text stringlengths 8 1.01M |
|---|
Instructor(s)
Course Description
László
Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems.
The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare |
A complete practical math and physics course for aviation related trades using everyday examples to explain each facet of the subject. Many sets of subjects are covered, each of which can be considered as an area of physics which is then solved through the application of basic math. The amount of math presented is suitable for the tasks at hand and for understanding the function and maintenance of aircraft systems. This is not an engineering level textbook. |
IntroductoryNormal 0 false false false MicrosoftInternetExplorer4 Lial/Hornsby/McGinnisrs"sIntroductory Algebra,8e, gives students the necessary tools to succeed in developmental math courses and prepares them for future math courses and the rest of their lives. The Lial developmental team creates a pattern for success by emphasizing problem-solving skills, vocabulary comprehension, real-world applications, and strong exercise sets. In keeping with its proven track record, this revision includes an effective new design, many new exercises and applications, and increased Summary Exercises to enhance comprehension and challenge studentsrs" knowledge of the subject matter. Prealgebra Review; The Real Number System; Equations, Inequalities, and Applications; Graphs of Linear Equations and Inequalities in Two Variables; Systems of Equations and Inequalities; Exponents and Polynomials; Factoring and Applications; Rational Expressions and Applications; Roots and Radicals; Quadratic Equations For all readers interested in introductory algebra. |
A unit designed to use the concepts of ecology and apply them to mathematics, divided into two sections. The first section gives an overview of the topic of ecology and the second section gives lesson plans: examples...
A unit that introduces flowcharting as a technique for solving math word problems in a logical, ordered sequence. Basic charting concepts of categorizing data and information in groups of input and output data,...
A 4-6 week unit for use with college-bound high school students, combining the introduction of chemistry with a methodical method of problem solving and a review of the mathematics needed for high school chemistry. It...
A unit that introduces elementary ideas included in probability theory, defining important words and ideas, presenting formulas for solving problems, and discussing permutations, combinations, and compound probability....
A unit that focuses on problem solving through real life situations that involveaviation. In spite of a variety of shapes and sizes all airplanes fly in the same way, and the problems of the aviation industry are... |
Do the exercises, then come up with your own exercises. The best exercises are the ones which test your understanding of two different books. (These are the ones you have to come up with.)
–
Qiaochu YuanFeb 20 '11 at 12:31
I definitely agree with the advice of "coming up with your own exercises". It is certainly the best way to learn mathematics. Let me also add the advice of "coming up with your own proofs of results in the text". If you find it difficult to come up with your own exercises, then it is also a good idea to search online or look at many different books to find good exercises.
–
Amitesh DattaJun 25 '11 at 1:35
1
@Quiaochu Yuan: What did you do if you could not solve ''your own exercise''? Normally, I got alot of my own problems when I study a new mathematical theory, and I could not answer them. Then I try to abandon them and come back in a beautiful day :D
–
ArsenalerMar 29 '12 at 2:12
Your question is probably appropriate for the nearly-in-beta-SE area51.stackexchange.com/proposals/64216/…. Check out the proposal and commit to it if you're interested. Then we can get it off the ground and get the site in beta!
–
Xoque55Mar 3 at 4:58
13 Answers
The only way is to put in a lot of time, to not give up, and to keep studying. As Agusti Roig mentions, the importance of doing exercises cannot be downplayed - working things out for yourself is absolutely necessary when trying understand things more deeply.
For me one of the most important things has been asking myself questions. Lots of questions Why does the theorem have theses hypothesis? Why this definition? What was the key idea in the proof? Can I apply this idea, this method of proof to other questions? For what kinds of questions will this method fail, and why does it fail? Is there another proof? Terence Tao has a good blog post about this titled "Ask yourself dumb questions – and answer them.
The more time you spend thinking about a subject, the better you will understand it.
Try to learn a subject you find more difficult by reading more then just your notes from class. You can rent math books from your local libary or even at your school.
In my case I used to watch math videos about several subjects I had problems with and it helped me alot.
A place where you can find a collection of several math video website is:
As last almost all teachers say "practice, practice and practice" and it's true but practice the subjects with a focussed mind. Another extremely helpful website is Wolram Alpha, take some time to learn how to work with this website and it'll be a great help in checking your solved excersises and learning.
Mathematics nowaday is a very rich field and has many applications. Doing the exercises, fighting with your own questions... are very good advices. I just want to mention another interesting activity, that is finding the connections between various fields of maths, like the connections between commutative algebra and representation theory or commutative algebra and combinatorics... It may not have connections in the whole subject, but it may have in some specific theorems. Finding such connections can help us seeing the bigger picture and may be some astonishing proofs...In my case, it motivated me alots.
Spending lots of time doing math is necessary but not sufficient. To do math effectively, there must be an intensity to your study. I wear earplugs while I work, and use the StayFocusd extension to Chrome so that when the going gets tough, I have to actively decide to start dicking around by going through the somewhat involved process of disabling that app.
I also have to keep in mind that Wikipedia is not always my friend. It is rarely inaccurate, but the writing style is horrid and the notation is invariably different than that used in your text. Plus, when your text says something inscrutable, it's best to just battle it rather than pray to God that Wikipedia will have that magical statement that makes it facile. Once you're on Wikipedia, you can get hopelessly diverted for hours. Limit your Wikipedia time per day to (say) 15 minutes via the StayFocusd app.
When doing homework, write it out on paper, then TeX it up for submission to your professor. I cannot tell you how many times I've found huge gaps in my proofs while typing it up. Never TeX before writing a proof out completely on paper.
To add one more idea, which may work for some of you (it works great for me): try invent applications of what have you just learned. Naturally, they can be purely theoretical uses and have nothing to do with applied math.
What corollaries follows from the theorem? Does it allow you to gain any deep insights or to work out some intuition?
With what other lemmas you can combine it? What do you gain?
Can you construct a non-trivial example for it? Is the result meaningful in any way?
Sometimes: can you find a non-trivial example in real world (i.e. formulate the theorem using real-world entities, e.g. for a sphere you could use the globe, for some sequences you could use stock market prices, also there are many real-world posets, and all the probability theory fits into real life just perfect)?
What are the downsides of the theorem (e.g. is it only existential or maybe computationally impossible)? Are there any nice things that are just beyond the scope of the theorem? What would you need to have to close the gap, is it possible?
I have used that approach for quite some time with success in wide range of domains including not only calculus, functional analysis or topology, but also logic, abstract algebra, combinatorics and category theory. This also works in problem solving -- starting with special cases may help you a lot if you are stuck (this is also one of the advices given by Pólya in his famous How to Solve It).
I agree with tim. If ur a right brian learner, u should first get a general idea of what the topic is trying to do. Ex: calc 1 is all about integration and differentiation, after u get the general idea then work in the details
1) Work the proofs. Work them hard. I said work, and not learn, for a specific reason. Many students just think if you are able to recite the proof, it's ok.
What you have to do is (in my opinion) :
Understand which part of the proof is a key idea. Not all statements are equally important.
Understand why there is this condition, and not another one. Aka find counter-examples. It's one of the first exercice you should do. It can be really hard for some theorem, but it is very instructive. As already stated, ask yourself questions !
2) Do exercices. A lot of them. And by a lot, if you are undergrad, I mean a lot.
Never skip a correction even if you have the good results. You should always try to see differences between your answer and the book one.
Learn to be good in mental calculus. Yeah, it's annoying to work, but you have to do it.
Do not work only short exercises. Working problems helps to get the "big picture", especially when you mix tools like analysis and algebra together.
If you are stuck in an exercise after some time, ask help, dont put it away. Not be able to do an exercise on your own is the way to make some progress. Even the best mathematicians ask help to their collaborators.
But the most important point (third one) is to be patient, and to enjoy working. Math is not a quickly rewarding field, but it's worth it.
If "staring" means "I have no thoughts", then you are probably stuck at some tough place. Mathematics was developed for centuries, do not expect of yourself to develop it by your own in minutes. Put in words what you are stuck at, ask people.
I'd found revealing to switch between textbooks on the same subject, as textbooks have different strengths and weaknesses. However, this method has its own disadvantage, because you should integrate knowledge from different books on your own. They may use different notations etc.
I think different books may have different view point and in my case, if I get troubles with chapters, definitions,... I switch to other books. The advantage is that you can see the bigger picture and improves your synthesis ability :)
–
ArsenalerMar 29 '12 at 2:18
A math book usually represents a way of thinking about a topic, a perspective on that topic. Hence, you have to agree with the authors opinion on how to present the topic in order to get a useful learning approach. (Contrary, if you completely disagree with the book's perspective, you may regard it as a challenge.)
In my experience, learning achievements are enhanced if you let the knowledge flow through you own hands. This means you have to put down the content of the book in a way which fits your way of thinking best. The author will probably have a (slightly) different perspective than you have, due to taste and ability.
A good approach towards a book is: "The author is lying." - each line of the book has to be justified. If you can't do so, you do not understand the topic in full.
Furthermore, I have made the experience it is inevitable to spend lots of time with the matter. Difficult and inaccessible proofs may unveil if you read it over and over again (imo, good examples of these are Hörmander's books on linear pde).
I like your question. For me, I prefer to get a big picture first. If books that I have do not work for me in this way, perhaps because of my weak math background, I will search online for a comprehensive overview and mostly be led to Wikipedia. More details will be pursued when needed.
First, besides the book, you need paper and a pen. Second, you must do the exercices of the book. Third, you must do the exercises of the book. Fourth, you must do the exercices of the book. Fifth..., did I mention you must do the exercises of the book? -Do them! |
Synopses & Reviews
Publisher Comments:
Brushing up on math has never been easier!
Just about everyone can use some extra help improving or remembering basic math skills. Finally, all the information you need to master the basics, once and for all, is at your fingertips. Featuring several overviews of a multitude of mathematical concepts, as well as detailed learning plans, Mathematics Made Simple presents the information you need in clear, concise lessons that make math fun to study. Easy-to-use features include |
Integrated Mathematics I
Code:
MATH 541
Credits:
[4.0]
This course (along with MATH 542 and MATH 543) involves students in the process of integrating mathematics. This process enables teachers to deepen their understanding of the relationship among the various mathematical disciplines, thereby making this insight available for children and other teachers. Using concrete materials and examples, the following basic topics are dealt with: elementary number theory, algebra, groups, and transformational geometry. |
Algebra I – Unit 5
Ascension Parish Comprehensive Curriculum
Concept Correlation
Unit 5: Linear Functions and Their Graphs, Rates of Change, and Applications
Time Frame: Regular – 4 weeks
Block – 2 weeks
Big Picture: (Taken from Unit Description and Student Understanding)
This unit leads to the investigation of the role of functions in the development of algebraic thinking and modeling.
Heavy emphasis is given in this unit to understanding rates of change and graphing input-output relationships on the coordinate graph.
Emphasis is also given to geometric transformations as functions and using their constant difference to relate to slope of linear equations.
Students need to see functions as input-output relationships that have exactly one output for any given input.
Central to this unit is the study of rates of change, noting that the rate of change in graphs and tables is constant for linear relationships and for
each change of 1 unit in x, there is a constant amount of growth in y.
In Unit 4, this relationship for lines through the origin was tied to direct proportion. In this unit, emphasis is given to the formula and rate of
change of a direct proportion as y kx or k 1 . That is, as x changes 1, y changes k. Lines that do not run through the origin can be modeled
y x
by functions of the form kx b , which are just lines of proportion translated up b units. These relationships need to be seen in a wide variety
of settings.
Activities Documented GLEs
Guiding Questions The essential activities are GLEs
denoted by an asterisk. GLES Date and Method of
DOCUMENTATION
44 – Patterns and GLES
Concept 1: Linear Bloom's Level Assessment
Relationships, Slope (GQ 13, 14, 15) 13,15,25, Model real-life situations using 9
Graphs, Slope 37,40 linear expressions, equations,
24. Can students and inequalities (A-1-H) (D-2-
identify the *45 – Recognizing H) (P-5-H) (Analysis)
matched elements Linear Relationships Evaluate polynomial 12
9,23,39,40
in the domain/range (GQ 14, 15) expressions for given values of
for a given the variable (A-2-H)
function? *46 – Rate of Change 10,12,13, (Application)
25. Can students (GQ 14, 15) 15,23,25, Translate between the 13
describe the 29 characteristics defining a line
constant growth *47 – Graph Families 37,38,39, (i.e., slope, intercepts, points)
rate for a linear (GQ 14,15) 40
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
function in tables and both its equation and graph
and graphs, as well (A-2-H) (G-3-H) (Analysis)
as connecting it to
the coefficient on
Translate among tabular, 15
the x term in the
graphical, and algebraic
expression leading
representations of functions
to the linear graph?
and real-life situations (A-3-H)
26. Can students
DOCUMENTATION
(P-1-H) (P-2-H) (Analysis)
intuitively relate *48 – Slopes and y-
slope (rate of 38,40 Use coordinate methods to solve 23
intercepts (GQ 14, 15) and interpret problems (e.g.,
change) to m and
the y-intercept in slope as rate of change,
graphs to b for intercept as initial value,
linear intersection as common
relationships mx b solution, midpoint as
? equidistant) (G-2-H) (G-3-H)
(Analysis)
Explain slope as a 25
Concept 2: Functions representation of "rate of
24. Can students change" (G-3-H) (A-1-H)
identify the (Analysis)
matched elements *49 – What's a
in the domain/range function? (GQ 13, 16, 12, 35, 36
for a given 17)
function?
25. Can students
describe the
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
constant growth Create a scatter plot from a set 29
rate for a linear of data and determine if the
function in tables relationship is linear or non-
and graphs, as well linear (D-1-H) (D-6-H) (D-7-H)
as connecting it to *50 – Identify! (GQ 8, 12, 15, (Synthesis)
the coefficient on 13) 35, 36
Determine if a relation is a 35
the x term in the function and use appropriate
expression leading function notation (P-1-H)
to the linear graph? (Analysis)
26. Can students Identify the domain and range 36
intuitively relate of functions (P-1-H)
slope (rate of (Knowledge)
change) to m and
51 – Functions of 10, 15, 35, Analyze real-life relationships 37
the y-intercept in
Time (GQ 13, 14, 15) 36 that can be modeled by linear
graphs to b for
functions (P-1-H) (P-5-H)
linear
(Analysis)
relationships mx b
? Identify and describe the 38
27. Can students characteristics of families of
understand and linear functions, with and
apply the definition without technology (P-3-H)
of a function in (Knowledge)
evaluating Compare and contrast linear 39
expressions (output functions algebraically in terms
rules) as to whether *52 – Make that of their rates of change and
they are functions 10, 12, 13, intercepts (P-4-H) (Analysis)
Connection! (GQ 14,
or not? 15, 25, 36
15)
28. Can students apply Explain how the graph of a 40
the vertical line test linear function changes as the
to a graph to coefficients or constants are
determine whether changed in the function's
or not it is a symbolic representation (P-4-
function? H) (Synthesis)
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Unit 5 – Concept 1: Linear Relationships, Graphs, Slope (LCC Unit 3)
GLEs
*Bold GLEs are assessed in this unit
9 Model real-life situations using linear expressions, equations, and inequalities
(A-1-H) (D-2-H) (P-5-H) (Analysis)
12 Evaluate polynomial expressions for given values of the variable (A-2-H)
(Application)
13 Translate between the characteristics defining a line (i.e., slope, intercepts,
points) and both its equation and graph (A-2-H) (G-3-H) (Analysis)
15 Translate among tabular, graphical, and algebraic representations of
functions and real-life situations (A-3-H) (P-1-H) (P-2-H) (Analysis)
23 Use coordinate methods to solve and interpret problems (e.g., slope as rate of
change, intercept as initial value, intersection as common solution, midpoint as
equidistant) (G-2-H) (G-3-H) (Analysis)
25 Explain slope as a representation of "rate of change" (G-3-H) (A-1-H)
(Analysis)
29 Create a scatter plot from a set of data and determine if the relationship is
linear or non-linear (D-1-H) (D-6-H) (D-7-H) (Synthesis)
37 Analyze real-life relationships that can be modeled by linear functions (P-1-H)
(P-5-H) (Analysis)
38 Identify and describe the characteristics of families of linear functions, with
and without technology (P-3-H) (Knowledge)
39 Compare and contrast linear functions algebraically in terms of their rates of
change and intercepts (P-4-H) (Analysis)
40 Explain how the graph of a linear function changes as the coefficients or
constants are changed in the function's symbolic representation (P-4-H)
(Synthesis)
Purpose/Guiding Questions: Key Concepts and Vocabulary:
Identify the matched elements in the Perimeter
domain and range for a given Positive/Negative Slopes
function. Y-intercept
Describe the constant growth rate Families of Graphs
for a linear function in tables and Linear Relationships
graphs, as well as, connecting it to Rate of Change
the coefficient on the x term in the
expression leading to the linear
graph.
Intuitively relate slope (rate of
change) to m and the y-intercept in
graphs to b for linear relationships
mx + b.
62
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Assessment Ideas:
The student will generate the functional notation for a linear function expressed in x
and y.
For example: y = 2x + 3 => f(x) = 2x + 3
The student will generate a function's graph from an input-output table.
Given a graph that is a function of time, the student will write a story that relates to
the graph.
The students will answer open-ended questions such as:
Maria is hiking up a mountain. She monitors and records her distance every half
hour. Do you think the rates of change for every half hour are constant? Explain
your answer.
The student will solve constructed response items such as:
Signature Office Supplies is a regional distributor of graphing calculators. When
an order is received, a shipping company packs the calculators in a box. They
place the box on a scale which automatically finds the shipping cost. The cost C
depends on the number N of the calculators in the box, with rule
C 4.95 1.25 N .
A. Make a table showing the cost for 0 to 20 calculators.
B. How much would it cost to ship an empty box? (4.95) How is that information
shown in the table and the cost rule?
C. How much does a single calculator add to the cost of shipping a box? (1.25)
How is that information shown in the table and the cost rule?
D. Write and solve equations and inequalities to answer the following questions.
1. If the shipping cost is $17.45, how many calculators are in the box?
(10 calculators)
2. How many calculators can be shipped if the cost is to be held below
$25? (16 calculators)
3. What is the cost of shipping eight calculators? ($14.95)
E. What questions about shipping costs could be answered using the following
equation and inequality?
27.45 4.95 1.25N
4.95 1.25N 10
The students will complete journal writings using such topics as:
o A child's height is an example of a variable showing a positive rate of change
over time. Give two examples of a variable showing a negative rate of change
over time. Explain your answer.
o Explain why the graph of an equation of the form y kx always goes through
the origin. Give an example of a graph that shows direct variation and one that
does not show direct variation.
o Explain how you can tell if the relationship between two sets of data is linear.
Activity-Specific Assessments: Activities 20, 22
63
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Resources:
McDougal Littell: 4.4, 4.6
Graphic Organizers:
organizers/printable/6293.html and
4Sgod3TaxVg
Create your own organizers using:
and
Plato – Refer to end of Concept 1
Refer to Algebra I Groupwise Cabinet for activity-specific handouts, tests, and
materials.
64Activity 44: Patterns and Slope (LCC Unit 3)
(GLEs: 13, 15, 25)
Materials List: math learning log, paper, pencil, square algebra tiles, Patterns and Slope BLM,
graph paper
Have students use the Patterns and Slope BLM to complete this activity.
Divide students into groups and provide them with square algebra tiles. Have the students
arrange 3 tiles in a rectangle and record the width (x) and the perimeter (y) on the BLM. Have
the students fit 3 more tiles under the previous tiles and continue adding tiles, putting the
values in a table. Example:
Width(x) Perimeter(y)
1 8
2 10
3 12
4 14
Have students notice that the change in the y-values is the same, graphing the data and
deciding if it is linear. Ask students what changed in the pattern (the widths that keep
increasing) and what remained constant (the length of the sides added together (3+3)). Have
them write a formula to describe the pattern. ( y = 6 + 2x ) Guide students to conclude that
what remained constant in the pattern will be the constant in the formula and the rate of
change in the pattern will be the slope. Guide students to make a connection between the
tabular, graphical and algebraic representation of the slope.
In their math learning logs (view literacy strategy descriptions) have students respond to the
following prompt:
A child's height is an example of a variable showing a positive rate of change over time.
Give two examples of a variable showing a negative rate of change over time. Explain
your answer.
Have students share their answers with the class and combine a class list of all student
answers. Discuss the answers and have students determine whether the examples are indeed
negative rates of change.
*Activity 45: Recognizing Linear Relationships (LCC Unit 3)
(GLEs: 9, 39, 40)
Materials List: paper, pencil
65
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Provide students with several input-output tables (linear) paired with a graph of that same
data. Include examples of real-life linear relationships. (Examples of linear data sets can be
found in any algebra textbook.)
rise
Introduce slope as the concept of . Have students determine the slope of the line and then
run
investigate the change in the x-coordinates and the accompanying change in the y-coordinates.
Ask, Was a common difference found? How does this common difference in the y-
coordinates compare to the slope (rate of change) found for the line? Using this information,
have students conjecture how to determine if an input-output table defines a linear
relationship. (There is a common difference in the change in y over the change in x.)
Have students write a linear equation for each of the graphs. Have students compare the input-
output tables, the graphs, and the equations to see how the slope and y-intercepts affect each.
Activity–Specific Assessment
The student will find the rate of change between consecutive pairs of data.
Example:
x 1 3 4 7
y 3 7 9 15
Is the relationship shown by the data linear? (Yes) Explain your answer. (There is
a common difference between the change in y over the change in x. (2))
*Activity 46: Rate of Change (LCC Unit 3)
(GLEs: 10, 12, 13, 15, 23, 25, 39)
Materials List: paper, pencil, Rate of Change BLM, graph paper, straight edge
Use the Rate of Change BLM to introduce the following problem:
David owns a farm market. The amount a customer pays for sweet corn depends on the
number of ears that are purchased. David sells a dozen ears of corn for $3.00. Place the
students in groups and ask each group to make a table reflecting prices for purchases of 6,
12, 18, and 24 ears of corn.
Place students in groups and have each group complete the Rate of Change BLM. Students
will write and graph four ordered pairs that represent the number of ears of corn and the price
of the purchase. Have each group write an explanation of how the table was developed, how
the ordered pairs were determined, and how the graph was constructed.
After ensuring that each group has a valid product, ask the students to use a straightedge to
construct the line passing through the points on the graph. Looking at the line constructed, ask
each group to find the slope of the line. Review the idea that slope is an expression of a rate of
66
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
change. Ask students to explain the real-life meaning of the slope. (For every ear of corn
purchased, the price goes up $.25.)
Introduce the slope-intercept form of an equation. Have groups determine the equation of the
lines by examining the graph for the slope and y-intercept. Point out to the students that the
value of y (the price of the purchase) is determined by the value of x (the number of ears
purchased). Therefore, y is the dependent variable and x is the independent variable.
Point out to the student that the value of y will always increase as the value of x increases.
This is indicated by the fact that there is a positive slope. Also, point out that the y-intercept is
at the origin because no purchase would involve a zero price. Ask the students to use the
equation to find the price of a purchase of four ears of corn.
Have students participate in a math story chain (view literacy strategy descriptions) activity to
create word problems using real-life applications that are linear relationships. Students should
now be familiar with story chains after the activities in Units 1 and 2. A sample story chain
might be:
Student 1: Jimi wants to save money to buy a car.
Student 2: He has been mowing lawns to earn money
Student 3: He charges $30 per lawn.
Student 4: What is the rate of change of this linear relationship?
Have groups share their math story problems with the entire class and have the other groups
solve and critique the problems.
*Activity 47: Graph Families (LCC Unit 3)
(GLEs: 37, 38, 39, 40)
Materials List: paper, pencil, Graph Families BLM, graphing calculator
Activities 8 and 9 are a study of families of lines. A family of lines is defined as a group of
lines that share at least one common characteristic. For example, these lines may have
different slopes and the same y-intercept or different y-intercepts and the same slope. Parallel
and perpendicular lines are also examples of families of lines and will be studied in Unit 4.
Use the Graph Families BLM to complete this activity. First, generate a discussion on
families of linear graphs by describing the following situation.
Suppose you go to a gourmet coffee shop to buy coffee beans. At the store, you
find that one type of beans costs $6.00 per pound and another costs $8.00 per
pound.
Place the students in groups and have them complete the BLM through question 4. Ask each
group to share its findings, and ensure that each group finds the correct equations, slopes, and
y-intercepts. Have students complete questions 5 and 6 and then discuss the students'
conclusions.
67
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Have students use a graphing calculator to complete the remainder of the BLM. If a graphing
calculator is not available, have the students graph the equations by hand. The BLM will lead
students to discover that a line will get steeper as the absolute value of the slope is increased
and flatter as the slope is decreased. They will also observe the difference in lines with
positive and negative slopes. Examples of graphs of horizontal and vertical lines are also
included on the BLM.
Conclude the lesson by clarifying what is meant by the term family of lines and discussing
similarities and differences of the types of families.
Activity-Specific Assessment
The student will sort a set of linear functions into families based on slope
and y-intercept characteristics.
*Activity 48: Slopes and y-Intercepts (LCC Unit 3)
(GLEs: 38, 40)
Materials List: paper, pencil, Slopes and Y-intercepts BLM, graphing calculator
Have students use the Slopes and Y-intercepts BLM to complete this activity. After students
have completed the BLM, have a class discussion of their findings. Have students explain
how the changes in the y-intercepts affect the graphs. Have students explain the effects of the
change in the slope on the graphs. Have students make conjectures about positive and
negative slopes. Discuss the slopes of horizontal and vertical lines and the lines y x
and y x . Help students intuitively relate slope (rate of change) to m and the y-intercept in
graphs to b for each of these linear functions expressed as f ( x) mx b .
After activities 7, 8, and 9, have students participate in a professor know-it-all activity (view
literacy strategy descriptions). In a professor know-it-all activity, students assume roles of
know-it-alls or experts who are to provide answers to questions posed by their classmates.
Form groups of three or four students. Give them time to review the content covered in
activities 7, 8, and 9. Have the groups generate three to five questions about the content. Call
a group to the front of the class. These are the "know-it-alls." Invite questions from the other
groups. Have the chosen group huddle, discuss, and then answer the questions. After about 5
minutes, ask a new group to come up and repeat the process. The class should make sure the
know-it-all groups respond accurately and logically to their questions.
68
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Concept 1
PLATO Instructional Resources
GLE 9: Plato
o Alg. 1 P2-Eq. & Ineq.: Solving prob. In 1 var.
o Math Pro. Solving-Prob. & Stat.: Making the Grade
o Beginning Alg.-Math Sentences: Solv. Eq, Ab. Val..
o Beg. Alg. – Math Sentences: Word Problems I & II
o Pre-Alg.-Math Sentences: Lin. Eq. 2 Var/Sys.
GLE 15: Plato
o Alg. 2 P1 – Graphs & Lin. Eq.:ALL
GLE 23: Plato
o Alg 2 P1 –Graphs & Lin.
