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The Town lab is looking for motivated undergraduate students who are interested in gaining lab experience as a research assistant. Our lab focuses on the interface between two main systems of the body, the central nervous system and immune system. More specifically, our lab is interested in the innate immune system in Alzheimer's disease. There are projects focused on immune drug deliveries in Alzheimer rats, immune reactions to neural stem cell engraftments, and the basic cellular biology of microglia (the resident immune cells of the brain).
Freshmen and sophomores looking for multiple years of experience are highly encouraged to apply. Juniors with lab experience are also encouraged to apply. Animal handling experience is a bonus. Drosophila experience is also a bonus. We are asking students to dedicate at least 15 hours per week.
If you are interested, please send an email with a one paragraph description of your reasons for wanting to join the Town lab along with your CV to Allan Jensen allanjen@usc.edu
What does e + π mean and how can we evaluate it? What is the difference in the meaning of the equals sign between x2 −1 = 0, x2 −1 = (x−1)(x+1), (x2 −1)/(x−1) = x+1 and √x2 = x? What does it mean for a line to be straight? Are there lines that are not straight? In Math 499 we will be addressing these questions and more!
In this class we will explore the foundations of mathematics and how we acquire and process mathematical knowledge. We will revisit K-12 mathematics from the point of view of a mathematician. We will explore the roles of metaphors, models, and definitions. We will discuss the use of symbols and see that even in mathematics their meanings are often contextual. We will compare and contrast proofs and convincing arguments and think about the roles they play in developing and understanding mathematics. We will discuss the relationship between mathematics and our physical world and how we use mathematics to understand the physical world. We will consider various algorithms common in K- 12 mathematics and discuss why and how they work. We also will read and discuss the literature on how K-12 mathematics is taught and how we learn and process that knowledge. Throughout the semester, you will also the opportunity to observe and participate in classes at AUGUSTUS HAWKINS High School. This is a new school with a modern curriculum implementing an initiative called the Algebra Project.
This class has no prerequisites. In particular, it is not necessary to have taken any college level math classes; you are only expected to know how to count (albeit fairly well!). However, students must be willing to engage with the material at a mathematically sophisticated level. There will be very little lecturing. There will be a lot of discussion, group work, and both oral and written presentations. This class will be valuable for math majors, anyone with an interest in teaching mathematics, and sociology and psychology majors interested in the science of learning.
Characterizing the sequence, function, and evolution of genomes is a central focus of modern biology. In this course, we will learn about the core questions and methods of genome scientists. We will discuss techniques for comprehensively examining organisms at the levels of DNA, RNA, proteins, and metabolites. We will also talk about how this information is used to determine the molecular basis of phenotypes, such as evolutionary adaptations, crop improvements, and human disease. Lastly, we will spend time on the relationship between genomics and synthetic biology, which is a field that seeks to engineer new features into existing organisms or build new organisms based on present knowledge. The goal of this course is for students to walk away conversant in modern genomics techniques and the biological problems genome researchers hope to solveThe Fall 2013 Career Fair is here! Each year, more than 400 organizations seeking to employ USC students from diverse disciplines attend our career fairs. All students are encouraged to attend and explore the wide variety of internship and full-time employment opportunities that are represented:
Thursday, September 19, 2013
10:00 am – 2:30 pm
Trousdale Parkway
Part-time, Full-Time, and Internship positions available from over 150 companies. Log-in to connect SC for more information.
Assistantships are available as part of a Directed Research Course or can be done on a volunteer basis. Assistants work on studies examining the role of emotional factors that influence tobacco, alcohol and drug use, as well as other behaviors that impact health (e.g. exercise and diet). Undergraduate assistantships are a great way to gain initial exposure to research in preparation for medical school and graduate school in psychology, neuroscience and public health.
We are currently looking for research assistants who are either fluent in Spanish or have a full day of availability in fall 2013. To get a better understanding of our lab, please check out our website (
3 paid URAP internships: Seeking 3 talented undergrads (biology/pre-med, math/engineering, and computer science/engineering) for a multidisciplinary cancer simulation team. The team will work to make powerful 3-D computer models of cancer user friendly enough for diverse research teams, while testing and refining simulations of invasive breast cancer, stem cell biology, and chemotherapy. Publication and indepdendent study opportunities available. Applications due May 10, interviews May 13-17, and project to run summer 2013-spring 2014. See details in the attached flyer or at MathCancer.org, and apply as instructed to Paul.Macklin@usc.edu.
Requirements: Should be a junior or advanced sophomore with a 3.5+ GPA. One position in biology, pre-med or related. One position in math or engineering or related. One position in computer science or engineering or related. Same flyer for all 3 positions. |
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Sample Chapter
Assembling Your Tools
In This Chapter
* Giving names to the basic numbers
* Reading the signs - and interpreting the language
* Operating in a timely fashion
You've probably heard the word algebra on many occasions, and you
knew that it had something to do with mathematics. Perhaps you remember
that algebra has enough information to require taking two separate high
school algebra classes - Algebra I and Algebra II. But what exactly
is algebra? What is it really used for?
This book answers these questions and more, providing the straight scoop
on some of the contributions to algebra's development, what it's good
for, how algebra is used, and what tools you need to make it happen. In
this chapter, you find some of the basics necessary to more easily find
your way through the different topics in this book. I also point you
toward these topics.
In a nutshell, algebra is a way of generalizing arithmetic.
Through the use of variables (letters representing numbers) and
formulas or equations involving those variables, you solve problems. The
problems may be in terms of practical applications, or they may be
puzzles for the pure pleasure of the solving. Algebra uses positive and
negative numbers, integers, fractions, operations, and symbols to
analyze the relationships between values. It's a systematic study of
numbers and their relationship, and it uses specific rules.
Beginning with the Basics: Numbers
Where would mathematics and algebra be without numbers? A part of
everyday life, numbers are the basic building blocks of algebra. Numbers
give you a value to work with. Where would civilization be today if not
for numbers? Without numbers to figure the distances, slants, heights,
and directions, the pyramids would never have been built. Without
numbers to figure out navigational points, the Vikings would never have
left Scandinavia. Without numbers to examine distance in space,
humankind could not have landed on the moon.
Even the simple tasks and the most common of circumstances require a
knowledge of numbers. Suppose that you wanted to figure the amount of
gasoline it takes to get from home to work and back each day. You need a
number for the total miles between your home and business and another
number for the total miles your car can run on a gallon of gasoline.
The different sets of numbers are important because what they look like
and how they behave can set the scene for particular situations or help
to solve particular problems. It's sometimes really convenient to
declare, "I'm only going to look at whole-number answers," because whole
numbers do not include fractions or negatives. You could easily end up
with a fraction if you're working through a problem that involves a
number of cars or people. Who wants half a car or, heaven forbid, a
third of a person?
Algebra uses different sets of numbers, in different circumstances. I
describe the different types of numbers here.
Really real numbers
Real numbers are just what the name implies. In contrast to
imaginary numbers, they represent real values - no pretend or
make-believe. Real numbers cover the gamut and can take on any form -
fractions or whole numbers, decimal numbers that can go on forever and
ever without end, positives and negatives. The variations on the theme
are endless.
Counting on natural numbers
A natural number (also called a counting number) is a
number that comes naturally. What numbers did you first use? Remember
someone asking, "How old are you?" You proudly held up four fingers and
said, "Four!" The natural numbers are the numbers starting with 1 and
going up by ones: 1, 2, 3, 4, 5, 6, 7, and so on into infinity. You'll
find lots of counting numbers in Chapter 6, where I discuss prime
numbers and factorizations.
Wholly whole numbers
Whole numbers aren't a whole lot different from natural numbers.
Whole numbers are just all the natural numbers plus a 0: 0, 1, 2, 3, 4,
5, and so on into infinity.
Whole numbers act like natural numbers and are used when whole amounts
(no fractions) are required. Zero can also indicate none. Algebraic
problems often require you to round the answer to the nearest whole
number. This makes perfect sense when the problem involves people, cars,
animals, houses, or anything that shouldn't be cut into pieces.
Integrating integers
Integers allow you to broaden your horizons a bit. Integers incorporate
all the qualities of whole numbers and their opposites (called their
additive inverses). Integers can be described as being
positive and negative whole numbers: ... -3, -2, -1, 0, 1, 2, 3,....
Integers are popular in algebra. When you solve a long, complicated
problem and come up with an integer, you can be joyous because your
answer is probably right. After all, it's not a fraction! This doesn't
mean that answers in algebra can't be fractions or decimals. It's just
that most textbooks and reference books try to stick with nice answers
to increase the comfort level and avoid confusion. This is my plan in
this book, too. After all, who wants a messy answer, even though, in
real life, that's more often the case. I use integers in Chapters 8 and
9, where you find out how to solve equations.
Being reasonable: Rational numbers
Rational numbers act rationally! What does that mean? In this case,
acting rationally means that the decimal equivalent of the rational
number behaves. The decimal ends somewhere, or it has a repeating
pattern to it. That's what constitutes "behaving."
Some rational numbers have decimals that end such as: 3.4, 5.77623,
-4.5. Other rational numbers have decimals that repeat the same pattern,
such as 3.164164164, or 0.666666666. The horizontal bar over the 164 and
the 6 lets you know that these numbers repeat forever.
In all cases, rational numbers can be written as fractions. Each
rational number has a fraction that it's equal to. So one definition of
a rational number is any number that can be written as a
fraction, p/q, where p and q are integers (except
q can't be 0). If a number can't be written as a fraction, then
it isn't a rational number. Rational numbers appear in Chapter 13, where
you see quadratic equations, and in Part IV, where the applications are
presented.
Restraining irrational numbers
Irrational numbers are just what you may expect from their name - the
opposite of rational numbers. An irrational number cannot be
written as a fraction, and decimal values for irrationals never end and
never have a nice pattern to them. Whew! Talk about irrational! For
example, pi, with its never-ending decimal places, is irrational.
Irrational numbers are often created when using the quadratic formula,
as you see in Chapter 13.
Picking out primes and composites
A number is considered to be prime if it can be divided evenly
only by 1 and by itself. The first prime numbers are: 2, 3, 5, 7, 11,
13, 17, 19, 23, 29, 31, and so on. The only prime number that's even is
2, the first prime number. Mathematicians have been studying prime
numbers for centuries, and prime numbers have them stumped. No one has
ever found a formula for producing all the primes. Mathematicians just
assume that prime numbers go on forever.
A number is composite if it isn't prime - if it can be divided by
at least one number other than 1 and itself. So the number 12 is
composite because it's divisible by 1, 2, 3, 4, 6, and 12. Chapter 6
deals with primes, but you also see them in Chapters 8 and 10, where I
show you how to factor primes out of expressions.
Speaking in Algebra
Algebra and symbols in algebra are like a foreign language. They all
mean something and can be translated back and forth as needed. It's
important to know the vocabulary in a foreign language; it's just as
important in algebra.
An expression is any combination of values and
operations that can be used to show how things belong together and
compare to one another. 2[chi square] + 4x is an example of an
expression. You see distributions over expressions in Chapter 7.
A term, such as 4xy, is a grouping together of
one or more factors (variables and/or numbers). Multiplication is
the only thing connecting the number with the variables. Addition and
subtraction, on the other hand, separate terms from one another. For
example, the expression 3xy + 5x - 6 has three
terms.
An equation uses a sign to show a relationship - that
two things are equal. By using an equation, tough problems can be
reduced to easier problems and simpler answers. An example of an
equation is 2[x.sup.2] + 4x = 7. See the chapters in Part
III for more information on equations.
An operation is an action performed upon one or two
numbers to produce a resulting number. Operations are addition,
subtraction, multiplication, division, square roots, and so on. See
Chapter 5 for more on operations.
A variable is a letter representing some unknown; a
variable always represents a number, but it varies until it's
written in an equation or inequality. (An inequality is a
comparison of two values. For more on inequalities, turn to Chapter 15.)
Then the fate of the variable is set - it can be solved for, and its
value becomes the solution of the equation. By convention,
mathematicians usually assign letters at the end of the alphabet to be
variables (such as x, y, and z).
A constant is a value or number that never changes in
an equation - it's constantly the same. Five is a constant because it is
what it is. A variable can be a constant if it is assigned a definite
value. Usually, a variable representing a constant is one of the first
letters in the alphabet. In the equation a]x.sup.2] +
bx + c = 0, a, b, and c are constants and
the x is the variable. The value of x depends on what
a, b, and c are assigned to be.
An exponent is a small number written slightly above
and to the right of a variable or number, such as the 2 in the
expression [3.sup.2]. It's used to show repeated multiplication. An
exponent is also called the power of the value. For more on
exponents, see Chapter 4.
Taking Aim at Algebra Operations
In algebra today, a variable represents the unknown. (You can see more
on variables in the "Speaking in Algebra" section earlier in this
chapter.) Before the use of symbols caught on, problems were written out
in long, wordy expressions. Actually, using letters, signs, and
operations was a huge breakthrough. First, a few operations were used,
and then algebra became fully symbolic. Nowadays, you may see some words
alongside the operations to explain and help you understand, like having
subtitles in a movie.
By doing what early mathematicians did - letting a variable represent a
value, then throwing in some operations (addition, subtraction,
multiplication, and division), and then using some specific rules that
have been established over the years - you have a solid, organized
system for simplifying, solving, comparing, or confirming an equation.
That's what algebra is all about: That's what algebra's good for.
Deciphering the symbols
The basics of algebra involve symbols. Algebra uses symbols for
quantities, operations, relations, or grouping. The symbols are
shorthand and are much more efficient than writing out the words or
meanings. But you need to know what the symbols represent, and the
following list shares some of that info. The operations are covered
thoroughly in Chapter 5.
+ means add or find the sum, more than, or
increased by; the result of addition is the sum. It also
is used to indicate a positive number.
- means subtract or minus or decreased
by or less than; the result is the difference. It's
also used to indicate a negative number.
x means multiply or times. The values being
multiplied together are the multipliers or factors; the
result is the product. Some other symbols meaning multiply
can be grouping symbols: ( ), , { }, ?, *. In algebra, the x symbol is
used infrequently because it can be confused with the variable x.
The dot is popular because it's easy to write. The grouping symbols are
used when you need to contain many terms or a messy expression. By
themselves, the grouping symbols don't mean to multiply, but if you put
a value in front of a grouping symbol, it means to multiply.
? means divide. The number that's going into the
dividend is the divisor. The result is the
quotient. Other signs that indicate division are the fraction
line and slash, /.
[square root of] means to take the square root of
something - to find the number, which, multiplied by itself, gives you
the number under the sign. (See Chapter 4 for more on square roots.)
|| means to find the absolute value of a number, which
is the number itself or its distance from 0 on the number line. (For
more on absolute value, turn to Chapter 2.)
[pi] is the Greek letter pi that refers to the irrational
number: 3.14159.... It represents the relationship between the diameter
and circumference of a circle.
Grouping
When a car manufacturer puts together a car, several different things
have to be done first. The engine experts have to construct the engine
with all its parts. The body of the car has to be mounted onto the
chassis and secured, too. Other car specialists have to perform the
tasks that they specialize in as well. When these tasks are all
accomplished in order, then the car can be put together. The same thing
is true in algebra. You have to do what's inside the grouping
symbol before you can use the result in the rest of the equation.
Grouping symbols tell you that you have to deal with the
terms inside the grouping symbols before you deal with the
larger problem. If the problem contains grouped items, do what's inside
a grouping symbol first, and then follow the order of operations. The
grouping symbols are
Parentheses (): Parentheses are the most commonly used
symbols for grouping.
Brackets and braces {}: Brackets and braces are also
used frequently for grouping and have the same effect as parentheses.
Using the different types of symbols helps when there's more than one
grouping in a problem. It's easier to tell where a group starts and
ends.
Radical [square root of]: This is used for finding
roots.
Fraction line (called the vinculum): The
fraction line also acts as a grouping symbol - everything above the line
(in the numerator) is grouped together, and everything below the
line (in the denominator) is grouped together.
Even though the order of operations and grouping-symbol rules are fairly
straightforward, it's hard to describe, in words, all the situations
that can come up in these problems. The examples in Chapters 5 and 7
should clear up any questions you may have.
Defining relationships
Algebra is all about relationships - not the he-loves-me-he-loves-me-not
kind of relationship - but the relationships between numbers or among
the terms of an equation. Although algebraic relationships can be just
as complicated as romantic ones, you have a better chance of
understanding an algebraic relationship. The symbols for the
relationships are given here. The equations are found in Chapters 11
through 14, and inequalities are found in Chapter 15. |
Teaching Complex Systems with Mathematica
Streamlines of wind direction over North America 2 February 2009, created by "Cloudruns" using Mathematica modeling program. Image from Wikipedia.