GLE 25: Plato
o Alg 2 P1- Graphs & Lin. Eq.: ALL
GLE 37: Plato
o Algebra 2 Pt 2 – Func/Graphs: Equa/Graphs p1
GLE 38: Plato
o Alg. 1 P1 –Intro to Func.: ALL
GLE 39: Plato
o Alg 2 P1- Graphs & Lin. Eq.: ALL
GLE 40: Plato
o Alg 2 P1 – Graphs & Lin. Eq.: ALL
69
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Unit 5 – Concept 2: Functions (LCC Unit 3)
GLEs
*Bold GLEs are assessed in this unit.
8 Use order of operations to simplify or rewrite variable expressions (A-1-H) (A-2-
H) (Application)
10 Identify independent and dependent variables in real-life relationships (A-1-H)
(Knowledge)
12 Evaluate polynomial expressions for given values of the variable (A-2-H)
(Application)
13 Translate between the characteristics defining a line (i.e., slope, intercepts, points)
and both its equation and graph (A-2-H) (G-3-H) (Analysis)
15 Translate among tabular, graphical, and algebraic representations of functions and
real-life situations (A-3-H) (P-1-H) (P-2-H) (Analysis)
25 Explain slope as a representation of "rate of change" (G-3-H) (A-1-H) (Analysis)
35 Determine if a relation is a function and use appropriate function notation (P-
1-H) (Analysis)
36 Identify the domain and range of functions (P-1-H) (Knowledge)
Purpose/Guiding Questions: Key Concepts and Vocabulary:
Understand and apply the Function
definition of a function in Domain/Range
evaluating expressions (output Function Notation
rules) as to whether they are Vertical Line Test
functions or not. Relations
Apply the vertical line test to a
graph to determine if it is a
function or not
Assessment Ideas:
The students will use the definition of a function and/or the vertical line test to
determine which of several relations are functions
The student will make a poster of a function represented in three different ways and
describe the domain and range of the function.
The students will complete journal writings using such topics as:
o Sketch the graph of a relation that is not a function and explain why it is not a
function.
o Explain algebraically and graphically why y 2 x 2 7 is a function.
o Explain why the vertical line test works.
Activity-Specific Assessments: Activities 1, 3, 4
Resources:
McDougal Littell: 1.7, 4.2, 4.8
Graphic Organizers:
organizers/printable/6293.html and
70
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
4Sgod3TaxVg
Create your own organizers using:
and
Plato – Refer to end of Concept 2
Refer to Algebra I Groupwise Cabinet for activity-specific handouts, tests, and
materials.
71*Activity 49: What's a Function? (LCC Unit 3)
(GLEs: 12, 35, 36)
Materials List: paper, pencil, Vocabulary Self-Awareness Chart BLM, What is a Function?
BLM, calculator (optional)
Have students maintain a vocabulary self-awareness chart (view literacy strategy
descriptions) for this unit. Vocabulary self-awareness is valuable because it highlights
students' understanding of what they know, as well as what they still need to learn, in order to
fully comprehend the concept. Students indicate their understanding of a term/concept, but
then adjust or change the marking to reflect their change in understanding. The objective is to
have all terms marked with a + at the end. A sample chart is included in the blackline
masters. Be sure to allow students to revisit their self-awareness charts often to monitor their
developing knowledge about important concepts.
Have students use the What is a Function? BLM to complete this activity.
The BLM first provides examples of relations that are and are not functions (that are labeled
as such) including real-life examples, input/output tables, mapping diagrams, and equations.
Pose the question: "What is a function?" and then have students use a Think-Pair-Share
process to help them determine what is significant in the tables. After giving students time to
complete page 1, lead a discussion which results in the definition of a function (for every
input there is exactly one output) and have students write the definition in the blank at the top
of page 2.
The next section of the BLM repeats the activity with graphs that are and are not functions.
Introduce the vertical line test. Ask students to explain why this vertical line test for functions
is the same as the definition they used to see if the set of ordered pairs was a function.
The third section of the BLM can be used to help students define the domain and range of a
function. After students have looked at the first example, have them discuss with a partner
what they believe are the definitions of domain and range. Discuss with the class the correct
definitions of domain and range. The BLM then provides examples in which students write
the domain and range for three different relations.
Introduce function notation ( f x ), The function f(x) = 2x +3 is provided and students are
asked to find f -2 , f -1 , f 0 . Give students additional input-output rules in the form of
two-variable equations for more practice as needed.
The last section of the BLM asks students to determine if the set of ordered pairs in the
input/output tables generated using f(x) = 2x +3 satisfies the definition of a function (i.e., for
each element in the domain there is exactly one element in the range). Tell students to plot the
ordered pairs and connect them and determine the domain and range. Now have students draw
72
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
several vertical lines through the input values to illustrate the idea that for a function, a
vertical line intersects the graph of a function at exactly one point.
Provide closure to the activity by summarizing and reviewing the major concepts presented in
the activity.
Activity-Specific Assessment
The students will decide if the following relations are functions:
a. number of tickets sold for a benefit play and amount of money made (yes)
b. students' height and grade point averages (no)
c. amount of your monthly loan payment and the number of years you pay
back the loan (no)
d. cost of electricity to run an air conditioner during peak usage hours and the
number of hours it runs (yes)
e. time it takes to travel 50 miles and the speed of the vehicle (yes)
*Activity 50: Identify! (LCC Unit 3)
(GLEs: 8, 12, 15, 35, and 36)
Materials List: paper, pencil, Identify BLM, calculator
Give students the Identify BLM. One page contains a set of linear equations and the other
containing a set of ordered pairs. Have students identify the domain and range of each
relation. Have students work in pairs to determine which domain-range pairs match which
given equation on the second page of the BLM.
The set of linear equations includes some that depict real-world scenarios. These linear
equations also include some that are in unsimplified form (e.g., 3 y 3(4 x 2) 2 y 3 ) so
that students can have practice in using order of operations when they plug a value in for one
of the variables and solve for the other.
Have students determine which relations are also functions. For those relations they determine
to be functions, have students identify the independent and dependent variables and rewrite
the linear function using function notation. For example, if students determine that 3x y 8
is a linear function, then they could rewrite it as h( x) 3x 8 .
Activity 51: Functions of Time (LCC Unit 3)
(GLEs: 10, 15, 35, 36)
Materials List: paper, pencil, computer with spreadsheet program or a posterboard, supplies
needed for time functions chosen for this activity
Have students collect and graph data about something that changes over time. (Ex. The
temperature at each hour of the day, the height of a pedal on a bicycle when being ridden, the
number of cars in a fast food parking lot at different times of the day, the length of a plastic
73
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
grow creature as it sits in water, etc.) Have students organize the data in a spreadsheet and
make a graph of the data. Have them identify the domain and range of the function.
Then have the students construct a PowerPoint® presentation and present their findings to the
class, perhaps first showing their graphs to the class without labels to see if other students can
guess what they observed. (If technology is not available, have students construct the table
and graph by hand on a posterboard.)
Activity-Specific Assessment
The student will write a report explaining the procedures and the conclusions
of the investigation. The teacher will provide the student a rubric to use
when he/she writes the report including questions that must be answered in
the report such as: How did you decide on values to use for your axes? And
what did you and your partner learn about collecting and graphing data? (A
sample rubric is included at the end of this unit.)
*Activity 52: Make that Connection! (LCC Unit 3)
Materials List: paper, pencil, calculator, graph paper
(GLEs: 10, 12, 13, 15, 25, 36)
Have students generate a table of values for a given linear function expressed as
f ( x) mx b . An example would be the cost of renting a car is $25 plus $0.35 per mile.
Have students label the input value column of the table "Independent Variable" and the output
value column "Dependent Variable." Have students select their own domain values for the
independent variable and generate the range values for the dependent variable.
Next, have students calculate the differences in successive values of the dependent variable,
and find a constant difference. Then have them relate this constant difference to the slope of
the linear function. Next, have students graph the ordered pairs and connect them with a
straight line. Finally, discuss with the students the connections between the table of values,
the constant difference found, the graph, and the function notation. Last, have students do the
same activity using a linear function that models a real-world application.
For example, students could investigate the connections between the algebraic representation
of a cost function, the table of values, and the graph.
74
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Activity-Specific Assessment
The student will solve constructed response items such as:
Suppose a new refrigerator costs $1000. Electricity to run the refrigerator costs about
$68 per year. The total cost of the refrigerator is a function of the number of years it is
used.
a. Identify the independent and dependent variables
b. State the reasonable domain and range of the function.
c. Write an equation for the function. ( C 1000 68 N )
d. Make a table of values for the function.
e. Graph the function.
f. Label the constant difference (slope) on each of the representations of the
function.
75
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Sample Rubric for
Activity 51
Functions of Time Project
Rubric
Directions: Write a report explaining the procedures and the conclusion of your function of time
investigation. In your report, the following questions must be answered:
1. What did you investigate?
2. How did you and your partner decide what to investigate?
3. What is the domain and range of your function?
4. Did you see any patterns in the relationship you observed?
5. How did you decide what values to use for your axes?
6. How did you divide up the work between you and your partner?
7. Did you have any problems conducting your investigation? If so, explain.
(Teachers may wish to add other questions to ensure understanding of the investigation.)
This rubric must be handed in with your final project.
Name__________________________________
Spreadsheet/Table
Demonstrates Spreadsheet/table Spreadsheet/table Spreadsheet/table Spreadsheet/table
mastery of is constructed is constructed is constructed is constructed
constructing a with 1 – 2 errors with 3 errors with 4 - 5 errors with many errors
spreadsheet/table
with no errors
4 points 3 points 2 points 1 points 0 points
Graph
Graph is Graph is Graph has 3 Graph has 4 -5 Graph is
exemplary. Title sufficient but has errors. errors. constructed with
is included, axes 1 - 2 errors in many errors.
are labeled construction.
appropriately, all
points are plotted
correctly.
4 points 3 points 2 points 1 point 0 points
Report
Report is Report is Report is Report is Report is
exemplary. All constructed with constructed with constructed with insufficient as
questions are few grammatical grammatical many explanation of
answered errors or one errors or 2 -3 grammatical project.
thoroughly. No question was not questions were errors or 4
grammatical answered not answered questions were
errors. thoroughly. thoroughly. not answered
thoroughly.
12 points 9 points 6 points 3 points 0 points
76
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 5
Concept 2
PLATO Instructional Resources
GLE 12: Plato
o Inter. Alg.-Rational Exp: Evaluating
GLE 26: Plato
o Geometry & Measurement 2-Trans, Symm, Area:..
GLE 35: Plato
o Algebra 1 Pt. 1 Intro. To functions: Functions
GLE 36: Plato
o Algebra 1 Pt. 1- Intro. To Functions: Desc. Func…
77
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications
Algebra I – Unit 578
Algebra I – Unit 5 – Linear Functions and Their Graphs, Rates of Change, and Applications |
Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "…a good, solid instructional text on the basic tools of numerical analysis." |
Fractals: A Very Short Introduction (Very Short Introductions)
by Kenneth Falconer Publisher Comments
From the contours of coastlines to the outlines of clouds, and the branching of trees, fractal shapes can be found everywhere in nature. In this Very Short Introduction, Kenneth Falconer explains the basic concepts of fractal geometry, which produced a... (read more)
Fractals
by John Briggs Publisher Comments
Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them... (read more)
Complex Spaces in Finsler, Lagrange and Hamilton Geometries
by Gheorghe Munteanu Publisher Comments
This book presents the most recent advances in complex Finsler geometry and related geometries: the geometry of complex Lagrange, Hamilton and Cartan Spaces. The last three spaces were initially introduced to and have been investigated by the author of... (read more)
Modern Geometry / With CD (02 Edition)
by David A. Thomas Publisher Comments
MODERN GEOMETRY was written to provide undergraduate and graduate level mathematics education students with an introduction to both Euclidean and non-Euclidean geometries, appropriate to their needs as future junior and senior high school mathematics... (read more)
Topos Theory (Dover Books on Mathematics)
by P. T. Johnstone Publisher Comments
One of the best books on a relatively new branch of mathematics, this text is the work of a leading authority in the field of topos theory. Suitable for advanced undergraduates and graduate students of mathematics, the treatment focuses on how topos... (read more)
Convex Polyhedra (Springer Monographs in Mathematics)
by A. D. Alexandrov Publisher Comments
This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems... (read more)
Analytical Conics
by Barry Spain Publisher Comments
This concise text introduces students to analytical geometry, covering basic ideas and methods. Readily intelligible to any student with a sound mathematical background, it is designed both for undergraduates and for math majors. It will prove... (read more)
Three Lectures on Fermat's Last Theorem
by Louis Joel Mordell Publisher Comments
Attempted by the greatest mathematicians including Euler, Legendre, Gauss, Abel, Dirichlet, Cauchy, and Kummer, and here is Mordell. Considered a classic, and unabridged.... (read more)
Geometric Analysis and Applications to Quantum Field Theory
by Peter Bouwknegt Publisher Comments
In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric... (read more)
Schaum's Outline of Geometry (4TH 09 - Old Edition)
by Barnett Rich Publisher Comments
Schaum's has Satisfied Students for 50 Years. Now Schaum's Biggest Sellers are in New Editions! For half a century, more than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's celebrates |
MathematicsCalc is arbitrary precision C-like arithmetic system that is a calculator, an algorithm prototyper and mathematical research tool. Calc comes with a rich set of builtin mathematical and programmatic functions |
Synopses & Reviews
Publisher Comments:
REAs High School Tutors is a series of useful and practical study guides. Each High School Tutor provides practice and understanding of various math, science, and history subjects, making them challenging and interesting. Hundreds of solved problems with step-by-step detailed solutions are included to meet the needs of high school students. REAs Pre-Algebra High School Tutor study guide helps high school student succeed:
Covers all the Pre-Algebra topics taught in classrooms
Makes Pre-Algebra easy to learn, easy to understand, and easy to study
An essential companion to any high school textbook
Superb study guide for quizzes and exams
An excellent aid when working on homework
Helps students grasp a subject fully
Indexed for easy topic searches
REAs High School Tutors make it easy to learn difficult subjects!
Synopsis: |
This excellent site, from LessonCorner, helps educators create customized math worksheets for students of all levels. Creating worksheets is free, and visitors can also name them what they wish and print them to...
This course, designed for Miami Dade Community College, integrates arithmetic and beginning algebra for the undergraduate student. By applying math to real-life situations most students experience during college, the...
This site from the Center for Cultural Design will help students understand the connection between musical rhythms and mathematic ratios. The site also provides some background on Latino-Carribean music and the...
Based at the University of Plymouth, the Centre for Innovation in Mathematics Teaching has developed many instructional materials designed to help both novice and experienced math teachers. This particular area of the...
This document from SpaceTEC National Aerospace Technical Education Center is one of three handbooks for people preparing for mechanic certification with airframe or powerplant ratings, or both. This particular volume... |
Description
When you have the right math teacher, learning math can be painless and even fun Let "Basic Math and Pre-Algebra Workbook For Dummies" teach you how to overcome your fear of math and approach the subject correctly and directly. A lot of the topics that probably inspired fear before will seem simple when you realize that you can solve math problems, from basic addition to algebraic equations. Lots of students feel they got lost somewhere between learning to count to ten and their first day in an... algebra class, but help is here Begin with basic topics like interpreting patterns, navigating the number line, rounding numbers, and estimating answers. You will learn and review the basics of addition, subtraction, multiplication, and division. Do remainders make you nervous? You'll find an easy and painless way to understand long division. Discover how to apply the commutative, associative, and distributive properties, and finally understand basic geometry and algebra. Find out how to: Properly use negative numbers, units, inequalities, exponents, square roots, and absolute value Round numbers and estimate answers Solve problems with fractions, decimals, and percentages Navigate basic geometry Complete algebraic expressions and equations Understand statistics and sets Uncover the mystery of FOILing Answer sample questions and check your answers Complete with lists of ten alternative numeral and number systems, ten curious types of numbers, and ten geometric solids to cut and fold, "Basic Math and Pre-Algebra Workbook" "For Dummies" will demystify math and help you start solving problems in no time |
Essential Mathematics for Economic Analysis - 2nd edition
Summary: Essential Mathematics for Economic Analysis provides an invaluable introduction to mathematical analysis and linear algebra for economists. Its main purpose is to help students acquire the mathematical skills they need in order to read the less technical literature associated with economic problems. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics usually taught in undergraduate course...show mores on mathematics for economists. Features
Large number of examples throughout the book help to link abstract mathematics with real life
Extremely clear writing style without sacrificing mathematical precision and rigour ensures that students gain a thorough understanding of the use of mathematics to analyse economic problems.
Extensive number of problems and exercises at the end of each section with solutions to odd-numbered questions at the back of the book, allowing students to constantly practice what they are learning to reinforce their understanding.
New To This Edition
Most chapters have been revised and updated. They now include additional problem material and many more examples
Key concepts and techniques placed in colour and boxes to outline their importance
New chapter 17 on Linear Programming
Extensive resources for instructors and students on the companion website at including Instructors Manual with tests; Excel supplement with exercises; Excel supp Answers for lecturers; Downloadable Exam style problems which can be set as assignments for students |
Get a better grade with PRECALCULUS! With a focus on teaching the essentials, this mathematics text provides you with the fundamentals necessary to ...Show synopsisGet a better grade with PRECALCULUS! With a focus on teaching the essentials, this mathematics text provides you with the fundamentals necessary to be successful in this course and your future calculus course. Exercises and examples are presented the way that you will encounter them in calculus so that you are truly prepared for your next course. Learning tools found throughout the text such as exercises, calculus connections, and true and false questions help you master difficult concepts 464 p. Contains: Illustrations. Precalculus |
Descriptions This OxBox contains all you need to deliver engaging GCSE lessons, bringing the new GCSE curriculum to life, and to plan your schemes of work. Title Oxford GCSE Maths for OCR: Interactive...
Title: A Level Maths Essentials: Mechanics 1 for Edexcel Book and CD-ROM. Isbn 13: 9780582836754. And buy all the books you love. We are committed to post all products you order the same or next worki...
All about Shape and Space is designed to help children aged 6 to 8 develop their maths and ICT skills through a variety of fun, stimulating activities:Pattern and design – generate patterns and apply ... |
Thinking through Mathematics: Engaging students with inquiry- based learning
Book 2 builds on students increasing experience of the world and growing capability for mathematical thinking. More complex inquiries increase the focus on prediction, defining parameters, and collecting evidence to form and communicate conclusions. |
An introduction to mathematical functions, suitable for Mathematics students from grade 8 onwards. This educational game uses 60 images to help students to recognize the graphs of the basic mathematical functions, y = x, sin(x), cos(x), tan(x), exp(x), log(x) and sinc(x) and their reciprocals, reflections and powers.
Students hear the name of a function and choose the matching graph. After six right in a row, Race Mode starts automatically. It asks questions at speed to test the students' memory and comprehension of the functions just covered, before continuing with new functions. At the end of the race, students can see how well they have done relative to their other races. The game gradually focuses on any functions that the students have difficulty recognizing, and speeds up as competence is gained.
By contrast to Race Mode, Story Mode slowly introduces new functions by saying them as the graphs are shown, allowing students to quietly look, listen and learn.
The game is controlled by on-screen gestures which are simple to demonstrate and easy to use, and the game can be played without voice prompts.
* 60 graphs of 4 variations each of 15 mathematical functions * Reciprocals, reflections and powers * Race Mode tests memory and comprehension * Story Mode allows students to look, listen and learn * Slideshow Mode displays each function in its variationsXFunction is an app designed to facilitate the study of one-variable functions. XFunction allows you to display graph of a function, move on it, zoom in or out areas of interest, see the value of the function at the point touched. But the strength of Xfunction is in the way and speed with which you can do all that. Thanks to a simple and intuitive interface, XFunction guides you when inserting the function ensuring the correctness of that as you type. Syntactic errors due to bad typing, typically present in applications of this kind will belong only to the past. So from now thanks to XFunction draw the graph of a function becomes an easy game.
Mathematic's application essential for students of all ages with formulas of trigonometry. The arguments covered vary from the graphical representation of functions (sin, cos ..), domains, codomain, roots etc etc.
This application will allow you to have somethings about Trigonometry always with you , to clear doubts and in preparation for tests or exams.
A simple app that draws 3D graphs. The free version supports graphs in the form y = f(x, y), but the paid version supports other forms, including functions in cylindrical and spherical polar coordinates, parametric surfaces, and parametric curvesSelect Simple ODE Solver mode if your problem has only an equation or System ODEs mode if you has a System or Ordinary equations.
1) Enter the initial value for the independent variable, x0. 2) Enter the final value for the independent variable, xn. 3) Enter the step size for the method, h. 4) Enter the given initial value of the independent variable y0. 5) Select from the combo the integration method (default Euler method is selected). 6) Enter the function f(x, y) of your problem, for example. |
It is true that only schematics versions of 'life problems' lead to general mathematical theory. However: (a) the students bring 'life' into the classroom with them. (b) the process of moving from life to the APPROPRIATE' schematic is part of mathematics (applied mathematics).
Isn't there room for some movement in the class which involves some 'life' (open-ended messy problems of potential complexity) and the theory? Even when I think I have already done this - I have been struck by what happens when students ('good students') try to work back from the theory to a real, physical example. The experience reveals a lot of misunderstanding. The learning which happens then seems essential to a well-rounded course of mathematics. |
Differentiate-fundamental-and-derived-quantities
Best Results From
Yahoo Answers
From Omilili
A Review of Jean Jacques Rousseau's 'On the Origin of Equality'
Of the fundamental tenets of "equality" today, derive from this small booklet written by the French Philosopher quantities of food, or for preparing proper housing for the winter. It could be argued that, the increase A Review of Jean Jacques Rousseau's 'On the Origin of Equality' By Johann Luther As I read through Jean Jacques Rousseau'...
From Yahoo Answers
Question:I was wondering if any body could explain some advanced college math classes, what they are about, how they fit in to the how spectrum of math courses, and/or why you have to take them after you complete calc 3.
Ones in my college are Differential Equations 1 and 2, Linear Algebra, Modern Algebra, College Geometry, Advanced Calculus, Theory of Numbers, and Complex Variables. Only brief descriptions are given in the course catalog.
Answers:I have taken all these courses but it is just too much to type out the descriptions. Here are a couple from Wolfram...Go there and search by title.
Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems. Contour integration, for example, provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration.
The key result in complex analysis is the Cauchy integral theorem, which is the reason that single-variable complex analysis has so many nice results. A single example of the unexpected power of complex analysis is Picard's great theorem, which states that an analytic function assumes every complex number, with possibly one exception, infinitely often in any neighborhood of an essential singularity!
A fundamental result of complex analysis is the Cauchy-Riemann equations, which give the conditions a function must satisfy in order for a complex generalization of the derivative, the so-called complex derivative, to exist. When the complex derivative is defined "everywhere," the function is said to be analytic.
Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and engineering. Confusingly, linear algebra is not actually an algebra in the technical sense of the word "algebra" (i.e., a vector space over a field , and so on).
The matrix and determinant are extremely useful tools of linear algebra. One central problem of linear algebra is the solution of the matrix equation
for . While this can, in theory, be solved using a matrix inverse
other techniques such as Gaussian elimination are numerically more robust.
In addition to being used to describe the study of linear sets of equations, the term "linear algebra" is also used to describe a particular type of algebra. In particular, a linear algebra over a field has the structure of a ring with all the usual axioms for an inner addition and an inner multiplication together with distributive laws, therefore giving it more structure than a ring. A linear algebra also admits an outer operation of multiplication by scalars (that are elements of the underlying field ). For example, the set of all linear transformations from a vector space to itself over a field forms a linear algebra over . Another example of a linear algebra is the set of all real square matrices over the field of the real numbers.
Answers:Dear, you can not get all these e books for free on internet. Better buy these books. These books are copyright material and can not be downloaded for free even if available in the form of e books.
Try these web sites:
Try these web sites also
hsj
Question:A firm has the following average cost function:
AC= 50+ 10/Q
a) Show by differentiation that AC decreases indefinitely as Q increases. Give an economoic interpertation of this phenomenon.
b) Write down the equation for total cost. hence, write down the equation for total variable cost and average variable costs. state the value of fixed costs.
c) Write down the equation for marginal costs. Comment on the relatioinship between TC and MC in this example.
5stars answers
Answers:1. So why are you asking this economics question in the math section?
2. Parts a and b are completely independent. Which have you tried and how far did you get?
If you don't know how to differentiate:
average cost = total cost / quantity
so you can determine total cost as a function of average cost and quantity. From there:
And:
From Youtube
Units, Measurements and Theory of Errors - Concept Builder 1
The measurement is any physical quantity, either fundamental or derived, requires a 'reference standard' called Unit. The international system of unit is SI unit, which has seven fundamental unit and it is rational coherent and metric. Learn more at
Cardiomyogenic differentiation of Mesenchymal Stem cells (KUM2/9-15c)
Mesenchymal stem cells derived from bone marrow are capable of differentiating into cardiomyocytes. However the characteristics of the stem cells are poorly understood, and how the progeny of multipotent cells adopt one fate among several possible fates remains a fundamental question. A hierarchical model has been proposed on the in vitro differentiation of mesenchymal stem cells. Yamada and Umezawa show that mesenchymal stem cells in culture consisted of a mixture of at least three types of cells, ie, cardiac myoblasts, cardiac progenitors and multipotent stem cells, and suggest that commitment of a single-cell-derived stem cell toward a cardiac lineage is stochastic by a follow-up study of individual cells.
CalTech: Derivatives P2 chosen
CalTech: Derivatives P3. chosen |
Naive Lie Theory - 10 edition
Summary: In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called ''classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.This naive approach to Lie theory is originally due ...show moreto von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994). ...show less
201045 +$3.99 s/h
New
El Pinarillo Books Morden,
2010 Paperback New Book New and in stock. 10/19/2010 |
Absorb Mathematics
Absorb Mathematics is an excellent interactive course written by Kadie Armstrong, a mathematician. The lessons in it contain interactivity, explanations, and quiz questions. The course concentrates on geometry and trigonometry but includes a few other topics as well. While most of the content is accessible by a fee only, some lessons are available as free samples.
Maisonet Math
Worksheets and online quizzes on a variety of geometry (and other) topics. Look for the links in the left sidebar for Angles, Area, Circumference, Geometry, Transformations, and Volume.
A High School First Course in Euclidean Plane Geometry
This is a high school geometry course by Charles Aboughantous. It is based on Euclid's five postulates and his most common theorems. It promotes the art and the skills of developing logical proofs. Practice problems are included at the end of each chapter in three groups: geometric construction problems, computational problems, and theorematical problems. The answers to the computational problems are included at the end of the book. The solutions manual of the book contains detailed solutions to all the problems in the book. It is free to home schooled students upon proof of purchase of the book. Samples are found at |
Cart
Archive | Double-Slash
eBook version of the Algebra Survival Guide is HERE! Check it out on Amazon.com Price is 20% lower than that of the paperback version, and the e-version has several unique advantages over the paperback book.
Factoring by grouping is one of the trickier skills in Algebra 1. But by using a special form of notation, the double-slash, students can do this skill with greater ease. This post explains how this notation can help students tackle this challenging form of factoring.