Mathematica is a tool for engineering analysis and modeling, and can be used for applications as varied as simple calculator operations to large-scale programming. Mathematica integrates a numeric and symbolic computational engine, graphics system, programming language, documentation system, and advanced connectivity to other applications. The Mathematica product site (more info) includes a description of Mathematica, key elements of the tool, a tour of its features, technical requirements, revision history and a free trial version of the calculation tool. |
Geometry
Standard Objective Taught
Kansas Standards, 2004
Standard 1 use numerical and computational concepts and procedures in a variety of situations.
demonstrate number sense for real numbers and algebraic expressions in a variety
S1.B1 R/M of situations.
know, explain, and use equivalent representations for rational numbers and simple
algebraic expressions including integers, fractions, decimals, percents, and ratios;
rational number bases with integer exponents; rational numbers written in scientific
1.1.K1 R notation with integer exponents; time; and money ($).
generate and/or solve real-world problems using equivalent representations of real
numbers and algebraic expressions ($), e.g., a math classroom needs 30 books and
15 calculators. If B represents the cost of a book and C represents the cost of a
calculator, generate two different expressions to represent the cost of books and
1.1.A1 R calculators for 9 math classrooms.
determine whether or not solutions to real-world problems using real numbers and
algebraic expressions are reasonable ($), e.g., in January, a business gave its
employees a 10% raise. The following year, due to the sluggish economy, the
employees decided to take a 10% reduction in their salary. Is it reasonable to say
1.1.A2 R they are now making the same wage they made prior to the 10% raise.
demonstrate an understanding of the real number system; recognizes, applies, and
S1.B2 explain their properties; and extend these properties to algebraic expressions.
explain and illustrate the relationship between the subsets of the real number system
[natural (counting) numbers, whole numbers, integers, rational numbers, irrational
1.2.K1 R numbers] using mathematical models, e.g., number lines or Venn diagrams.
identify all the subsets of the real number system [natural (counting) numbers, whole
numbers, integers, rational numbers, irrational numbers] to which a given number
1.2.K2 R belongs.
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: commutative (a +
b = b + a and ab = ba), associative [a + (b + c) = (a + b) + c and a(bc) = (ab)c],
distributive [a (b + c) = ab + ac], and substitution properties (if a = 2, then 3a = 3 x 2
*1.2.K3a R/M = 6) ($).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: identity properties
for addition and multiplication and inverse properties of addition and multiplication
(additive identity: a + 0 = a, multiplicative identity: a o 1 = a, additive inverse: +5 + -5
*1.2.K3b R/M = 0, multiplicative inverse: 8 x 1/8 = 1) ($).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: symmetric
*1.2.K3c R/M property of equality (if a = b, then b = a) ($).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: addition and
multiplication properties of equality (if a = b, then a + c = b + c and if a = b, then ac =
bc) and inequalities (if a > b, then a + c > b + c and if a > b, and c > 0 then ac > bc)
*1.2.K3d R/M ($).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: zero product
*1.2.K3e R/M property (if ab = 0, then a = 0 and/or b = 0) ($).
use and describe the following property with the real number system: transitive
1.2.K4a R/M property (if a = b and b = c, then a = c) ($).
use and describe the following property with the real number system: reflexive
1.2.K4b R/M property (a = a) ($).
1
Geometry
generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: commutative, associative, distributive,
and substitution properties, e.g., the chorus is sponsoring a trip to an amusement
park. They need to purchase 15 adult tickets at $6 each and 15 student tickets at $4
each. How much money will the chorus need for tickets? Solve this problem two
1.2.A1a R ways ($).
generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: identity and inverse properties of
addition and multiplication, e.g., the purchase price (P) of a series EE Savings Bond
is found by the formula ½ F = P where F is the face value of the bond. Use the
1.2.A1b R formula to find the face value of a savings bond purchased for $500 ($).
generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: symmetric property of equality, e.g.,
Sam took a $15 check to the bank and received a $10 bill and a $5 bill. Later Sam
took a $10 bill and a $5 bill to the bank and received a check for $15. $ addition and
multiplication properties of equality, e.g., the total price for the purchase of three
shirts in $62.54 including tax. If the tax is $3.89, what is the cost of one shirt, if all
1.2.A1c R shirts cost the same? ($).
generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: addition and multiplication properties of
equality, e.g., the total price for the purchase of three shirts is $62.54 including tax.
1.2.A1d R If the tax is $3.89, what is the cost of one shirt? ($).
generate and/or solve real-world problems with real numbers using the concepts of
these properties to explain reasoning:zero product property, e.g., Jenny was thinking
of two numbers. Jenny said that the product of the two numbers was 0. What could
1.2.A1e R you deduct from this statement? Explain your reasoning ($).
analyze and evaluate the advantages and disadvantages of using integers, whole
numbers, fractions (including mixed numbers), decimals or irrational numbers and
their rational approximations in solving a given real-world problem ($), e.g., a store
sells CDs for $12.99 each. Knowing that the sales tax is 7%, Marie estimates the
cost of a CD plus tax to be $14.30. She selects nine CDs. The clerk tells Marie her
1.2.A2 R bill is $157.18. How can Marie explain to the clerk she has been overcharged?
S1.B3 use computational estimation with real numbers in a variety of situations.
estimate real number quantities using various computational methods including
1.3.K1 R mental math, paper and pencil, concrete objects, and/or appropriate technology ($).
use various estimation strategies and explain how they were used to estimate real
1.3.K2 R number quantities and algebraic expressions ($).
know and explain why a decimal representation of an irrational number is an
1.3.K3 R approximate value.
1.3.K4 R know and explain between which two consecutive integers an irrational number lies.
adjust original rational number estimate of a real-world problem based on additional
information (a frame of reference) ($), e.g., estimate how long it takes to walk from
*1.3.A1 R here to there; time how long it takes to take five steps and adjust your estimate.
estimate to check whether or not the result of a real-world problem using real
numbers and/or algebraic expressions is reasonable and make predictions based on
the information ($), e.g., if you have a $4,000 debt on a credit card and the minimum
1.3.A2 R of $30 is paid per month, is it reasonable to pay off the debt in 10 years?
determine if a real-world problem calls for an exact or approximate answer and
perform the appropriate computation using various computational methods including
mental mathematics, paper and pencil, concrete objects, and/or appropriate
technology ($), e.g., do you need an exact or an approximate answer in calculating
the area of the walls to determine the number of rolls of wallpaper needed to paper a
1.3.A3 R room? What would you do if you were wallpapering 2 rooms?
2
Geometry
explain the impact of estimation on the result of a real-world problem
(underestimate, overestimate, range of estimates) ($), e.g., if the weight of 25 pieces
of paper was measured as 530.6 grams, what would the weight of 2,000 pieces of
paper equal to the nearest gram? If the student were to estimate the weight of one
piece of paper as about 20 grams and then multiply this by 2,000 rather than multiply
the weight of 25 pieces of paper by 80; the answer would differ by about 2,400
grams. In general, multiplying or dividing by a rounded number will cause greater
1.3.A4 R discrepancies than rounding after multiplying or dividing.
model, perform, and explain computation with real numbers and polynomials in a
S1.B4 variety of situations.
compute with efficiency and accuracy using various computational methods
1.4.K1 R including mental math, paper and pencil, concrete objects, and appropriate
perform and explain the following computational procedure: addition, subtraction,
1.4.K2a R/M multiplication, and division using the order of operations (N).
perform and explain the following computational procedure: multiplication or division
1.4.K2bi R to find a percent of a number, e.g., what is 0.5% of 10? ($).
perform and explain the following computational procedure: multiplication or division
to find percent of increase and decrease, e.g., a college raises its tuition form $1,320
1.4.K2bii R per year to $1,425 per year. What percent is the change in tuition? ($).
perform and explain the following computational procedure: multiplication or division
1.4.K2biii R to find percent one number is of another number, e.g., 89 is what percent of 82? ($).
perform and explain the following computational procedure: multiplication or division
to find a number when a percent of the number is given, e.g., 80 is 32% of what
1.4.K2biv R number? ($).
perform and explain the following computational procedure: manipulation of variable
quantities within an equation or inequality (2.4.K1d), e.g., 5x - 3y = 20 could be
1.4.K2c R written as 5x - 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3.
perform and explain the following computational procedure: simplification of radical
expressions (without rationalizing denominators) including square roots of perfect
1.4.K2d R square monomials and cube roots of perfect cubic monomials.
perform and explain the following computational procedure: simplification or
evaluation of real numbers and algebraic monomial expressions raised to a whole
1.4.K2e R number power and algebraic binomial expressions squared or cubed.
perform and explain the following computational procedure: simplification of
products and quotients of real number and algebraic monomial expressions using
1.4.K2f R the properties of exponents.
find prime factors, greatest common factor, multiples, and the least common multiple
1.4.K3 R of algebraic expressions. applications from business, chemistry, and physics that involve
addition, subtraction, multiplication, division, squares, and square roots when the
formulae are given as part of the problem and variables are defined, e.g., given F =
ma, where F = force in newtons, m = mass in kilograms, a = acceleration in meters
*1.4.A1a R per second squared. Find the acceleration if a force of 20 newtons is applied to a volume and surface area given the measurement formulas of
rectangular solids and cylinders, e.g., a silo has a diameter of 8 feet and a height of
*1.4.A1b R 20 feet. How many cubic feet of grain can it store? ($ probabilities, e.g., if the probability of getting a defective light bulb is
1.4.A1c R 2%, and you buy 150 light bulbs, how many would you expect to be defective? ($).
3
Geometry*1.4.A1d R concepts with application of percents ($) (O simple exponential growth and decay (excluding logarithms) and
economics, e.g., a population of cells doubles every 20 years. If there are 20 cells to
start with, how long will it take for there to be more than 150 cells? or If the radiation
level is now 400 and it decays by ½ or its half-life is 8 hours, how long will it take for
1.4.A1e R the radiation level to be below an acceptable level of 5? ($).
Standard 2 use algebraic concepts and procedures in a variety of situations.
recognize, describe, extend, develop, and explain the general rule of a pattern in
S2.B1 R/M variety of situations arithmetic and geometric
2.1.K1a R/M sequences using real numbers and/or exponents; e.g., radioactive half-lives patterns using geometric
2.1.K1b I/R/M figures algebraic patterns
including consecutive number patterns or equations of functions, e.g., n, n + 1, n + 2,
2.1.K1c I/R/M ... or f(n) = 2n - 1 special patterns, e.g.,
2.1.K1d I/R Pascal's triangle and the Fibonacci sequence.
2.1.K2 R/M generate and explain a pattern.
recognize the same general pattern presented in different representations [numeric
2.1.A1 I/R/M (list or table), visual (picture, table, or graph), and written] ($).
use variables, symbols, real numbers, and algebraic expressions to solve equations
S2.B2 R and inequalities in variety of situations.
know and explain the use of variables as parameters for a specific variable situation,
2.2.K1 R/M e.g., the m and b in y = mx + b.
manipulate variable quantities within an equation or inequality, e.g., 5x - 3y = 20
2.2.K2 R could be written as 5x - 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3.
2.2.K3a R solve linear equations and inequalities both analytically and graphically ($) (N).
represent real-world problems using variables, symbols, expressions, equations,
2.2.A1 R inequalities, and simple systems of linear equations ($).
represent and/or solve real-world problems with linear equations and inequalities
both analytically and graphically, e.g., tickets for a school play are $5 for adults and
$3 for students. You need to sell at least $65 in tickets. Give an inequality and a
*2.2.A2a R graph that represents this situation and three possible solutions ($) (N).
S2.B3 R analyze functions in a variety of situations.
evaluate and analyze functions using various methods including mental math, paper
2.3.K1 R and pencil, concrete objects, and graphing utilities or other appropriate technology.
determine whether a graph, list of ordered pairs, table of values, or rule represents a
2.3.K3 R function.
recognize how changes in the constant and/or slope within a linear function changes
*2.3.K6 R/M the appearance of a graph ($).
2.3.K7 R use function notation.
4
Geometry
2.3.K8 R evaluate function(s) given a specific domain ($).
interpret the meaning of the x- and y- intercepts, slope, and/or points on and off the
*2.3.A2 R line on a graph in the context of a real-world situation ($) (O).
analyze the effects of parameter changes (scale changes or restricted domains) on
2.3.A3a R the appearance of a function's graph.
analyze how changes in the constants and/or slope within a linear function affects
2.3.A3b R the appearance of a graph.
develop and use mathematical models to represent and justify mathematical
relationships found in a variety of situations involving tenth grade knowledge and
S2.B4 R skills.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: factor trees
2.4.K1b R to model least common multiple, greatest common factor, and prime factorization.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: algebraic
expressions to model relationships between two successive numbers in a sequence
2.4.K1c R or other numerical patterns.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: coordinate
planes to model relationships between ordered pairs and equations and inequalities
2.4.K1f R and linear and quadratic functions ($).
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include:
2.4.K1g R constructions to model geometric theorems and properties.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: two- and
three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets,
or solids) and real-world objects to model perimeter, area, volume, and surface
area, properties of two- and three-dimensional figures, and isometric views of three-
2.4.K1h R/M dimensional figures.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: scale
2.4.K1i R/M drawings to model large and small real-world objects.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: frequency
tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single
and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms,
2.4.K1l R and matrices to organize and display data ($).
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: Venn
2.4.K1m R diagrams to sort data and show relationships.
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: process models (concrete objects,
pictures, diagrams, flowcharts, number lines, hundred charts, measurement tools,
multiplication arrays, division sets, or coordinate grids) to model computational
procedures, algebraic relationships, mathematical relationships, and problem
2.4.A1a R situations and to solve equations ($).
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: equations and inequalities to
2.4.A1c R model numerical and geometric relationships ($).
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: function tables to model numerical
2.4.A1d R and algebraic relationships ($).
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: coordinate planes to model
relationships between ordered pairs and equations and inequalities and linear and
2.4.A1e R quadratic functions ($).
5
Geometry
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: two- and three-dimensional
geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-
world objects to model perimeter, area, volume, and surface area, properties of two-
2.4.A1f R/M and three-dimensional figures and isometric views of three-dimensional figures.
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: scale drawings to model large and
2.4.A1g R/M small real-world objects.
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: frequency tables, bar graphs, line
graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-
leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to describe,
2.4.A1i R interpret, and analyze data ($).
use the mathematical modeling process to analyze and make inferences about real-
2.4.A2 R world situations ($).
Standard 3 use geometric concepts and procedures in a variety of situations.
recognize geometric figures and compare and justify their properties of geometric
S3.B1 I/R/M figures in a variety of situations.
recognize and compare properties of two-and three-dimensional figures using
concrete objects, constructions, drawings, appropriate terminology, and appropriate
3.1.K1 I/R/M technology.
3.1.K2a I/R/M discuss properties of regular polygons related to angle measures.
3.1.K2b I/R/M discuss properties of regular polygons related to diagonals.
recognize and describe the symmetries (point, line, plane) that exist in three-
3.1.K3 I/R/M dimensional figures.
recognize that similar figures have congruent angles, and their corresponding sides
3.1.K4 I/R/M are proportional.
3.1.K5a I/R/M use the Pythagorean Theorem to determine if a triangle is a right triangle.
3.1.K5b I/R/M use the Pythagorean Theorem to find a missing side of a right triangle.
recognize and describe congruence of triangles using: Side-Side-Side (SSS), Angle-
3.1.K6a I/R/M Side-Angle (ASA), Side-Angle-Side (SAS), and Angle-Angle-Side (AAS).
recognize and describe the ratios of the sides in special right triangles: 30°-60°-90°
3.1.K6b I/R/M and 45°-45°-90°.
recognize, describe, and compare the relationships of the angles formed when
3.1.K7 I/R/M parallel lines are cut by a transversal.
recognize and identify parts of a circle: arcs, chords, sectors of circles, secant and
3.1.K8 I/R/M tangent lines, central and inscribed angles.
solve real-world problems by using the properties of corresponding parts of similar
3.1.A1a I/R/M and congruent figures, e.g., scale drawings, map reading, or proportions.
solve real-world problems by applying the Pythagorean Theorem, e.g., when
checking for square corners on concrete forms for a foundation, determine if a right
*3.1.A1b I/R/M angle is formed by using the Pythagorean Theorem (O).
solve real-world problems by using properties of parallel lines, e.g., street
3.1.A1c I/R/M intersections.
use deductive reasoning to justify the relationships between the sides of 30°-60°-90°
3.1.A2 I/R/M and 45°-45°-90° triangles using the ratios of sides of similar triangles.
understand the concepts of and develop a formal or informal proof through
understanding of the difference between a statement verified by proof (theorem) and
3.1.A3 I/R a statement supported by examples.
S3.B2 estimate, measure, and use geometric formulas in a variety of situations.
determine and use real number approximations (estimations) for length, width,
weight, volume, temperature, time, distance, perimeter, area, surface area, and
3.2.K1 R,M angle measurement using standard and nonstandard units of measure ($).
select and use measurement tools, units of measure, and level of precision
appropriate for a given situation to find accurate real number representations for
length, weight, volume, temperature, time, distance, area, surface area, mass,
3.2.K2 R,M midpoint, and angle measurements ($).
6
Geometry
approximate conversions between customary and metric systems given the
3.2.K3 R conversion unit or formula.
state, recognize, and apply formulas for perimeter and area of squares, rectangle,
3.2.K4a R,M and triangles ($).
state, recognize, and apply formulas for circumference and area of circles; volume of
3.2.K4b I,R,M rectangular solids ($).
use given measurement formulas to find perimeter, area, volume, and surface area
3.2.K5 I,R,M of two- and three-dimensional figures (regular and irregular).
recognize and apply properties of corresponding parts of similar and congruent
3.2.K6 I,R,M figures to find measurements of missing sides.
know, explain, and use ratios and proportions to describe rates of change ($), e.g.,
3.2.K7 R,M miles per gallon, meters per second, calories per ounce, or rise over run.
solve real-world problems by converting within the customary and the metric
systems, e.g., Marti and Ginger are making a huge batch of cookies and so they are
multiplying their favorite recipe quite a few times. They find that they need 45
3.2.A1a R tablespoons of liquid. To the nearest ¼ of a cup, how many cups would be needed?
solve real-world problems by finding the perimeter and the area of circles, squares,
rectangles, triangles, parallelograms, and trapezoids, e.g., a track is made up of a
rectangle with dimensions 100 meters by 50 meters with semicircles at each end
(having a diameter of 50 meters). What is the distance of one lap around the inside
3.2.A1b R,M lane of the track? ($).
solve real-world problems by finding the volume and the surface area of rectangular
solids and cylinders, e.g., a car engine has 6 cylinders. Each cylinder has a height of
3.2.A1c I,R,M 8.4 cm and a diameter of 8.8 cm. What is the total volume of the cylinders? ($).
solve real-world problems by using the Pythagorean theorem, e.g., a baseball
diamond is a square with 90 feet between each base. What is the approximate
3.2.A1d I,R,M distance from home plate to second base? ($).
solve real-world problems by using rates of change, e.g., the equation w = -52 + 1.6t
can be used to approximate the wind chill temperatures for a wind speed of 40 mph.
Find the wind chill temperature (w) when the actual temperature (t) is 32 degrees.
3.2.A1e R,M What part of the equation represents the rate of change? ($).
estimate to check whether or not measurements or calculations for length, weight,
volume, temperature, time, distance, perimeter, area, surface area, and angle
measurement in real-world problems are reasonable and adjust original
measurement or estimation based on additional information (a frame of reference)
3.2.A2 R ($).
use indirect measurements to measure inaccessible objects, e.g., you are standing
next to the railroad tracks and a train passes. The number of cars in the train can be
determined if you know how long it takes for one car to pass and the length of time
3.2.A3 R the whole train takes to pass you.
recognize and apply transformations on two- and three-dimensional figures in a
S3.B3 variety of situations.
describe and perform single and multiple transformations [refection, rotation,
translation, reduction (contraction/shrinking), enlargement (magnification/growing)]
3.3.K1 I,R,M on two- and three-dimensional figures.
recognize a three-dimensional figure created by rotating a simple two-dimensional
figure around a fixed line, e.g., a rectangle rotated about one of its edges generates
a cylinder; an isosceles triangle rotated about a fixed line that runs from the vertex to
3.3.K2 I the midpoint of its base generates a cone.
3.3.K3 I generate a two-dimensional representation of a three-dimensional figure.
determine where and how an object or a shape can be tessellated using single or
3.3.K4 i multiple transformations and create a tessellation.
analyze the impact of transformations on the perimeter and area of circles,
rectangles, and triangles and volume of rectangular prisms and cylinders, e.g.,
reducing by a factor of ½ multiplies an area by a factor of ¼ and multiplies the
volume by a factor of 1/8, whereas, rotating a geometric figure does not change
*3.3.A1 I,R,M perimeter or area.
7
Geometry
describe and draw a simple three-dimensional shape after undergoing one specified
3.3.A2 I,R transformation without using concrete objects to perform the transformation.
3.3.A3 I use a variety of scales to view and analyze two- and three-dimensional figures.
analyze and explain transformations using such things as sketches and coordinate
3.3.A4 I,R systems.
use an algebraic perspective to analyze the geometry of two- and three-dimensional
S3.B4 figures in a variety of situations.
recognize and examine two- and three-dimensional figures and their attributes
including the graphs of functions on a coordinate plane using various methods
including mental math, paper and pencil, concrete objects, and graphing utilities or
3.4.K1 I other appropriate technology.
determine if a given point lies on the graph of a given line or parabola without
3.4.K2 R graphing and justify the answer.
calculate the slope of a line from a list of ordered pairs on the line and explain how
3.4.K3 R,M the graph of the line is related to its slope.
find and explain the relationship between the slopes of parallel and perpendicular
lines, e.g., the equation of a line 2x + 3y = 12. The slope of this line is -2/3. What is
*3.4.K4 R,M the slope of a line perpendicular to this line.
3.4.K5 I,R,M use the Pythagorean Theorem to find distance (may use the distance formula).
recognize the equation of a line and transform the equation into slope-intercept form
*3.4.K6 R,M in order to identify the slope and y-intercept and use this information to graph the line.
translate between the written, numeric, algebraic, and geometric representations of a
real-world problem ($), e.g., given a situation, write a function rule, make a T-table of
3.4.A2 R the algebraic relationship, and graph the order pairs.
recognize and explain the effects of scale changes on the appearance of the graph
3.4.A3 R of an equation involving a line or parabola.
analyze how changes in the constants and/or leading coefficients within the equation
3.4.A4 R of a line or parabola affects the appearance of the graph of the equation.
Standard 4 use concepts and procedures of data analysis in a variety of situations.
collect, organize, display, explain, and interpret numerical (rational) and non-
S4.B2 numerical data sets in a variety of situations. frequency tables and
4.2.K1a R line plots bar, line, and circle
4.2.K1b R graphs Venn diagrams or
4.2.K1c R other pictorial displays ($).
organize, display, and read quantitative (numerical) and qualitative (non-numerical)
data in a clear, organized, and accurate manner including a title, labels, categories,
4.2.K1d R and rational number intervals using the following data display: charts and tables ($).
explain how the reader's bias, measurement errors, and display distortions can
4.2.K2 R affect the interpretation of data.
approximate a line of best fit given a scatter plot, make predictions, and analyze
4.2.A6 R decisions using the equation of that line.
REVISED 5/4/11 |
books.google.com - This is an exposition of the analytic theory of continued fractions in the complex domain with emphasis on applications and computational methods.... Fractions |
Pre-calculus A Concise Course
9780618627196
ISBN:
0618627197
Edition: 1 Pub Date: 2006 Publisher: Houghton Mifflin College Div
Summary: With the same design and feature sets as the market leading "Precalculus," 7/e, this new concise text provides both students and instructors with sound, consistently structured explanations of the mathematical concepts. "Precalculus: A Concise Course" is designed to offer a cost-effective, one-semester alternative to the traditional two-semester precalculus text. It contains the features that have made the Larson/Hos...tetler series a complete solution for both students and instructors: interesting applications, pedagogically effective design, and innovative technology combined with an abundance of carefully developed examples with worked-out solutions and exercises. In addition: "Side-by-Side Example Solutions" for select examples include multiple problem solving approaches--such as algebraic, graphical, and numerical--to appeal to a variety of teaching and learning styles."Checkpoints" after each Example/Solution refer students to similar drills in the Section Exercises, giving students the opportunity to practice and reinforce the concepts they just learned. Answers to Checkpoints are included at the back of the book."Vocabulary Checks" open every set of Section Exercises. This review of mathematical terms, formulas, and theorems provides regular assessment and reinforcement of students' understanding of algebraic language and concepts."Exercise Sets" are carefully developed to improve the categorization of problems from "basic skill-building" to "challenging;" improve the pairing of similar odd- and even-numbered exercises; update all real data; and add real-life and real-data applications."New!" "Make a Decision" applications--presented throughout the text at the end of selectedexercise sets--are based on large sets of real data. These extended modeling applications give students the opportunity to use all the mathematical concepts and techniques they've learned and apply them to large sets of real date--analyzing it, graphing it, and making conjectures about its behavior. These applications are featured in Eduspace and the Online Learning Center in an interactive format."Eduspace, powered by Blackboard," Houghton Mifflin's online learning environment, brings your students quality online homework, tutorials, multimedia, and testing that correspond to the "Precalculus: A Concise Course" text. This content is paired with the recognized course management tools of Blackboard.
Larson, Ron is the author of Pre-calculus A Concise Course, published 2006 under ISBN 9780618627196 and 0618627197. Fifty seven Pre-calculus A Concise Course textbooks are available for sale on ValoreBooks.com, twenty nine used from the cheapest price of $0.35, or buy new starting at $60 |
Elementary and Intermediate Algebra: Discovery and Visualization
Third Edition
Elaine Hubbard - Kennesaw State University
Ronald D. Robinson
This
new program will help you understand the best uses for the technology
supplements that accompany your textbook. Click the icons above or
the links to the left for more information or to access any of the
web-based products.
Student Solutions Manual Link to a sample chapter with detailed, step-by-step solutions to odd-numbered exercises in the text.
Graphing Calculator Keystroke Guide This Guide is designed for students using a Texas Instruments TI-83 Plus or TI-86 graphing calculator in conjunction with the textbook Elementary and Intermediate Algebra: Discovery and Visualization, Third Edition, by Hubbard and Robinson. |
More About
This Textbook
Overview
"Encyclopedia of Mathematics is a useful reference providing current and accurate information on the subject for high school and college students. Comprehensive coverage includes significant discoveries in mathematics, in addition to definitions of basic terms, thought-provoking essays, and capsule biographies of notable scientists in mathematics - all presenting a wide range of valuable information compiled into a single source. Written in easy-to-understand language, the encyclopedia explains the importance of mathematics to society and includes summaries of notable events throughout history related to the subject." "Featuring more than 800 cross-referenced entries, the encyclopedia includes six essays, interspersed throughout the text, that discuss the evolution of algebra and equations, calculus, functions, geometry, probability and statistics, and trigonometry. The encyclopedia also includes three helpful appendixes - bibliographies and Web resources, a chronology of notable discoveries in mathematics, and an extensive list of associations that provide information about mathematics - as well as a comprehensive index." Encyclopedia of Mathematics is an indispensable resource that will meet the specific demands of students, interested laypeople, and professionals who need accurate and straightforward information on historical or current issues in |
What can I do with a major in...Mathematics?
Mathematics is one of the oldest and most fundamental sciences. Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems. Mathematics falls into two broad classes—theoretical (pure) mathematics and applied mathematics. |
An examination of the principles of Fourier analysis. It offers a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. more... |
The Math of Life
Applied mathematics is the language of science, technology and engineering. It provides the grammar, syntax and punctuation for quantitative composition of the physics and chemistry man uses to understand and control reality. It is also a study within itself.
10:48 am June 24, 2011
Sandy wrote :
Nowadays, students are very likely to avoid STEM, especially math. Students should take math from school level so that they don't have to face any problem in future. Schools also should take the matter seriously. Unfortunately most of the public schools do not do so. Students can try online math tutoring services like tutorteddy.com for free math help / solutions (video / text) if schools cannot offer.They can also try tutorteddy math curriculum for intelligence math testing. |
Title of Instructional Materials: Holt McDougal Alg I ... they are not integrated into
the lessons themselves. ... 1. Make sense of problems and persevere in solving
them. Mathematically proficient students ... |
G. MSC# for Areas of Specialization and Competencies in Topics of specified at point H: 1. 2. 3. 4. 5. 6. 7.
(e.g. MSC# for 'Algebraic Geometry' is MSC 14XX. The information about the MSC - avalable at
-------------------------------------------------------- |
Performs useful calculations such as finding the Area, Common Factors of a set of numbers, Distance between two points, Quadratic Roots, Midpoint, Perimeter, Find all the primes up to and including a number, the slope of a line, and the volume of a cube, cone, cylinder, and sphere.Finds the area of a Rectangle, Circle, Triangle, Oval, Cylinder, Cone, and Pyramid.Formula for each function is displayed at the top of the screen for easy reference. Easy to use, convenient and powerful math program. Great for math class and home work!An easy and convenient handwriting recognition system allows numbers to be entered by just writing on the screen with your finger |
Hello everyone!. Ever since I have started algebra 1 help at school I never seem to be able to get through it well. I am excellent at all the other branches, but this particular topic seems to be my weakness. Can some one assist me in understanding it properly?
Being a teacher, this is a comment I usually hear from students. algebra 1 help is not one of the most popular topics amongst kids. I never encourage my pupils to get pre made answers from the web, however I do encourage them to use Algebrator. I have developed a liking for this software over the years. It helps the children learn math in a convenient way.
I must agree that Algebrator is a great thing and the best program of this kind you can find. I was amazed when after weeks of anger I simply typed in graphing inequalities and that was the end of my problems with math. It's also so good that you can use the software for any level: I have been using it for several years now, I used it in Algebra 2 and in Algebra 2 also! Just try it and see it for yourself!
I remember having often faced problems with quadratic formula, perfect square trinomial and function composition. A truly great piece of algebra program is Algebrator software. By simply typing in a problem from workbook a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Algebra 1, College Algebra and College Algebra. I greatly recommend the program.
All, Thanks a lot for the guidance that you have offered. I just had a look at the Algebrator available at: The best part that I liked was the money back guarantee that they are extending there. I went ahead and purchased Algebrator. It is really user friendly and turns up to be a remarkable tool for Basic Math. |
Differential Equations: Matrices and Models
This book provides a modern study of differential equations. Matrix algebra is presented along with many of the elementary numerical techniques needed for computer implementation of its procedures. The author reviews models that generate the differential equations and presents methods used to calculate the solution. MATLAB commands that a student might use are listed in the first appendix. A supplemental lab manual, Explorations in Differential Equations Using MATLAB, provides the student with problems and projects for exploration and experimentation. The manual can be ordered from Prentice Hall using ISBN 0-13-374760-3.
Free Mathematical Modeling Technical Kit
Learn how you can quickly build accurate mathematical models based on data or scientific principles. |
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Primary Navigation
Mathematics and Quantitative Literacy (3 Crs.)
Students will have the "ability to understand numerical data and use mathematical methods for analysis and problem solving" (PASSHE BOG Policy 1993-01). Mathematics is the science of numbers and their operations, interrelations, combinations, generalizations and abstractions and of space configurations and their structure, measurement, transformations and generalizations. |
Friendly Introduction to Mathematical Logic
9780130107053
ISBN:
0130107050
Pub Date: 1999 Publisher: Prentice Hall PTR
Summary: For a one-quarter/one-semester, junior/senior-level course in Mathematical Logic. With the idea that mathematical logic is absolutely central to mathematics, this tightly focused, elementary text discusses concepts that are used by mathematicians in every branch of the subjecta subject with increasing applications and intrinsic interest. It features an inviting writing style and a mathematical approach with precise s...tatements of theorems and correct proofs. Students are introduced to the main results of mathematical logicresults that are central to the understanding of mathematics as a whole.
Leary, Christopher C. is the author of Friendly Introduction to Mathematical Logic, published 1999 under ISBN 9780130107053 and 0130107050. Six Friendly Introduction to Mathematical Logic textbooks are available for sale on ValoreBooks.com, three used from the cheapest price of $43.00, or buy new starting at $251.28 |
5069657 / ISBN-13: 9780205069651
Elementary Number Theory
This text provides a simple account of classical number theory, as well as some of the historical background in which the subject evolved. It is ...Show synopsisThis text provides a simple account of classical number theory, as well as some of the historical background in which the subject evolved. It is intended for use in a one-semester, undergraduate number theory course taken primarily by mathematics majors and students preparing to be secondary school teachers. Although the text was written with this readership in mind, very few formal prerequisites are required. Much of the text can be read by students with a sound background in high school mathematics |
August 29, 2006
Algebra - Tuesday, August 29We reviewed over last night's homework and took notes on 2.4 and 2.5, one step equations, adding, subtracting, multiplying and dividing. We played equation bingo and began our homework in class. Homework is p.19 (13 - 29, odd), p. 24, (13 - 29, odd). We will have a quiz tomorrow on 1.2 - 1.5.
August 28, 2006
Algebra - Monday, August 28
Chapter tests were passed back today and go home for a parent's signature and test corrections. We went over section 2.1 on the real number line, Homework is worksheet 2.1, both top and bottom sections. We will also have a quiz on Thursday over 2.1 - 2.4.
Something new! Check out the attachment which are our notes from today:
Check it out!! I have sent a copy of today's notes that you can review if you were absent or just wanted to review. Let me know how it works.
Quizzes were passed back today. We went over 1.2 and 1.3.
Homework is p. 10, 13-33, odd
p. 14, 15 - 39, odd ***Remember, to check your answers in the back of the book PRIOR to class tomorrow.
We will have a quiz on Wednesday on 1.2 - 1.5.
August 24, 2006
Algebra - Thursday, August 24
We went over last night's homework and did review work for the chapter one test tomorrow. We took a "mock" test to see how we would do. There is no assigned homework, but you can review problems in each section(do the last ones in each section which are generally the most challenging).
We reviewed for the quiz tomorrow by working on dry erase boards and completing a math crossword puzzle. No assigned homework, but you can review for the quiz by practicing adding, subtracting, multiplying and dividing integers. Go online and google integers, there are tons of websites that will have practice problems!
August 23, 2006
Quizzes were passed back and we reviewed over journal entries. We went over the homework and took notes on 1.5. We practiced translating verbal expressions into algebraic expressions on dry erase boards.
Homework is p. 35, 13 - 47, odd
p. 38, 65 - 71, odd, 75, 77
Remember, the chapter one test is on Friday!
We went over worksheet , "You Write the Rules."
We went over sections 2.4 and 2.5, Adding more integers and subtracting integers.
We did a class activity (magic circle) in partners. Those that were able to solve the puzzle received a bonus points pass.
Homework is a worksheet on +, - integers, all of it. We will have a quiz on Friday on adding, subtracting, multiplying and dividing integersAugust 18, 2006
BAG - Friday, August 18
The finish of our first week! A great start! We went over homework, took and graded our first quiz on decimals and reviewed over multiplying and dividing fractions....Homework is page 603 and 604, do the first column down on the left on both pages.
Thanks for a great first week! Enjoy your weekend.
A terrific kick off this week! I think we have covered the majority of the housekeeping and are ready to dive in. Today, we checked homework and took notes on 1.3, Order of Operations. We did worksheet 1.2 together in class. There will be a quiz on Monday on sections 1.1 - 1.3 and worksheet 1.2. Homework is worksheet 1.2 which we started in class.