Combining like terms confuses many students. But by using a special notation, the double-slash, students get a visual aid that helps them combine like terms with greater care. This post shows how to use the double-slash to combine like terms. And it offers practice problems and their solutions, too.
The double-slash notation comes to the rescue in algebra once again. In this post we learn how this clever notation device helps students combine positive and negative numbers, the trickiest pre-algebra concept of all. Read to find out how you can use this notation to make this concept easier for your students or children.
Algebra is an area of math that leads many students to make mistakes. Using a simple "Double-Slash" mark helps students wall off parts of algebra expressions from other parts, so that they avoid making mistakes. This post and the next several post will help educators learn how to use the "Double-Slash."
Algebraic expressions are covered with mental "land mines." Step the wrong way, and an expression will blow up on the page, making it impossible for students to move in the right direction. Fortunately there's a simple thing students can do to succeed at simplifying algebraic expressions, and that simple something is using what I call the "Double-Slash." This is the first in several blog posts that show educators how to use the "Double-Slash" as part of their everyday algebra instruction.
Welcome!
Here at Singing Turtle Press, we believe everyone should succeed at math, no matter how math phobic, no matter how right-brained, no matter what. Our products help students K-12 and beyond, including English language learners, and adults returning to college.
"I'm a returning college adult now in the fourth week of my College Algebra course. The Algebra Survival Guide has FINALLY filled in the gaps in my earlier education. Thank you to the third power. Thirty years of math phobia gone in three hours of reading."
— Mary Ellen Kirian, Lake Oswego, OR |
Queens, NY
Ticket Information
Who's Going
Event Details
Wayne State University of Detroit, MI is proud to offer a workshop for high school mathematics teachers. The course builds on algebraic modeling concepts developed in Algebra II, and all of the material presented is developed around real-world contexts that answers the question - When will I ever use this? It is designed for a wide range of student mathematical abilities.
There is no cost for participation in the workshop. Participants will gain access to materials including a full textbook, curriculum, and online support which can be implemented in any school as a fourth year mathematics course.
With more than 50 schools across Michigan, North Carolina, California, Georgia, and New York participating in the curriculum, the analytics course has proven to be popular amongst teachers, administrators, and students alike. As the only curriculum which seeks to answer the question of, "When will I ever use this?", partners have said the following about this opportunity:
Parents:
1). I don't know what you are doing but for the first time my child enjoys and finds success doing mathematics.
2). I hated math when I was in school. I wish I had had this course when I was in high school.
Students:
1). I like this course because it's the first time I have ever been asked my opinion in a math class. Some of the problems were really cool because it was my choice of what was most important, and I could see how different choices played out.
2). I used some of the tools that I learned to make a decision about which boy I would take to prom. I got to understand how to weigh variables, and how to use math to make better decisions.
Teachers:
1). I love this course. For the first time, I have not been scared to answer the question, How will I use this in my life. THANK YOU!!!!
2). This course has been a blessing. Even with an extreme range of student's abilities in my classroom, the content was interesting enough to keep the attention of the mathematic all stars, as well as some of my mathematically challenged students. The blend of application based learning with the real-world contexts made all of the students fascinated by the power of mathematic application to various industries and professions. |
The Calculus Tutor DVD Series will help students understand the fundamental elements of calculus- -how to take algebra and extends it to include rates of change between quantities. Concepts are introduced in an easy to understand way and step-by-step example problems help students understand each part of the process.
This lesson begins with introducing a limit that's then used to present the formal mathematical definition of the derivative. Grades 9-12. 26 minutes on DVD. |
Course Description: Math 8 for 7th Graders is an advanced seventh grade course designed to prepare students for the rigor of high school mathematics classes. This Common Core standards-based course completes the middle school curriculum's intent to help students make the transition from concrete arithmetic to abstract algebraic thinking. Math 8 for 7th Graders includes pre-algebra concepts and skills that set high expectations for all students. It makes provisions for enrichment and acceleration for advanced students. The course emphasizes algebraic thinking and applies it to other aspects of mathematics including Algebra I in the eighth grade or Math 8 : |
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able... more... |
Math Department
The Mathematics Department offers courses from Elementary Algebra through Calculus as well as Linear Algebra, Sequences and Series, Differential Equations, and Statistics. Before taking a math course students are required to take the math placement test to determine where they will start in the math sequence. The math faculty at Whatcom strive to create a learning environment conducive to student success by employing a variety of innovative and effective methods of instruction and educational support. |
Discrete Mathemetics
9780618415380
0618415386
Summary: Discrete Mathematics combines a balance of theory and applications with mathematical rigor and an accessible writing style. The author uses a range of examples to teach core concepts, while corresponding exercises allow students to apply what they learn. Throughout the text, engaging anecdotes and topics of interest inform as well as motivate learners. The text is ideal for one- or two-semester courses and for studen...ts who are typically mathematics, mathematics education, or computer science majors. Part I teaches student how to write proofs; Part II focuses on computation and problem solving. The second half of the book may also be suitable for introductory courses in combinatorics and graph theory.
Ferland is the author of Discrete Mathemetics, published 2008 under ISBN 9780618415380 and 0618415386. Four hundred ninety seven Discrete Mathemetics textbooks are available for sale on ValoreBooks.com, one hundred twenty used from the cheapest price of $61.03, or buy new starting at $184.60 |
anSets, Sequences and Mappings: The Basic Concepts of Analysis by Kenneth Anderson, Dick Wick Hall This text bridges the gap between beginning and advanced calculus. It offers a systematic development of the real number system and careful treatment of mappings, sequences, limits, continuity, and metric spaces. 1963 edition.
Product Description:Bonus Editorial Feature:
Hermann Weyl: The Search for Beautiful Truths
One |
Algebra 1, Algebra 2, Geometry, Advanced Mathematics, and Calculus each contain a series of lessons covering all areas of general math. Advanced Mathematics is a comprehensive precalculus course that includes advanced algebra, geometry, trigonometry, discrete mathematics, and mathematical analysis. Each lesson in the Saxon math program presents a small portion of math content (called an increment) that builds on prior knowledge and understanding.
Homeschool kits for the upper grades math programs include a textbook and Homeschool Packet (with test forms, textbook answers, and test answers), and a Solutions Manual is also available.
Saxon Teacher, a CD-ROM supplement that offers lesson instruction videos and video problem solutions in a convenient player, is also available for all Algebra 1 (3rd Edition), Algebra 2 (3rd Edition), Geometry, and Advanced Math.
By using Algebra 1and 2 (3rd Edition) and Advanced Math (2nd Edition), students can receive credit for one year of Euclidean geometry. This is the recommended path.
Students who are interested in taking the Saxon Geometry course may choose the 4th Edition Algebra 1 and Algebra 2 courses, which are designed to accompany Geometry. Featuring the same incremental approach that is the hallmark of the Saxon program, the 4th Edition Algebra 1 and Algebra 2 textbooks feature more algebra and precalculus content and fewer geometry lessons than their 3rd Edition counterparts.
<< Use the Product Offers on the left to navigate through this category. |
Linear Algebra : Introduction - 2nd edition
Summary: In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete and computational, and leads the reader to a choice of major applications (Markov chains, least-squares approximation, and solution of differential equations using Jordan normal form).
The first three chapters address the basics: matrices, vector s...show morepaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructor's taste and to the length of the course. Bronson's approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at the end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed features, this text will be a pleasure for professionals, teachers, and37.00 +$3.99 s/h
New
Webe Books Rushville, IL
PAPERBACK New 0120887843 Excellent condition. Never been used. **FREE** Delivery tracking with every book purchased |
Synopses & Reviews
Publisher Comments:
If mathematics is a language, then taking a topology course at the undergraduate level is cramming vocabulary and memorizing irregular verbs: a necessary, but not always exciting exercise one has to go through before one can read great works of literature in the original language. The present book grew out of notes for an introductory topology course at the University of Alberta. It provides a concise introduction to set-theoretic topology (and to a tiny little bit of algebraic topology). It is accessible to undergraduates from the second year on, but even beginning graduate students can benefit from some parts. Great care has been devoted to the selection of examples that are not self-serving, but already accessible for students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In some points, the book treats its material differently than other texts on the subject: * Baire's theorem is derived from Bourbaki's Mittag-Leffler theorem; * Nets are used extensively, in particular for an intuitive proof of Tychonoff's theorem; * A short and elegant, but little known proof for the Stone-Weierstrass theorem is given.
Synopsis:
Synopsis:
"Synopsis"
by Springer,"Synopsis"
by Springer, |
More About
This Textbook
Overview
Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples.
No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.
Related Subjects
Meet the Author
Mi Lu received her MS and PhD in electrical engineering from Rice University, Houston. She joined the Department of Electrical Engineering at Texas A&M University in 1987 and is currently a professor. Her research interests include computer arithmetic, parallel computing, parallel computer architectures, VLSI algorithms, and computer networks. She has published over one hundred technical papers, and has served as associate editor of the Journal of Computing and Information and the Information Sciences Journal. She was conference chairperson of the Fifth, Sixth, and Seventh International Conferences on Computer Science and Informatics. She served on the panel of the National Science Foundation, the panel of the IEEE Workshop on Imprecise and Approximate Computation, and many conference program committees. She is the chairperson of sixty research advisory committees for masters and doctoral students. Dr. Lu is a registered professional engineer and a senior member of the IEEE. She has been recognized in Who's Who |
Nature of Mathematics
Written for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl ...Show synopsisWritten for liberal arts students and based on the belief that learning to solve problems is the principal reason for studying mathematics, Karl Smith introduces students to Polya's problem-solving techniques and shows them how to use these techniques to solve unfamiliar problems that they encounter in their own lives. Through the emphasis on problem solving and estimation, along with numerous in-text study aids, students are assisted in understanding the concepts and mastering the techniques. In addition to the problem-solving emphasis, "The Nature Of Mathematics, 12e, International Edition" is renowned for its clear writing, coverage of historical topics, selection of topics, level, and excellent applications problems. Smith includes material on such practical real-world topics as finances (e.g. amortization, installment buying, annuities) and voting and apportionment. With the help of this text, thousands of students have 'experienced' mathematics rather than just do problems-and benefited from a writing style that boosts their confidence and fosters their ability to use mathematics effectively in their everyday livesFine. Shrink wrapped and unopened. Includes supplemental or...Fine. Shrink wrapped and unopened. Includes supplemental or companion materials if applicableFine. 1285563948 Used, but looks brand new. Only very slight...Fine. 1285563948 Annotated Edition. All orders ship SAME or NEXT...Very good.The title of this book does not indicate that it is the teacher's edition, neither is this reflected in the photo. If you read the entire description it is confusing. It does state that the teacher's edition is the same as the student edition, but does not in any way indicate that you are |
See What's Inside
Product Description
What is the relationship between fractions and rational numbers? Can you explain why the product of two fractions between 0 and 1 is less than either factor? How are rational numbers related to irrational numbers, which your students will study in later grades?
How much do you know… and how much do you need to know?
Helping your upper elementary school students develop a robust understanding of rational numbers requires that you understand this mathematics deeply. But what does that mean?
This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to rational numbersFocus on the ideas that you need to understand thoroughly to teach confidentlyFocus in High School Mathematics: Geometry mathematical reasoning. It is organized around one big idea, supported by multiple smaller, interconnected ideas—essential understandings.Taking you beyond a simple introduction to mathematical reasoning expressions, equations, and functions. It is organized around five big ideas, supported by multiple smaller, interconnected ideas—essential understandings.Taking you beyond a simple introduction to expressions, equations, and functions geometry. It is organized around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers highest quality for all students through vision, leadership, professional development, and research. |
Role an importance of mathematics especially calculas in business?
Detailed project about 6-7 pages discription
Asked By: JAck - 11/21/2012
Best Answer - Chosen by Asker
You need to write a project about 7 pages long? You should probably start with and opening paragraph explaining the many areas of business where calculus is used, such as in accounting, actuary, statistics, real estate, finance, insurance, physical sciences research, construction, architecture, computer |
Everyone could use some help improving their math skills at one time or another! Refresh your memory on a host of various mathematic functions, including fractions, decimals, percents, algebra, equations, graphs, probability, geometry and trigonometry. Step by Step instructions and practical application problems help keep information easy to understand and relevant to everyday life. Multiple choice tests help to monitor progress and a final test allows you to see where you still need improvement. 280 pages with glossary and index.
Customer Reviews for Mathematics Made Simple, Sixth Edition
This product has not yet been reviewed. Click here to continue to the product details page. |
Mathematical Tools for Physicists is a unique collection of 18 carefully reviewed articles, each one written by a renowned expert working in the relevant field. The result is beneficial to both advanced students as well as scientists at work; the former will appreciate it as a comprehensive introduction, while the latter will use it as a ready reference.... more...Contains some of the invited lectures presented at the International Conference Analysis, PDEs and Applications, held in Rome in July 2008, and dedicated to Vladimir G Maz'ya on the occasion of his 70th birthday. This title present surveys as well as fresh results in the areas in which Maz'ya gave seminal contributions. more...
This volume continues the tradition of the Advances series. It contains contributions from experts in the field of atomic, molecular, and optical (AMO) physics. The articles contain some review material, but are intended to provide a comprehensive picture of recent important developments in AMO physics. Both theoretical and experimental articles are... more...
What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt . With his trademark combination... more... |
Books
Matrices
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site,
codingthematrix.com
provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics.
Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program
The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool.
This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems
Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.
"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine. This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.
The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.
This work shows that linear algebra is a natural language for special relativity. Requiring a minimum of expertise beyond basic matrix theory, the authors use full-color illustrations to introduce inertial frames and Minkowski diagrams that explain the nature of simultaneity, why faster-than-light travel is impossible, and the proper way to add velocities. We resolve the twin paradox, the train-in-tunnel paradox, the pea-shooter paradox and the lesser-known accommodating universe paradox and the bug-rivet paradox that shows how rigidity is incompatible with special relativity. Since Einstein, in his seminal 1905 paper introducing the theory of special relativity, acknowledged his debt to Clerk Maxwell, we fully develop Maxwell's four equations that unify the theories of electricity, optics, and magnetism.These equations also lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell himself was unaware that light was a special case of electromagnetic waves.) Several chapters are devoted to early experiments of Roemer, Fizeau, and de Sitter in their efforts to measure the speed of light along with the Michelson-Morley experiment abolishing the necessity of a universal aether. The exposition is thorough, but not overly technical, and bountifully illustrated by cartoons. Supplemental interactive animations are found at Special-Relativity-Illustrated.com. This book is be suitable for a one-semester general-education introduction to special relativity. It is especially well-suited to self-study by interested laypersons or use as a supplement to a more traditional text.
Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame., and scientists.
"This book is intended to teach useful matrix algebra to 'students, teachers, consultants, researchers, and practitioners' in 'statistics and other quantitative methods'.The author concentrates on practical matters, and writes in a friendly and informal style . . . this is a useful and enjoyable book to have at hand." -Biometrics
This book is an easy-to-understand guide to matrix algebra and its uses in statistical analysis. The material is presented in an explanatory style rather than the formal theorem-proof format. This self-contained text includes numerous applied illustrations, numerical examples, and exercises.
Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results.
The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book also includes polynomial interpolation at Chebyshev points, use of the MATLAB package Chebfun, and a section on the fast Fourier transform. Supplementary materials are available online. |
books.google.co.uk - This... and Fundamental Concepts of Mathematics
Foundations and Fundamental Concepts of Mathematics
This as bases for understanding the changing nature of mathematics. Among the topics covered in this wide-ranging text are: mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, the real numbers system, sets, logic and philosophy and more. The emphasis on axiomatic procedures provides important background for studying and applying more advanced topics, while the inclusion of the historical roots of both algebra and geometry provides essential information for prospective teachers of school mathematics. The readable style and sets of challenging exercises from the popular earlier editions have been continued and extended in the present edition, making this a very welcome and useful version of a classic treatment of the foundations of mathematics. "A truly satisfying book." — Dr. Bruce E. Meserve, Professor Emeritus, University of Vermont.
LibraryThing Review
User Review - LibraryThing
This is an excellent book tracing the history of deductive procedures and key concepts relevant to the foundation of modern mathematics, specific focus on deductive axiomatics and the utility of generality. The book starts with babylonian and egyptian empirical mathematics which were based upon experience and induction, contrast them to deduction, and then moves onto material axiomatics and Euclids elements. Next we encounter non-euclidiean geometry as a shaking up in the foundations of math, and then we encounter generalizations of geometry and hilberts axiomatic treatment of geometry. Following this we get an introduction to algebraic structure with comments on algebra before it was realized that the laws of "normal" algebra could be dropped (eg: commutation) -- called here "the liberation of algebra, analagous to the liberation of geometry (dropping the parallel postulate) -- to give way to new (and useful) structures such as Hamilton's Quaternions, and Caley's Matrices. Fields, and ordered fields are presented. Groups are presented along with their utility to geometry. In the problems you can get introduced to other structures as well, such as rings. Next up we get a full statement of the formal axiomatic method and it's importance to pure mathematics. Pure mathematics is contrasted to applied mathematics which in this view is verifying concrete models or interpretations of a pure systems. Illuminatings examples are given. Finally in the last three chapters you see an overview of how to construct the real numbers based on the smaller axiom set of the naturals following a chain of definitional introductions naturals => integers => rationals => reals => complex numbers and what this means for the foundations of math. Then you get a brief intro to set theory and logic along discussions on some of the philosophic issues. Splendid book. You can read this with no background whatsoever and you will come away having learned many important concepts and notions which will serve you very well if you continue to take the path of exploring the world of mathematics.
Cool little history that starts in the ancient world and works through modern development of formal axiomatics (Gödel noted as crushing formal axiomatics, which everyone noted and then yawned).Read full review
book.store.bg - Foundations and Fundamental Concepts of ... Like the title says, Eves' text is a historical analysis and introduction to the foundations and fundamental concepts of mathematics. If you are interested ... import.book.store.bg/ product/ id-048669609X/ foundations-and-fundamental-concepts-of-mathematics.html?printthispage=1 |
Essential Math Methods F/phy.>intl Ed.<
9780120598786
ISBN:
0120598787
Publisher: Elsevier Science & Technology Books
Summary: This new, more accessible version of Arfken/Weber's blockbuster bestseller Mathematical Methods for Physicists 5/e is the most comprehensive and modern resource for using mathematics to solve physics problems. New features: * Many detailed, worked-out examples illustrate how to use and apply mathematical techniques to solve physics problems * Frequent and thorough explanations help readers understand, recall, and app...ly the theory * Introductions and review material provide context and extra support for key ideas * Many routine problems reinforce basic, foundational concepts and computations REVIEWERS SAY: "Examples are excellent. They cover a wide range of physics problems." - Bing Zhou, University of Michigan "The ideas are communicated very well and it is easy to understand...It has a more modern treatment than most, has a very complete range of topics and each is treated in sufficient detail....I'm not aware of another better book at this level..." -Gary Wysin, Kansas State University[read more] |
I'm taking a college Calculus course for the first time in my life, and I find that everything is just easier than it was for me when I was taking my college course in Linear Algebra. When I spoke to my friend about this, he said that a possibility was that Calculus is more intuitive, and I am just naturally more atoned to that kind of thinking. Is there any possibility to this, and if so, could someone explain it further?
If it was a proper first course in linear algebra, it was quite proof-intensive, while a typical first/second year calculus course focuses more on computation rather than rigorously proving theorems. In general, proof-based courses are harder than computation, as they require a thorough understanding and a certain amount of creativity, whereas computation is more often than not a purely mechanical process thag can be completed after memorising a set of "rules".
I wasn't allowed to use one, and frankly a calculator wasn't that useful unless it would integrate and do derivatives for you. Even then I found letting something do this for you ends up making you prone to other types of mistakes.
I took AP Calculus BC (I'm told it is the equivalent of Calc I, II, and III) and there were times we were sometimes allowed to have our calculator. If it was something you can do easily with a program, chances are we would not be allowed a calculator e.g. we were not allowed a calculator for Euler's Method.
The people I know who took BC covered material in calc II but not to a similar depth whatsoever, it is important to note that I took a very rigourous first year calculus course in which we proved everything we used and every test/exam was focused around proofs.
I agree. I remember feeling totally out of my league in linear algebra but I breezed through college calc courses. Flash forward some 10+ years to last summer when I taught a basic course on linear algebra and diff eq and wondered why I ever thought lin alg was hard. Guess I just wasn't ready for it at the time. Wish I had been as my prof was a pretty awesome guy.
At my school, the department mandates that you take Calc II (MATH220) before you take either, but LA is MATH203 whereas Calc III is MATH221, and apparently our school uses their numbering system somehow to rate the difficulty of the course (which I never understood, seeing as graph theory and discrete math II was "MATH307" but Calculus II was 220, despite the latter being far more work-intensive).
I hated linear algebra, cool concepts but for some reason they put way too much emphasis on row reducing matrices (at least in linear algebra 1). That shit is boring. I've always found calculus interesting.
I agree. For my homework problems I don't want to have to find the singular value decomposition of a bunch of matrices or find orthogonal bases for all the eigenspaces, but that's always what the homework was. Suuuuper boring.
Believe it or not, that helps you build intuition on what is actually happening. If you just have someone throw the equations at you without describing what is going on you wouldn't get the concepts as well.
I somewhat disagree. Many of the algorithms used for finding some factorization or other don't really show the theory behind what's happening. For example, the orthogonal diagonalization of a symmetric matrix. I can sit at my desk all day finding one orthonormal basis of eigenvectors after another to put in a matrix P, and then putting the eigenvalues in D, but it won't build any more fundamental understanding of the theory.
All I can say is chugging through this stuff helped me out. It wasn't a complete picture though, as maybe you are pointing out. Matlab helped a lot too since you could sort of pause between operations and look at the objects in memory different ways.
I am not sure I understand here. Do you get points for being better than other people at the structure of proofs, or do you get points for the proof being correct? Is it heavily curved?
Generally, a good proofs course is supposed to grade you on structure and results, and I have rarely been in one that curved the grade. I would say my experience has been 30 percent of the grade for one problem is on the structure, and 70 percent is on the result being correct (with partial credit awarded for whatever is correct). So for example, if half my proof is right and then I made some mistake, but the structure is good, I may get like 6-7 points out of 10 for that problem.
I'm just good at math tests, so I would show up and figure things out on the test. I'd write down what I thought the correct answer was and then get a good grade. I didn't look at tests or think about the tests as deeply as you are. I just knew if I showed up and tried my best on proof based tests, everything would work out.
Originally you made it sound like as long as you were better than the other students at the format of proofs you did ok. I was just commenting that that isn't the best way to run a math class.
You should be graded on results, not how much better you are than other people. If its wrong its wrong. It doesn't seem like you were saying that after all. I also frequently show up and just do the tests without much preparation. That's not a problem.
I really liked linear algebra for engineers. After the first quiz in week two on row reduction by hand we were shown how to use our TIs to do it and then moved on to applications. Helped immensely with the physics courses.
I find algebra easier too. For me it is more logical and the proofs are more intuitive. Calculus is much more abstract for me and the proofs are very complex and harder for me to grasp (especially in multivariable calculus).
To be clear, are we talking about abstract algebra or the class they teach in high school and freshman year of college where you learn about absolute value, polynomials, factoring and "find x?" I realize that these are actually the same thing, but I hope you understand what I mean here.
Yes, I am talking about the abstract algebra (we call it only algebra where I live). From reading this thread I found out that Calculus is taught here differently than in the USA - our calculus is based heavily on theory and proofs from the begining. That is why I find abstract algebra easier.
Most calculus and diff eq relies on algorithms to solve equations and some equation manipulation. You were always given something to start with (equation, word problem, etc) and generally asked to find a given final product (volume, value, antiderivative). The equations and functions you use are extensions of the arithmetic and variable polynomial algebra we've been taught for the past 12 grades of our lives.
Algebra, however, generally asks for "truth" in the form of proofs. Otherwise, it also deals with non-numeric elements, which does not obey the communicative properties we are so familiar with.
I felt a lot the same way in term of intuition. Though, I think it's more to do with how we've been taught (unless you were taught New Math).
I was thinking about this recently, why calc theory isn't included in calc1/2/~3. I think their purpose is to motivate applications, because there is a fuckton of them, and half of your upper level courses will explain calculus (real/complex analysis, topology) further or require their use (differential __________, Fourier analysis). So you really have to hold onto what it's for. Calc is so f-ing useful, and so the uses are highlighted by the bunches of physics word problems. It's also very visual-- you can draw out every aspect of a calc problem. Linear algebra is taught with rigor in mind. CS may appreciate it more.
I think a lot of calculus is more intuitive than linear algebra (I mean, how many people have a real intuitive understanding of what a singular matrix is?). But perhaps also your professor hasn't pushed you enough yet in the applications of calculus. One of the problems I recall from my first year calculus class was to prove that at any time, there are two opposite points on the Earth that have the same temperature (assume temperature is a continuous function). See if you can figure it out before googling for the answer (I couldn't do it).
They actually put that as the last problem on my Calc 1 final. I think I got it at last minute (I know it now, but I'm not certain if my rushed last-minute scribbling when I figured it out back then had been fully correct), but from the groaning of the others, it wasn't a well-solved problem.
Most of the other questions on the test were "calculate ____" types. I think most are just prepped for that and not for more abstract ones.
Linear algebra really clicked for me as an undergraduate because my professor made us use Matlab. We still had to do stuff by hand on smaller matrices, but using Matlab and being able to look at different objects stored in memory and how they change when you do different operations was very useful.
I really wish I'd been introduced to Matlab then, as it probably would have helped me as well. Now, as a computer vision engineer, I use it most days in my work (I've even got a Matlab decal on my car's bumper!).
Props bro! I worked in computer vision during my graduate career as a research assistant. I have a couple papers on it I was co-author on but we didn't get stellar results compared to the new Pitt-patt or the stuff Dr. Pantic is doing now. We were a few percentage points better that state of art for our recognition rates but that changed like one or two conferences after our results were published. I was on the math side here, using wavelets and such to construct features.
Yeah, I was really lucky to have such an awesome professor. The guy didn't have his PhD yet, and he worked at a community college, but I haven't had a better professor at teaching the material nor preparing you for later courses. He was a hard ass on the homework but it was to our benefit.
For example, I was way ahead of everyone else in my numerical analysis classes because we learned Matlab in his Diff. Eq. and Linear Algebra classes. Even when I took the graduate level numerical class there were people that had never seen it before.
This, and also I find calculus really interesting. Before hearing anything about calculus I wouldn't even imagine how to compute work over a distance for an increasing force, my first guess it would be an insanely hard computation. It's like magic for me, of which you understand the workings.
I think it depends a lot on your personal preference, but also on your teachers.
With me, it was just the opposite. The teacher I had at the Calculus course was pretty bad, he just recited the demonstrations and had a rule that all questions must wait for the seminar, no questions were allowed during his course. So there were usually three or four days between the time when we were exposed to the information and the time we could ask for clarifications.