August 17, 2006
BAG - Thursday, August 17
We went over the homework from yesterday on adding, subtracting, multiplying and dividing decimals. There will be a brief quiz tomorrow on this. We went over adding and subtracting fractions using the bob sled method to help identify least common denominators.
Homework is p. 602, 1 - 39, odd.
** with your homework!!
Here we go! We did a brief review over vocabulary in sections 1.1 and 1.2. We practiced using the graphing calculators and learning how to raise a base to a power. There will be a quiz on Monday on 1.1 - 1.3.
Presents for tonight: p. 6, 19 - 29, odd, 35, 37, 45, 47
p. 8, (mixed practice), 51-61, odd
p. 12, 17 - 61, odd
p. 14, 73 - 83, odd
with your homework!!
August 16, 2006
BAG - Wednesday, August 16
I do believe we have wrapped up the first of the year technicalities and details and are ready to dive in! Textbooks were issued today and should be covered.
We did a brief review of decimals, adding, subtracting, multiplying and dividing. Homework is p. 600, 21 - 47, odd and p. 601, 21 - 47, odd.
Happy 3rd day of school! I think we have just about covered all the beginning of the year necessities. A couple more email addresses, signed letters and we will be off and running. We finished the pretest today and from the feedback I am getting, I will get to teach lots this year!! I love it! Textbooks were passed out today and should be covered. Other than that, we will dive in tomorrow, so be ready!
August 15, 2006
Tuesday, August 15
I hope everyone has had a smooth transition over the last couple of days. If you haven't brought in your signed syllabus (algebra needs the signed letter also), please have that ready for tomorrow. We continued to work on the pre-test today. No homework... |
New GCSE Maths - Homework Book Higher 1: Edexcel Linear (A)
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Collins New GCSE Maths Homework Books are excellent companions to Collins New GCSE Maths Student Books. Following the familiar structure and layout of the Student Book, the Homework Book provides extensive practice of all the elements of the new curriculum at Grades D to A* to ensure that your students achieve the best grades in mathematics.
About this resource
Collins New GCSE Maths EDEXCEL Linear Homework Book Higher 1 is written by experienced teachers and examiners, and provides comprehensive practice for all the topics covered in Collins New GCSE Maths EDEXCEL Linear Student Book Higher 1. It fully supports your students in learning the new 2010 GCSE Maths EDEXCEL specification and will ensure that they achieve the best grades:
• Provide excellent additional practice for all topics covered in the Student Book with brand-new questions not found in the Student Book • Enable students to assess their own progress through each chapter with familiar colour-coded grades in every exercise • Extend students' thinking and problem-solving skills with open-ended investigative tasks at the end of every chapter • Assess students' work with answers to homework questions conveniently located in Collins New GCSE Maths EDEXCEL Linear Teacher's Pack Higher 1 • Give students easy reference to the clear explanations and examples in their textbooks with a free CD-ROM of Collins New GCSE Maths EDEXCEL Linear Student Book Higher 1 with every Homework Book |
algebra 1, algebra 2 and calculus algebra 1, algebra 2 and calculus, algebra 2 and calculus algebra 1, algebra 2 and geometry |
Quantitative Literacy Area Goals
GenEd Quantitative Literacy courses present mathematical thinking as a tool for solving everyday problems, and as a way of understanding how to represent aspects of a complexworld. They are designed to prepare students as citizens and voters to have the ability to think critically about quantitative statements, to recognize when they are misleading or false, and to appreciate how they relate to significant social or political issues. While computation may be part a QL course, the primary focus is not computational skills.
Quantitative Literacy courses are intended to teach students how to:
Understand quantitative models that describe real world phenomena and recognize limitations of those models;
Perform simple mathematical computations associated with a quantitative model and make conclusions based on the results;
Recognize, use, and appreciate mathematical thinking for solving problems that are part of everyday life;
Understand the various sources of uncertainty and error in empirical data;
Retrieve, organize, and analyze data associated with a quantitative model; and
Communicate logical arguments and their conclusions.
Courses
Critical Reasoning and Problem Solving
MATH 0828
The course teaches students how to deal with and solve complex problems by confronting them with critical analysis. We look at these problems both from an historical perspective and the practical view of how and when these types of problems affect the students' everyday lives. The course takes students through several key mathematical disciplines, including probability and statistics, including the hallmark of probability – reasoning under uncertainty – as well as set theory and counting techniques and graphing, especially with Venn diagrams, a skill they will find beneficial as the world turns to technology and graphics. For example, when we introduce probability, we cover the first dramatic application of the discipline, Mendel's discovery of the centuries-old problem of explaining the scientific laws of heredity as he gives birth to genetics. We also cover Mendel's use of statistics. This leads us to study modern uses of the same concepts in areas such as medicine – how to evaluate statistical studies and how to analyze topics such as false positives – as well as the application of DNA in areas such as how it has significantly changed our justice system.
Digital Mapping: From Mercator to Mashups
COMMUNITY & REGIONAL PLANNING 0821, GEOGRAPHY & URBAN STUDIES 0821Investing for the Future
ELECTRICAL ENGINEERING 0822, FINANCE 0822
Thinking about investing but don't know what to do or where to start? Mystified by a 401(k) versus a Roth IRA selection? Confused by the choice of mutual funds, index versus actively managed, load versus no load? And what about exchange traded funds (ETFs)? Want to prepare for your financial future, but not sure how? Learn what it really means to invest in your future, beginning with how to compute what you need for the future such as college or retirement. Then learn how to connect the dots between risk, return, and cost of investing. This class will teach you about seemingly complicated financial topics in a very comprehensible manner that will help you make informed financial decisions to ensure a secure financial future.
Math for a Digital World
COMPUTER & INFORMATION SCIENCES 0823, 0923, MATH 0823, 0923
How can I tell if an Email message is really from my bank? If I do online banking, can other people see the information? Does playing the lottery make sense? Does it make sense to draw for an inside straight? How can polling results differ so much from the election — or do they? Sometimes the winner of an election in the US gets much less than 50% of the vote. Would it make sense to have a run-off in such cases? How long will the world's oil last, assuming that we use more each year. How long will a million dollars last you, assuming it earns interest until you spend it? If you bought your text online, could someone tap into the Internet and get your credit card number when it's transmitted? Why does the VIN on your car have so many digits?
Mathematical Patterns
MATH 0824, 0924
News stories, everyday situations, and puzzling vignettes will be used to illuminate basic math concepts. Learn probability, for example, by discussing the gambler's fallacy and gambler's ruin, the drunkard's random walks, the Monty Hall problem, the St. Petersburg paradox, the hot hand, monkeys randomly typing on a typewriter, and many others. A similar approach involving estimation problems and puzzles will be taken in the units on basic numeracy and logic. Throughout the course, lectures and readings will examine the mathematical angles of stories in the news, suggesting fresh perspectives, questions, and ideas on current issues from Google searches to the randomness of the iPod shuffle.
Quantitative Methods in the Social Sciences
Psychological, political, social, and economic arguments and knowledge frequently depend on the use of numerical data. A psychologist might hypothesize that I.Q. is attributable toenvironmental or genetic factors; a politician might claim that hand gun control legislation will reduce crime; a sociologist might assert that social mobility is more limited in the United States than in other countries, and an economist might declare that globalization lowers the incomes of U.S. workers. How can we evaluate these arguments? Using examples from psychology, sociology, political science, and economics, students will examine how social science methods and statistics help us understand the social world. The goal is to become critical consumers of quantitative material that appears in scholarship, the media, and everyday life.
Statistics in the News
STATISTICS O826
Through discussion of approximately 50 news articles, learn basic principles of statistics. This course focuses on the relevance, interpretation and usage of statistics in the news media. It has no quantitative prerequisites and involves more reading than math aptitude. Statistics deals with the study of variability, uncertainty, and decision-making, and has applicability to most other disciplines and everyday life. |
Presents an introduction to MuPAD - a modern Computer Algebra System. This book shows how we can use it in various areas of mathematics. It devotes a chapter to the graphical visualization of mathematical concepts. It is a resource for conducting workshops on using Computer Algebra Systems to explore and visualize mathematical concepts.Introduces the reader to Mathematica's various approximate numbers, their arithmetic and the common numerical analysis operations such as numerical integration, root-finding, equation solving, minimization, and differential equation solving. This resource is useful for practitioners, professionals, and researchers. more... |
Adrian Timofeev. The Integration of Functions. by Adrian Timofeev
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Integration is the algebraic method of finding the integral. I was fun of Math and I conducted research in mathematics in my free time. I worked as adviser of Central Bank of the USSR in 1920-s and I was arrested during the Great Terror in 1930-s.
I started writing of this book in 1931 in terrible Verhneuralsk prison in Russia. This book is in Russian and my dream is to translate it in English.
GCSE Maths Teachers Pack V10 by Clive W. Humphris
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Approx. 24,990 words.
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Published on November 11, 2013.
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GCSE Maths Teachers Pack12 Zeros by Marc Zev
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Approx. 2,940 words.
Language:
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Published on August 25, 2013.
Category:
Nonfiction » Education and Study Guides » Study guides - Mathematics.
How much is a trillion? How high would a stack of a trillion dollars be? How much space would a trillion candies might take up? How many people can a trillion kernels of popped corn feed? These questions, and more, are posed, answered and explained in words and math.
Vedic Mathematics Made Easy by Dhaval Bathia
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Approx. 44,920 words.
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This International Bestselling book on Vedic Mathematics which will help you do calculations and solve complicated math questions in a matter of a few seconds. Extremely helpful for students giving GMAT, GRE, CAT, SAT, CET and other entrance exams. Over 150,000 copies sold in 14 languages worldwide |
Differential Geometry : A Geometric Introduction - 98 edition
Summary: The only book that introduces differential geometry through a combination of an intuitive geometric foundation, a rigorous connection with the standard formalisms, computer exercises with Maple, and a problems-based approach. Starting with basic geometric ideas, Differential Geometry uses basic intuitive geometry as a starting point to make the material more accessible and the formalism more meaningful. The book presents topics through problems to provide re...show moreaders with a deeper understanding. And, it introduces hyperbolic geometry in the first chapter rather than in a closing chapter as in other books. An important reference and resource book for any reader who needs to understand the foundations of differential geometry3675 +$3.99 s/h
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This Textbook
Overview
Despite the fact that Maple V has become one of the most popular computer algebra systems on the market, surprisingly few users realize its potential in the field of scientific visualization. The purpose of this book is to equip the reader with a variety of graphics tools needed on the voyage of discovery into the complex and often beautiful world of curves and surfaces. A comprehensive treatment of Maple's graphics commands and structures is combined with an introduction to the main aspects of visual perception. Top priority is given to the use of light, color, perspective, and geometric transformations. Numerous examples, accompanied by pictures (many in color), cover all aspects of Maple graphics. The examples can be easily customized to suit the individual needs of the reader. The approach is context independent, and as such will appeal to students, educators, and researchers in a broad spectrum of scientific disciplines. For the general user at any level of experience, this book can serve as a comprehensive reference manual. For the beginner, it offers a user- friendly elementary introduction to the subject, with mathematical requirements kept to a minimum. For those interested in advanced mathematical visualization, it explains how to maximize Maple's graphical capabilities. In particular, this book shows how to turn Maple into an excellent modeling tool capable of generating elaborate surfaces that conventional modelers cannot produce. These surfaces can be exported to an external ray tracer (e.g. POV-ray) for sophisticated photo-realistic rendering. All of the Maple code segments which are presented in the book, as well as high-resolution pictures showing alternative renderings of some of the book's color plates, are included on the accompanying DOS diskette |
MTG Foundation Courses for Class 8 - Chemistry
Quick Overview
• Exhaustive coverage of the topics that help building Foundation for IIT/AIEEE/PMT while studying class 8th syllabus • Each concept of class 8th is explained with solved examples, illustrations activities and concept maps. • Complete practice of a topic through variety of questions such as MCQs, Fill in the blanks, True-False, Matrix Match, Assertion and Reason, Passage comprehension, Subjective problems of different weightage. • Solved NCERT questions. • In short, a complete study package to prepare you to ace in school exams and competitive exams as well.
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The Mathematics Today Group, now registered as MTG Learning Media Pvt. Ltd. is the pioneer in education publishing business in India catering to the needs of IIT and PMT aspirants. It publishes five monthly magazines viz. Mathematics Today, Physics for You, Chemistry Today, Biology Today and Current Currents and other relevant educational books |
High-Level Algebra and Geometry Tasks: Resources for Both Student and Teacher Learning
Summary: High-level mathematical tasks provide opportunities for students
to develop deep mathematical understanding, however, such tasks are
difficult for teachers to implement effectively. This module offers
practical suggestions as well as four algebra and geometry tasks, and
detailed lesson guides, that can support teachers' efforts to provide such
opportunities for their students.
High-level math tasks provide critical opportunities for students to develop mathematical understanding as well as learn about the nature of mathematics and how one engages in it. Such tasks, however, are difficult for teachers to implement effectively. Through thoughtful pre-planning, purposeful implementation, and deliberate reflection on one's practice, teachers are better able to implement such tasks and support student learning. This module discusses various components of this process: (a) the characteristics of high-level tasks, (b) effective implementation of lessons around high-level tasks.
In order to assist teachers as they work to transform their practice, a set of four tasks as well as their Lesson Guides (LG's) -- which are detailed suggestions for how each task might be enacted – are provided. The detailed lesson guides permit teachers to study, use and internalize instructional practices long before they may feel prepared to design similar lessons themselves. Specific questions and strategies that can support
the learning of ELLs are also highlighted on the lesson guides. It is intended that, over time, teachers will generalize these practices to their instruction more broadly and design and enact similar lessons.
This module provides four high-level tasks, two of which are suitable for use in Algebra 1 and two are suitable for use in Geometry.
Geometry
This module will guide the reader through Custom T-Shirts and its Lesson Guide in order to ground the discussion and illustrate the features of the resources available.
High-Level Mathematical Tasks
To determine whether or not a task is high-level it is necessary to consider both the kind of thinking and the level of thinking that is required of students as they engage with and solve the task (Stein, Smith, Henningsen and Silver, 2000; Stein and Smith, 1998). It is important to keep in mind that a "high-level" mathematical task is not the same as a "difficult" task. A high-level task is one that requires students to put forth some cognitive effort as they work to understand, make connections to, and build upon, mathematical concepts and ideas. Students are required to represent the mathematical ideas in multiple ways and make connections between the representation of underlying mathematical ideas in tables, graphs, verbal explanations, equations, and both real-world and mathematical contexts. High-level tasks should also allow for multiple entry points, opportunities for students to begin working on the task using a variety of approaches and techniques.
A specific mathematical procedure might be suggested or implied, however a high-level task would require students to make sense of the procedure by making connections to underlying mathematical ideas and structures. Students might also be required to develop a unique pathway or procedure for solving the task as they explore underlying mathematical concepts, processes, or relationships. In short, high-level tasks promote thinking, reasoning, and mathematical sense-making (Stein, Smith, Henningsen, Silver, 2000). Conversely, tasks that can be solved by simply reproducing memorized facts or applying learned procedures would not be categorized as high-level, even if the facts or procedures are complex or difficult for a particular student.
Why is it important for students to have an opportunity to engage in high-level tasks? The tasks in which students engage determines what they learn. Lappan and Briars contend that "there is no decision that teachers make that has a greater impact on students' opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics" (Lappan and Briars, 1995, p. 138). Providing opportunities for students to build new understanding by drawing upon their prior knowledge as they work to solve rich tasks helps students build the connections between mathematical ideas that are important for developing deep understanding.
High-level tasks also address important socio-cognitive needs in a heterogeneous classroom as they "enable more students to contribute ideas and feel valued" (Boaler, 2006, p. 42). It is important to keep in mind, however, that for a task to be a high-level task for a particular group of students, it must be able to form a bridge between their prior knowledge and experiences and the mathematical understanding that the teacher wants them to construct. Therefore a task that might be high-level for one group of students might be routine for another group, and impossible for yet another group. In addition, although low-level tasks may provide an opportunity for students to develop procedural fluency, this is only one strand of mathematical proficiency that today's students must develop – the other strands are conceptual understanding, strategic competence, adaptive reasoning, and a productive disposition (Kilpatrick, et al., 2001). High-level tasks work on all five strands as an interconnected whole.
The Custom T-Shirts task, which can be used to introduce Pre-Algebra or Algebra 1 students to linear functions, will be used to illustrate our discussion.
The pricing plan of a t-shirt company embodies the important mathematical concepts of constant (y-intercept) and rate of change (slope) that are foundational to students' understanding of linear functions.
The four prompts provide entry points for students as they build upon their understanding of arithmetic processes and generalize from these procedures to build their algebraic representations.
While the prompts help students organize their work, they do not give away the solution paths -- student still must make sense of the mathematical ideas for themselves.
Students construct tables, graphs and equations, and will work to connect the various representations as they construct their explanations and listen to their peer' ideas.
The task is at the appropriate level of difficulty for students who are in the process of transition between arithmetic and algebra.
The homework provides an opportunity for students to continue to think about the mathematical ideas that were the focus of this task and to begin to think about the roles of the constant and the coefficient in different representations of a linear function.
Implementing High-level Tasks
Although high-level tasks provide important opportunities for student learning, merely selecting a high-level task and presenting it to students does not guarantee that students will engage with the challenging aspects of the task (Stein and Smith, 1998). The characteristics of a high-level task are often not lived out in classrooms because the practices that students need to engage in and the instructional practices that teachers must be able to use are challenging for both students and teachers (Stein, Grover and Henningsen, 1996). As a result, time that teachers spend thinking through the lesson beforehand, both individually and with other teachers, can help ensure that the cognitive demands of the task will be maintained as the lesson unfolds.
Smith, Bill and Hughes (in press) have developed the Thinking Through the Lesson Protocol (TTLP) that provides prompts that promote detailed and thoughtful planning by teachers. It "provides a framework for developing or reflecting on lessons that use students' mathematical thinking as the critical ingredient in developing their understanding of key disciplinary ideas" (Smith, Bill and Hughes, in press). The TTLP divides the planning process into three phases: selecting and setting up the task, supporting student's exploration of the task, and sharing and discussing the task. The Lesson Guides (LG) presented in this module were developed using this protocol and provide examples of ways that the TTLP can help structure your planning.
Phase One: Selecting and Setting up the Task
One of the key components of planning is identifying the mathematical goals of the lesson - what students are to learn or be in the process of learning as they engage in the task, not what they will do. The TTLP also prompts the teacher to consider: how the task builds on students' prior knowledge, the ways that students might solve the task, the errors and misconceptions that might surface, and the expectations for how students will engage with the task.
The Lesson Guide that accompanies Custom T-Shirts will be used to illustrate how these are taken into consideration when planning to implement the task.
The Lesson Overview and Set-Up Phase of the LG (pages 1 and 2) discusses:
The overall flow of the lesson
NCTM Standards that the task addresses
Mathematical and Academic Language Goals of the lesson
Assumption of prior knowledge.
How the task can be introduced and expectations set so that students understand what they are expected to do, however the cognitive challenge of the task has not been removed.
Phase Two: Supporting Students' Exploration of the Task
It is important to carefully think about how you will support student learning during the Explore phase of the lesson. The TTLP underscores the central role of questioning in this process, however it also recognizes that constructing good questions as one is also reacting and responding to students is not easy. Considering possible questions that you could ask as you plan the lesson is crucial (Smith, Bill and Hughes, in press). The TTLP suggests that a teacher's carefully crafted questioning can serve many purposes: questions can help floundering students get started, focus student thinking on key mathematical ideas of the lesson, support the sharing and building of ideas by small groups, and challenge and assist students in clarifying misconceptions or errors.
advance student thinking and understanding towards the mathematical goals of the lesson.
In order for this to occur the teacher must circulate and monitor what is occurring in all of the groups. This also provides an opportunity for the teacher to begin to construct a plan for how the whole-class discussion can be built upon the emerging ideas.
The Lesson Guide that accompanies Custom T-Shirts will be used to illustrate these points.
Ask students to explain their thinking and reasoning to you and to their peers;
Ask students to listen to each other's explanations and to rephrase what each other has said;
Support students' use of mathematical language.
What you could look for as you monitor small-group work so that you can orchestrate the whole group discussion to build on student ideas, and move towards the mathematical goals of the lesson.
Different ways that students might approach the task and possible questions that you can ask them to assess their understanding and to advance their thinking towards the mathematical goals of the lesson (questioning strategies are discussed in more detail below).
Possible misconceptions and errors that you can anticipate, and possible questions that prompt them to revisit their notions and begin to correct their own thinking.
As you examine the Explore Phase of the LG you will also note that:
it is suggested that you begin with an assessing question. As teachers we often assume that we understand the thinking that has gone into a particular piece of student work. However, students frequently approach a problem in a novel way, and it is important to determine this before you try to move a student's thinking forward. Also, having students put their thinking into words is important in its own right.
advancing questions should consider not only mathematical concepts, but also strategies, representations, and connections among representations. Advancing questions should also keep the goals of the lesson in mind.
IT IS IMPORTANT TO NOTE THAT THE LG IS NOT A SCRIPT, but provides a way to consider the type of planning that will help support task implementation, and student learning (see Smith, Bill and Hughes, in press, for a more detailed discussion of the TTLP as a tool for planning).
Phase Three: Sharing and Discussing the Task
After students have had the opportunity to explore the mathematical ideas underlying the task, it is crucial for the teacher to bring the class together to examine, analyze, and connect the various ideas that surface and to focus the discussion on the key mathematical ideas (Sherin, 2000; Smith, Bill and Hughes, in press). By thinking ahead of time about how you could orchestrate the class discussion around the ideas that might surface during small-group work, you will be able to make decisions about: the student work that you will select for presentation as you monitor small-group work; the order in which you will have the students present their solutions; and the questions you might ask so that students will make connections between different strategies and representations and make sense of the key mathematical ideas. It is also important that you consider what you will expect to see and hear in the student discussion of the mathematics that will indicate that students understand those mathematical ideas, and what your next steps will be.
Note: It is not expected that each student, or each group, will have completely solved the task prior to the Sharing and Discussing of the task. By carefully selecting and sequencing the work, and orchestrating the discussion around the key ideas, a story can be built and the class as a whole will have an opportunity to continue to work to construct and analyze the mathematical ideas. The teacher plays a crucial role in this process (Sherin, 2000; Smith, Bill and Hughes, in press).
The Lesson Guide that accompanies Custom T-Shirts will be used to illustrate these points.
By allowing different groups to chart and present different segments of their solution, you can ensure that a wider variety of students' input is honored and incorporated into the discussion. This is also a time saving device, since it is not always necessary for each group to construct a chart that contains all parts of the solution.
Mathematical ideas and rationale
The LG is not a script to be followed, but a discussion of possible ways in which a lesson might unfold. The LG presents a rationale for one particular set of decisions, and the mathematical ideas that are linked to that decision. In your practice you may make different decisions – the lesson to be learned here, however, is that all decisions should keep the mathematical goals of the lesson in mind.
Possible questions and student responses
The questions are provided as a starting point for discussion, with the idea of asking students to explain their thinking, model their solution processes so that they are made explicit for other students to see, and to make connections among various representations.
Possible student responses allow the "student voice" to come alive and to illustrate how mathematical language might be incorporated in their explanations. These are meant only as an ideal to which you might aim over the course of the year. Initially students should be allowed to express their thinking in ways that make sense to them. It is then your job to explicitly link mathematical vocabulary to their ideas, to create charts in the classroom that display the vocabulary for students to refer to, and that you press students to use, and take ownership of, this language.
Homework is also provided so that students will continue to think about, and build upon, the mathematical ideas explored in the lesson, and to form a link to the following day's exploration and continued learning
Development supported by The James Irvine Foundation.
References
Boaler, J. and Brodie, K. (2004). The importance, nature, and impact of teacher questions. In McDougall, D.E. & Ross, J. A. (Eds.), Proceedings of the Twenty-Sixth Annual Meeting of the North American Chapter of the International Group for Psychology of Mathematics Education, Vol. 2, pp. 773-782. Toronto, Ontario |
Appendix 1. Mathspeak - Pg. 151
A1 Mathspeak The purpose of this appendix is to give a quick summary of everyday mathematical terminology. First of all, a set is a collection of things (called its members or elements), the collection being regarded as a single object. We write "x S" to say that x is a member of S; we write "x S" to say that it is not. / For example, there is the set S whose members are the prime numbers between 0 and 10. This set has four elements, the numbers 2, 3, 5, and 7. We can name this set conveniently by listing the members within braces (curly brackets): S = {2, 3, 5, 7} An important part of the set concept is that what a set is depends solely on what its members are, and not on how we might choose to name them. We might choose to name the elements in a different order {2, 3, 5, 7} = {7, 5, 3, 2} |
Elementary Statistics Using the Graphing Calculator : For the TI-83/84 Statistics Using the Graphing Calculator is written for the introductory statistics course in which the TI-83 or TI-84 Plus graphing calculator is used. It is appropriate for students majoring in any field, and the use of algebra is minimal, although completion of an elementary algebra course is recommended. The hallmarks of Triola's other texts are present here: a friendly writing style, an abundance of relevant exercises with real data, and an emphasis on interpretation of statistical results. In addition, this text provides TI-83 and TI-84 Plus calculator instructions, screen displays and projects. |
Springboard 7 Sample UnitPlansAlgebra 2 UnitPlan - Year 7 catch up programme Teaching objectives A. Understand and use the relationships between the four ...
UnitPlanAlgebra 1 Class Description: This is the foundation and bridge course to high school mathematics. This class is a study of the language, concepts, and ...
Differentiated Unit -Algebra Strand- th This three ses on the fundamental knowledge, reasoning, ents will need as a foundation to the more -depth, ed study ... Differentiated Unit.pdf
Pre-Algebra Mathematics Support Curriculum Unit 1: Wind Power Summary The first unit of the summer mathematics support program asks students to design a wind turbine ...
Algebra I is a comprehensive course that provides an in-depth exploration of key algebraic concepts. Through a u0022Discovery-Confirmation-Practiceu0022 based exploration of ... |
eighty five Calculus One and Several Variables textboo...ks |
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 class.
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Adding Words to Algebra
While some calculations may be described with words - think of the
perimeter calculation example, many calculations can be represented or
given by an algebraic expression or formula that is best seen and grasped
in a silences in a glance. Formulas like the compound interest or growth
formula and like the quadratic formulas fall in this category of being
seen and grasped in silence. The use and development of formulas for
lengths, areas, volumes, speed, distance, time, simple interest, compound
growth and even or odd numbers, introduces students to the shorthand role
of letters and symbols in mathematics.
A. Naming and Identifying Formulas
Outside of algebra, a picture is worth a thousand words. Inside, formulas
to awkward to read aloud term by term may also be worth a thousand words.
However, both pictures and formulas may be named or identified with
words. Outside of algebra, the phrase Mona Lisa identifies a painting of
Leonardo da Vinci. Inside of algebra, formulas may be identified by name
In these phrases, the words formulas, expression and calculation may be
used interchangeable.
In dealing with fractions, we may speak of general and/or efficient
methods or formulas for adding, subtracting, multiplying and dividing. At
the higher level in the mathematical subject of calculus, the phrases
product rules, quotient rule, chain rule, integration by parts
identify operations with words.
Words to name or identify formulas and operations is a simple way to
expand the role of words in mathematics.
B. Talking about Numbers, Amounts and Quantities
Following the appearance of algebra and logic in and apart from
mathematics education, the oral element introduce above may expand. The
first skill for algebra which I introduced in fall 1983 emphasized that
we can talk about numbers, amounts and quantities without doing any
arithmetic and even apart from or parallel to the use of letters and
symbols to denote them. So we may talk about and describe numbers,
amounts and quantities as being known or not, measure-able or not,
private or not, confidential or not, forgotten or not, constant or not,
and varying or not. Some of these descriptive terms are not usually part
of mathematics, but their presence suggests how we may understand and
explain the concepts of a numbers, amount or quantity being known or not,
constant or not, or variable or not. I have written an essay What is
a Variable that informally introduces and expands the concept before
algebra begins. While pure mathematics and logic introduce technical
definitions of what is a variable, those definitions are too complex for
people just learning algebra. In the first instance, when a letter that
denotes a number, amount or quantity that is unknown, constant or
variable then the letter too will be called an unknown, constant or
variable, respectively. And in the use of formulas, letters often denote
numbers or measure whose value is to be given or found. What I am
advocating here is a simpler use of language, a use closer to everyday
use. While numbers, amounts and quantities may be described or talked
about apart from algebra or the use of letters to denote them or their
values, doing so while denoting them by letters or symbols expands the
role of words in algebra and so in mathematics.
C. Using Formulas etc Forwards and Backwards.
A theme that transcend algebra. A Fourth Skill For Algebra.
Every formula met in mathematics, accounting, science, technology etc may
be used directly and indirectly, that is forwards and backwards.
The simple message that the forward and backward use of formulas
(direct and indirect use) is part of high school mathematics and
beyond names a required skill and allows us to recognize, identify
and thus emphasize the most frequent pattern in high school mathematics
and beyond.
This message needs to be given explicitly and early in secondary
mathematics. Otherwise the underlying skill become part of the hidden, or
silent and unspoken, agenda in mathematics courses.
Teachers: Consider combining the a two page lesson on
solving
literal equtions with the message above and the examples and
exercises indicated below. The page banner above was Forward and
Backward use of equations but it now reflects the purplemath
lesson, Solving Literal Equations.
First Site Example
Direct and Indirect Use of the Rectangle Area Computation Formula
Volume 2, Chapter 10, in discussing Direct use of A =WL assumes W and L are given.
Indirect use assumes A and one of W and L is given, and leads to the
calculation or formulas W = A/L or L = A/W. The explanation of those
formulas is a step towards algebraic reasoning - the direct and indirect
or forward and backward use of formulas.
More Examples: Formulas for perimeters and areas
of squares, circles, triangles, rectangles etc can be used forwards and
backwards. Finding the value of a proportionality constant k say in an
equation y = k x represents an indirect or backwards use of an
equation, a pre-requisite to further forward and backward use of the
equation y = kx. The calculation of parameters a and b in y = ax + b
(or y = mx +b) represents another backward use of a formula or
equation. Quebec students in secondary III have met the forward and
backward use of the Pythogorean equation
c2=a2+b2 where c is the length of the
hypotenuse and the two numbers a and b are the lengths of the other two
sides (legs) of a right triangle.
To Do: : Post some details and exercises here to
further illustrate and emphasize the forward and backward use of common
formulas.
Chapter 10 before the forward and backward use of a formula goes further
in showing how to describe a the calculation of a box V = H(WL) and show
how to employ substitution (a new concept for students) to go between
this formula and V = HA where A = WL. Details are given in the chapter.
The details may be easier to grasp if numerical examples are added to
this exposition.
Seeing how a box volume formula V = hA and V = h (WL)
can be transformed into each other illustrates and may introduce the
notion of equivalent expressions. The law applied here is A = WL is a
geometric law rather than an algebraic law (like the distributive law).
None, the idea that an expression represents a number or quantity and
that there may be more than one ways to compute the number or quantity
is key to the notion of equivalence. Students thus see how substitution
in formulas leads to new formulas, how arithmetic patterns may be used
to use formulas directly and indirectly, and how algebraic solutions
may be more general or powerful than arithmetic solutions.
Algebraic Exercises:
Find a formula for the area of square in terms of its perimeter
(easy)
Find a formula for the area of circle in terms of its perimeter
(easy)
Find a formula for the perimeter of square in terms of its areas
(harder)
Find a formula for the perimeter of circle in terms of its areas
(harder)
The exercises will be easier after reading the first sections of Chapter
15 and Chapter 14 in Volume 2, Three Skills for Algebra ] |
Suggestions about Learning Mathematica
Getting Started
As with any other computer system, there are a few points that you need to get straight before you can even start using Mathematica. For example, you absolutely must know how to type your input to Mathematica. To find out these kinds of basic points, you should read at least the first section of Part 1 in this book.
Once you know the basics, you can begin to get a feeling for Mathematica by typing in some examples from this book. Always be sure that you type in exactly what appears in the book--do not change any capitalization, bracketing, etc.
After you have tried a few examples from the book, you should start experimenting for yourself. Change the examples slightly, and see what happens. You should look at each piece of output carefully, and try to understand why it came out as it did.
After you have run through some simple examples, you should be ready to take the next step: learning to go through what is needed to solve a complete problem with Mathematica.
Solving a Complete Problem
You will probably find it best to start by picking a specific problem to work on. Pick a problem that you understand well--preferably one whose solution you could easily reproduce by hand. Then go through each step in solving the problem, learning what you need to know about Mathematica to do it. Always be ready to experiment with simple cases, and understand the results you get with these, before going back to your original problem.
In going through the steps to solve your problem, you will learn about various specific features of Mathematica, typically from sections of Part 1. After you have done a few problems with Mathematica, you should get a feeling for many of the basic features of the system.
When you have built up a reasonable knowledge of the features of Mathematica, you should go back and learn about the overall structure of the Mathematica system. You can do this by systematically reading Part 2 of this book. What you will discover is that many of the features that seemed unrelated actually fit together into a coherent overall structure. Knowing this structure will make it much easier for you to understand and remember the specific features you have already learned.
The Principles of Mathematica
You should not try to learn the overall structure of Mathematica too early. Unless you have had broad experience with advanced computer languages or pure mathematics, you will probably find Part 2 difficult to understand at first. You will find the structure and principles it describes difficult to remember, and you will always be wondering why particular aspects of them might be useful. However, if you first get some practical experience with Mathematica, you will find the overall structure much easier to grasp. You should realize that the principles on which Mathematica is built are very general, and it is usually difficult to understand such general principles before you have seen specific examples.
One of the most important aspects of Mathematica is that it applies a fairly small number of principles as widely as possible. This means that even though you have used a particular feature only in a specific situation, the principle on which that feature is based can probably be applied in many other situations. One reason it is so important to understand the underlying principles of Mathematica is that by doing so you can leverage your knowledge of specific features into a more general context. As an example, you may first learn about transformation rules in the context of algebraic expressions.
But the basic principle of transformation rules applies to any symbolic expression. Thus you can also use such rules to modify the structure of, say, an expression that represents a Mathematica graphics object.
Changing the Way You Work
Learning to use Mathematica well involves changing the way you solve problems. When you move from pencil and paper to Mathematica the balance of what aspects of problem solving are difficult changes. With pencil and paper, you can often get by with a fairly imprecise initial formulation of your problem. Then when you actually do calculations in solving the problem, you can usually fix up the formulation as you go along. However, the calculations you do have to be fairly simple, and you cannot afford to try out many different cases.