The Algebra teacher however was one of the best I've had, and very passionate about his subject, so although Algebra might be considered more difficult, I loved every minute of it and it felt much easier than Calculus.
I have found higher level math easier in the sense I always wanted to know why something was true. (i.e the proof) Any proof has always gathered my intrest. Another problem for me is I haven't had an algebra course since high school because I took college Algebra in high school for the credit. I will be a Senior undergrad with a Major in Math next year as well.
TL;DR: I'm the same way because its been so long since an algebra class.
Isn't algebra like a piece of cake for you though? I found after taking calculus I-III, diff. eq., and linear algebra I basically can do anything with algebra that has ever come in front of me so far. I remember having 2-3 pages of algebra just for one problem a lot of the time in my calculus classes. The truly hard classes were my senior and graduate level proofs classes since a lot of the time it was trying to find a trick or use some magical form where everything falls out. These were not immediately apparent most of the time.
Calculus and Linear Algebra are not mutually exclusive - in fact it is natural to extend calculus to more than 2-3 dimensions, at which point you should be representing everything with vectors and matrices. Calculus in school probably comes off easier to a lot of people because it is taught in low dimensional space and is easy to visualize.
Well Linear Algebra is a natural extension to Calculus III really (in terms of difficulty). Some people are thrown off by having "Algebra" in the course title. I was unaware that you could even take Linear Algebra before Calc III, much less Calc I.
I sometimes find that I have a very strong sense of geometric intuition that makes calculus and graph theory very easy to envision, but that I sometimes struggle with memorizing and computation. Even so, I think it's fair to say that because it's math, it's all the same thing, only examined from different lenses - a function can be represented as a matrix, or a set, or a geometric picture, or a discrete graph, so saying "is linear algebra more intuitive than calculus" is like asking if "cooking spaghetti" is more intuitive than boiling water, putting noodles in and then screening them through a colander.
If your math classes only involve learning algorithms (how to do integration by parts, or take derivatives, or matrix transformations), I suppose it's possible that some algorithms are easier than the others. But my experience teaches me that mathematical intuition in writing proofs can involve being able to engage universality - for example, that an isomorphism can be between to graphs, two matrices, or two sets, but the idea of structure preservation is common to all of them.
Me too regarding 3 and 2. I took calc 2 in high school and struggled through it, I did fail a final but because it was high school the overall grade ended up okay. I also ended up getting a 5 on the AP test which shocked me! Then calc 3 was my first college math class and I found it really easy (and I know many others didn't, so I don't think it was just an easy teacher). I think it would make so much more sense to put calc 1 and calc 3 material together, and then do some of the harder topics from calc 2 last.
I did extremely well in Calc 1 and 2. I took those in high school with a teacher that really cared about each student, and it all clicked to me. She always went over homework, which I think was the biggest help of all. Calc 3 in college consisted of teacher missing 3 classes, webassigns with no explanation for why I got something wrong, and the whole "help yourself" mentality that college teachers show off. I got an A average on the webassigns, but the exams were too big and they had stuff that we learned three weeks back. Final was cumulative too.
My first exam was a 60. No one did well on this, but I did much worse than the average, so no excuse. Second exam was a 97, and I had a "much better than expected" face going on. The final could replace your lowest exam grade if you did better on it, and I did, but it was like a 79 or something. Since this was like 50% of the grade for me (because it replaced first exam), that weight brought be down to a B-.
I've always done well in math classes, but the sheer amount of info in a semester with a whole new dimension just took a toll on my ability to remember things for an exam. I liked the calculus of Calc 3. Not dot product or cross product or anything that wasn't differentiation or integration.
The classes I always ended up being disappointed in myself for were always low level math courses. That damned C in Calc 3, all cause I failed the final, and that damned C for not caring about linear algebra.
When I was younger I could visualize continuous field transforms, so calculus was much easier. As I grew older, my skills in analysis, grammar, and proofs grew much stronger and now I find algebra easier. |
Series
Lessons: 30
Total Time: 7h 33m
Use: Watch Online & Download
Access Period: Unlimited
Created At: 01/20/2012
Last Updated At: 12/23/2013
Here is your help for Beginning Algebra and Geometry. Very basic math instruction gets you started. It's your to keep. Use it and share it as much as you'd like. Remember the best way to learn math is to teach it to someone else. So, now, you learn it and then you teach it. You may be surprised what a good learning strategy that is. You will be the one helping others with their math!
This series includes the Beginning Algebra Series AND the Basic Geometry Series. It is a better buy for your money than buying each one separately. Get them while you can and have them when you need them. I am happy for you to share them with a friend.
These math help lessons are especially for people who really, really struggle with math. I use repetition and very basic examples to show you how to work the problems. If you are a math whiz, this is not what you need.
Every Algebra video has a video guide sheet and a worksheet for you to practice. The answers are for you to check your work. Never move to the next concept until you understand the one you are working on. If you do, you will be building on a weak foundation and it WILL come back to haunt you.
It is my wish that having these videos in your virtual library will give you that extra personal touch we all need. You may stream them from this site as often as needed or you may download them. They are yours to keep. And share.
Hope you enjoy using them and being successful as you begin to learn Algebra and Geometry! Have fun!
About this Author
Welcome! I'm so glad you are here! Math help is here for you when you need it.
I believe that using these Algebra and Geometry videos will help you understand the basics of Algebra and Geometry.
Some students try very hard and still struggle to pass math. They start off strong but things quickly begin to fall apart. That happens as soon as the student becomes lost. Teenagers who find themselves in this position often let it "get away from them" before they seek help. Because Math is always a class of stepping stones, it rarely gets better without help.
I urge you to seek help from your child's teacher first. Always. These Algebra and Geometry videos can help too. You can watch...
Below are the descriptions for each of the lessons included in the
series:
How To Add Like Terms
Remember back in elementary school when math made sense? This video helps you feel that way about math again. Starting with "adding like terms", you can build a strong foundation so you can understand math from now on!
Learning to "add like terms" is one of the first things you learn in Algebra. This algebra video lesson explains addition in a way that anyone can understand.
When you need Math help, it is best to start with something you already know. Since it's easy to understand addition in Arithmetic, this video starts there and shows you how much Algebra is like Arithmetic.
I repeat things a lot because I know that helps. You need to practice a lot because that helps too.
Print out the Guide and Practice along with Answers for you to check your work. If you've never done Algebra before, this is a good place to start! It is fail-proof.
Learn To Multiply in Algebra
Just like in Arithmetic, you have to Add, Subtract, Multiply, and Divide in Algebra. It's not really harder, it's just different.
This video shows you how to multiply. It shows you the signs, the symbols, and the terminology. It doesn't confuse things with negatives. That comes later.
Print the Guide to work as you watch the video.
Then print the Practice for....you guessed it...more practice. I challenge you to "get better" at Algebra by practicing, practicing, practicing. Okay? Give it a try. You'll be glad you did.
What Are Integers Anyway?
This video will show you exactly what integers are!
Arithmetic uses only positive numbers and zero. Algebra uses negative numbers too! This is a big deal! Since Algebra uses "integers" all the time you really need to know everything about them.
The number line is a picture of the real numbers. You will see the difference in counting numbers, whole numbers, and integers. The number line is the basis of all rules involving integers and is essential to add, subtract, multiply, and divide with positive and negative numbers.
If you've studied Algebra before you know you must know your sign rules. I will explain them to you with a number line. Once that makes sense, then the rules are nice shortcuts to know.
Remember it takes a lot of practice and that is where you come in. Work along with me as you watch the video and continue to practice until you are an expert yourself!
Print the Practice and Answers and try my Fail-Proof approach. Repeat, Repeat, Repeat until you can teach it to someone else.
Adding Positive and Negative Numbers
Note: You can buy just this lesson or the entire series.
I'm just going to tell you the truth. You must be able to work with negative numbers or you will never get good at Algebra. On this video I show you how to combine positive and negative numbers. First I explain it the long way so you can add integers even if you don't "know your sign rules". However, you will get very tired of having to do everything the looooong way. That's why there are rules, or shortcuts.
You'll love the rules because they will save you so much time! But first you must understand where they come from and then... learn them 'by heart'. You will be a much better Algebra student once you know the sign rules. Until you know them really well, you will struggle.
Watch my video and I will explain how they work and why. You will understand. I make it easy. LOL.
This is where it all starts.
Once again, this video lesson is great math help whether you are brand new to Algebra or just reviewing the subject to pass a test or go back to school. This video is the most important one to help you move into more advanced math topics.
Work along with me. Then download the sheets and practice, practice, practice. Watch the video as many times as you need to.
Multiplying Positive And Negative Numbers
This video is about the "M" word. I hate telling students to memorize something but this time....that's the truth. You have to memorize these three rules.
If you want to be successful in Algebra you must learn to add, subtract, multiply, and divide with positive and negative numbers. This video shows you how these rules work and how to use them.
As you watch this video, make sure each step is clear to you. If it is not, pause the lesson, rewind, and watch again. Download the PDF and work right along with me.
In the end you will know these rules "as well as you know your name". That is what it takes to move forward with a good foundation.
The best math help you can find anywhere allows you to work at your own pace, encourages repetition, and talks to you 1:1. That is what this video offers you.
Multiplying Positive and Negative Numbers Cont'd
Once you learn the signs laws for multiplying by heart, you can learn to handle more complex problems. This video is a more in depth look at multiplication. Whether you are multiplying fractions and any number of terms, it is easy to apply the rules, once you know them!
It takes practice with these problems until they become second nature. You will learn a few shortcuts which you can use, not only to save time, but to check your problems and catch sign errors. Since one sign error can ruin an entire problem, you have to "get" this or forever fail Algebra. That's the cold hard truth.
Work the problems along with me and keep practicing. That is the way to success.
Solving Linear Equations
Once you have learned the basic of the language of Algebra you will quickly start solving equations. The first equations you will solve are linear equations. This video breaks down the process of solving linear equations into easy-to-follow steps.
The equations on this video are all one step equations. The examples show you how to use the inverse operation to get the variable by itself. The goal is always to get the variable on a side by itself.
As you move into any advanced math class you will always need to solve equations. This video is paced slowly to provide the first important steps for the foundation you will need. Stay tuned for more videos on solving equations.
Work along with me and use all the downloadable practice.
Solving Two Step Linear Equations
When you first get started in Algebra, one of the first things you learn to do is solve equations. This video solves equations that require two steps. It shows you how to know which step to do first and how to check to see if your answer is correct.
Equations in Algebra get to be much longer and 'more complicated' than these. This is where you start so that you will have the foundation to move ahead. If you are absent from school when your teacher explains this process, this video will help you 'catch up' quickly. Whew! That's a good feeling. Being lost and getting behind is no fun!
How To Solve Linear Inequalities
Now that you have learned to solve linear equations, let's take a look at inequalities. There are very few differences in solving linear inequalities and solving linear equations so this will be easy for you to understand with a little practice.
Several examples are included on this video to show you step-by-step how to proceed. They are not intended to be difficult but to show you how they differ from equations. Watch me work the problems first, then go back and work them by yourself. Compare your answers to mine.
Even though linear inequalities can get much longer and more complex than these examples, they are worked the same way. The better you become at solving linear equations, the better you will be with inequalities.
Equations are, at all times, stating that two quantities are equal. Inequalities are stating that, given two quantities, they may be unequal...and if they are, the inequality sign will tell you which one is larger.
If Inequality statements are brand new to you, they are first introduced on the Number Line video.
Meaning Of Exponents
Exponents are everywhere in Algebra. You just can't get very far without understanding what they are and how they work. When you watch this video you will learn exactly that.
Exponents are wonderful shortcuts and they speak a language of their own. Always begin at the beginning, at the most basic level. You will have a good foundation that way and you will build your confidence in mathematics.
Download the Guide and along with me as you watch the video. Pat yourself on the back every time you are correct. I know that will be most of the time. :) If it isn't, ask me to slow down or repeat something for you by stopping the video and replaying what you need to hear and see again.
The download the Practice Sheet.
Master these little, tiny numbers and they will never defeat you.
Laws Of Exponents
Once you really understand what exponents are, it's time to learn how to use them. Whenever you notice the same thing occuring over and over again in math, you can expect to find a law.
Exponent Laws are derived from patterns that show up every time you use the meaning of exponents. When you multiply, patterns show up. When you divide, patterns show up. When you raise a power to another power, patterns show up.
This video will explain each one of these patterns and show you exactly how they work. Then you will learn the Laws of Exponents. It is information you really need to practice until it becomes natural.
Work the "Guide" as you watch the video. Then work the Practice page.
Parallel Lines And Angles
Parallel lines are everywhere you look in Geometry. They are found in squares, rectangles, and parallelograms. The information you gain through parallel lines is mostly about angles so this video will focus on angles formed by parallels.
Students like this section because there are patterns which are easy to see. Once you see the patterns and learn the names of the angles you can work almost any problem with parallel lines.
Just remember. Whenever you see lines that are parallel, it is all about the angles formed by the transversal. Look for them!
Point, Line, Plane
Well, this is where you start in Geometry. You're going to learn a lot more about a point, a line, and a plane than you can imagine. Actually it is impossible to "define" these terms so we will just describe them and make sure you know all about them.
If I can find a "Pointalism" picture from one of my students, I will post it here...just for fun.
Seriously, all geometric figures are made up of points. We connect points to form shapes of all kinds. So without points, lines, and planes Geometry would not exist.
Stick with me and you'll be off to a good start!
Postulates and Theorems
Even the words sound intimidating! What are Postulates and Theorems anyway? They've been around for a long time and contain all the "rules" of Geometry. This video explains the difference between Postulates and Theorems in a way that is not as strange as they sound.
Once you know your Postulates, Theorems, and definitions, there is nothing in Geometry that you cannot do. Isn't that a good feeling?
If-Then Statements
Geometry is just full of If-Then Statements! Usually they are called Conditional Statements. We all use if-then statements everyday as we go about our day. This video will help you see what conditional statements are actually saying to you...in Geometry.
Converse statements, Inverse statements, and Contrapositive statements all start with a Conditional statement. What ARE all those kinds of statements? This video will tell you. That way, when you see it on your SAT, you will know exactly what it is talking about. Gotta speak the language to have any shot at success.
We will see what happens to a statement when we swith the if-then parts, or if we make them both negative.
You probably know "hypothesis" and "conclusion" from Science. That will help too.
Introduction To Angles
You hear people talking about angles all the time but what, exactly, are they? I know it sounds like a simple questions, and it is really, but looking closely at the definition will start you off with a firm footing in Geometry. Math help isn't really very helpful if it skips too much material and starts you off in the dark!
This video will define "angle" for you and show you exactly what an angle is and what makes an angle. Then it will talk with you about different kinds of angles so when you come across these terms, you will know what they are talking about.
For example, if I go on and on about adjacent angles, and you have no idea what that means...it really doesn't matter what else I say because you will be lost. That's what happens in many classrooms. Always ask when there is something you don't understand.
However, there is only so much time in a "regular" classoom so it's impossible for your teacher to stay on the basics for very long. Me? I can stay on them as long as I want to. And you can replay me as many times as it takes.
More About Angles
When you listen to your teacher in Geometry,she, or he, will mention angles every day about a hundred times! You see, then, how important they are. If you don't want to get lost, stick with this video until you really understand all of it.
The Angle Addition Postulates is explained on this math help video. There are a lot of times you need to add angles together. It might seem kind of obvious but it is necessary to learn how to add them, how to name them, and what allows you to add them. That's where the Angle Addition Postulate comes in. Your book might call it something else similar.
Some pairs of angles are called complementary. Some pairs are called supplementary. And some pairs are called Linear Pairs. Whew! That's a lot of different pairs of angles. Not hard though. You'll see.
Watch the video whenever you need to review these terms and again right before the test.
Kinds Of Triangles
Triangles are one of the most familiar shapes in the world. As simple as a triangle is, there are several different kinds of triangles and they have different properties. We will also look at the interior, the exterior, as well as the triangle itself.
In this video you will learn all about each type of triangle. You will learn about their angles and their sides and the relationships between sides and angles. Make sure you commit all definitions to memory so when you need to write a proof involving a triangle, you will have all the tools you need.
Enjoy this lesson. It's very straightforward and not difficult at all. Just get all the details and terminology! Success is in the details!
180 Degrees In A Triangle
In this video you will learn two very important theorems about triangles. Not only will you learn the theorems but you will see me prove them. As I walk you through the proofs you will become more comfortable with writing your own proofs in the future. Right now just focus on learning these two concepts.
Ever wondered why there were 180 degrees in every triangle? No matter the size, type, or location of a triangle, the angles always add up to 180 degrees. This video will show you why. This is a theorem you must, must, must learn. Or else....as they say!
Another theorem on this video is the Exterior Angle Theorem. I am proving this theorem for you by writing a formal proof. Watch me, listen carefully, follow the steps. It is intended only to help you get more comfortable with proofs.
The more comfortable you get, the less you will freak out when you have to write a proof of your own. It's coming you know. Better to get all these basics out of the way first!
Work hard!
How To Prove Vertical Angles Are Congruent
Vertical angles! We love them! They are so easy to use and provide a real comfort level when beginning Geometry. This proof shows you "why" vertical angles are congruent. It proves that they are 'always' congruent. If you need to see how and why vertical angles are congruent, watch this.
Once this theorem is proven, it can be used anytime in the future when you have vertical angles. First of all make sure you recognize vertical angles so you will know when you have them. Then be on the look out for them!
Vertical angles are formed whenever two lines cross (intersect). You will find them hidden in many drawings that contain more than two lines. That is why you want to look for them. Think of it as a puzzle and keep your eyes open for vertical angles.
After this video you will understand why they are always congruent and you will understand how to work with them. Whenever you get a problem with vertical angles, go ahead and mark them congruent as soon as you sketch the drawing. Don't draw too small. The more you can actually see, the better and quicker solutions will begin to come together.
Enjoy working with vertical angles. They usually lead you to more information to help you solve a problem.
Properties Used In Proofs
Many students have trouble writing proofs by themselves. One essential step when writing Geometry proofs is knowing the definitions, properties, and theorems. This video explains the most used properties.
Whether in Geometry or Algebra, for example, the Addition Property of Equality is used over and over.
Very simply put, you use this property whenever you add the same value to both sides of an equaition.
In this video you will see examples of this property plus the Subtraction Property of Equality, Multiplication Property of Equality, and Division Property of Equality.
Other properties that occur frequently are the Reflexive Property, Symmetric Property, and Transitive Property.
Watch the video. Refer back to it as often as you need to until these properties are as easy as pie and as clear as day!
Commutative, Associative, Distributive, Identity
This video explains the Commutative, Associative, and Distributive Properties. They are not very fun or interesting,to tell you the truth, but you need to know them. When I first learned them I thought they were pointless. I didn't understand why in the world they were in every math course I took. You may be like that too. Eventually, as you take more and more math classes, you will see that they never go away...and you'll begin to understand why you need these properties. This video lesson is more like eating your veggies than eating dessert! Just telling you the truth.
3rd Angle Of A Triangle Proof
It's fairly obvious that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. However, how to write the proof may not be so obvious. For that matter, how to write ANY proof may not be so obvious!
That is probably the understatement of the world! Most students find proofs to be very difficult. This video "illustrates" a proof but doesn't really teach you how to write a proof. That will need a video all it's own! Coming soon.
For now, the most important part of this video is to get the concept of the 3rd angle...and, thank goodness, that IS very easy to get.
Learn this theorem. Do not worry if you cannot write the proof as I did. Try to follow me though. At this stage, being able to just follow my proof is enough. The concept is important to know. The proof...just follow me for now.
Algebraic Examples In Geometry
Sometimes you just need extra practice in solving geometry problems using algebra. Most students like this part of Geometry more than proofs and definitons. Do you?
You have four problems to solve on this video. Work them along with me. One is vertical angles. One uses angle bisector. A third problem uses linear pairs and the last problem uses supplementary angles.
First of all, solve for x. Then find the measure of the angle. It is so easy to double check these and know for sure if you are right. I think you'll like these.
As I say in the videa "Math is not a spectator sport." You can't just watch and just listen if you want to really learn and remember what you learn. You have to do the problems too. Work them with me, then work them by yourself.
Midpoint
Well, now that we've gotten started in Geometry we'll just forge ahead and talk more about points, lines, and planes. What happens when two lines intersect? What does intersect mean? What is a midpoint of a line segment? If two line segments are congruent, what does that mean about the length of each?
This might be more detail that you really want to know but, just stay with me. In the long run you will be so glad you are comfortable with all these details about distance, length, and congruence.
Geometry is all about logical thinking. It is about moving from one fact logically to another fact and being able to back them up. You can back up your geometry facts with definitions, Postulates, and Theorems...but you can't make it up and you can't go by "how things look".
If you agree not to just "go by how things look", that means that we understand everything must have a valid reason.
Bisectors and Vertical Angles
As you study Geometry you will become best friends with bisectors and vertical angles! This video makes sure you know what they are and how to recognize them. I will first define them for you and then show you many examples. Once you see what they are and how they work, geometry math problems will be so much easier for you to do. Some will seem "flat out" easy!
Algebra examples are included in this geometry video lesson. They are great practice. You will surely have these type problems in your class at school. Watch me work them, then work them on your own until you totally "get it".
This video introduces you to vertical angles. It makes sure you know what vertical angles are. It teaches you that vertical angles are formed whenever two lines cross.
Bisectors of segments and angles are found throughout Geometry. This lesson helps you know what both kinds of bisectors are....for sure, before you start using them in theorems and postulates.
If you need a good foundational video to begin your study of geometry, this is one that is essential.
Using Algebra To Find Angle Measures
Did you like Algebra? I hope so, because, many times in Geometry you are asked to solve for x. So if you thought you could get away from Algebra, oops, you were wrong! If you liked Algebra you are probably cheering to get back where you are comfortable.
You must also know your geometry definitions to know how to set up your algebra equation. Solving the equation is almost always easy...once it is set up. The hard part comes when you are trying to set it up! The more definitions (in Geometry) that you really understand, the easier it is to set up your equation. Watch me and you'll see what I mean.
In this video I will work problems with angle bisectors that form angles with equal measures. Also we'll work with linear pairs and supplementary angles.
Bisectors and Vertical Angles
Before you can start working problems with bisectors and vertical angles you have to know what they are. My teaching methods help you learn by seeing and hearing the information. I use a lot of repetition and drawings to help you learn.
This video introduces you to vertical angles. It makes sure you know what vertical angles are. It teaches you that vertical angles are formed when two lines cross.
Bisectors of segments and angles are found throughout Geometry. This lesson helps you know what a bisector is....for sure, before you start using them in theorems and postulates.
If you need a good foundational video to begin your study of geometry, this one is essential.
Parallel And Perpendicular Lines - Proofs
This video proves two theorems.
1. If two lines are perpendicular to the same line, then they are parallel.
2. If two lines are parallel to the same line, then they are parallel.
Follow along with me as I prove these two concepts. We certainly don't have time to prove every theorem but these two are proven here. They are not necessarily the most important but they may help you learn how proofs work.
After you work through them with me, turn off the screen and try it by yourself. Copy the 'given' and the drawing before you turn off the screen.
Even if the proof itself is confusing, and even if you can't prove it by yourself, it's okay for now. The important thing right now is to be able to understand how each step flows logically from the previous step.
"How To Write A Proof" will come later. :)
Examples With Parallel Lines and Triangles
Parallel lines form many angles when cut by another line called a transversal. You can imagine how many angles are formed when you have more than one transversal! All those angles have names, thank goodness, so we can keep them straight! Such pairs are the alternate interior angles, corresponding angles, and same side interior angles. And what about the converses of these postulates?
In this video you will learn all these angles and more. You will see how they show up in triangle problems. Once you learn all the names and how they work, you'll be looking everywhere for parallel lines because you'll find them easy problems to work.
Geometry will, sooner or later, start fitting together like a big jigsaw puzzle. It is not very enjoyable until that happens. As long as it makes no sense it will be a dreaded subject. But once you begin to see how it all fits together, you will begin to like it...a lot!
Watch, work the problems, watch again as many times as you need. Master this material and you'll be on your way to smoother sailing!
Supplementary Files:
Once you purchase this series you will have access to these files:
Guide_and_Practice_Combining_Like_Terms.pdf
ANSWERS_Combining_Like_Terms.pdf
Multiplying_In_Algebra_Guide.pdf
Practice_Multiplying_In_Algebra.pdf
ANSWER__How_To_Multiply_In_Algebra.pdf
Practice_For_Number_Line_and_Integers.pdf
ANSWERS_Number_Line_and_Integers.pdf
Guide_Positive_and_Negative_Numbers.pdf
Practice_for_Adding_Postive_and_Negative_Numbers.pdf
ANSWERS_Positive_and_Negative_Numbers.pdf
Guide_Multiplication_Sign_Rules.pdf
Practice_Multiplication_Sign_Rules.pdf
ANSWERS_Mult_Signs_Rules.pdf
Guide_Mult_With_Sign_Numbers_Cont.pdf
Practice_Mult_With_Sign_Numbers_cont.pdf
ANSWERS_Mult_of_Sign_Numbers_cont.pdf
Practice_for_Solving_One_Step_Linear_Equation.pdf
Guide_Solving_Linear_Equations.pdf
ANSWERS_One_Step_Equations.pdf
Guide_and_Practice_2-Step_Equation.pdf
ANSWERS_Two_Step_Linear_Equations.pdf
Guide_Inequalities.pdf
Practice_Solving_Inequalities.pdf
ANSWERS_Solving_Inequalities.pdf
Practice_Meaning_of_Exp.pdf
Meaning_Of_Exponents_Guide.pdf
ANSWERS_Meaning_of_Exp.pdf
Laws_Of_Exponents_Guide.pdf
Practice_Laws_Of_Exponents.pdf
ANSWERS_Exp_Practice.pdf
Buy Now and Start Learning
Buy this series to watch it immediately. View it as many times as you
need and download it to your computer or iPod (most lessons).
Satisfaction's guaranteed, so go get started! |
Your solution to MATH word PROBLEMS! Find yourself stuck on the tracks when two trains are traveling at different speeds? Help has arrived! Math Word Problems Demystified , Second Edition is your ticket to problem-solving success. Based on mathematician George Polya's proven four-step process, this practical guide helps you master the basic procedures and develop a plan of action you can use to solve many different types of word problems. ...
ELEMENTARY STATISTICS: A BRIEF VERSION TI-84 Plus ...
Elementary Statistics: A Step By Step Approach is for introductory statistics courses with a basic algebra prerequisite. The text follows a nontheoretical approach, explaining concepts intuitively and supporting them with abundant examples. In recent editions, Al Bluman has placed more emphasis on conceptual understanding and understanding results, which is also reflected in the online homework environment, Connect Math Hosted by ALEKS. ...
Preempt your anxiety about PRE-ALGEBRA! Ready to learn math fundamentals but can't seem to get your brain to function? No problem! Add Pre-Algebra Demystified , Second Edition, to the equation and you'll solve your dilemma in no time. Written in a step-by-step format, this practical guide begins by covering whole numbers, integers, fractions, decimals, and percents. You'll move on to expressions, equations, measurement, and graphing. ...
"Elementary Statistics: A Brief Version, 4th Edition" is a shorter version of Allan Bluman's popular text "Elementary Statistics: A Step by Step Approach, 6th edition". This softcover edition includes all the features of the longer book, but is designed for a course in which the time available limits the number of topics covered. The book is written for general beginning statistics courses with a basic algebra prerequisite. The book uses a ...
"Elementary Statistics: A Brief Version", is a shorter version of the popular text "Elementary Statistics: A Step by Step Approach". This softcover edition includes all the features of the longer book, but it is designed for a course in which the time available limits the number of topics covered. It is for general beginning statistics courses with a basic algebra prerequisite. The book is non-theoretical, explaining concepts intuitively and ...
ELEMENTARY STATISTICS: A STEP BY STEP APPROACH features increased emphasis on Excel, MINITAB, and the TI-83 Plus graphing calculator, computing technologies commonly used in such coureses.
Say goodbye to dry presentations, grueling formulas, and abstract theories that would put Einstein to sleep -- now there's an easier way to master the disciplines you really need to know. McGraw-Hill's Demystified Series teaches complex subjects in a unique, easy-to-absorb manner, and is perfect for users without formal training or unlimited time. They're also the most time-efficient, interestingly written "brush-ups" you can find. ...
STUDENT SOLUTIONS MANUAL FOR ELEMENTARY STATISTICS: A STEP-BY-STEP APPROACH By Sally Robinson of South Plains College, this manual contains detailed solutions to all odd-numbered text problems and answers to all quiz questions.
Connect Statistics Hosted by ALEKS Corporation is an exciting, new assignment and assessment platform combining the strengths of McGraw-Hill Higher Education and ALEKS Corporation. Connect Statistics Hosted by ALEKS is the first platform on the market to combine an artificially-intelligent, diagnostic assessment with an intuitive ehomework platform designed to meet your needs. Connect Statistics Hosted by ALEKS Corporation is the culmination of ...
Word problems are the most difficult part of any math course –- and the most important to both the SATs and other standardized tests. This book teaches proven methods for analyzing and solving any type of math word problem.
Stack the odds in your favor for mastering probability Don't leave your knowledge of probability to chance. Instead, turn to Probability Demystified , Second Edition, for learning fundamental concepts and theories step-by-step. This practical guide eases you into the subject of probability using familiar items such as coins, cards, and dice. As you progress, you will master concepts such as addition and multiplication rules, odds |
Calvert Education Store
Advanced math students benefit from placement in our comprehensive Algebra 1 course. Our Lesson Manual contains detailed instructions and easy-to-follow examples. Although parents remain involved, the Lesson Manual is written to the student. Our solutions manual provides step-by-step answers to textbook problems. Also included are lessons to teach the use of graphing calculators and a download for an easy-to-use computer program that replaces expensive graphing calculators. |
Advanced Modern Algebra - 02 edition
Algebra is used by virtually all mathematicians, be they analysts, combinatorists, computer scientists, geometers, logicians, number theorists, or topologists. Nowadays, everyone agrees that some knowledge of linear algebra, groups, and commutative rings is necessary, and these topics are introduced in undergraduate courses. We continue their study.
This book can be used as a text for the first year of graduate algebra, but it is much more than that. It can also serve more advanced graduate students wishing to learn topics on their own; while not reaching the frontiers, the book does provide a sense of the successes and methods arising in an area. Finally, this is a reference containing many of the standard theorems and definitions that users of algebra need to know. Thus, the book is not only an appetizer, but a hearty meal as well.
Let me now address readers and instructors who use the book as a text for a beginning graduate course. If I could assume that everyone had already read my book, A First Course in Abstract Algebra, then the prerequisites for this book would be plain. But this is not a realistic assumption; different undergraduate courses introducing abstract algebra abound, as do texts for these courses. For many, linear algebra concentrates on matrices and vector spaces over the real numbers, with an emphasis on computing solutions of linear systems of equations; other courses may treat vector spaces over arbitrary fields, as well as Jordan and rational canonical forms. Some courses discuss the Sylow theorems; some do not; some courses classify finite fields; some do not.
To accommodate readers having different backgrounds, the first three chapters contain many familiar results, with many proofs merely sketched. The first chapter contains the fundamental theorem of arithmetic, congruences, De Moivre's theorem, roots of unity, cyclotomic polynomials, and some standard notions of set theory, such as equivalence relations and verification of the group axioms for symmetric groups. The next two chapters contain both familiar and unfamiliar material. "New" results, that is, results rarely taught in a first course, have complete proofs, while proofs of "old" results are usually sketched. In more detail, Chapter 2 is an introduction to group theory, reviewing permutations, Lagrange's theorem, quotient groups, the isomorphism theorems, and groups acting on sets. Chapter 3 is an introduction to commutative rings, reviewing domains, fraction fields, polynomial rings in one variable, quotient rings, isomorphism theorems, irreducible polynomials, finite fields, and some linear algebra over arbitrary fields. Readers may use "older" portions of these chapters to refresh their memory of this material (and also to see my notational choices); on the other hand, these chapters can also serve as a guide for learning what may have been omitted from an earlier course (complete proofs can be found in A First Course in Abstract Algebra). This format gives more freedom to an instructor, for there is a variety of choices for the starting point of a course of lectures, depending on what best fits the backgrounds of the students in a class. I expect that most instructors would begin a course somewhere in the middle of Chapter 2 and, afterwards, would continue from some point in the middle of Chapter 3. Finally, this format is convenient for the author, because it allows me to refer back to these earlier results in the midst of a discussion or a proof. Proofs in subsequent chapters are complete and are not sketched.
I have tried to write clear and complete proofs, omitting only those parts that are truly routine; thus, it is not necessary for an instructor to expound every detail in lectures, for students should be able to read the text.
When I was a student, Birkhoff and Mac Lane's A Survey of Modern Algebra was the text for my first algebra course, and van der Waerden's Modern Algebra was the text for my second course. Both are excellent books (I have called this book Advanced Modern Algebra in homage to them), but times have changed since their first appearance: Birkhoff and Mac Lane's book first appeared in 1941, and van der Waerden's book first appeared in 1930. There are today major directions that either did not exist over 60 years ago, or that were not then recognized to be so important. These new directions involve algebraic geometry, computers; homology, and representations (A Survey of Modern Algebra has been rewritten as Mac Lane-Birkhoff, Algebra, Macmillan, New York, 1967, and this version introduces categorical methods; category theory emerged from algebraic topology, but was then used by Grothendieck to revolutionize algebraic geometry).
Here is a more detailed account of the later chapters of this book.
Chapter 4 discusses fields, beginning with an introduction to Galois theory, the interrelationship between rings and groups. We prove the insolvability of the general polynomial of degree 5, the fundamental theorem of Galois theory, and applications, such as a proof of the fundamental theorem of algebra, and Galois's theorem that a polynomial over a field of characteristic 0 is solvable by radicals if and only if its Galois group is a solvable group.
Chapter 6 introduces prime and maximal ideals in commutative rings; Gauss's theorem that R x is a UFD when R is a UFD; Hilbert's basis theorem, applications of Zorn's lemma to commutative algebra (a proof of the equivalence of Zorn's lemma and the axiom of choice is in the appendix), inseparability, transcendence bases, Lüroth's theorem, affine varieties, including a proof of the Nullstellensatz for uncountable algebraically closed fields (the full Nullstellensatz, for varieties over arbitrary algebraically closed fields, is proved in Chapter 11); primary decomposition; Gröbner bases. Chapters 5 and 6 overlap two chapters of A First Course in Abstract Algebra, but these chapters are not covered in most undergraduate courses.
Chapter 8 introduces noncommutative rings, proving Wedderburn's theorem that finite division rings are commutative, as well as the Wedderburn-Artin theorem classifying semisimple rings. Modules over noncommutative rings are discussed, along with tensor products, flat modules, and bilinear forms. We also introduce character theory, using it to prove Burnside's theorem that finite groups of order pmqn are solvable. We then introduce multiply transitive groups and Frobenius groups, and we prove that Frobenius kernels are normal subgroups of Frobenius groups.
Chapter 9 considers finitely generated modules over PIDs (generalizing earlier theorems about finite abelian groups), and then goes on to apply these results to rational, Jordan, and Smith canonical forms for matrices over a field (the Smith normal form enables one to compute elementary divisors of a matrix). We also classify projective, injective, and flat modules over PIDs. A discussion of graded k-algebras, for k a commutative ring, leads to tensor algebras, central simple algebras and the Brauer group, exterior algebra (including Grassman algebras and the binomial theorem), determinants, differential forms, and an introduction to Lie algebra.
Chapter 10 introduces homological methods,beginning with semidirect products and the extension problem for groups. We then present Schreier's solution of the extension problem using factor sets, culminating in the Schur-Zassenhaus lemma. This is followed by axioms characterizing Tor and Ext (existence of these functors is proved with derived functors), some cohomology of groups, a bit of crossed product algebras, and an introduction to spectral sequences.
Chapter 11 returns to commutative rings, discussing localization, integral extensions, the general Nullstellensatz (using Jacobson rings), Dedekind rings, homological dimensions, the theorem of Serre characterizing regular local rings as those noetherian local rings of finite global dimension, the theorem of Auslander and Buchsbaum that regular local rings are UFDs.
Each generation should survey algebra to make it serve the present time.
Ships same day or next business day! UPS85 +$3.99 s/h
VeryGood
Bookbyte-OR Salem, OR
Has minor wear and/or markings. SKU:9780130878687-3-0
$13.45 +$3.99 s/h
LikeNew
Bookbyte-OR Salem, OR
Almost new condition. SKU:9780130878687-2-079 +$3.99 s/h
Good
Books Revisited Chatham, NJ
Possible retired library copy, some have markings or writing.
$79 |
Appendix A Mathematical concepts
The purpose of this Appendix is to give a brief description of some of the mathematical concepts mentioned in this document. For a more thorough treatment of modular arithmetic and basic number theory, consider any undergraduate textbook in elementary algebra. For more information about groups, rings, and fields, we recommend [Fra98]. For more details on analysis and the theory of limits, consult any undergraduate textbook in analysis. A good introduction to complexity theory is given in [GJ79]. |
Sign in to YouTube
This is the fourth part of the lecture for understanding Permutations and Combinations in Maths for preparing for JEE, AIEEE, BITS and other engineering exams. The lectures are taught by IITians themselves to help the aspirants. Collegepedia.in is uploading these lectures to help students learn in a better way. Visit collegepedia.in . We are on facebook as well. For rest of the videos, Check out our channel COLLEGEPEDIAIN on youtube |
more details
Smith (Santa Rosa Junior College) covers the nature of problem solving and treats problems in logic, set theory and counting, probability, statistics, geometry, measurement, growth, networks, and graph theory in this text for undergraduates. Each chapter includes exercise sets of some 60 color-illustrated exercises each, designed to appeal to undergraduate students. Students should have a background in beginning algebra, and preferably intermediate algebra. Annotation (c) Book News, Inc., Portland, OR (booknews.com) |
Examples of java.lang.Math Methods
Here is an example program that exercises most of the routines in
java.lang.Math. If your high school math is a little
rusty, don't worry if you don't remember the exact meaning of
logarithms or cosines. Just know that they're here in Java if you
need them. |
TAUGHT BY
Mohammed Kaabar is interested in several programming languages such as Scala, C++, C, JavaScript, Python, HTML 5 and MATLAB Programming.
He became IEEE Student Member, IEEE Computer Society Member, IEEE Electron Devices Society Member, IEEE Women in Engineering Society Member and IEEE Communications Society Member, in 2011 and 2012, respectively. In 2011 & 2012, he participated in several competitions, conferences, research papers and projects. In 2011, he attended also a three-month course in numerical approximation techniques including error analysis, root finding, interpolation, function approximation, numerical differentiation, numerical integration and numerical solutions of initial value problems. Ultimately, he worked on several projects such as "PCA Implementation and Classification of Data in Recognition of Arabic Sign Language Alphabet using Polynomial Classifiers" and "Modeling a GaAs MESFET Device Structure using Silvaco Software:Athena and Atlas". For more information about him, please visit his personal website:
SHARE
Advanced Numerical Analysis
In this course, you will be Introduced to several numerical approximation methods such as interpolation: divided difference, polynomial approximations, iterative methods for
solving linear systems, numerical differentiation and numerical integration.
During five weeks of the course, you will be learning these methods and compare them as well.
The course is divided into five weeks where each week you will
find a set of video lectures posted with a PDF version of lecture notes
as well.
You are welcome to take this course if you want to learn and study the advanced numerical analysis methods.
Use the divided difference to interpolate and approximate functions by polynomials.
Use the iterative methods with algorithms to implement several numerical methods.
Apply the midpoint rule for finding numerical integration.
Apply the trapezoidal rule for finding numerical integration.
Use the divided difference formula to proof the approximation part and error part in the basic quadrature rules.
The ability to use computer software such as Maple to apply several numerical methods and approximations.
What is the target audience?
Anyone who wants to learn advanced methods in numerical analysis.
Students who had a background in the bascis of numerical analysis.
Students who had a background in the linear algebra.
CURRICULUM
SECTION 1:
Week 1: Solutions of Equations in One Variable
1
Newton's Method for Systems
In this lecture, you will be introduced to newton's method for system using inverse jacobian with partial derivatives and vectors. At the end of this lecture, you will given an example of how to use newton's method for system in order to solve system of linear equations.
30:40
2
Müller's Method
In this
lecture, you will be introduced to muller's method and how to use it to approximate a function in the neighborhood of the root by quadratic poloynomial. At the end of
this lecture, you will given an example of how to use muller's method
for solving system of linear equations.
30:08
SECTION 2:
Week 2: Interpolation and Polynomial Approximation
3
Divided Difference (Part I)
In this
lecture, you will be introduced to interpolation: divided difference method and how to use it to construct polynomial of order (n) . At the end of
this lecture, you will given an example of how to use divided difference method in order to construct polynomial of order (n).
39:18
4
Divided Difference (Part II)
In
this
lecture, you will be introduced to interpolation: divided difference
method and how to use it to find the distance between two points using both delta notation and del notation . At the
end of
this lecture, you will given an example of how to find the squared and cubic distance between two points using both delta notation and del notation.
23:24
5
Evenly-Spaced Data
In
this
lecture, you will be introduced to the concept of evenly-spaced data and. In addition, you will given several examples about evenly-spaced data.
23:22
6
Newton's Forward Divided Difference
In
this
lecture, you will be introduced to newton's forward divided difference using binomial coefficient notation. In addition, you will given an example of how to use newton's forward divided difference to approximate a polynomial at a point not in the table of data.
32:51
7
Newton's Backward Divided Difference
In
this
lecture, you will be introduced to newton's backward divided difference using binomial coefficient notation.
18:08
SECTION 3:
Week 3: Spline Interpolation
8
Linear Spline Interpolation
In this lecture, you will be introduced to spline interpolation in
general and linear splines in particular. Then, you will given an
example about linear spline interpolation, and how to use Maple 11 to
solve it.
28:59
9
Quadratic Spline Interpolation
In this lecture, you will be introduced to quadratic splines.
Then, you will given an example about quadratic spline interpolation,
and how to use Maple 11 to solve it.
29:46
10
Cubic Spline Interpolation
In this lecture, you will be introduced to cubic splines. Then,
you will given an example about cubic spline interpolation, and how to
use Maple 11 to solve it.
18:48
11
Problem Set
This problem set is a review for the material of week 3.
I highly recommend you to solve this problem set before looking at problem set solutions.
GOOD LUCK!
3 pages
12
Problem Set Solutions
After you are done with solving the problem set, please review your
answers with the given solutions in order to learn from your mistakes.
GOOD LUCK!
4 pages
SECTION 4:
Week 4: Iterative Methods for Solving Linear Systems
13
Jacobi Method
In
this
lecture, you will be introduced to jacobi method which is one of the iterative methods for solving linear systems. In addition, you will given an
example of how to use jacobi method to solve a system of linear equations.
17:16
14
Gauss-Siedel Method (Part I)
In
this
lecture, you will be introduced to gauss-siedel method which is one of the iterative methods for solving linear systems.
17:01
15
Gauss-Siedel Method (Part II)
In this lecture, you will be introduced to whether matrix is diagonally dominant or not in order to use it for applying gauss-siedel method. Moreover, several examples about that were given.
10:43
16
Successive Over Relaxation (SOR) Method (Part I54
17
Successive Over Relaxation (SOR) Method (Part II14:10
18
Successive Over Relaxation (SOR) Method (Part III48
SECTION 5:
Week 5: Numerical Integration and Differentiation
19
Basic Quadrature Rules (Midpoint Rule)
In this lecture, you will be introduced to the midpoint rule which is one of the basic quadrature rules. Moreover, you will be introduced the proofs of both approximation part and error of midpoint rule.
18:09
20
Basic Quadrature Rules (Trapezoidal Rule)
In this lecture, you will be introduced to the trapezoidal rule which is one of the basic quadrature rules. Moreover, you will be introduced the proofs of both approximation part and error of trapezoidal rule.
20:40
SECTION 6:
Week 6: Wrapping Up
21
Course Conclusion
In this lecture, you will given a summary of all topics discussed in the Advanced numerical analysis course.
01:32
SECTION 7:
Week 7: Optional Final Exam
22
Advanced Numerical Analysis Final Exam
20 questions
REVIEWS
9
0
0
0
0
AVERAGE RATING
NUMBER OF RATINGS
Amazing Advanced Course
This is a great course to learn about advanced topics in numerical analysis in very easy way because the instructor of this course makes everything easy to follow and gives an excellent coverage of the topics in his lectures. He also has a great knowledge of all topics of the course with all their applications because he teaches these topics using all modern education tools in order to make his students understand everything in the course and love the course in general and all courses related to numerical analysis.
Thanks Mohammed Kaabar for teaching this advanced version of your introductory course "Introduction to Numerical Analysis".
I really enjoyed this course and I found it very helpful for understanding advanced numerical approximation techniques that can be used in several real life applications. In addition, the instructor makes the course topics very interesting because he teaches the course material in an excellent way by explaining first the concept, giving many examples about that concept, and then comparing between this concept and other discussed concepts.
Great Course
The Advanced Numerical Analysis course is a great course and very helpful in our life as well as it includes amazing topics in advanced numerical analysis such as newton's method, Muller's method, Divided difference, iterative methods and numerical integration & differentiation. In addition, the instructor is excellent because he taught the material of this course in an excellent way that makes everyone understands the course material easily without any difficulty.
Amazing Advanced Course in Numerical Analysis
This is an amazing course for anyone interested in mathematics, statistics, advanced numerical analysis and engineering because it can benefit them to solve complex mathematical, physical and engineering problems. I highly recommend everyone to register this advanced version of "Introduction to Numerical Analysis" course if you want to learn advanced topics in numerical analysis.
Thank you for offering Advanced Numerical Analysis
Thanks for offering this excellent course. I really liked this course so much because you made a huge effort in order to offer for us a free online course in advanced numerical analysis, and I learned several topics in advanced numerical analysis such as muller's method, newton's method using vector and inverse jacobian, divided differences, jacobi method, gauss-siedel method, SOR method and numerical integration and differentiation. |
Algebra and Trigonometry : Graphs and Models -Text Only - 4th edition
Summary: The authors help students "see the math" through their focus on functions; visual emphasis; side-by-side algebraic and graphical solutions; real-data applications; and examples and exercises. By remaining focused on today's students and their needs, the authors lead students to mathematical understanding and, ultimately, success in class69 +$3.99 s/h
Good
Dream Books Company, LLC Englewood, CO
2009 Hardcover Good Used book with normal wear and tear and may contain writing. Stock photo may be different from actual book coverGoodwillnyonline Astoria, NY
GoodGood
Susies Books Garner, NC
2009 Hardcover COVER SHOWS WEAR This book looks good. It is like any used book you would expect to find in a used book shop |
...I Algebra 1 covers many different topics that are just built upon in Geometry, Algebra 1, pre-calculus, and beyond |
Elementary Algebra for College Students - 8th edition
Summary: Today's students are visual learners, and Angel/Runde offers a visual presentation to help them succeed in math. Visual examples and diagrams are used to explain concepts and procedures. New Understanding Algebra boxes and an innovative color coding system for variables and notation keep students focused. Short, clear sentences reinforce the presentation of each topic and help students overcome language barriers to learn math. Real Numbers; Solving Linear Equations and Inequalities; ...show moreApplications of Algebra; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Graphing Linear Equations; Systems of Linear Equations; Roots and Radicals; Quadratic Equations For all readers interested in algebra20.6122.51 +$3.99 s/h
Acceptable
newrecycleabook centerville, OH
0321620933 used book - book appears to be recovered - has some used book stickers - free tracking number with every order. book may have some writing or highlighting, or used book stickers on front o...show morer back ...show less
$30.9050 +$3.99 s/h
Good
kelseyskorner Ferndale, WA
Solid binding. Pages have minimal markings-otherwise in good clean condition. Good clean cover. Good hardcover book14 |
Solutions from Every Perspective: Using Mathematica to Enhance Students' Understanding of Math Concepts
Richard Breheret
One of Richard Breheret's biggest challenges as a high school math teacher is finding a way to help students arrive at answers from different perspectives, whether algebraic or formal, while integrating concepts from primary school to high school. In French. |
Highly interactive tutorials and self-test system for individual e-learning, home schooling, college and high school computer learning centers, and distance learning. The product emphasizes on building problem-solving skills....
Solve common machine shop and other trades trigonometry and math problems at a price every trades person can afford! As a machinist or CNC programmer, you often have to use trigonometry to calculate hole positions,...
The RealEstateManager Basic component for Joomla allows you to manage and maintain a flats and houses database with easy on a Joomla-based website. Because RealEstateManager incorporates Lend-Return management, buying request... |
Mathematical Problem Solving in North Texas
That object is called a polynomial, it is simple and has very nice properties.
In our lecture we present a unified view of polynomials. This will help you understand concepts covered in school much better and much faster. There will be plenty of tricky Olympiad problems related to them and it will be fun!!
Like this:
The AMC 10A/12A is on February 4th and the AMC 10B/12B is on February 19th. If you'd like a chance to learn some interesting tips and techniques to help with these competitions, then please join us for this enlightening Math Circle. Adrian Andreescu, Vinjai Vale, and Dr. Titu Andreescu will be presenting problems to challenge and delight.
If you have yet to sign up for these tests and your school does not offer them, there is still room for both dates (these testing sites are not sponsored by Metroplex Math Circle). Registration will be held outside the math circle room, ECSS 2.201.
Matrices are an extremely useful concept – they are widely used in many areas of mathematics, science, engineering, and data analysis. This talk will provide a peek into what can be done with matrices in a few of these contexts. We will start by discussing what a matrix is, how the basic arithmetic operations are defined, and some useful properties, and then we'll explore some simple applications in linear algebra, geometry, and data analysis.
Like this:
Please join Dr. Titu Andreescu and Mathew Crawford as they offer an American Regions Mathematics League (ARML) session for students interested in learning more about the contest and wishing to be exposed to the types of problems they would encounter. This will be a very interactive math circle where students will have the opportunity to work together to solve interesting problems. Here is the plan for this first practice as detailed by Mathew Crawford:
We plan to talk about our goals for the team.
Discuss the rules and format for ARML, the primary event for the Metroplex Math Team
Practice three of the four rounds from a past ARML contest (Individual, Team, and Relay)
We will practice the fourth ARML round (the Power Round) as the Metroplex Math Team participates in the ARML Power Contest the following weekend.
For this first contest, we're picking an ARML contest that isn't from the past few years both in hopes that fewer students have seen the problems and also because the problems from older contests are a little more accessible to beginners. We plan to use more recent practice problems as the team progresses.
Veterans of ARML are encouraged to show up to this first practice to help make new students comfortable with the process and also because leadership matters—and we will practice like we play, as a team.
If you know of talented high school students or extremely motivated younger students in the Dallas Metroplex area who may want to attend this event, please pass this link along.
Research is one of the more difficult aspects of education to provide for students. New research, by its nature, often involves large time commitments, and there are additional skills involved in communicating research that take time to develop. As a result, many students find the nature of research to be mysterious and simply don't know how to get started. That's a shame, because mathematical exploration rewards us on many levels.
One solution is to create problems (pun intended). In this talk, we will take a look at a few cool problems (some of the really cool ones, in fact) and discuss how they were or might have been the result of "miniature research projects". We will then ourselves participate in the process. We will start with some brainstorming, playing, and doodling, just to see where it leads. We will synthesize some of the ideas into original problems and challenges of our own. It is even possible that some of the ideas lead to more interesting projects.
This talk is friendly for a very wide audience. If you know some math, you can play, and playing is part of the research process!
We will present an attractive crossroad of mechanics and mathematics. We will talk about interesting problems of billiards on triangular and elliptical tables. Video clips illustrating the subject will be demonstrated. We will provide basic definitions and some historical background.
About the lecturer: Vladimir Dragovic is a professor of Mathematics at UT Dallas. He has been a full research professor and the Head of the Department of Mechanics of the Mathematical Institute of the Serbian Academy of Sciences and Arts. He served as the Director of the Mathematical High School in Belgrade (2004-2008), known as one of the world's most successful schools in the IMO competitions (
**Please note: Math Circle will be on winter break from December 21, 2013 through January 4, 2014. We will resume with a talk by Mathew Crawford on January 11, 2014 (see schedule). |
Algebra and Trigonometry
Book Description: The Eighth Edition of this highly dependable book retains its best features–accuracy, precision, depth, and abundant exercise sets–while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Trigonometric Functions; Exponential and Logarithmic Functions; Analytic Geometry; Analytic Trigonometry; Counting and Probability; and more. For individuals with an interest in learning algebra and trigonometry as it applies to their everyday lives |
Andrew Baines, J. M. Bond
Publication Year:
28/06/2007
Subject:
School Textbooks & Study Guides
Format:
Pamphlet
Subject 2:
School Textbooks & Study Guides: Maths, Science & Technical
Language:
English
ISBN:
9780748781133
EAN:
9780748781133
Detailed item information
Description
Bond Assessment is the only series of graded practice papers for age 6 to 11+ in all four subjects commonly assessed in entrance examinations. Providing thorough and continuous practice of key Maths skills, these essential study guides really can help children succeed.
Key Features
Author(s)
Andrew Baines, J. M. Bond
Publisher
Nelson Thornes Ltd
Date of Publication
28/06/2007
Language(s)
English
Format
Pamphlet
ISBN-10
0748781137
ISBN-13
9780748781133
Genre
School Textbooks & Study Guides: Maths, Science & Technical
Publication Data
Place of Publication
Cheltenham
Country of Publication
United Kingdom
Imprint
Nelson Thornes Ltd
Out-of-print date
17/05/2012
Content Note
Illustrations
Dimensions
Weight
148 g
Width
190 mm
Height
248 mm
Spine
6 mm
Pagination
76 |
Mathematics Education and Resource Center
The Mathematics Education and Resource Center (MERC) is a free service available to support cadets in math studies. There will be tutors on-hand for help in the following mathematics courses:
MA105/MA106 - Introduction to Probability and Statistics I & II
MA103 - Fundamentals of Matrix Algebra
MA114 - Pre-Calculus
MA123/MA124 - Calculus & Analytic Geometry I & II
MA125/MA126 - Quantitative Methods I& II
MA215 - Multivariable Calculus
MA311 - Differential Equations
Location: 700 Level of Preston Library, Open Math Lab (OML).