When you use Mathematica, on the other hand, the initial formulation of your problem has to be quite precise. However, once you have the formulation, you can easily do many different calculations with it. This means that you can effectively carry out many mathematical experiments on your problem. By looking at the results you get, you can then refine the original formulation of your problem.
There are typically many different ways to formulate a given prob- lem in Mathematica. In almost all cases, however, the most direct and simple formulations will be best. The more you can formulate your problem in Mathematica from the beginning, the better. Often, in fact, you will find that formulating your problem directly in Mathematica is better than first trying to set up a traditional mathematical formulation, say an algebraic one. The main point is that Mathematica allows you to express not only traditional mathematical operations, but also algorithmic and structural ones. This greater range of possibilities gives you a better chance of being able to find a direct way to represent your original problem.
Writing Programs
For most of the more sophisticated problems that you want to solve with Mathematica, you will have to create Mathematica programs. Mathematica supports several types of programming, and you have to choose which one to use in each case. It turns out that no single type of programming suits all cases well. As a result, it is very important that you learn several different types of programming.
If you already know a traditional programming language such as BASIC, C, Fortran, Perl or Java, you will probably find it easiest to learn procedural programming in Mathematica, using Do, For and so on. But while almost any Mathematica program can, in principle, be written in a procedural way, this is rarely the best approach. In a symbolic system like Mathematica, functional and rule-based programming typically yields programs that are more efficient, and easier to understand.
If you find yourself using procedural programming a lot, you should make an active effort to convert at least some of your programs to other types. At first, you may find functional and rule-based programs difficult to understand. But after a while, you will find that their global structure is usually much easier to grasp than procedural programs. And as your experience with Mathematica grows over a period of months or years, you will probably find that you write more and more of your programs in non-procedural ways.
Learning the Whole System
As you proceed in using and learning Mathematica, it is important to remember that Mathematica is a large system. Although after a while you should know all of its basic principles, you may never learn the details of all its features. As a result, even after you have had a great deal of experience with Mathematica, you will undoubtedly still find it useful to look through this book. When you do so, you are quite likely to notice features that you never noticed before, but that with your experience, you can now see how to use.
How to Read This Book
If at all possible, you should read this book in conjunction with using an actual Mathematica system. When you see examples in the book, you should try them out on your computer.
You can get a basic feeling for what Mathematica does by looking at "A Tour of Mathematica" in Section T.0. You may also find it useful to try out examples from this Tour with your own copy of Mathematica.
Whatever your background, you should make sure to look at the first three or four sections in Part 1 before you start to use Mathematica on your own. These sections describe the basics that you need to know in order to use Mathematica at any level.
The remainder of Part 1 shows you how to do many different kinds of computations with Mathematica. If you are trying to do a specific calculation, you will often find it sufficient just to look at the sections of Part 1 that discuss the features of Mathematica you need to use. A good approach is to try and find examples in the book which are close to what you want to do.
The emphasis in Part 1 is on using the basic functions that are built into Mathematica to carry out various different kinds of computations.
Part 2, on the other hand, discusses the basic structure and principles that underlie all of Mathematica. Rather than describing a sequence of specific features, Part 2 takes a more global approach. If you want to learn how to create your own Mathematica functions, you should read Part 2.
Part 3 is intended for those with more sophisticated mathematical interests and knowledge. It covers the more advanced mathematical features of Mathematica, as well as describing some features already mentioned in Part 1 in greater mathematical detail.
Each part of the book is divided into sections and subsections. There are two special kinds of subsections, indicated by the following headings:
• Advanced Topic: Advanced material which can be omitted on a first reading.
• Special Topic: Material relevant only for certain users or certain computer systems.
The main parts in this book are intended to be pedagogical, and can meaningfully be read in a sequential fashion. The Appendix, however, is intended solely for reference purposes. Once you are familiar with Mathematica, you will probably find the list of functions in the Appendix the best place to look up details you need.
About the Examples in This Book
All the examples given in this book were generated by running an actual copy of Mathematica Version 5.1. If you have a copy of this version, you should be able to reproduce the examples on your computer as they appear in the book.
There are, however, a few points to watch:
• Until you are familiar with Mathematica, make sure to type the input exactly as it appears in the book. Do not change any of the capital letters or brackets. Later, you will learn what things you can change. When you start out, however, it is important that you do not make any changes; otherwise you may not get the same results as in the book.
• Never type the prompt In[n]:= that begins each input line. Type only the text that follows this prompt.
• You will see that the lines in each dialog are numbered in sequence. Most subsections in the book contain separate dialogs. To make sure you get exactly what the book says, you should start a new Mathematica session each time the book does.
• Some "Special Topic" subsections give examples that may be specific to particular computer systems.
• Any examples that involve random numbers will generally give different results than in the book, since the sequence of random numbers produced by Mathematica is different in every session.
• Some examples that use machine-precision arithmetic may come out differently on different computer systems. This is a result of differences in floating-point hardware. If you use arbitrary-precision Mathematica numbers, you should not see differences.
• Almost all of the examples show output as it would be generated in StandardForm with a notebook interface to Mathematica. Output with a text-based interface will look similar, but not identical.
• Almost all of the examples in this book assume that your computer or terminal uses a standard U.S. ASCII character set. If you cannot find some of the characters you need on your keyboard, or if Mathematica prints out different characters than you see in the book, you will need to look at your computer documentation to find the correspondence with the character set you are using. The most common problem is that the dollar sign character (Shift-4) may come out as your local currency character.
• If the version of Mathematica is more recent than the one used to produce this book, then it is possible that some results you get may be different.
• Most of the examples in "A Tour of Mathematica", as well as Parts 1 and 2, are chosen so as to be fairly quick to execute. Assuming you have a machine with a clock speed of over about 1 GHz (and most machines produced in 2003 or later do), then almost none of the examples should take anything more than a small fraction of a second to execute. If they do, there is probably something wrong. Section 1.3.12 describes how to stop the calculation.
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT. SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION. |
This book combines the teaching of the MATLAB® programming language with the presentation and development of carefully selected electrical and computer engineering (ECE) fundamentals. This is what distinguishes it from other books concerned with MATLAB®: it is directed specifically to ECE concerns. Students will see, quite explicitly, how and why MATLAB® is well suited to solve practical ECE problems.
This book is intended primarily for the freshman or sophomore ECE major who has no programming experience, no background in EE or CE, and is required to learn MATLAB® programming. It can be used for a course about MATLAB® or an introduction to electrical and computer engineering, where learning MATLAB® programming is strongly emphasized. A first course in calculus, usually taken concurrently, is essential.
The distinguishing feature of this book is that about 15% of this MATLAB® book develops ECE fundamentals gradually, from very basic principles. Because these fundamentals are interwoven throughout, MATLAB® can be applied to solve relevant, practical problems. The plentiful, in-depth example problems to which MATLAB® is applied were carefully chosen so that results obtained with MATLAB® also provide insights about the fundamentals.
With this "feedback approach" to learning MATLAB®, ECE students also gain a head start in learning some core subjects in the EE and CE curricula. There are nearly 200 examples and over 80 programs that demonstrate how solutions of practical problems can be obtained with MATLAB®. After using this book, the ECE student will be well prepared to apply MATLAB® in all coursework that is commonly included in EE and CE curricula.
Roland Priemer received the Ph.D. degree in Electrical Engineering from the Illinois Institute of Technology in 1969. Over the past forty years he has been a faculty member in the Electrical and Computer Engineering (ECE) Department of the University of Illinois at Chicago (UIC), during which time he has also consulted for numerous local, national and international corporations and laboratories. His research interests concern optimal and adaptive digital signal processing, fuzzy logic, neural networks, microprocessor based design and biomedical signal processing. He has published over 100 articles in journals and proceedings of conferences. Professor Priemer has mentored over 150 graduate students at the PhD and MS levels. He holds 3 patents. In 1991 he published the book: Introductory Digital Signal Processing, and has contributed chapters to several other books. At UIC he introduced the graduate level courses: Optimal and Adaptive Digital Filters (1982) and Fuzzy Logic (1994), and the undergraduate level courses: Microprocessor Based Design (1983), Digital Signal Processing (1984), Statistical Digital Signal Processing (2001) and Introduction to Electrical and Computer Engineering (2005). From 1999 through 2010 he was Director of Undergraduate Studies in the ECE Department.
Roland Priemer received: the UIC Excellence in Teaching Award in 2004, the College of Engineering Excellence in Teaching Award in 2006 and the College of Engineering Harold Simon Award for Excellence in Teaching in 2008. Presently, Roland Priemer is an Associate Professor, Emeritus in the ECE Department at UIC, where he teaches the course: Introduction to Electrical and Computer Engineering to freshman students. |
By Dan Kalman
Uncommon Mathematical Excursions is for anyone who knows and appreciates the basics of algebra, geometry, and calculus, and would like to learn more. It offers teachers an opportunity to deepen their knowledge of mathematics, not by exploring the far reaches of the subject, but by returning to the core. More generally, for the old hand and new devotee alike, this book will surprise, intrigue, and delight readers with unexpected aspects of old and familiar subjects. The book is particularly recommended for professional development and continuing education of secondary and college mathematics teachers.
Table of Contents
Preface
Acknowledgements
I. The Province of Polynomia
Horners Form
Polynomial Potpourri
Polynomial Roots and Coefficients
Solving Polynomial Equations
II. Maxiministan
Leveling with Lagrange: Constrained Maxima and Minima with Lagrangian Functions
A Maxmini Miscellany
Envelopes and the Ladder Problem
Deflection on an Ellipse
III. The Calculusian Republic
A Generalized Logarithm for Exponential-Linear Equations
Envelopes and Asymptotes
Derivatives Without Limits
Two Calculusian Miracles
References
Index
About the Author
About the Author
Dan Kalman has been writing about and teaching mathematics for 30 years. A graduate of Harvey Mudd College (BS, 1974) and the University of Wisconsin (PhD, 1980) he is a Professor of Mathematics at American University, Washington, DC. He previously held faculty positions at the University of Wisconsin, Green Bay, and Augustana College, Sioux Falls, among other institutions, and worked for several years as an applied mathematician at the Aerospace Corporation. He also served for one year as an Associate Executive Director of the MAA. Kalman's mathematical writing has been recognized with multiple MAA awards: Allendoerfer Awards in 1998 and 2002, Pólya Awards in 1994 and 2002, and an Evans Award in 1997. He is the author of one previous book, Elementary Mathematical Models, published by the MAA in 1997. Kalman has served on the Editorial Boards for several MAA publications, including Mathematics Magazine, MAA FOCUS, Math Horizons, and the Spectrum and Classroom Resource Materials book series. |
Elementary Probability for perfect one-semester introduction to probability, for students who are familiar with basic calculus. The lively style reflects the author's philosophy that the best way to learn probability is to see it in action, and he gives over 200 examples from genetics, sports, finance, and current events. This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is des... MOREigned for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author's philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of applications not found in other books, from areas as broad ranging as genetics, sports, finance, and inventory management. Explains probability using genetics, sports, finance, current events and more. |
This book arose from lectures repeatedly given by the author at the Friedrich Schiller University Jena. It is intended for students who have a working knowledge of the calculus as well as the theory of ordinary differential equations. We give a brief description of the characteristic features of this book. It is divided into two parts:
Geometric tomography deals with the retrieval of information about a geometric object from data concerning its projections (shadows) on planes or cross-sections by planes. It is a geometric relative of computerized tomography, which reconstructs an image from X-rays of a human patient. The subject overlaps with convex geometry and employs many tools from that area, including some formulas from integral geometry. |
B.3.2 Major Data Analysis Project
This project ties together the data analysis pieces from the previous two and one-half years of mathematics courses. Students will work in small groups on this project off and on for several weeks. Their work should include formulating a good question, then collecting, analyzing, and interpreting the data. While students work on their projects, the course will continue with several independent topics. Class time should occasionally be spent discussing the ongoing projects and verifying student progress.
Instructional Days (suggested)
15 - 18 days
Click on subtopics below to see resources from the Ohio Resource Center |
NEW DIRECTIONS; The Hand-Held Calculus
NOT SO MANY years have passed since arithmetic teachers faced up to the grim prospect of classrooms full of cheap electronic calculators, enabling students to sidestep the painstaking memorization of multiplication tables. What would happen, educators wondered, when these students went on to try the rigors of calculus? If they skipped the agony of long division, how would they manage such necessities as the differentiation of sine functions and the graphing of polynomials?
Now calculus itself is facing a crisis. The crisis has been long in coming, and its causes are as complex as the subject itself, but for some teachers it will boil down to a single astonishing fact: the calculator has caught up. New hand-held models can do precisely what students spend the bulk of their time trying to master in traditional courses. It can manipulate algebraic symbols, differentiate functions and turn obscure-looking equations into graphs on a tiny display screen.
''Just the existence of this calculator is an incredible thing,'' said Ronald G. Douglas, dean of the physical sciences at the State University of New York at Stony Brook. ''On most examinations that are now given in calculus, that calculator could get a B, or at worst a C+. It's a real opportunity, but it means that the calculus course will have to change.''
Such calculators, now selling for around $200 but sure to drop in price, will require many educators to rethink their curriculums. But the calculators are just the most visible challenge to the old ways of teaching calculus. The role of this venerable, 300-year-old mainstay of mathematics and physics has already been under attack - for example, from those who believe that other forms of mathematics are better suited to the needs of modern science in an era of digital computers.
As a result, government agencies and mathematics associations have begun a sweeping effort to overhaul the teaching of calculus at universities nationwide. Their goal is to devise what the Mathematical Association of America calls - unlikely as it may sound rrxhto students who have endured the old version - ''a lean and lively calculus.''
They know that the weighty and dull calculus will be a hard beast to kill. They have held a series of conferences and workshops, including a major national conference in Washington late last month, that are supported by the National Research Council, a branch of the National Academy of Sciences, and the Sloan Foundation, based in New York City. Next year the National Science Foundation hopes to sponsor three pilot projects to chart a new approach. Few institutions will remain unaffected. The teaching of calculus has grown into a vast enterprise, as more than a half-million students discover each year. Since the early 70's, that number has been rising. The subject has widely become a prerequisite not just for math, physics and engineering but also for biology and ''softer'' sciences like economics. At some universities, even those hoping to major in psychology and political science must confront calculus.
Its study is traditionally daunting, even for those well prepared by high school courses. In many cases, educators acknowledge, the introductory course acts less as a gateway than as a filter, screening out students who might otherwise be able to carry on in their majors. |
Applied mathematics
Definition
The study of the application of mathematical principles to domains outside of mathematics itself. Although the branches of mathematics within this categorization change with time, applied mathematics typically involves the use of differential equations, numerical analysis, and statistics with areas of knowledge such as engineering, biology, physics, computer science, economics, and finance |
Calculus : Single and Multivariable - 5th edition
Summary: Calculus teachers recognize Calculus as the leading resource among the ''reform'' projects that employ the rule of four and streamline the curriculum in order to deepen conceptual understanding. The fifth edition uses all strands of the ''Rule of Four'' - graphical, numeric, symbolic/algebraic, and verbal/applied presentations - to make concepts easier to understand. The book focuses on exploring fundamental ideas rather than comprehensive coverage of multiple similar cases that are ...show morenot fundamentally unique. Readers will also gain access to WileyPLUS, an online tool that allows for extensive drills and practice. Calculus teachers will build on their understanding in the field and discover new ways to present concepts to their students76 |
InterpolIn the mathematical subfield of numerical analysis, interpolation is a procedure that assists in "reading between the lines" in a set of tables by constructing new data points from existing points. This rigorous presentation includes such topics as displacement symbols and differences, divided differences, formulas of interpolation, much more. 1950 edition. |
Beginning and Intermediate Algebra - 6th edition
Summary: The new edition of BEGINNING & INTERMEDIATE ALGEBRA is an exciting and innovative revision that takes an already successful book and makes it more compelling for today's users. The new edition has been thoroughly updated with a new interior design and other pedagogical features that make the book both easier to read and easier to use. Known for its clear writing and an engaging, accessible approach that makes algebra relevant, BEGINNING & INTERMEDIATE ALGEBRA helps users to develop p...show moreroblem-solving skills and strategies that they can use in their everyday lives. The new edition welcomes two new co-authors Rosemary Karr and Marilyn Massey who along with David Gustafson have developed a learning plan to help users succeed in Beginning Algebra and transition to the next level in their coursework120.90 +$3.99 s/h
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College Geometry : Using the Geometer's Sketchpad - 12 edition
Summary: From two authors who embrace technology in the classroom and value the role of collaborative learning comes College Geometry Using The Geometer's Sketchpad. The book's truly discovery-based approach guides readers to learn geometry through explorations of topics ranging from triangles and circles to transformational, taxicab, and hyperbolic geometries. In the process, readers hone their understanding of geometry and their ability to write rigorous mathematical proofs.
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Short description
Math is a special and important learning in education. Even though Math is hard to some people, it is not hard to learn if you follow a good guide. This book is a good guide that will help high/middle school students learn basic and advanced skills with important concepts and skills carefully designed into questions and solution for students to master. This book will escort you to your success.
.. (Read more) and skills are all carefully designed into questions for students to master. Every question is solved with important details. Through the progress in each topic, students are expected to learn what they are required and in the meantime excel among their peers.