No appointments necessary.
Fall Semester Hours
Daytime: Monday through Friday, 1200-1600 hours
Evening: Sunday through Thursday, 1800-2300 hours
At the Mathematics Education and Resource Center, our mission is to: support our Cadet Corps in their pursuit of mathematical studies, engage our VMI faculty and staff in their goals of maintaining rigor and excellence in their respective disciplines, and work with our community in their desire for productive, inspired, and healthy citizens. |
Plantation, FL Chemistry functions such as Ln and Exponential functions are also explained in the subject. The focus on differences become crucial when dealing with advanced mathematics. Calculus branches into two sections, differential and integral calculus. |
Mathaid inter active Probability and Statistics tutorial is a new java-based package for e-lear ning and home schooling. It guides the user through all steps of the learning process, from theoretical concepts, exam ples, problem-solving...
- that science project ormaths homework help. The student calculator graphically displays many of the standard mathematic formula and has the ability to edit graphically, lines, circles, triangles and many...
Learn and Practice Basic Maths in quick bursts with this Windows based application. Then compare your best times with people all around the world at Suitable for Primary School children or anyone wanting...
- launched its new productInter office Instant Messenger & Organizer known as ?IMO? which is a replacement of inter com. Now the aim of IMO is to reduce telephone calls within organizations. Instead of instant...
- Minimize Boolean and propositionalformulae up to 8 variables Convert Boolean formulae into SOP, POS and decimal notation Work with Karnaugh map, truth table and sets of terms Highlight minimized term on Karnaugh...
- having difficulty with basicmaths ? Dont know where to start? Then try this handy little game to get your child on track, or to give them a real edge. This game is very effective at making them learn their sums the old fashioned...
- multiplication, division, and complexformulas with unlimited number of operations and operands. For example, you can type in Edit Window such formula ((12.55+10.05+8.45+17.35)/30)*0.7-(13.45+15.76+2.05)*0.33... |
Abstract After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. To develop the student's problem-solving skills, the book works through a large number of examples and economic applications. This streamlined third edition offers an array of new and updated examples. Additionally, lengthier proofs and examples are provided on the book's website. The book and the Web material are cross-referenced in the text. A Student Solutions Manual is available in e-book form, and instructors are able to access online the Instructor's Manual, which includes PowerPoint slides16225 and published in 2011.
Lists
Statistics
Corrections
When requesting a correction, please mention this item's handle: RePEc:mtp:titles:0262516225 |
Math Assessment
We use COMPASS, a computerized assessment to help place you into Math courses. There are 4 possible areas you will be assessed in: numerical skills/prealgebra, algebra, college algebra, and trigonometry. Where you will begin depends on your Math background. Please talk with our Assessment Center staff about the last level of math you completed.
You may bring your own calculator provided it meets the requirements as listed in Using Calculator |
Formats
Book Description
Publication Date: May 18 1998 | Series: Economist BooksProduct Description
From the Publisher
A handy reference to stay on top of global economic trends. In today's global arena it is imperative that business people keep abreast of the economics of nations around the world. Every day features the release of a new barrage of updated economic indicators and figures that carry often hidden messages about the direction of segments of the economy. This pocket reference enables readers to quickly revisit the meaning and impact of late breaking economic news and to make better decisions based on the looming economic terrain.
From the Inside Flap
Crucial to business success, numerical methods are often viewed as too complex to understand, much less use. They are, in fact, far less complicated, able to be broken down into stepby-step instructions and processed by basic computing devices. This invaluable resource from the publishers of The Economist, the leading international business journal, simplifies and demystifies the numbers game, illustrating just how straightforward—and relatively easy—it really is. Taking you clearly and concisely through numerous fundamental functions, both elementary and advanced, The Economist Numbers Guide arms you with the tools necessary to not only approach numbers with more confidence, but solve financial problems more easily, analyze information more accurately, and make decisions more effectively. Covering finance and investment, forecasting techniques, hypothesis testing, linear programming, and a host of other important topics, it shows you how to handle everything from figuring interest and quantifying risk to projecting inflation and evaluating investment opportunities. In addition to the basic mechanics of numerical techniques, the Guide takes a look at their practical applications, including their role in stock control, simulation, and project management. To help you sidestep potentially costly mistakes, it also highlights common errors to avoid, such as rounding incorrectly and bypassing time series selection. Along with sample calculations, concise definitions, and clear explanations, as well as more than 100 charts, graphs, and tables, The Economist Numbers Guide features an A-to-Z dictionary that encompasses key terms—from autocorrelation to zero sum game—and provides useful reference material on such essentials as conversion factors and formulae for calculating areas and volumes. In-depth and easy-to-use, this is an indispensable reference for business and numbers success.
I have read cover-to-cover a previous edition of this book (when it was published by Wiley in 1998) and recently had an opportunity to carefully peruse this current edition (5th ed. by Bloomberg Press???). What I found is that this is a strange case of how a great book (the 1998 edition) turned into merely a good book (this 5th edition). Because of this regression toward the average, I deducted one star from my review (but still feel that it is good enough for 4 stars).
As you may have noticed, I really loved the older edition of The Economist Numbers Guide that I thankfully own. It is a great overview and introduction of mathematics as it relates to business. There are a lot of great things about that edition of this book. One of the things I admired about it was the range of topics covered, from interest rates and basic probability/statistics all the way up to Markov Chains, linear programming, and marginal analysis. It is hard to find the breadth of topics covered in that book elsewhere - whether all in one book or in any combination of books.
So I found it perplexing that this 5th edition dedacted some materials and topics covered in older editions. Gone are the interesting discussion of descriptive statistics for sets of data that do not easily conform to any of the standard probability distributions (e.g., where median is the best measure of the 'average' and substitutes must be used for the more common parameters such as standard deviation). I have a hard time finding anything coherent much less accessible on those topics elsewhere so it is a shame that they were left off of the 5th edition.
The only new material (not previously present) is a short blurb on public-key cryptography.
While that topic is interesting to me and the limited discussion was illuminating and mathematically sound, it seemed a rather quixotic choice to put in when some interesting materials in previous editions were left off and new material that would have been more useful to the targeted audience have yet to be added.
What I mean by useful material that have yet to be added is that both the 1998 edition and this edition don't have some materials that I would think naturally ought to be added. E.g., the section on finance & investment mathematics is mostly devoted to various discussions on interest rate/time value of money & basic probability. I think adding material on CAPM (although CAPM Beta is defined in the book's very helpful glossary section), option/derivative pricing, financial portfolio optimization, and other topics in financial mathematics/engineering would make a great and natural addition to this book.
Some problems common to both the prior and current edition of this book are the occassional (relatively rare) typos. They are usually minor (although they are most annoyingly frequent in the section on time value of money / interest rates).
Another flaw in both the older and newer editions is that there are gaps in the expository material that don't make much sense. To be fair, this book is designed to be a brief intro/overview into a wide swathe of topics so it wouldn't be reasonable to expect that the author go into great detail on every topic. However, there are instances - e.g., the example on mixed strategies in game theory - where one or two additional sentences would help novices to understand (e.g., how did you get the the mixed strategy probabilities? author should have added a couple of more lines about how the system of equations are interrelated with one another when determining mixed strategies).
Having said all of that, let me reiterate that BOTH the old and the new edition of The Economist Numbers Guide is a wonderful resource for people interested in business mathematics. The sections on decision-making and forecasting are especially of value since they are so wonderfully explained here and a comparable set of explanations are hard to find elsewhere.
In future editions, I just hope that the author heeds my advice about bringing back some topics in older editions, correcting a few errors & lapses, and adding some material that would fit in with what has otherwise been an excellent series of books.
This book provides concise and clear definitions of business analytics with practical applications. Excellent for the neophyte in business math. Helpful index and glossary to get started. Good guide to use if learning stats or marketing research. |
Getting Started with MATLAB 7 : A Quick Introduction for Scientists and EngineersRG Familiarizes users with MATLAB in just a few hours though self-guided lessons RG Discusses new features and applications in MATLAB 7 RG Covers elementary, advanced, and special functions RG Includes numerous new examples and problems RG Supplements any course that uses MATLAB RG Works as a stand-alone tutorial and reference MATLAB, a software package for high-performance numerical computation and visualization, is one of the most widely used tools in engineering field today. Its broad appeal lies in its interactive environment with hundreds of built-in functions for technical computation, graphics, and animation. In addition, it provides easy extensibility with its own high-level programming language. Enhanced by fun and appealing illustrations,Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers employs a casual, accessible writing style that shows users how to enjoy using MATLAB.
Rudra Pratap is Professor of Mechanical Engineering at the Indian Institute of Science in Bangalore. |
12 total
5 5
4 2
3 1
2 1
1 3
Unfortunately App will not even open on my phone, it will simply stop responding before it's even done loading.A Google User A Google User
Dosent even deserve a star Just not helpful
A Google User A Google UserSimilar
You will use it from high school all the way to graduate school and beyond.
Features
Includes both Calculus I and II Clear and concise explanations Difficult concepts are explained in simple terms Illustrated with graphs and diagrams Search for the words or phrases Access the guide anytime, anywhere - at home, on the train, in the subway. Use your down time to prepare for an exam. Always have the guide available for a quick reference. Table of Contents
Introduction: Functions
Limits and Continuity: Limit of a Sequence | Limit of a Function | Limit of a function at infinity | Continuity | Classification of Discontinuities
PreCalculus Buddy is a reference manual for students in technical and engineering programs. The app covers hundreds of definitions and rules, and has an user friendly and intuitive interface. Many of the sections contain schematics for easier understanding.
Differentiation is all about finding rates of change (derivative) of one quantity compared to another. We need differentiation when the rate of change is not constant. Derivative Calculator computes a derivative of a given function with respect to a given variable using analytical differentiation. In calculus, the subtraction rule in differentiation is a method of finding the derivative of a function that is the subtraction of two other functions for which derivatives exist. The subtraction rule in integration follows from it. The rule itself is a direct consequence of differentiation. In calculus, the product rule of derivatives is a method of finding the derivative of a function that is the multiplication of two other functions for which derivatives exist. The product rule in integration follows from it. The rule itself is a direct consequence of differentiation. In calculus, the quotient rule of derivatives is a method of finding the derivative of a function that is the division of two other functions for which derivatives exist. The quotient rule in integration follows from it. The rule itself is a direct consequence of differentiation. In calculus, the power rule of derivatives is a method of finding the derivative of a function that is the multiplication of two other functions for which derivatives exist. The rule itself is a direct consequence of differentiation In calculus, the chain rule of derivatives is a method of finding the derivative of a function that is the composition of two functions for which derivatives exist. The rule itself is a direct consequence of differentiation.. In calculus, the sum rule in differentiation is a method of finding the derivative of a function that is the sum of two other functions for which derivatives exist. The sum rule in integration follows from it. The rule itself is a direct consequence of differentiation. Trapezoidal / Trapezium Rule is a method of finding an approximate value for an numerical integral, based on finding the sum of the areas of trapezia. Trapezium rule is also known as method of approximate integration. A slight underestimate will often be cancelled by a similar slight overestimate from another trapezium. Using narrower intervals will improve accuracy. Simpson's 1/3 Rule Numerical Integration is used to estimate the value of a definite integral. It works by creating an even number of intervals and fitting a parabola in each pair of intervals. Simpson's rule provides the exact result for a quadratic function or parabola. Romberg's Method Numerical Integration is based on the trapezoidal rule, where we use two estimates of an integral to compute a third integral that is more accurate than the previous integrals. This is called Richardson's extrapolation.
A perfect tool for college going students and mathematicians.
Disclaimer: This app used web Api of calculation from with Due permission
With more than nine million copies sold, Twenty-Four Hours a Day, the classic daily meditation book from Hazelden, is a mainstay for those recovering from addiction to alcohol and other drugs.
Featuring the complete collection of thoughts, meditations, and prayers presented in the book, the 24 Hours application for your Android device makes it easy to focus on your sobriety anywhere, at any time. Practicing the Twelve Steps has never been more accessible.
PRESS the "Today" button to access the message synched to that exact day of the year
CUSTOMIZE the size of the font presented, for reading ease
SEARCH a wide selection of recovery books and resources through a direct link to Hazelden's online bookstore
Hazelden is a nonprofit organization dedicated to helping people heal from addiction. Proceeds from this application and other Hazelden resources fund initiatives to help those struggling with addiction and related life issues.
Study Guide To Calculus is the complete guide, covering the basics to the advanced, full of pictures and useful reference guides to get you all the information you need to have a compete understanding. Refer to the Screenshots to get a look at the wealth of information within the study guide. 100% Money Back Guarantee, if you are not 100% Satisfied return in the first 24hours for a full refund
Calculus may not seem very important to you but the lessons and skills you learn will be with for your whole lifetime!
Calculus is the mathematical study of continuous change. It helps you practice and develop your logic/reasoning skills. It throws challenging problems your way which make you think. Although you may never use calculus ever again after school or college, you will definitely hold on to the lessons that calculus teaches you.
Things like time management, how to be organized, how to accomplish things on time, how to perform under pressure, how to be responsible are just some of the things Calculus helps you become proficient in. Traits that will help you succeed.
Calculus plays a big role in most universities today as students in the fields of economics, science, business, engineering, computer science, and so on are all required to take Calculus as prerequisites.
Our Pre-Calculus guide is a preliminary version of Calculus containing over 300 rules, definitions, and examples that provides you with a broad and general introduction of this subject. A valuable pocket reference to have on your phone.
Even if you dont use Calculus, this app sure is a cool way to show-off some high IQ!
Like all our 'phoneflips', this fast and lightweight application navigates quick, has NO Adverts, NO In-App purchasing, never needs an internet connection and will not take up much space on your phone!
Start reading on your favorite Android device in seconds with BAM Reader 2, a free app by Books-A-Million, one of the nation's largest book retailers. Shop the Books-A-Million online store directly from your Android device to get the newest releases and latest bestsellers from today's top authors.
You can easily customize your reading experience by choosing a background color, font size, and either portrait or landscape format.
With BAM Reader 2, you can read eBooks previously purchased from Booksamillion.com.
.
The Wolfram Calculus Course Assistant is powered by the Wolfram|Alpha computational knowledge engine and is created by Wolfram Research, makers of Mathematica—the world's leading software system for mathematical research and education.
The Wolfram Calculus Course Assistant draws on the computational power of Wolfram|Alpha's supercomputers over a 2G, 3G, 4G, or Wi-Fi connection. |
Most students will begin their study of mathematics with one of the two calculus sequences:
(i) Calculus: Math 161, 162, 263, and 264; the traditional sequence.
(ii) Analysis: Math 165, 166, and 267; a calculus sequence which uses a more sophisticated and rigorous approach and integrates multivariate calculus with single variable calculus.
Individuals who do not start their college mathematics with one of the above calculus sequences should take Math 105 or 110, depending on their major interests.
Careful attention should be given to the proper placement in the calculus sequence. Students having a high school calculus background should consider taking the Analysis sequence, Math 165, 166, and 267. The Analysis sequence covers approximately the same material as that contained in the standard Calculus sequence, Math 161, 162, 263 and 264. However, the Analysis sequence builds on one year of successful high school calculus and presents the material with a more rigorous conceptual approach and a significantly different order of presentation. Students who scored at least 4 on the AB or 3 on the BC Advanced Placement exams in high school should take Math 165. It is highly recommended that students begin their college calculus during the fall term of their freshman year.
Placement into Calculus II, III, or IV via AP credit is not allowed.
Credit will not be allowed for both Math 161 and 165. Moreover, credit will not be allowed for any course that is taken after the successful completion of another course for which the first course was a prerequisite.
Major Sequence in Mathematics:
A minimum of eleven course units in mathematics to include:
1) One of the calculus sequences (i) or (ii).
2) Math 200 and 215. Both Math 200 and Math 215 should be completed by the end of the second year. Students should consult with a mathematics advisor in order to determine the best time for them to take these courses.
And a minimum of six courses that satisfy the following requirements:
3) Two courses selected from Math 405, 410, 415, 425, 440, or 470. Students must take at least one 400-level course in mathematics in their senior year. Students are allowed to take more than two 400-level courses.
Math 105, 106, 110, 135, 235, 397, 495, and 499 will not count towards the Mathematics major or minor.
Mathematics majors and minors who desire secondary certificates and/or middle school and area teaching endorsements should apply to the Teacher Education Program in their sophomore year. Those students should also refer to the Educational Studies curriculum description in this Catalog and the Teacher Education Handbook ( for further information.
The Department of Mathematics maintains two computer labs. A Mathematics Learning Center (MLC) is also maintained throughout the academic year. It is staffed with student assistants under faculty supervision and is open to students enrolled in most first-year courses.
105 Mathematical Concepts for Elementary Teachers I The study of number systems (whole, integer, rational, and real), intuitive geometry, and measurement. Open only to elementary education majors. This is not a methods course. Will not count towards the major or minor in mathematics. Prerequisite: two years of high school algebra and one year of high school geometry. Offered each fall.
106 Mathematical Concepts for Elementary Teachers II (FR) A continuation of Math 105. Topics to be covered include measurement, informal geometry, probability, and statistics. This is not a methods course. Will not count toward the major or minor in mathematics. Prerequisite: 105. Offered each spring.
110 Finite Mathematics (FR) Topics to be selected from solving systems of linear equations using Gaussian and Gauss-Jordan Elimination, matrix algebra, linear programming, probability, mathematics of finance, statistics, and Markov chains. Will not count toward the major or minor in mathematics. Prerequisite: two years of high school algebra and one year of high school geometry. Offered each semester.
135 Applications of Sets, Logic, and Recursion (FR) Introduction to functional programming and discrete mathematics. Sets, functions, and relations. Basic logic including formal derivations in propositional and predicate logic. Recursion and mathematical induction. Programming material: Data types and structures, list processing, functional and recursive programming. No prerequisites. Will not count towards the major or minor in mathematics. Cross-listed with Computer Science 135. Offered each year.
161 Calculus I (FR) Beginning calculus: A rigorous study of limits, continuity and differential calculus of functions of one variable. Prerequisite: four years of high school mathematics including trigonometry. Offered each semester.
162 Calculus II (FR) Further topics in one variable calculus: introduction to integration, applications of the definite integral, techniques of integration. Prerequisite: 161. Offered each semester.
165 Analysis I (FR) Careful study of the real number system, basic topology of the real line, the plane, and three-dimensional space; sequences and their limits; sequential limits of functions from Rn to R; equivalence of the sequential and delta-epsilon limit definitions for functions of one variable. Prerequisite: One year of high school calculus including trigonometry. Students who scored at least 4 on the AB or 3 on the BC Advanced Placement exams in high school should take this course. Offered each fall.
166 Analysis II A continuation of Math 165 to include: Differential calculus of vector-valued functions, vector fields, differentiation for functions of several variables, and integration for functions of one variable. Prerequisite: 165. Offered each spring.
300 Mathematical Modeling This course demonstrates the applicability of mathematics in the formulation and analysis of mathematical models used to solve real world problems. Students are expected to write the results of the models obtained in technical reports and to give oral presentations. This course is taught with the aid of a computer lab. Prerequisite: one of the courses 263 or 267, 215, and at least one additional mathematics course at the 200- or 300-level. Offered each fall.
303 Regression and Time Series This course introduces statistical methods used in practice: simple and multiple linear regressions, hypothesis testing and confidence intervals in the linear regression models, autoregressive and ARIMA models, data analysis and forecasting with time series models. Prerequisite: 325 or one of the following: Biology 209, Economics 227, Psychology 227, or Sociology 227. Offered in spring as needed.
337 Algorithmic Number Theory This course introduces the mathematics necessary to understand public key cryptography. Students will prove results from number theory and analyze algorithms to determine their running times. Topics include modular arithmetic, units and squares modulo integers, Fermat's little theorem, determining primality, and factoring composites. Offered in alternate years.
340 Differential Equations Topics may include, but are not limited to, first-order equations, linear higher order equations, systems of differential equations, series solutions, Laplace transforms, and other selected topics. Prerequisite: 263 or 166. Offered each spring.
370/470 Topics in Mathematics Topics in pure and applied mathematics not covered in other offerings. Math 470 will be proof oriented. May be repeated for different topics. Prerequisite: varies with the topic. Offered as needed.
397 Internship This course provides opportunities for junior and senior mathematics majors to apply skills acquired in the classroom to a job-related experience in various professional areas and locations. Will not count towards the major or minor in mathematics. Prerequisite: consent of department head. Offered as needed.
410 Introduction to Complex Analysis This course provides a rigorous introduction to the theory of functions of a complex variable, which extends Calculus to the complex domain. Topics covered include complex numbers, analytic functions, integrals, power series, elementary complex functions, mappings by elementary functions, elementary conformal mappings, Cauchy's Integral Theorem, the Residue theorem, and harmonic functions. Prerequisites: 200, 215, and either 264 or 267. Offered in spring of even-numbered years.
415 Introduction to Real Analysis A rigorous study of the real number system, functions, limits, continuity, derivatives, integrals, sequences, and series. Prerequisite: 200, 215, and either 263 or 267. Offered fall of odd-numbered years.
495 Directed Study Individual directed readings on a topic of interest to the student. This course is a preparation for Math 499 (Research/Thesis).The course requires a significant review of the literature that culminates in a committee-reviewed manuscript. Will not count towards the major or minor in mathematics. Prerequisite: two courses in mathematics at the 300-level or higher. Requires permission of department chair and faculty research advisor. Open only to mathematics majors with a cumulative GPA of 3.5 or higher in mathematics. Offered each semester.
499 Research/Thesis Experimental or theoretical examination of a significant problem in a topic of interest to the student that is not normally part of the curriculum. It includes as a requirement the preparation of a significant paper. Prerequisite: consent of department chair. Offered each semester. |
Introduction Infinite Sequences Infinite Series and Convergence Taylor Series and Taylor Polynomials The Integral Test Comparison Tests for Positive-Term Series Alternating Series and Absolute Convergence Power Series Power Series Computations Series Solutions of Differential Equations
12. Vectors and Matrices
Vectors in the Plane Rectangular Coordinates and Three-Dimensional Vectors The Cross Product of Vectors Lines and Planes in Space Curves and Motions in Space Curvature and Acceleration Cylinders and Quadric Surfaces Cylindrical and Spherical Coordinates
Double Integrals Double Integrals over More General Regions Area and Volume by Double Integration Double Integrals in Polar Coordinates Applications of Double Integrals Triple Integrals Integration in Cylindrical and Spherical Coordinates Surface Area Change of Variables in Multiple Integrals
PAPERBACK Fair 01303396792377 |
int... read more
Introduction to Vector and Tensor Analysis by Robert C. Wrede Examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, and more. 1963 edition.
About Vectors by Banesh Hoffmann No calculus needed, but this is not an elementary book. Introduces vectors, algebraic notation and basic ideas, vector algebra, and scalars. Includes 386 exercises.
Geometry and Light: The Science of Invisibility by Ulf Leonhardt, Thomas Philbin Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010Vectors, Tensors and the Basic Equations of Fluid Mechanics by Rutherford Aris Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.
The Variational Principles of Mechanics by Cornelius Lanczos Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.
Product Description:
introduces readers to the study of this subject by the methods of vector algebra. The next section explores the many aspects of the theory of mechanics adaptable to the use of vectors, and a full discussion of the vector operator "nabla" proceeds to a treatment of potential theory and Laplace's equation. This includes applications to the theories of gravitation, hydrodynamics, and electricity. A brief chapter on four-dimensional vectors concludes the text.
Unabridged republication of the ninth edition, originally published by Oliver and Boyd, Edinburgh, 1957 |
Algebra 1 CP
Intro to Algebra
Technology Stuff
Intro to Algebra Class Expectations
A successful year in
mathematics will require that we work together.Your active participation is essential.On this sheet you will find important information about your math class:my expectations, your responsibilities, as
well as helpful suggestions to help you to do your best this year in math.Keep this sheet in the front of your notebook
to refer back to during the year.
Student
Responsibilities
Attend
class every day and be on time.If you miss a class, it is your
responsibility to obtain make-up work. Unexcused absences and tardies will
result in disciplinary action, and under these circumstances, no make-up
will be allowed.
Be
prepared for class.You must have your notebook, a pencil,
the previous night's homework and a willing attitude with you every
day.Calculators are not necessary all
the time but would be good to have within reach.
Contribute
to a cooperative learning experience.Mathematics should not be
learned in isolation.Actively
participating in discussions and activities, either as an entire class or
within small groups, will allow others to learn from you, and you from
them.
Complete
all assignments to the best of your ability.Practice
is essential for learning mathematics, and it is important that you arrive
to class each day having taken the time to attempt every homework problem.
Seek extra help when necessary.Asking
questions is important!Use your
classmates as resources, or ask me for help.
Classroom
Expectations and Grading
Binder – Your binder should be a three-ring binder with
dividers. Each of us is an individual so how you organize you binder is up
to you. Each quarter you will have 2 to 4 binder quizzes to test whether
your binder is organized. Some suggestions to help organize your binder: Each
day of class notes should begin with a date and title. In class worksheets
should also be dated and kept with that days notes. Practice should be
dated and kept in chronological order with all problems answered and
corrected if necessary.
Practice – Practice will be assigned and check
daily.It will be accepted only if
it is neat, organized, and all work is shown.Each assignment is worth a total of 5
points. If you do not have the homework or it is incomplete you will be
expected to return (with your lunch) during your lunch block to complete
your work and a score of 4 out of 5 will be given for the assignment. Any
work not completed by the end of the day due will not be accepted and a
score of 0 out of 5 will be given. If you are absent due to illness, the
assignment will be due the day after you return to school, unless
extenuating circumstances exist.
Technology – Technology assignments will have students using websites and programs
to complete and created tasks pertaining to skills and topics we are
covering in class. Some examples are: posting
to your blog, contributing to a wiki, creating a podcast, completing a
survey, creating a Scratch program, and gathering data through internet searches.
Daily Comps – Daily Comps are short 4 question quizzes given at the start of each day
that cover material and skills previously covered in class. Each daily
comp is worth 10 points. If you are absent the daily comp will be exempted and you do not have to make it up.
Tests,
Quizzes, Projects – You will always be given warning as to when a test/quiz will be given. I do not give "pop" quizzes.
Extra
Help – If you need some extra
help, it is your responsibility to arrange a time in advance with me
before school, during a lunch period, or after school when we can both
meet. Don't wait until you are in
over your head before you ask for help.
Sometimes the biggest of problems can be cured with a simple fix. Extra help needs to be arranged at least
one day in advance. Bring your binder with you when coming for extra help. |
Teaching algebra is quite demanding and difficult for both the new teacher and the students. Confidence is a great help. The following suggestions will help build success based on being confident, thorough and thoughtful.