The material in this book comes from the experience and learning in China. Students will learn what Chinese students learn and practice in middle school and high school Math. This is a training that builds up the high reputation in Math study in China and hopefully this book can escort you to your success. |
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Math
Linear algebra
Matrices, vectors, vector spaces, transformations, eigenvectors/values
We will begin our journey through linear algebra by defining and conceptualizing what a vector is (rather than starting with matrices and matrix operations like in a more basic algebra course) and defining some basic operations (like addition, subtraction and scalar multiplication).
Given a set of vectors, what other vectors can you create by adding and/or subtracting scalar multiples of those vectors. The set of vectors that you can create through these linear combinations of the original set is called the "span" of the set.
If no vector in a set can be created from a linear combination of the other vectors in the set, then we say that the set in linearly independent. Linearly independent sets are great because there aren't any extra, unnecessary vectors lying around in the set. :)
In this tutorial, we'll define what a "subspace" is --essentially a subset of vectors that has some special properties. We'll then think of a set of vectors that can most efficiently be use to construct a subspace which we will call a "basis".
In this tutorial, we define two ways to "multiply" vectors-- the dot product and the cross product. As we progress, we'll get an intuitive feel for their meaning, how they can used and how the two vector products relate to each other.
This tutorial is a bit of an excursion back to you Algebra II days when you first solved systems of equations (and possibly used matrices to do so). In this tutorial, we did a bit deeper than you may have then, with emphasis on valid row operations and getting a matrix into reduced row echelon form.
We will define matrix-vector multiplication and think about the set of vectors that satisfy Ax=0 for a given matrix A (this is the null space of A). We then proceed to think about the linear combinations of the columns of a matrix (column space). Both of these ideas help us think the possible solutions to the Matrix-vector equation Ax=b. |
Trigonometry
Book Description: The emphasis of the textbook is on understanding the definitions and principles of trigonometry and their application to problem solving. Identities are introduced early in Chapter 1. They are reviewed often and are then covered in more detail in Chapter 5. Also, exact values of the trigonometric functions are emphasized throughout the textbook. There are numerous calculator notes placed throughout |
People, I need some help with my algebra assignment. It's a really long one having almost 30 questions and it covers topics such as math review sheets grade 6, math review sheets grade 6 and math review sheets grade 6. I've been trying to solve those questions since the past 4 days now and still haven't been able to solve even a single one of them. Our teacher gave us this homework and went on a vacation, so basically we are all on our own now. Can anyone help me get started? Can anyone solve some sample questions for me based on those topics; such solutions would help me solve my own questions as well.
First of all, let me welcome you to the world of math review sheets grade 6. You need not worry; this subject seems to be tough because of the many new symbols that it has. Once you learn the basics, it becomes fun. Algebrator is the most used tool amongst beginners and professionals. You must buy yourself a copy if you are serious at learning this subject.
Algebrator is the program that I have used through several algebra classes - Algebra 1, Algebra 1 and Pre Algebra. It is a really a great piece of math software. I remember of going through difficulties with difference of squares, conversion of units and 3x3 system of equations. I would simply type in a problem homework, click on Solve – and step by step solution to my algebra homework. I highly recommend the program. |
KS4, A level - the site provides help with problems in mathematics and statistics. Students can send a question and receive an email back with hints and general advice on tackling the problem. It is also possible to access an archive of selected past questions and responses. A maths chat room is also available on occasions.
-aimed at students studying for the higher tier of GCSE maths, the main site covers revision tips and provides resources in number, shape and space, statistics and probability, graphs, algebra and trigonometry. There is also a formula sheet and some coursework practise questions. A level students should follow the link to a comprehensive set of revision resources.
AS/A2 - revision themes are organised under the headings of Pure Maths and Statistics. Quicklearn guides are provided, followed by tests on understanding. Finally, there is a revision summary that can be printed out. An effective and well-organised site.
- features around 400 interactive GCSE maths exam questions, answers and explanations developed from exam board papers and practice papers. Each question is randomised so that whenever the page is visited the details are different. Exam advice is included and any user can contact the site directly to request more explanation of topics |
Summary: Provides completely worked-out solutions to all odd-numbered exercises within the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer$96.95 |
IGCSE Mathematics is a new text book written specifically for the Cambridge International Examinations syllabus.
Long description
IGCSE Mathematics is a new text book written specifically for the Cambridge International Examinations syllabus. It has been written and trialled by experienced IGCSE teachers and endorsed by CIE, ensuring that it is up to date and comprehensive in its coverage of the syllabus.
Product details
Author:
Karen Morrison
Subtitle:
Igcse
Format:
Trade paperback
Publisher:
Cambridge University Press
ISBN:
9780521011136
Series Title:
Cambridge International Examinations
Pages:
308
Width (mm):
188
Length (mm):
245
Table of Contents:
Introduction
Module
Working with numbers
Module
Algebra
Module
Graphs and functions
Module
Geometry
Module
Trigonometry
Module
Statistics
Module
Probability
Module
Transformations
Answers |
Thousands of math problems and questions with solutions and detailed explanations are included. Free math tutorials and problems to help you explore and gain deep understanding of math, calculus, trigonometry and geometry topics.
This website is specifically focused on teaching mathematics. It provides teachers with specific lessons focused on pre calculus, calculus, geometry, trigonometry and applied mathematics. In addition to important links and resources there are online tools such as an online graphing calculator, tutorial problems and answers and downloadable graph paper. - Karrie Jones
Free analytical and interactive math, calculus, geometry and trigonometry tutorials and problems with solutions. Thousands of problems and examples with detailed solutions and answers are included in this site. Also explore topics in mathematics using jav
This website contains math problems, tutorials, etc. for all types of math. It could be very helpful when needed some extra questions to put on an exam. Also, since it has all math courses, it can be helpful for any class that I teach jav
Free analytical and interactive math, calculus, geometry and trigonometry tutorials and problems with solutions. Thousands of problems and examples with detailed solutions and answers are included in this site. Also explore topics in mathematics using java applets. |
082645223 Mathematics 11-18
It has been speculated that all learners are capable of sophisticated mathematical thought if given supportive environments and challenging stimuli. Inclusive Mathematics 11-18 provides a timely guide for teachers wishing to eradicate underachievement and to ensure that all students, whatever their learning styles, backgrounds or abilities, benefit as fully as possible from their teaching |
066947 to Go: A Mathematics Handbook (Math Handbooks)
Algebra To Go is a unique new handbook designed to help demystify algebra for students. Modeled after the Math On Call handbook, Algebra To Go is a student-friendly resource that covers key and often complex math topics in a way that's clear and easily understandable for students - from numeration and number theory to estimation, linear and non-linear equations, geometry, and data |
Maple by Example, Third Edition , is a reference/text with CD for beginning and experienced students, professional engineers, and other Maple users. This new edition has been updated to be compatible with the most recent release of the Maple software. Coverage includes built-in Maple commands used in courses and practices that involve calculus, linear,... more...
Quantum Probability and Related Topics is a series of volumes based on material discussed at the various QP conferences. It aims to provide an update on the rapidly growing field of classical probability, quantum physics and functional analysis. more...
This volume contains the latest results in the fields of quantum probability and infinite dimensional analysis. The contributions range from classical probability, 'pure' functional analysis and foundations of quantum mechanics to applications in mathematical physics, quantum information theory and modern mathematical finance. This diversity... more...
This volume includes new topics such as the stochastic limit approach to nonequilibrium states, a new algebraic approach to relativistic nonequilibrium local states, classical and quantum features of weak chaos, transports in quantum billiards, the Welcher–Weg puzzle with a decaying atom, and the topics related to the quantum Zeno effect.TheX and the City , a book of diverse and accessible math-based topics, uses basic modeling to explore a wide range of entertaining questions about urban life. How do you estimate the number of dental or doctor's offices, gas stations, restaurants, or movie theaters in a city of a given size? How can mathematics be used to maximize traffic flow through... more... |
Acceleration is both a buzz-word and a set of solutions in developmental mathematics. In a basic way, the New Life model is based on acceleration to college mathematics for most of our students. The courses in the New Life model — Mathematical Literacy and Algebraic Literacy — are being well received; dozens of colleges have implemented one or both courses.
However, we are resisting a simple change that promises significant improvement at little risk — eliminating any college course prior to the level of beginning algebra or mathematical literacy. I'm talking about courses called pre-algebra, basic math, and or arithmetic. I believe that these courses have insignificant benefits while presenting risks to students.
The vast majority of these courses focus on procedural skills in a few content domains (decimals, fractions, percents, very basic geometry, and perhaps extremely limited algebraic skills). Historically, these courses are a relatively recent development from a remedial point of view:
The myth that we must fill all student deficiencies before they can take a college-level math course.
We all have deficiencies; human beings have a capacity to function in spite of them. We tend to accept without question the surface logic that says a student needs to master arithmetic before they can master algebra. [The New Life courses do not de-emphasize algebra; our focus is on diverse mathematics and understanding, including algebra.] A course like beginning algebra or Math Lit continues to be one of the key gatekeepers to college success.
At the global level, I have never seen any study reporting a large correlation between pre-algebra (or arithmetic) skills and success in beginning algebra; sure, there are a few studies (including my own) that show a significant correlation … due primarily to large sample sizes. Significance does not show a meaningful relationship in all cases. A correlation of 0.2 to 0.3 is only connected with 5% to 10% of the variation in outcomes; other student factors (like high school GPA) have larger correlations.
At the micro level, we often justify a pre-algebra course by justifying the components. Fractions are needed before algebra, because the algebra course covers rational expressions. Other content areas have similar rationales. This justification has two major problems:
The need in the target course is artificially imposed in many cases ('needed for calculus, so we do this in beginning algebra'). [This is a pre-calculus course has the responsibility for this need.]
The pre-algebra content is almost always a procedurally bound, right answer obsessed quick tour with no known transfer to an algebraic setting.
When the New Life model was developed, we did not assume any particular content connections. We looked at the content of Mathematical Literacy, and determined that nature of the knowledge needed before students would have a reasonable chance of success. The list of prerequisites to Math Lit is quite short:
Understand various meanings for basic operations, including relating each to diverse contextual situations
Use arithmetic operations to solve stated problems (with and without the aid of technology)
Order real numbers across types (decimal, fractional, and percent), including correct placement on a number line
Use number sense and estimation to determine the reasonableness of an answer
Apply understandings of signed-numbers (integers in particular)
For the vast majority of students, any gaps in these areas can be handled by just-in-time remediation. This list certainly does not justify a prerequisite course. A similar analysis from a beginning algebra reference would yield a similar list, I believe.
In spite of what we know, we continue to offer courses before beginning algebra or Math Lit, and continue to require students to pass them before progressing in the sequence.
This has been a long-debated topic in AMATYC — why does an arithmetic-based course need to be a prerequisite to algebra? Essentially, I think this is our problem — these courses are security blankets for us. We feel like we are doing the safe thing and helping our students by giving them this 'chance to be successful'; we believe that these courses offer real benefits for students, even though the data is pretty clear that they do not (in general).
It is uncomfortable, perhaps even scary, for us to consider the possibility that all students be placed into beginning algebra or Mathematical Literacy. We worry about the risk. We seem unconvinced that another math course in a sequence is creating known risks and problems for our students.
We can easily see the problem by a simulation. Let's assume that 70% of the students pass pre-algebra, that 80% of those continue to beginning algebra (or Math Lit), and 60% of these pass.
Enter pre-algebra, pass beginning algebra … about 34%
Compare this to these same students starting out in beginning algebra. There is no sequence; the percent who pass beginning algebra is simply the pass rate for a group with somewhat higher risk.
Skip pre-algebra, pass beginning algebra … about 40% to 50%
The real world is not as rosy as the first scenario. At my college, less than 50% of our pre-algebra passers complete beginning algebra (and a fourth of these barely pass, having little chance at the next level).
We should be very upset by the situation. Few researchers talk about this, but we know. Pre-algebra (and arithmetic) courses tend to have a higher (sometimes much higher) proportion of minority students, as well as people with employment and economic problems. Community colleges are supposed to be about upward mobility; instead, we've created a system which has been shown to keep certain groups from advancing.
Let go of that security blanket called pre-algebra (or arithmetic). Take the very small risk of helping a lot more students get though their mathematics and their program. Completion leads to economic opportunity. Let's get out of the way, as much as possible!
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The AMATYC "New Life Project" has a curricular vision that includes two new courses that can replace the traditional developmental mathematics courses. The first of the new courses is Mathematical Literacy for College Students (often shortened to just Mathematical Literacy, or even MLCS); this course shares content with the Carnegie Foundation Pathways (Quantway™ and Statway™) and with the Dana Center (Foundations of Mathematical Reasoning).
With the New Life Project, our work is based on faculty making choices and working with publishers to develop materials. Currently, two commercial texts are available for MLCS (either published or soon-to-be published); some faculty have also custom published their own materials, or adapted existing materials. The initial MLCS pilots started about two years ago.
As of fall 2013, here is a summary of the known MLCS course implementations (number of sections):
State
count
AL
1
AZ
2
CA
12
CO
29
GA
1
IA
19
IL
31
MA
7
MI
7
NY
26
TX
18
The actual total is definitely higher than this (153 sections), as we know of other colleges using one of the new Math Lit textbooks. A few more colleges are implementing MLCS in Spring 2014, and several more colleges are implementing Fall 2014.
I think it is worth noting that all of this progress is being made without special grants; no mandates are involved, and we have no 'staff' in the New Life project. What we do have — dozens of dedicated faculty, willing colleges, and publishers willing to work with us.
The New Life Project is a voluntary effort (AMATYC Developmental Mathematics Committee) with considerable collaboration with the Carnegie Foundation and the Dana Center — especially in providing curricular expertise to those organizations. We can be proud of this progress and our work together.
The use of Mathematical Literacy will continue to grow. Our work will increase the emphasis on the second course — Algebraic Literacy; for information on Algebraic Literacy, you can see a presentation from this year's Summit on Developmental Mathematics at
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Like humans in general, our students develop expectations based on experience. Habits form, often without awareness or conscious effort. Behaviors exhibit, which are used to measure knowledge. In assessments, we often confuse correct behavior with correct knowledge.
Symbolic work can be difficult for novices. We (experts) see large amounts of information in short symbolic statements. For a novice, symbols are like a map to a city never visited — yes, we can remember how to get from point A to point B on the map … but without any understanding of what these points mean in the city.
On a recent test in my beginning algebra classes, two mistakes were made by at least 20% of the students (one or both):
-3² + 5² = 2^4 = 16
8^6 divided by 8^2 = 1^6
The first error is a coincidental 'right answer' for a very wrong method. The second one, not at all. Both involve over-generalizations of 'same number' rules. Obviously, there is a very high probability that the students making one or both of these errors have low study skills or habits (like not doing any practice outside of class).
My concern is not these particular students, nor these particular errors. My concern is our overall approach to mathematics. We tend to take one of these approaches to symbolism in mathematics:
Emphasize context and reasoning, and measure understanding by correctly completing related problems with differences in details.
Some reform models take approach #2 to the extreme — very few symbolic procedures are introduced, and most of what is done is arithmetic; algebraic models are used but carried out with technology more than symbolic procedures. We need to learn how to balance the 'symbols' and 'reasoning' aspects of mathematics — and be willing to embrace both as critical in all mathematics courses.
Clearly, there is much (perhaps a majority) of our traditional algebra curriculum that involves symbolic work without a purpose now or in the student's future. I seriously doubt that solving a radical equation by squaring each side twice will ever be a survival skill in a student's future.
Just as clearly (to me, at least), many of our students will need good understanding of various symbolic structures in mathematics, in future science courses (hard science and soft science). Terms, exponents, coefficients, subscripts, groupings, equations, inequalities … are involved in stating properties in sciences and in using predictive models.
When we assess the mastery of symbolism, we need to deal with much more than 'correct answers'. In the ideal situation, assessments would be done in a one-on-one verbal interview so the expert can probe into the novice's understanding based on the individual learner. Lacking that luxury, we will need to use diverse assessment tools that deal with process and connections, as well as answers.
Sadly, I had integrated some of this assessment into the beginning algebra class about two weeks ago — dealing with the adding terms error (first error above). On a worksheet, students were faced with adding like terms (10x^4 + 6x^4) before we had dealt with them formally in class. Something like half the students added the exponents as well as adding the 'terms' (coefficients). About 40% of these students apparently maintained this erroneous method up until the test.
Correct answers are only correlated with correct knowledge; students are always seeking the simplest rules for achieving correct answers — which can lead to totally wrong rules. Mathematical symbolism can be a window into the houses where students keep their math knowledge. Too often, however, symbolism is confused with the knowledge and correct answers stop the assessment process.
We need to slow down our courses. Learning mathematics is not a fast or spontaneous activity. Learning mathematics is hard work for both us and our students.
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This semester, we have more than 150 sections of Mathematical Literacy offered at colleges across the country … and these are outside of the grant-related work (such as Quantway™). In other words, the New Life Mathematical Literacy course is now the most implemented reform math course in the United States.
Getting to this point is the result of the incredible effort of dozens of math faculty, many of whom have been members of the New Life wiki at Our work has not involved large grants from foundations; rather, collaboration and local initiative have allowed us to create significant change.
However, change is not the same as progress. Progress involves sustained efforts which achieve explicit goals. We have achieved more than other efforts … but we "are not there yet".
Where are we headed? How will we know when we have arrived? These are not questions for which we create singular responses and data-based conclusions; these are questions for a profession to use as standards for our work.