Ad
Steps
1
Attend school district training to get copies of teaching suggestions and example assignments for the the first unit, etc. Often you will receive more assignments from the district math consultants (not strictly supervisors, but advisers or sorts) as some kind of academic math coordinator, services person.
Ad
2
Use the school districts scope and sequence materials or manual which tells you when and what to teach, and how many days to spend on various topics.
3
Realize that the district produced scope and sequence usually does not go straight through the book and has extra assignments.
4
Read over the publishers similar kind of scope and sequence, but it goes straight through the book and has fewer "extras".
5
Prepare or obtain a syllabus that covers the subject to give to the students.
6
Make a Lesson Plan: Introduce the topic, demonstrate, use student centered guided practice in classroom work sessions; perhaps using groups may work for you.
7
Teach students using algebra concepts that are ordered and clarified. Review and reteach a little bit each day.
8
Do not teach a "book", but it is an important tool and reference (teach the students).
9
Lecture less, and facilitate more. Use some special real world activity for each unit.
10
Use math vocabulary "all the time" with some duplication with simpler terms, but not just the simple words: so students will know that you think the vocabulary is important.
11
Teach algebraic thinking with patterns of growth or decay with data, multiple representations, visual/sketch, graphing and expressing a relation or function.
12
Find examples of math in the real world (slope, roof pitch, percent hill grades) and other things in everyday life (cubic yards of soil, sand, concrete) and in sports (statistics), jobs, etc.
13
Have answers when students argue that math is useless and doesn't have anything to do with everyday life. Say that:
"It helps you have options in life like you have to take one or two math courses for almost all degrees in college."
"It is needed in the military to pass tests for technical work."
"You never know whether you will end up in some kind of technical work where math is needed."
"You will need math to help your children and grandchildren with school lessons."
"Math describes the real world with stunning accuracy and simplicity. In the words of Galileo, 'Mathematics is the language with which God has written the universe.'"
"Math is fundamentally the study of patterns, many of which are beautiful in themselves. Sometimes, math is useful as art is useful.
14
Motivate students to do homework, use it as a small part of the grade. Some small extra credit system may help.
15
Use "Hands-On" activities planned for each major unit. Math needs to not just be abstract. Engage students in learning by providing manipulative activities that get students moving and manipulating math.
Use a classroom "algebra-football field" to have the students walk through to explain the movements on a number line and for graphing of positive and negative integers (zero at what would usually be the 50 yard line) or make quadrants, with (0,0) at the origin, etc.
16
Test only what is taught: Make students accountable by testing as needed and as required by the school district and by the state with occasional short quizzes.
17
Reteach with a review and retest if needed, but do it while trying to keep making some progress on new materials.
18
Be happy about even small student successes when the have the "Eureka moment!" or "I got it!" and never stop being enthusiastic. Let students see and believe that math is cool, exciting and fun to you.
Classroom Procedures
1
Post just a few class rules, about 5 or 6, not twenty. Tell them that you will decide questions about rules, but that you try to be consistent and fair.
2
Make a set classroom procedures for roll call, tardies that do not take much time. Restrict hall passes to urgent use, not for going to lockers and such.
3
Calculators can be a help or a hindrance, and are useful, but some uses of the calculator are too advanced while students are learning the basic principles.
4
Check out and get back calculators which will require a carefully planned and executed system to be accountable.
Use a visual check at a glance that proves that the calculators are all there. Just keeping them in an ordinary box is not effective.
One system is a hanging set of shallow pockets so that the screen shows above the pocket (this can be ordered on the internet) where the calculator covers are removed and put away, or someone may swipe calculators and leave only the covers, and it is not obvious at a glance.
Another system is a box with 30 to 40 numbered slots.
5
Teach from bell to bell: That means, no free time, and no free class periods in general.
Tips
It is very crucial to have students use the same calculator every time or they will remove batteries and punch the screens, and trash them and you would hardly catch the tricksters.
The textbook publisher usually puts out some extra work in worksheet form and perhaps you can have access to these. If you make some of your own worksheets, the publisher material may help so you can cut and paste copies on paper or on screen.
Develop a kind of "Math Olympics Day": with gathering data, measuring, drawing, graphing and calculating -- for finding and using a relation and seeing if it is a function, set parameters for x, and y.
Ad
Warnings
Worksheets usually do not cover the subject well. They skip around.
Understanding vocabulary to be able to interpret and decide what to do to answer a question and solve a problem can be the key to doing well on testing.
Copied assignments can be useful, but be sure your class is not a "worksheet mill" where you give odds and ends of worksheets |
Does the thought of starting high school math make you think that you've just been sentenced to four years of Math Prison? Mom and Dad say that you should keep taking math courses all through high school, but it just doesn't seem to make sense. You're spending hours everyday on subjects like Algebra and Geometry, and many times Mom and Dad don't even understand it themselves! If you're not going to be an engineer or work in some highly technical field, then how much math do you really need anyway? Why not just break out of Algebra prison and study some practical subjects? If you've ever felt this way, or if Mom and Dad have felt this way, you both owe it to yourselves to invest just 55 minutes to find out whether this Algebra stuff is right for you. |
Miller's Algebra for the Clueless
Student tested and approved! If you suffer from math anxiety, then sign up for private tutoring with Bob Miller! Do sets, theorems, and equations ...Show synopsisStudent tested and approved! If you suffer from math anxiety, then sign up for private tutoring with Bob Miller! Do sets, theorems, and equations leave your head spinning? If so, you are like hundreds of thousands of other students who face math--especially, algebra--with fear. Luckily, there is a cure: Bob Miller's Clueless series! Like the teacher you always wished you had (but never thought existed), Bo [ Miller brings a combination of knowledge, empathy, and fun to the often-troubling subject of algebra. He breaks down the learning process in an easy, nontechnical way and builds it up again using his own unique methods. "Basically, the Clueless books are my notes. Exactly the way I teach: friendly, clear...with some humor and plenty of emotion!!" Meant to bridge the gulf between the student, the textbook, and the teacher, Algebra for the Clueless is packed with all the information you need to conquer algebra. This extensive guide gives you: anxiety-reducing features on every page; easy-to-grasp methods that make algebra understandable; bite-sized math portions that fit short study sessions (and short attention spans); full explanations of basic principles to make hard problems easy; quick tips for solving difficult problems; . "I am always delighted when a student tells me that he or she hated math...but taking a class with me has made math understandable...even enjoyable." Now it's your turn. Sharpen your #2 pencils, and let Bob Miller show you how to never be clueless |
As part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, CollegeAlgebra: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format.
Factor fearlessly, conquer the quadratic formula, and solve linear equations There's no doubt that algebra can be easy to some while extremely challenging to others. If you're vexed by variables, Algebra I For Dummies, 2nd Edition provides the plain-English, easy-to-follow guidance you need to get the right solution every time! |
Assessing the Math in Risk Management
Mathematics and Statistics for Financial Risk Management is a practical guide to modern financial risk management for both practitioners and academics. The recent financial crisis and its impact on the broader economy underscore the importance of financial risk management in today's world. At the same time, financial products and investment strategies are becoming increasingly complex. Today, it is more important than ever that risk managers possess a sound understanding of mathematics and statistics. In a concise and easy-to-read style, each chapter of this book introduces a different topic in mathematics or statistics. As different techniques are introduced, sample problems and application sections demonstrate how these techniques can be applied to actual risk management problems. Exercises at the end of each chapter and the accompanying solutions at the end of the book allow readers to practice the techniques they are learning and monitor their progress. A companion website includes interactive Excel spreadsheet examples and templates. This comprehensive resource covers basic statistical concepts from volatility and Bayes' Law to regression analysis and hypothesis testing.
Widely used risk models, including Value-at-Risk, factor analysis, Monte Carlo simulations, and stress testing are also explored. A chapter on time series analysis introduces interest rate modeling, GARCH, and jump-diffusion models. Bond pricing, portfolio credit risk, optimal hedging, and many other financial risk topics are covered as well. If you're looking for a book that will help you understand the mathematics and statistics of financial risk management, look no further.
Other Editions...
You might also like...
Teaches the fundamental ideas of decision analysis, without an overly technical explanation of the mathematics used in decision analysis. This title incorporates and implements the powerful DecisionTools[registered] software by Palisade Corporation, the world's leading toolkit for risk and decision analysis.
This is the first of two volumes of Dale Jorgenson's empirical studies of consumer behaviour. It focuses on an econometric model of demand obtained by aggregating over a population of consumers with heterogeneous preferences.
The number of obese adults in the United States has doubled and the number of obese children almost tripled, which may lead to increased medical expenditures, productivity loss, and stress on the health care system. This title provides a foundation for evaluating the costs and benefits of various proposals designed to control obesity rates.
Books By Author Michael B. Miller
Offering a comprehensive social history of the Bon Marche, the Parisian department store that was the largest in the world before 1914, this title explores the bourgeois identities, ambitions, and anxieties that the emporia so vividly dramatized.
Author Biography - Michael B. Miller
Michael B. Miller studied economics at the American University of Paris and the University of Oxford before starting a career in finance. He has worked in risk management for more than ten years, most recently as the chief risk officer for a hedge fund in New York City |
These authors understand what it takes to be successful in mathematics, the skills that students bring to this course, and the way that technology can be used to enhance learning without sacrificing math skills. As a result, they have created a textbook with an overall learning system involving preparation, practice, and review to help students get the most out of the time they put into studying. In sum, Sullivan and Sullivan's Precalculus: Enhanced with Graphing Utilities gives students a model for success in mathematicsYour opinion is important! Do you want more or less ability to customize your Pearson instructional materials; and, should they be more or less digital? |
Fibonacci and Catalan Numbers
:
An Introduction
Overview
Discover the properties and real-world applications of the Fibonacci and the Catalan numbers
With clear explanations and easy-to-follow examples, Fibonacci and Catalan Numbers: An Introduction offers a fascinating overview of these topics that is accessible to a broad range of readers.
Beginning with a historical development of each topic, the book guides readers through the essential properties of the Fibonacci numbers, offering many introductory-level examples. The author explains the relationship of the Fibonacci numbers to compositions and palindromes, tilings, graph theory, and the Lucas numbers.
The book proceeds to explore the Catalan numbers, with the author drawing from their history to provide a solid foundation of the underlying properties. The relationship of the Catalan numbers to various concepts is then presented in examples dealing with partial orders, total orders, topological sorting, graph theory, rooted-ordered binary trees, pattern avoidance, and the Narayana numbers.
Author Information
RALPH P. GRIMALDI, PhD, is Professor of Mathematics at Rose-Hulman Institute of Technology. With more than forty years of experience in academia, Dr. Grimaldi has published numerous articles in discrete mathematics, combinatorics, and graph theory. Over the past twenty years, he has developed and led mini-courses and workshops examining the Fibonacci and the Catalan numbers.
Customer Reviews
9780470631577
There are no customer reviews available at this time. Would you like to write a review? |
Book Information
What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching--supported by Rogawski's "Calculus Second Edition"--the most successful new calculus text in 25 years Widely adopted in its first edition, Rogawski's "Calculus" worked for instructors and students by balancing formal precision with a guiding conceptual "Calculus" success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.
Book description
What's the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching—supported by Rogawski's Calculus Second Edition—the most successful new calculus text in 25 years!
Widely adopted in its first edition, Rogawski's Calculus worked for instructors and students by balancing formal precision with a guiding conceptual focus.
Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.
Now Rogawski's Calculus success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning |
There are to things I know of for hw answers one is called myalgebra.com And the other on is an app for iPods and what not its called mathaway or something like that, the little app thing is red and it has an M on it:) |
'How about having a math tutor with you anytime, anywhere? Using HMH Math On the Spot, you can choose from hundreds of video...
see more
'How about having a math tutor with you anytime, anywhere? Using HMH Math On the Spot, you can choose from hundreds of video lessons and topics from Grade 6 to Algebra 2. Whether you are studying negative numbers, linear equations, the Pythagorean Theorem, or polynomial functions, On the Spot video tutorials give you the detailed help you need where and when you need it. Aligned to the Common Core State Standards, HMH Math On the Spot video tutorials feature Dr. Edward Burger, whose instructional style has earned him numerous awards. In 2006, Reader's Digest honored him in its annual "״100 Best of America״" special issue as "״Best Math Teacher.״" In 2010, Dr. Burger won the Robert Foster Cherry Award for Great Teaching for his "״proven record as an extraordinary teacher and distinguished scholar." Selected videos also feature Ms. Freddie Renfro, a math teacher, supervisor, and coordinator with more than 35 years experience in math education. Features:• More than 1400 available videos organized, with over 100 topics covering algebra, geometry, numbers and operations, statistics, probability, and much more. • Purchase only the topics you need with over 40 topics for Middle School and over 60 for High School, each with multiple sets of video lessons.• Customize your instruction by building your own playlists and choosing your favorites.• Fully aligned to the Common Core State Standards for Mathematics • Available with English and Spanish audio narration and closed-captioning (Grades 6, 7, 8, and Algebra 1)'This is a free app, but some topics must be purchased.
Web-based resources on Numerical Methods are presented for engineering undergraduates. It is dedicated to reaching a large...
see more
Web-based resources on Numerical Methods are presented for engineering undergraduates. It is dedicated to reaching a large audience of undergraduate students through its holistic but customized approach. Holistically, the resources review background information; present numerical methods through youtube videos, notes, presentations, simulations and assessments; show how what they learned is applied in real life; tell stories to illustrate special topics and pitfalls; and give historical perspectives. From a customized perspective, the user can choose a major of choice - Chemical, Civil, Computer, Electrical, General, Industrial or Mechanical Engineering, and a language of choice - Maple, Mathcad, Matlab, Mathematica to illustrate algorithms, convergence and pitfalls of the numerical methods.
Just for the Kids - California (JFTK-CA) is an affiliate of the National Center for Educational Accountability (NCEA). This...
see more
Just for the Kids - California (JFTK-CA) is an affiliate of the National Center for Educational Accountability (NCEA). This site provides free, easy to understand data on every public school in California to help schools and communities raise student achievement. The JFTK-CA School Improvement System does three things: -Provides clear and accurate data charts based on publicly available information from the California Standards Test for Language Arts and Mathematics. -Helps schools benchmark their performance against the top ten performing schools in the state, region and county that have comparable student populations. -Connects schools to higher performing schools to learn what works as well as a Best Practice Framework and self-audit tool to help set measurable, attainable goals for improvement.
Enable your school districts' math instructors to teach mathematics clearly and effectively while they employ the full power...
see more
Enable your school districts' math instructors to teach mathematics clearly and effectively while they employ the full power of your chosen math textbooks and curriculum approach. Professional development programs in mathematics from LessonLab give teachers an in-depth understanding of the concepts they teach so that they can appeal to students' different approaches to learning math and better anticipate their needs.
Students are helping NASA explore lunar plant growth through NASA's Engineering Design Challenge: Lunar Plant Growth Chamber. The challenge calls on elementary, middle and high school students to design, build and evaluate lunar plant growth chambers. The project supports NASA's goal of attracting and retaining students in science, technology, engineering and mathematics disciplines.
NCES has released a new research and development report, Mapping 2005 State Proficiency Standards Onto the NAEP Scales.This...
see more
NCES has released a new research and development report, Mapping 2005 State Proficiency Standards Onto the NAEP Scales.This report presents the results of applying a methodology for mapping state proficiency standards in reading and mathematics onto the appropriate NAEP scale, employing data from the 2004–05 academic year. The mapping exercise was carried out for both grades 4 and 8. For each of the four subject and grade combinations, the NAEP score equivalents to the states' proficiency standards vary widely, spanning a range of 60 to 80 NAEP score points. Although there is an essential ambiguity in any attempt to place state standards on a common scale, the ranking of the NAEP score equivalents to the states' proficiency standards offers an indicator of the relative stringency of those standards.
This site contains links to a wide variety of online calculators. There is an alphabetical listing as well as a listing...
see more
This site contains links to a wide variety of online calculators. There is an alphabetical listing as well as a listing according to discipline (mathematics, statistics, science and engineering, from astrophysics to car prices to camera optical properties). The author claims that the site 'contains over "13,760" calculators created by over "2,575" very "CREATIVE" Individuals, Businesses & Tax Supported Entities World Wide.' |
This is a free, online textbook offered in conjunction with MIT's OpenCourseWare. "Over the last 100 years, the mathematical...
see more
This is a free, online textbook that is a wikibook. "This book will help you learn how to do mathematics using Algebra. It...
see more
This is a free, onlne textbook. According to the authors, "We are two college mathematics professors who grew weary of...
see more
This is a free, onlne textbook. According to the authors, "We are two college mathematics professors who grew weary of forcing our students to purchase expensive college algebra textbooks whose mathematical content has slowly degraded over the years. Our solution? Write our own. The twist? We made our college algebra book free and we distribute it as a .pdf file under the Creative Commons License. What's more, the LaTeX source code is also available under the same license.״
״Prepares college students for the mathematics they need in the social sciences, computer science, business, economics, and...
see more
״Prepares college students for the mathematics they need in the social sciences, computer science, business, economics, and the physical sciences up to the pre-Calculus level. It is also intended to serve a course that has as its objective an introduction to, or review of, what is currently called "pre-Calculus" topics. Some of the topics that are amplified in modern discrete mathematics and finite mathematics courses are introduced
Elementary Algebra is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is...
see more
Elementary Algebra is a textbook that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques.
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The...
see more
It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated as it is the basis of all mathematical modeling used in applications found in all disciplines.Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Elementary Algebra, is the first part written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.John Redden's Elementary Algebra takes the best of the traditional, practice-driven algebra texts and combines it with modern amenities to influence learning, like online/inline video solutions, as well as, other media driven features that only a free online text can deliver. Using the online text in conjunction with a printed version of the text could promote greater understanding (at a lower cost than most algebra texts).From the traditional standpoint, John employs an early and often approach to real world applications, laying the foundation for students to translate problems described in words into mathematical equations. It also clearly lays out the steps required to build the skills needed to solve these equations and interpret the results. With robust and diverse exercise sets, students have the opportunity to solve plenty of practice problems. Elementary Algebra has applications incorporated into each and every exercise set. To do this John makes use of the classic "translating English sentences into mathematical statements" subsections in chapter 1 and as the text introduces new key terms.A more modernized element; embedded video examples, are present, but the importance of practice with pencil and paper is consistently stressed. This text respects the traditional approaches to algebra pedagogy while enhancing it with the technology available today.In addition, textual notation is introduced as a means to communicate solutions electronically throughout the text. While it is important to obtain the skills to solve problems correctly, it is just as important to communicate those solutions with others effectively in the modern era of instant communications.While algebra is one of the most diversely applied subjects, students often find it to be one of the more difficult hurdles in their education. With this in mind, John wrote Elementary Algebra from the ground up in an open and modular format, allowing the instructor to modify it and leverage their individual expertise as a means to maximize the student experience and success.
״At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a...
see more
״At first blush one might think that of all areas of mathematics certainly arithmetic should be the simplest, but it is a surprisingly deep subject. We assume that students have some familiarity with basic set theory, and calculus. But very little of this nature will be needed. To a great extent the book is self-contained. It requires only a certain amount of mathematical maturity. And, hopefully, the student's level of mathematical maturity will increase as the course progresses. Before the course is over students will be introduced to the symbolic programming language Maple which is an excellent tool for exploring number theoretic questions.״
Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty...
see more
Euclid's Elements form one of the most beautiful and influential works of science in the history of humankind. Its beauty lies in its logical development of geometry and other branches of mathematics. It has influenced all branches of science but none so much as mathematics and the exact sciences. The Elements have been studied 24 centuries in many languages starting, of course, in the original Greek, then in Arabic, Latin, and many modern languages.The text of all 13 Books is complete, and all of the figures are illustrated using the Geometry Applet, even those in the last three books on solid geometry that are three-dimensional. |
More About
This Textbook
Overview
This second edition of Tensors and Manifolds is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics, giving an introduction to the expanse of modern mathematics and its application in modern physics. It aims to fill the gap between the basic courses and the highly technical and specialized courses which both mathematics and physics students require in their advanced training, while simultaneously trying to promote, at an early stage, a better appreciation and understanding of each other's discipline. The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics. The existing material from the first edition has been reworked and extended in some sections to provide extra clarity, with additional problems. Four new chapters on Lie groups and fibre bundles have been included, leading to an exposition of gauge theory and the standard model of elementary particle physics. Mathematical rigour combined with an informal style makes this a very accessible book and will provide the reader with an enjoyable panorama of interesting mathematics and |
MTHS 640
A Mathematical Sampler
Fieldsteel,Adam
06/27/2005 - 08/10/2005
Monday & Wednesday 01:30 PM - 04:00 PM
Public Affairs Center 125
We will present a wide variety of topics from elementary mathematics, chosen for their striking beauty, but also for their bearing on issues of considerable importance. Some of the topics to be discussed are: the decomposition of integers into prime factors, the distribution of the prime numbers, countable and uncountable sets, combinatorial topology and geometry, irrational and transcendental numbers, constructions with straight-edge and compass and their limitations, geometric properties of curves and surfaces, and the isoperimetric inequality.
"Elementary" here means having few mathematical prerequisites. Our discussions will show that elementary arguments can yield startling and profound results. In addition, we will discuss problems which can be formulated in elementary terms, but whose only known solutions are quite sophisticated, and others for which no solution has yet been found.
The course is an attempt to enable students to experience mathematics as a creative enterprise by using examples of imaginative discoveries in mathematics, and by giving them a chance to explore subjects on their own.
The source for most of the course material is a book, an enchanting masterpiece of exposition, called The Enjoyment of Mathematics, which was written first in the 1920s by two distinguished mathematicians, Hans Rademacher and Otto Toeplitz, and which remains absolutely fresh and lively.
Grades will be based on written work, which will be regularly assigned throughout the term.
Adam Fieldsteel (A.B. Brown University; Ph.D. University of California, Berkeley) is professor of mathematics. His research focuses on ergodic theory and topological dynamics, and his recent publications include: (with A. Blokh), "Sets that force recurrence," Proceedings of the American Mathematical Society (2002); (with K. Dajani), "Equipartition of interval partitions and an application to number theory," Proceedings of the American Mathematical Society (2001); (with R. Hasfura), "Dyadic equivalence to completely positive entropy," Transactions of the American Mathematical Society (1998). Click here for more information about Adam Fieldsteel Rademacher & Toeplitz, THE ENJOYMENT OF MATHEMATICS (Dover), Paperback |
MA 135 College Algebra Schone, Jeffery
This class will be taught using a combination of lecture, demonstration, and discussion of sample math problems, exercises, and homework. The easiest way to understand the principles of math is through application and practice. Students are encouraged to work together on homework and take home exercises. Fundamental mathematics is critical to continue in higher level mathematic courses, thus practical real life applications will be used to help the student understand these principles. Students must read the Chapters prior to class discussion to fully comprehend the topics discussed in the classroom.
In order to learn mathematics, students must attempt a significant number of problems. Drill and practice are essential in order to succeed. In addition, the material should not be covered too quickly. Student comprehension always takes priority in the educational process.
Instructor Learning Outcomes
Given a set of lectures of a comprehensive review of basic algebraic concepts, the student will complete said problems to the satisfaction of the instructor.
Given a set of lectures on equations and inequalities, perform such problems to the satistifaction of the instructor.
Given a set of lectures on graphs and functions, complete such problems to the satisfaction of the instructor.
Given a set of lectures on polynomial and rational functions, complete such problems to the satisfaction of the instructor.
Given a set of lectures on inverse, exponential, and logarithmic functions, complete such problems to the satisfaction of the instructor.
Given a set of lectures on systems and matrices, perform such problems to the satisfaction of the instructor.
Given a set of lectures on conic sections and basic theorems of analytic geometry, perform such problems to the satisfaction of the instructor.
Class Assessment:
EXPECTATIONS: What are the things that the student needs to do in order to succeed in this course?
possible after each class session. Review your notes regularly throughout the
semester.
5. VOCABULARY, TERMINOLOGY, and NOTATION are extremely important in
learning
Reading Assignments: Read handouts as assigned. You may have to read a handout several times until you understand the material completely. Study these carefully and thoroughly, making sure that you follow and comprehend the reasoning behind each step of the procedure.
Behavior: Show respect for the instructor. Show respect for your classmates. Disruptive behavior will not be tolerated.
Responsibility: The student is entirely responsible for obtaining and learning any material missed because of absence. Get handouts and assignments from instructor. Get class notes from another student in the class.
The instructor reserves the right to make changes in the syllabus due to time constraints, speed of coverage, or other factors.
Grading:
All students are expected to be present and on time with homework assigned completed.
Predefined homework or exercise assignments are provided and reinforced at the end of each corresponding lesson/class for submission at the beginning of the next class.
Letter Grade Range
90-100% A
80-89% B
70-79% C
60-69% D
Below 60% F
Late Submission of Course Materials:
Assignments are due at the start of class unless otherwise agreed upon by the instructor.
Unexcused late assignments will not receive full credit.
Classroom Rules of Conduct:
Students are responsible for turning in their exercises/assignments on time. If any student cannot attend class, they are responsible for contacting the office or instructor PRIOR to the start of class. Excessive tardiness of the student will have a negative impact on their grade.
Since a portion of the students grade is dependent upon classroom participation and attendance, students are strongly encouraged to be there, on time, and participate in class discussions.
Course Topic/Dates/Assignments:
Prior to the start of each class, it is the student responsibility to review the chapter(s) discussed prior to class. This will help in participation, develop critical thinking and generate questions that will allow students to better understand the principles lectured.
A homework assignment listing will be given to each student at the beginning of the course and reviewed for understanding.
Week & Session
Chapter and Topic Covered
Quiz/Exam
Week 1
Session 1
Intro and Chapter 1: P. 3, P. 6, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6
Introduce yourself!
Week 2
Session 1
Chapter 2: 2.1, 2.2, 2.5, 2.6, 2.7, 2.8.
Chapter 1 Quiz
Week 3
Session 1
Chapter 3:3.1, 3.2, 3.3, 3.4, 3.5, 3.6
Chapter 2 Quiz
Week 4
Session 1
Chapter 3 (cont'd)
Midterm Examination Review
Chapter 3 Quiz
Week 5
Session 1
Midterm Examination
Chapter 4: 4.1, 4.2, 4.3, 4.4, 4.5
Midterm
Week 6
Session 1
Chapter 4 (cont'd)
Return and Review Midterm Exam
Chapter 4a Quiz
Week 6
Session 1
Chapter 5:5.1, 5.2, 5.3, 5.5
Chapter 4b Quiz
Week 7
Session 1
Chapter 7:7.1, 7.2, 7.3
Chapter 5 Quiz
Week 8
Session 1
Final Examination
You are finished penalty |
Editorial Reviews
From the Back Cover
Key Benefit: This student edition gives documentation to the powerful, industry-standard MATLAB technical computing environment, for use on personal computer. Key Topics: Includes coverage of all of the new MATLAB 5.0 features, which span the language, graphics, data analysis, and application and GUI development capabilities of MATLAB. MATLAB 5.0 includes over 500 mathematical, an engineering, and statistical functions including polynomial arithmetic; matrix manipulation, decomposition, and factorization; special matrices; data analysis functions; and integrated sparse matrix support. Covers the advanced visualization capabilities of MATLAB are included, such as 2-D, 3-D, and 4-D graphics; animation; light sources.
"The Student Edition of Matlab Version 5 User's Guide" bring to us a pratical and easy way apresentation to Matlab. Its language is easy to know. But this book present same fauls for me. It doesn't have exercises for the readers pratice. It show us few examples and repetitives. But they are goods. And, finally, I would like to see more pages about the simulink and blocksets. But in my opinion this book is a good way to you know Matlab and its comands. |
Most CiSE readers have probably used Maple, Mathematica, or Matlab for several years. With this review series, our goal is to help you now decide whether one of the others is better suited to your temperament and current practice than your original choice. For those of you new to integrative computing packages, our goal is to enable you to make an informed first choice.
In this installment, we begin to examine how these tools serve the professional work of undergraduate education. Within this context, we'd like to raise several significant issues for those teaching undergraduates to be scientists and engineers. We point to some exemplary materials and offer our own paradigms for major educational uses, which provide a framework for discussing the packages and drawing some implications for those issues in a concluding installment. In subsequent issues, we'll explore how the tools serve scientific and engineering research and communication.
We begin with the premise that science and engineering undergraduates should have experience in using modern computational tools. Indeed, this is already an explicit criterion for engineering schools' curricula in the US as prescribed by the Accreditation Board for Engineering and Technology (ABET; In this article, we examine the extent to which these tool packages so qualify: What kinds of computational experiences with them are appropriate for undergraduate students?
We're aware of the multiple goals that educational uses of computing technology must serve, as well as the challenge they present to a fair evaluation of computing software. Foremost in our minds as instructors experienced in the design of electronic instructional materials is the importance of appearance, simplicity, and user-interface functionality to the success of such materials. Yet, there are several types of user interfaces that connect users to different computing tasks according to different educational goals. This begs several questions: What are some major educational goals for science and engineering undergraduates? How are specific computing tasks related to those goals? How does each of the three productivity packages realize the required computations?
Undergraduates have a variety of learning styles and abilities, and they must simultaneously master material while learning how to learn. Ease of use in the packages' user interfaces as well as their adaptability to the variety of interactive mechanisms used in educational applications are key issues. Keep in mind, however, that the way and degree to which these are important depends on who the students are as well as the goals of the applications.
College and university instructors must be judicious in the type and intensity of development projects they undertake in creating educational materials, with respect to both the time and resources they dedicate. How well do these tool packages serve for materials-development work that faculty will likely perform alone? How efficient are they when fast response times are required for modifications? How expensive are they to purchase and, equally important, maintain?
Our approach to this review series is to describe the functions, features, and other elements these packages support and allow you to judge their value based on your values and objectives. To do this, we depart from making lists of features devoid of use-contexts, instead setting contexts in a variety of examples, both real and idealized. We've principally drawn the real examples from each company's Web site, but each is implemented in only one of the three packages. By examining explicit application software, albeit developed for an educational purpose that might not match your own, we hope to present examples that help you envision how applications you create could work in each package.
From our perspective, these examples provide a concrete feature set to which we can refer when discussing how each package would implement an idealized example. We define each example as a paradigmatic application directed to one of the following educational roles for computational productivity packages in science and engineering undergraduate education: content tutorials, simulations, and computational programming.
Maplesoft, Wolfram Research, and MathWorks all show evidence of wanting to maintain a position in the educational workplace. This is true in spite of the companies' self-histories in which only Maple claims to have had an academic birth and, as reported in the introductory article to this review series ( CiSE, Jan./Feb. 2005, pp. 8–16), has what most feels like an academic "personality." All three have an extensive number of exemplary educational applications available online:
• Maple (
• Mathematica (
• Matlab (
These examples are resources for instructors to borrow as models or for students to use to supplement their learning opportunities on their own.
The significance of these examples goes beyond evidence of the companies' commitment to education and is broader than their use as classroom materials. They also illustrate a great deal about each package's range of computing power, and new developers can learn how to harness that power by examining the code. If you're already using one package, you might also find it valuable to "test drive" applications built with the others.
In evaluating the packages' look, feel, and capabilities through these examples, we didn't feel a need to select the same type of examples from each. Rather, we chose examples that demonstrated interesting features, strengths, peculiar characteristics, and so on. For simplicity, we present the examples in alphabetical order by company name.
Maple
We selected precalculus and calculus tutorial applications because they reflect Maple's mathematical character, and a rather extensive range of such lessons are available on the Maple site for free download. Many educators involved in the New Calculus movement have adopted Maple for implementing their material, which means that using it inducts you into a community defined by its novel approach to teaching calculus, gives you access to comprehensive materials, and provides an opportunity for a major overhaul of your mathematics curriculum.
The Precalculus Study Guide is an exercise-based electronic textbook developed by Maplesoft and available for sale on the company's Web site. The educational material in the lessons fall into a category that we'll call "tutorials." They don't stretch Maple's computational power, but they could conceivably be used for remedial work in colleges. Among the subjects this study guide covers are graphing of lines, polynomials, and rational functions; roots and rational powers; and transcendental and piecewise-defined functions. The free downloads are less elegant versions of the textbook lessons, but they nicely illustrate the standard Maple worksheet format. This permits interleaving comments and questions (displayed in developer-formatted text) with Maple expressions and functions (displayed in system-formatted text and shown, following command prompts [>], in red in Figure 1).
The latest version of the Precalculus Study Guide includes 20 new tutorials, each using a GUI (Maplet) with buttons, input windows, graphical output windows, and so on. A GUI significantly alters the study guide's style, making it more congenial to exploration, but it lacks the more extensive text narrative possible with a worksheet because a GUI's advantages are diminished if the user must scroll to navigate it. Notice the complete absence of explanatory text in the window in Figure 2.
Figure 2. Maplet GUI example from Maplesoft's Precalculus Study Guide. The tutorials use input boxes, control buttons, and display windows to let users input values and immediately see the results of the calculation using variables with those values. Notice the absence of explanatory text.
Two of the educational issues we'll develop in this review are the costs and benefits of several material-delivery methods, including worksheets and GUIs. Distributing material through GUIs and worksheets is one way to take advantage of both. The Maple worksheet interface provides the user with immediate access to the Maple code and allows the user to change the code and explore additional options. The code's accessibility also provides a way to learn how to produce worksheets. However, the code for the Maplet tutorial lessons is one level removed from the user. Thus, the GUI protects the Maplet code from students' casual tampering (although it's fairly easy to access the code by moving to the Maple worksheet that generated the Maplet GUI).
The Calculus Study Guide, also available for purchase on the Maple site, is an electronic book to help those students taking their first course in calculus. The guide contains 31 Maple worksheets that give extensive coverage to five major subjects—limits, derivatives, application of derivatives, integrals, and applications of integrals—and 17 Maplet tutors that use the same GUI style as the Precalculus Study Guide. Other Maple course materials (including multivariable calculus, differential equations, partial differential equations, complex analysis, and matrix algebra) are also available for free download. Maplet tutors (for example, the Calculus 1 step-by-step differentiation problem solver) are useful as stand-alone student practice modules or for classroom demonstrations. An educational advantage of modularity in the packages is the ability for quick and responsive personalization of learning materials.
Mathematica
Mathematica has its own calculus tutor package, but we were prompted by the package's formalistic mathematical character and Wolfram's background as a physicist to select some physics applications. The company's Web site lists more than 750 Mathematica-related physics references (articles, books, demos, and courseware) available for download, so our application selection was somewhat arbitrary, but we did narrow the choices by eliminating examples written in earlier versions of Mathematica. In the end, we chose two examples from the quantum physics section: particle in a box and hydrogen atom.
These examples are part of a category of materials we call "visualizations." They don't use much of Mathematica's computational power, but they demonstrate an important component of all the packages: rendering of results. Moreover, the contents of these examples are standard topics in most college physics and quantum mechanics courses. Figure 3 shows the GUIs for these two visualizations. Each example calculates and plots the respective quantum mechanical solutions to the infinite-square potential well problem and the hydrogen atom from user-specified values. The examples include text explanations using standard mathematical notation for the equations together with output-graphing windows.
Figure 3. Mathematica GUI visualization examples from the Wolfram Research Web site. Quantum mechanical probability density distribution for (a) a particle in a box and (b) the hydrogen atom.
The Mathematica site also includes other interesting visualization examples. The optics example, for instance, displays a detailed solution to Maxwell's equations for electromagnetic waves sustained in a homogeneous and isotropic dielectric medium, expressing this solution in both Cartesian and spherical coordinates. This example also shows the solution as an animated wave traveling through this medium, bringing out some subtle features of traveling waves that really require animation to be apparent to the novice. This capability thus has high value in lessons for first-time quantum learners.
These lessons incorporate the recently developed GUI with its Web-based method of delivery—WebMathematica. (We briefly discuss alternative delivery systems for all three packages, emphasizing Web delivery, at the end of this section.)
Matlab
We first looked for engineering-like applications, such as systems operations, to test Matlab, which has been widely adopted by the professional engineering community. However, during our initial Google search of existing Matlab examples, we found an even better choice in Erik Cheever's Visualizing Phasors (the Matlab file is available for download directly from a Swarthmore College Web site
We selected this application for the Matlab example because it serves to mediate a particularly thorny learning task—understanding phasors—but also because our paradigmatic simulation example will be an exercise based on the behavior of AC electrical circuits analyzed using phasors.
Visualizing Phasors is a tool for depicting the relations between phasor and time graph representations of sinusoids. The user selects input parameters (voltage, impedance, and frequency) and then observes the corresponding time-dependent graphs of current and voltage (see Figure 4).
Figure 4. GUI with results from the Matlab simulation example. The Visualizing Phasors application shows a phasor diagram's relationship to its associated graphs of time behavior for the quantities represented by the phasors.
The tool then calculates the current's behavior through from the voltage applied across the impedance element by computing it from the AC generalization of Ohm's law. We will call this category of educational application a "simulation."
Given that Matlab's great strength is in the engineering community, however, we needed an engineering example as well. A compelling reason for this strong engineering bent comes from Matlab's numerical calculation capabilities. The syntax of its arithmetic representations is based on the matrix as the fundamental numerical construct (a real number is even represented as a 1 × 1 matrix, for example). Moreover, the development environment's architecture is geared toward computational programming as it uses multiple windows, command histories, search paths, and so on, which all favor code development.
A lab exercise developed by Jeff Holmes, a biomedical engineer, for his students at Columbia presents a nice example in which the educational objective—numerical problem solving—neatly dovetails with executable code that illustrates how to program in Matlab. For the lab experiment, the instructor furnishes students with a Matlab (M-code) file as a program for simulating the experiment they will perform. Students write their own Matlab programs to reduce their experimental data, and then use the M-code simulation to test their own computational algorithms. This application thus serves the dual educational roles of simulation and computational programming. The M-code and lab instructions are available for download at
Application Delivery
Except for the Mathematica Optics example, users would normally need to have the application package to execute the cases we've described here. However, Mathematica's Web-based delivery system lets us use the applications without buying the package—albeit with restricted ability to explore the code and no ability to modify it. Maple and Matlab have their own Web-based delivery systems, which are similar to Mathematica's though different in functionality. The Matlab Web Server lets developers deploy Web-based Matlab applications. The user sends data from a Web browser to the Matlab application running on a server for computation, and the server returns results for display by the user's Web browser. Maple TA is a Web-based system designed for creating tests, assignments, and exercises; it automatically assesses student responses and performance—a useful feature for educational users.
Web-based delivery is a relatively new feature in all three packages. It's especially useful for educational applications, such as tutorials and simulations, because it favors instructional developers who value borrowing and swapping materials freely. Moreover, it gives a more consistent, although constrained, look to user interfaces across packages and obviates students' need to have the tool packages to operate the applications. We'll discuss some of the differences between—and implications of—these Web-based interfaces more fully in the next installment.
Earlier, we singled out three roles for educational applications. To compare common application examples that compare how the packages work in educational settings, we'll invent one paradigm for each. Given our limited space, we'll develop the simulation role in considerably more depth than the tutorials and computations.
Simulation
The simulation example will be built around a lab-based scenario and will have features that spill over into the other two roles. It will serve as the baseline case.
We start with a definition of educational objectives:
• Enable students to collaborate in small groups as design and development teams.
• Serve as a medium for laboratory teaching assistants to interact with students in conducting "just in time" learning experiences.
• Provide properly motivated students with the opportunity for open-ended experimentation beyond the exercise's immediate requirements.
We then designed a paradigmatic exercise based on these goals. The flowchart in Figure 5 outlines such an exercise based on our objectives, specifications, and assumptions.
Figure Figures 5. Flowchart of the laboratory educational exercise specifying our "simulation" paradigm. Students complete the three branches to the exercise sequentially (moving from left to right) for the experiment.
This baseline case uses features that instructional applications generally need most. Our choices were animated visualizations, GUIs, text using standard mathematical notation, and interactive graphical output. With these features in mind, we chose to examine the behavior of AC electrical circuits, analyzed via phasors. The application should support the lab exercise by providing a prelab demonstration, in-lab design and simulation, and post-lab analysis and homework.
The application should visually display passive elements that students can arrange in circuits of their choice. The application should simulate the circuit's current/voltage behavior under a choice of applied AC voltages. This is similar to the popular SPICE (simulation program with integrated circuit emphasis) technology, which encodes a circuit-performance simulation directly from circuits designed in the form of a schematic. In addition, the application should provide the capability for graphical comparison of the results from the computer's simulation to data obtained by students from measurements on the physical circuits based on the design. Finally, it should have at least one Web-based implementation so that students can conduct it remotely from dorm rooms or public computer labs, as well as locally in the electricity lab.
We assume that, while in the lab, students will work collaboratively in groups and have access to a teaching assistant for help and advice. These assumptions favor graphics rather than text because graphical displays can, in the first instance, mediate group discussion more effectively. It is easier for several people to simultaneously look at and discuss graphical objects rather than text. In the second instance, graphical controls facilitate intervention by laboratory teaching assistants, who usually work over the shoulders of the group.
Tutorial
In the tutorial paradigm, we had a similar, but separate, set of educational objectives:
• Enable students to work individually.
• Serve as a medium for interactive learning.
• Provide properly motivated students with the opportunity for open-ended experimentation beyond the exercise's immediate requirements.
Here, individual activity replaces group work, and the interaction is between an individual learner and the organized material rather than between a group and a set of laboratory tools. In contrast to the baseline case, this situation favors easy readability and structural transparency of textual information. In consort with the baseline case, interactivity and open-endedness require embedded active objects, such as modifiable command statements and data containers.
With tutorials, our experience shows that the principal elements most needed are readable text using standard mathematical notation and interactive graphical output. In addition, sequential segments of the material should be organized by a clustering mechanism that lets the user alternatively "drill down" (open) and "reprise" (collapse) those segments, thus overlaying coarse-grained overviews on fine-grained details. The New User Guides for these three packages are good paradigms for tutorials. They conveniently furnish us with three realizations of the ideal and obviate the need for providing a set of detailed specifications. We can then simply evaluate the three package tutorials on how well they support our educational objectives.
Computational Programming
Proceeding to the last case, we developed the following educational objectives for the computational programming paradigm:
• Enable students to work individually or in groups.
• Serve as a medium for interactive learning of how to design, implement, and test computational algorithms.
Here, we must accommodate both individual and group work with multiple interactions—among students, among students and programming tools, and among students and numerical analysis methods and algorithms. In contrast to the baseline case, this situation favors a congenial code development environment, a full and flexible programming "language," and the existence of and access to numerical analysis information and tools. This case also demands ease of transport for code segments and modules among students and with the broader user community.
In computational programming, a paradigm is actually a complete program development environment. In this case, we conveniently have three realizations of this ideal—namely, the development environments for Maple, Mathematica, and Matlab, themselves. Again, we can simply evaluate these package environments on how they support our educational objectives.
This review project has grown in size beyond our original estimate. Happily, this means that we've uncovered lots of interesting material. Unfortunately, it also means that we had to split the print edition into two installments. In the July/August issue of CiSE, we'll continue this discussion by examining the inner workings of these tool packages. We'll describe the tools' flexibility, facility, and accessibility from the instructor-developer's standpoint. We'll also discuss the experiences of instructor-users, referring to specific parts of the paradigmatic applications described here. This should provide a comparison of the effort involved and the outcomes achievable using each of the three packages for common end applications. We hope these observations and conclusions will carry some implications about the cost and benefits of using each package in a variety of educational contexts.
Researchers and developers, remember that we'll be continuing this series in September/October with a review of the packages from the perspective of scientists and engineers at work.
Also, keep in mind that the project of constructing this review series is an experiment in determining what is useful to you, our readers, for use in your own work. As we promised earlier, CiSE will soon be soliciting your feedback on the new Tech Review format through an online "usability" evaluation—part of the magazine's renewed effort to evolve along with those whom we serve. We look forward to your cooperation in this effort.
Norman Chonacky, most recently a senior research scientist in environmental engineering at Columbia, is currently a research fellow in the Center for UN Studies at Yale. Chonacky received a PhD in physics from the University of Wisconsin, Madison. He is a member of the American Association of Physics Teachers (AAPT), the American Physical Society (APS), the IEEE Computer Society, the American Society for Engineering Education (ASEE), and the American Association for the Advancement of Science (AAAS). Contact him at cise-editor@aip.org.
David Winch is emeritus professor of physics at Kalamazoo College. His research interests are focused on educational technologies. Winch received a PhD in physics from Clarkson University. He is coauthor of Physics: Cinema Classics (ZTEK, videodisc/CD 1993, DVD/CD 2004). Contact him at dmwinch@kitcarson.net. |
Attend: Enrichment
Princeton University Math Club students and others show high school (and advanced middle school) students how fun and fascinating math can be. Students will hear talks on a wide range of topics outside the traditional school curriculum such as topology, number theory and combinatorics. Difficulty will vary. The group meets the second...
Princeton University Math Club students and others show students in grades 6-12 how fun and fascinating math can be. Designed for students who have a basic understanding of algebra, the series will integrate lectures with hands-on activities to illustrate how seemingly simple games and puzzles lay the foundation for many advanced topics...
Director Robert Greenwald investigates |
Summary: Ideal for mathematics majors and prospective secondary school teachers, Euclidean and Transformational Geometry provides a complete and solid presentation of Euclidean geometry with an emphasis on how to solve challenging problems. The author examines various strategies and heuristics for approaching proofs and discusses the process students should follow to determine how to proceed from one step to the next, through numerous problem solving techniques. A large col...show morelection of problems, varying in level of difficulty, are integrated throughout the text, and suggested hints for the more challenging problems appear in the instructor's solutions manual for use at instructor's discretion. ...show less
4-1 Ratio, Proportion and Similar Polygons 4-2 Further Applications of the Side Splitting Theorem and Similarity 4-3 Areas of Similar Figures 4-4 The Golden Ratio and the Construction of a Regular Pentagon 4-5 Circumference and Area of a Circle 4-6 Other Recursive Formulas for Evaluating p 4-7 Trigonometric Functions
New Book. Shipped from UK within 4 to 14 business days. Established seller since 2000.
$82104136136.75160.65 |
Schaum's Outlines present all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.
Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader... |
Product Description
Students will receive a full semester of informal geometry with real-world, abstract and interdisciplinary applications, as well as traditional Algebra 2 topics such as angles, perimeters, and proportional segments; negative exponents; quadratic equations; metric conversions; logarithms; and advanced factoring.
Saxon Teacher provides comprehensive lesson instructions that feature complete solutions to every practice problem, problem set, and test problem, with step-by-step explanations and helpful hints. These CD-ROMs contain hundreds of hours of instruction, allowing students to see and hear actual textbook problems being worked on a digital whiteboard. A slider button allows students to skip problems they don't need help on, or rewind, pause, or fast-forward to get to the sections they'd like to access. Problem set questions can be watched individually after the being worked by the student; the practice set is one continuous video that allows for easy solution review. For use with Algebra 2 3rd Edition. Four Lesson CDs and 1 Test Solutions CD included.
Product Reviews
teacher on CD-ROM doesn't always explain enough
The CD-ROM is helpful in that it goes over every problem in the book. Our frustration is that the teacher often skips steps, so if we aren't understanding how to find an answer, she doesn't really help us! We need more explanation than she gives. I'm ordering the teacher manual on top of this kit, so I have step by step answers.
November 23, 2010
The Saxon Teacher DVD is wonderful!
I am using this Algebra II kit to teach Algebra II at our homeschool co-op. Though I have strong math skills, it's been 25 years since I've taken Algebra II, so I got the DVD to use when I get to concepts that I've completely forgotten. The DVD is really well done. The video is of a teacher teaching each lesson on a white board, clearly explaining the concepts. Then under each lesson is a menu that allows you to choose specific problems from each lesson to watch the teacher solve the problem.
Similar to Teaching Textbooks, but I prefer Saxon Teacher and Saxon's straight forward approach.
As a side note - the 3rd edition textbook has identical problems to the 2nd edition so students in my class can use either text. The 2nd edition text has nice reference info (formulas, etc) on the end pages that the 3rd edition does not have. The 2nd and 3rd edition tests are similar, but not the exact same problems.
November 17, 2010
I purchased this product for my daughter who has struggled the last two years with Algebra I. The first year we tried ABeka, that did not work at all. Last year we tried the DIVE cds which were some better but she still struggled. I am happy to say that this year she is flourishing. She is doing it all on her own and is understanding the material and is making good grades as well. This product has been great for her. I highly recommend it!
October 22, 2009 |
first and second year undergraduate students in mathematics, the physical sciences, and engineering, and written by two authorities in the field, this book will be required reading for courses that follow a 'problem-solving' approach to teaching calculus. The main philosophy of calculus is presented through many examples and applications to explain its abstract notions and concepts. A solutions manual demonstrating the workings of each example accompanies the book. |
More About
This Textbook
Overview
This book provides a concise yet comprehensive and self-contained introduction to Grobner basis theory and its applications to various current research topics in commutative algebra. It especially aims to help young researchers become acquainted with fundamental tools and techniques related to Grobner bases which are used in commutative algebra and to arouse their interest in exploring further topics such as toric rings, Koszul and Rees algebras, determinantal ideal theory, binomial edge ideals, and their applications to statistics. The book can be used for graduate courses and self-study. More than 100 problems will help the readers to better understand the main theoretical results and will inspire them to further investigate the topics studied |
Transform Linear Algebra
Book Description: This book encourages readers to develop an intuitive understanding of the foundations of Linear Algebra. An emphasis on the concepts of Linear Algebra and Matrix Theory conveys the structure and nature of Linear Spaces and of Linear Transformations. Almost every chapter has three sections: a lecture followed by problems, theoretical and mathematical enrichment, and applications to and from Linear Algebra. Specific chapter topics cover linear transformations; row reduction; linear equations; subspaces; linear dependence, bases, and dimension; composition of maps, matrix inverse and transpose; coordinate vectors, basis change; determinants, …l-matrices; matrix eigenvalues; orthogonal bases and orthogonal matrices; symmetric and normal matrix eigenvalues; singular values; and basic numerical linear algebra techniques. For individuals in fields related to economics, engineering, science, or |
Schedule of Classes
Additional Information on Select Fall 2014 Courses
This will be a course on algebraic and enumerative combinatorics. The focus will be on counting and homology in partially ordered sets and lattices. We will start with basic counting methods: what to do when you meet an integer sequence, recursions, generating functions, the standard counting numbers, and using databases like OEIS [online encyclopedia of integer sequences] . More advanced topics include Moebius functions, characteristic polynomials, chain and no-broken-circuit complexes. We will also study specific examples: subspace and subgroup lattices, lattices of intersections of arrangements of hyperplanes, Bruhat orders, and permutahedrons. We will definitely not be doing CATegory theory.
We will not have an official textbook, but a useful reference is R. Graham, D. Knuth, and O.Patashnik, Concrete Mathematics, Addison-Wesley, 1989, 0-201-14236-8. |
This Web page is a collection of resources on Polynomials. The Web page includes narrated PowerPoint presentations on...
see more
This Web page is a collection of resources on Polynomials. The Web page includes narrated PowerPoint presentations on topics such as adding and subtracting polynomials, The FOIL Method, factoring a Quadratic Equation, and dividing a polynomial by a monomial. There is a link to a Blog on polynomials, which is a portal to numerous quality resources on polynomials. There is also a podcast that gives you a description of monomials, binomials, and polynomials.
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems...
see more
This is a resource that can be used in conjunction with an Abstract Algebra class. It contains definitions and theorems regarding abstract algebra. Included is a Table of Contents that lists the topics such as Integers, Functions, Groups, Polynomials, Galois Theory, Unique Factorization, etc. There is also a link to an online study guide for the topic.
This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of...
see more
This is a free online textbook designed for the Advanced Algebra instructor. According to the author, he "developed a set of in-class assignments, homework and lesson plans, that work for me and for other people who have tried them. The complete set comprises three separate books that work together:•The Homework and Activities Book contains in-class and homework assignments that are given to the students day-by-day." "•The" target=״_blank״ Concepts Book provides conceptual explanations, and is intended as a reference or review guide for students; it is not used when teaching the class." •The" target=״_blank״ Teacher's Guide provides detailed lesson plans; it is your guide to how the author "envisioned these materials being used when I created them (and how I use them myself) " target=״_blank״ Instructors should note that this book probably contains more information than you will be able to cover in a single school year."
This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to...
see more
This is the Conceptual Explanations part of Kenny Felder's course in Advanced Algebra II. It is intended for students to read on their own to refresh or clarify what they learned in class. This text is designed for use with the "Advanced Algebra II: Homework and Activities" ( and the "Advanced Algebra II: Teacher's Guide" ( collections to make up the entire course. |
1-1-90 other 3Students can rely on Moise's clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24 |
: A Combined Approach
With a reputation built on clear and concise exposition, numerous examples, and plentiful problem sets, Kaufmann and Schwitters' "Elementary and ...Show synopsisWith a reputation built on clear and concise exposition, numerous examples, and plentiful problem sets, Kaufmann and Schwitters' "Elementary and Intermediate Algebra, 6th edition, International Edition" consistently reinforces the following common thread: learn a skill; practice the skill to help solve equations; and then apply what you have learned to solve application problems. This traditional, straightforward approach has helped many students grasp and apply the fundamental problem-solving skills necessary for future mathematics courses. Algebraic ideas are developed in a logical sequence, and in an easy-to-read manner, without excessive vocabulary and formalism. The Sixth Edition's open and uncluttered design helps keep students focused on the concepts while minimizing distractions. Problems and examples reference a broad range of topics, as well as career areas such as electronics, mechanics, and health, showing students that mathematics is part of everyday life. The text's resource package-anchored by Enhanced WebAssign, an online homework management tool-saves instructors time while providing additional help and skill-building practice for students outside of class |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.