In the world of process and product design, one set of strategies involves having people seeing themselves in the situation that they are trying to create. For example, we might ask 100 math faculty to imagine that the mathematics curriculum works like it is supposed to. What does this look like? What does it sound like? What does it smell like?
For our work, here are some answers I would give to those questions about what we are trying to achieve:
Students text each other about the latest exciting math problem.
Students pass every math class unless something unexpected comes up.
Over 10% of students major in a STEM field and over 10% of degrees are awarded in STEM fields.
Students learn diverse mathematics, with understanding, in both pre-college and college math courses.
Fewer students are in college-prep math classes than are in college level math classes.
Half of the students who start in college-prep math classes change their goals to be more STEM-like.
Math faculty are the happiest faculty on campus.
Part of our difficulty has been that we have not had a goal in mind — beyond having higher pass rates. Higher pass rates is not a design standard; it's a production standard (and a poor one, at that).
Progress would exist if we would judge that we are substantially closer to achieving our goals. If we don't articulate our goals (like the 7 statements above), we can never have progress … because we are not directing our efforts towards anything. Change is cheap; progress is where the power is.
I started off this post thinking a next step, like getting the Algebraic Literacy course on the radar — and I still think that is very important. Or, thinking about salvaging the college algebra and pre-calculus curriculum, which is very important. I hope that you will be involved with one or both of those reform efforts. Overall, however, I am concluding that we need to have more conversations about our goals. What does progress look like? How do we know when we are there, as opposed to where we are now? |
Description
In addition to math, Saxon has an excellent physics book. Our son worked through it when he was 16 and it enabled him to write and pass the First Year University Physics Exam, allowing him to go directly into second year physics. I feel it is because he followed Saxon Math through their high school and Calculus courses and took Saxon Physics. I highly recommend this for anyone who is at all serious about these subjects. This Physics course is taught at an introductory level and does not require that the teacher have a background in physics. Anyone who has taught second-year algebra, especially Saxon's Algebra 2, can teach this book successfully. Saxon Homeschool Physics was written with both average and gifted students in mind.
The entire program is based on introducing a topic to a student and then allowing them to build upon that concept as they learn new ones. Topics are never dropped but are instead increased in complexity and practiced every day, providing the time required for concepts to become totally familiar
Additional Information
Please Note that there is a Solutions Manual available for this text. |
The Texas Instruments TI-34 MultiView Calculator was designed with educator input in mind. It's best used for middle grades math and science classes. Easy to use, students can compute, calculate, and analyze math and science problems quickly |
Why
Yes, but then they still can punch in the acos 37. The point is to teach them to get to the point of acos 37, and that can also be done with the solution being acos 2pi or something.
I
I really wish that my high school, and honestly even my undergraduate institution, had taken this sort of approach versus the number crunching nonsense.
Now that I'm taking graduate level courses, I realized how handicapped I was by my calculator. The courses feel much more difficult (actually have to work through the examples!) but they are so much more rewarding.
Applied "issue" without explaining what the issue actually is.
No.
I've never seen a complicated decimal number in my life. I don't even know what you are saying.
Really? Seeing as you introduced the statement "complicated terms of decimal places", do you think there's a chance that it's related to that?
It's also a matter of efficiency. It can take a while to manually work through complex problems and equations with little need to understand the exact how beyond knowing when it can be applied appropriately.
The Newton-Rhapson method: I made a program on my calculator automating the process. Taught me more about mathematics, about algorithms, and about numerical methods of solving problemsCalcul
I am currently in university, and my research is basically about numerical simulations. I used to be like you.
The Newton-Rhapson method: I made a program on my calculator automating the process. Taught me more about mathematics, about algorithms, and about numerical methods of solving problems.
What would teach you more about numerical methods is to actually be in a lab every week working on MATLAB on a computer and actually doing great.
What this will not teach you is why the method works. And that's what you really should have grasped.
I am happy to know you went above and beyond to program it and understand it.
Bottomline: If you understand the proof, you'll understand why it works. Not with a calculatorThe intended consequence of curve-sketching techniques and function graphing practice with calculators is so you can develop enough of an intuition to be able to visualize any function you are given.
Often
Bottomline: Graphing curves is great. But you aren't actually going to benefit from that during an examThis is a poor reason. I tutor a few high-school kids and I can come up with questions all day long with great simplifications but require a lot of thinking.
Bottomline: This is just a bad reason. A monkey could develop simplifiable questions.
You seem to have missed the point of your education if you don't understand what I am going to say next.
Calculators are there to make your job easy and faster. They aren't there to stand as a substitute for conceptual understanding or thinking.
It
I use WolframAlpha all day long and I use it to graph all sorts of things. I used to be like you actually. I ran to my Mathematica anytime I needed to get anything done. It became a lazy answer to everything.
This stopped after I got my first research job in 1st year university and my professor showed me why this is bad.
The
You are thinking about it right now as "I am just being efficient" but you are really just transferring the burden of thinking.
Curve-sketching is not a mundane activity like rote-calculation. It really forces you to understand how calculus works.
The
I therefore think that banning calculators will lead to an emphasis in rote memorisation of how to perform calculations rather than allowing teachers to focus on teaching what the calculator is actually doing, and why it works.
Computers
Well the article being discussed is for an examinations in primary school (age 11).
But the same principle can be extended to latter years, especially as the calculations become more tedious. For example solving linear systems of equations, matrix operations, certain classes of differential equations.
I can't think of any math for which primary school students would need calculators...
If they can't handle operations with numbers between 0 to 10, then it's stupid.
Computers are efficient only for complicated problems.
If kids need calculators for 5x3=15, we are teaching them to be slower than necessary.
I support computational methods for grade 10+ , but anything before that only encourages dependence. Calculators should be something you use because you want to be faster. Not something you use because you're helpless without it.
It's
Wait,
So basically the calculator is an intermediate step that allows longer conceptual problems.
That
The GCSE maths papers at the moment do a good job of balance. One non calculator paper, one calculator paper.
and not the numerical value of that answer.
My point above addresses this. Surely now you see that in more involved questions, that require you to do something more with acos37, having the decimal value would be beneficial.
EDIT: I just re-read your comment
Use simple numbers, that evaluate to a 1 or a 2 or a 0.
I'm sorry but this line leads me to believe that you don't really understand what you are talking about.
I can do most of my A-level maths without a calculator thanks to this; he knows what he's talking about. If you use pi/3, pi/6 or pi/4 (or degree equivalents) for angles all trig becomes very simple to calculate without making the questions easier (although admittedly they won't calculate to something as nice as an integer except for tan(pi/4)).
Also exact form means fewer rounding errors and therefore the paper becomes easier to mark, from a practical perspective. I can't actually think of anything that would always require decimals and therefore calculators (percentages maybe?). |
+ By ongolearn.com
This is for students in High School/College learning algebra. If you are a beginner in algebra you might be thinking X+Y=XY, Is not it? But it's not. The beauty of algebra is, it deals with variables, expressions & equations. You will come to know various formulas. For example if you know (a+b)^3= a^3+b^3+3a^2b+3ab^2. You can calculate any number to the powers 2,3,4…in a fraction of seconds. In the above equation a ,b are variables. So you can calculate (1.034)^3 also using that formula. Just feed a=1& b=.034 IMathPractice Algebra's 3 steps method of teaching has sections like Tutorial, Practice Skills, Practice Test & Algebra Challenge. Under tutorial it teaches you.
Numbers Types of Number like real number, integer, negative number, complex number Addition, Subtraction, Multiplication & Division of Real Number Addition, Subtraction, Multiplication & Division of Negative Number Addition, Subtraction, Multiplication & Division of Complex Number Properties of Number
Under Practice Skills, You will be able to practice all the above learned skills with help. There are answer & steps to get the answer for each question.
Under Practice Test, You will be able to practice all the skills in specified timed environment. There is a timer. You need to finish within that time.
Under Algebra Challenge You will be prepared to compete with others. It contains 50 questions & time allotted is 1 hour.
There are around 210 questions to practice for in lite version.
What's new in version 1.3? Bug reported in comment section has been removed.
Note:Currently the app is in English only. We are working on translation to other languages. Please don't rate 1 only because it's not in your language.You can send your request to developer.
Tags:
algebra lite class, quien es el maestro del algebra.
Comments and ratings for Master Algebra Lite
(59 stars)
by A Google User on 03/11/2012
Hmmm well its oky if you want to practice it but not to learn it 3 stars
(59 stars)
by Aisling on 24/06/2012
This app is great in many ways. The tests contain a balanced mix of questions, from simple to challenging. However, once you've reached 40% of the total, a msg appears to tell you that you've passed. This msg covers the end of the questions, slowing you d |
Geometry Demystified
You can read this ebook online in eb20 format without having to download anything.
more
Say goodbye to dry presentations, grueling formulas, and abstract theory that would put Einstein to sleep - now there's an easier way to master chemistry, biology, trigonometry, and geometry. McGraw-Hill's ''Demystified'' series teaches complex subjects in a unique, easy-to-absorb manner and is designed for users without formal training, unlimited time, or genius IQs. Organized like self-teaching guides, they come complete with key points, background information, questions at the end of each chapter, and final exams. There's no better way to gain instant expertise! This book: will help users understand circle and triangle models; inverses of circular functions; graphs of functions; coordinate conversions; angles and distances; waves and phase; complex numbers; vectors; trigonometry in 3-space; and much more. less |
1)A subject, that in its elementry forms, can be quite useful to the average person, but around Algebra I, becomes pointless to people who aren't planning to enter a field of study focusing around math.
2)A class that many kids find tortous and confusing.
3)A class usually excelled in by: A)gifted peoples (like me lol) B)normal people who work their ass off to try and understand it or C) (this is j/k just laugh, don't hate) Asian kids.
1)People use simple math every time they count change.
2)Algebra I is totally killing my friends' grades.
3)Walk into a common high school math class and I bet you could pick out who will be doing well or not simply either by lack of friends or their features.
Short for mathematics - the logical study of quantity (numbers) and abstract structure (geometry), their operations, properties, applications, and how they all interrelate.
Aside from its incredible value in real-world applications (science, engineering, business, etc.), mathematics is also taught in schools because it's the best system to demonstrate and strengthen the vital concepts of deductive reasoning, objectivity, and abstract thinking.
People who are quick to say they hate math are typically those who had horrible math teachers/curricula in school, and never grasped the basic underlying concepts of math. Other reasons for an individual's poor math skills might include having a short attention span, no confidence to question what isn't understood, and the simple reinforcement by peers that it's OK to remain bad at math. But like a sonet or a piece of sheet music, mathematics reveals its beauty to those who speak its language.
1) A source of common teenage suicide. Mostly defined as an area of academic study- but is known to cause mental health problems such as hallucinations, dizziness, and minor cases of concussion (usually from banging your head on a desk) Many retired drill sargeants and arabian assasins take up professions as math teachers to let their steam out on innocent, unfortunate students that had come to actually learn a valuable life skill. Children- avoid math at all costs (!!)
2) A system of numbers and variables believed to be useful in everyday life
1) I had come to math class ony to find that my A+ average has been ruined by a fuckin' test with graphing inequalities... what fuckin' bitch said that
X+3X-2Y<8XY ??? SCREW MATH!!!
2) When I majored in math- i thought i had done a great thing, but it turns out my head is endlessly cluttered with meaningless numbers and symbols (!!!)
A subject that is easy to do and seduces you into it. Then it becomes substantially harder as you progress. Eventually, you will get gang raped by Algebra, Geometry, Calculus, Statistics, Linear Algebra, Multivariable calculus... watch the integral... |
Book summary
This book is concerned with the calculus of several variables and provides an introduction to elementary differential and difference equations. The emphasis is on practical problem-solving rather than the proof of formal theorems. Many worked examples are supplied as well as problems for the student to solve, together with their solutions. The techniques are illustrated with applications drawn chiefly from economics, statistics and operational research. Some elementary knowledge of the calculus of one variable is assumed but revision material is supplied throughout the text. A confident approach to problem-solving is not possible without some understanding of the background theory. In this book the theory is presented systematically but informally. Wherever possible, geometric arguments are used and the text is illustrated with numerous diagrams. Particular care has been taken to make the main body of the text suitable for students who are studying independently of a taught course. The book will interest students at universities and other higher education institutions. At the London School of Economics, the course on which this book is based is attended by students reading for a variety of different degrees and with a wide disparity in their previous levels of mathematical training. Some are graduates and some are first-year undergraduates. It is hoped that this book will attract a similar audience: not only of economists, statisticians and other social scientists but also physical scientists, engineers and mathematicians. [via] |
Prealgebra and Introductory Algebra, Books a la Carte agrave; la Carte also offer a great valuethis format costs 35% less than a new textbook. Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief.Prealgebra & Introductory Algebra, Third Editionwas written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like... MORE theStudent Organizer(available separately) and now includesStudent Resourcesin the back of the book to help students on their quest for success.
This edition features the exact same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value—this format costs significantly less than a new textbook.
Elayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Prealgebra & Introductory Algebra, Third Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer (available separately) and now includes Student Resources in the back of the book to help students on their quest for success. |
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Starting at $213 package consists of the textbook plus an access kit for MyMathLab/MyStatLab. This book presents the content and applications in an accessible manner while maintaining an appropriate level of rigor. The authors proceed from familiar material to new, and from concrete examples to general rules and formulas. This edition retains its focus on real-world problem solving, but has been refreshed with a wealth of new data in the examples and exercises-39% of the 623 examples are new or revised, and 28% of the 5,288 exercises are new or revised. MyMathLabprovides a wide range of homework, tutorial, and assessment tools that make it easy to manage your course online.
Table of Contents
Chapter 1: Algebra and Equations
1.1 The Real Numbers
1.2 Polynomials
1.3 Factoring
1.4 Rational Expressions
1.5 Exponents and Radicals
1.6 First-Degree Equations
1.7 Quadratic Equations
Chapter 1 Summary
Chapter 1 Review Exercises
Case Study 1: Consumers Often Defy Common Sense
Chapter 2: Graphs, Lines, and Inequalities
2.1 Graphs
2.2 Equations of Lines
2.3 Linear Models
2.4 Linear Inequalities
2.5 Polynomial and Rational Inequalities
Chapter 2 Summary
Chapter 2 Review Exercises
Case Study 2: Using Extrapolation to Predict Life Expectancy
Chapter 3: Functions and Graphs
3.1 Functions
3.2 Graphs of Functions
3.3 Applications of Linear Functions
3.4 Quadratic Functions
3.5 Applications of Quadratic Functions
3.6 Polynomial Functions
3.7 Rational Functions
Chapter 3 Summary
Chapter 3 Review Exercises
Case Study 3: Architectural Arches
Chapter 4: Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Applications of Exponential Functions
4.3 Logarithmic Functions
4.4 Logarithmic and Exponential Equations
Chapter 4 Summary
Chapter 4 Review Exercises
Case Study 4: Characteristics of the Monkeyface Prickleback
Chapter 5: Mathematics of Finance
5.1 Simple Interest and Discount
5.2 Compound Interest
5.3 Annuities, Future Value, and Sinking Funds
5.4 Annuities, Present Value, and Amortization
Chapter 5 Summary
Chapter 5 Review Exercises
Case Study 5: Continuous Compounding
Chapter 6: Systems of Linear Equations and Matrices
6.1 Systems of Two Linear Equations in Two Variables
6.2 Larger Systems of Linear Equations
6.3 Applications of Systems of Linear Equations
6.4 Basic Matrix Operations
6.5 Matrix Products and Inverses
6.6 Applications of Matrices
Chapter 6 Summary
Chapter 6 Review Exercises
Case Study 6: Matrix Operations and Airline Route Maps
Chapter 7: Linear Programming
7.1 Graphing Linear Inequalities in two Variables
7.2 Linear Programming: The Graphical Method
7.3 Applications of Linear Programming
7.4 The Simplex Method: Maximization
7.5 Maximization Applications
7.6 The Simplex Method: Duality and Minimization
7.7 The Simplex Method: Nonstandard Problems
Chapter 7 Summary
Chapter 7 Review Exercises
Case Study 7: Cooking with Linear Programming
Chapter 8: Sets and Probability
8.1 Sets
8.2 Applications of Venn Diagrams
8.3 Introduction to Probability
8.4 Basic Concepts of Probability
8.5 Conditional Probability and Independent Events
8.6 Bayes' Formula
Chapter 8 Summary
Chapter 8 Review Exercises
Case Study 8: Medical Diagnosis
Chapter 9: Counting, Probability Distributions, and Further Topics in Probability |
Synopses & Reviews
Publisher Comments:
"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples."--American Mathematical Monthly
A stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written in an informal style that does not sacrifice depth or challenge. Based on 20 years of teaching by the leading researcher in graph theory, it offers a solid foundation on the subject. This revised and augmented edition features new exercises, simplifications, and other improvements suggested by classroom users and reviewers. Topics include basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 ed.
Synopsis: |
ALEX Lesson Plans
Title: Systems of Linear Inequalities Project
Description:
The
Subject: Mathematics (9 - 12) Title: Systems of Linear Inequalities Project Description: The
Title: Systems of Equations: What Method Do You Prefer?
Description:
TheStandard(s): [MA2010] (8) 10: Analyze and solve pairs of simultaneous linear equations. [8-EE8] [MA2010] AL1 (9-12) 19: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. [A-REI5 ALC (9-12) 2: Solve application-based problems by developing and solving systems of linear equations and inequalities. (Alabama) (8 - 12) Title: Systems of Equations: What Method Do You Prefer? Description: The
Thinkfinity Lesson Plans
Title: Shedding the Light
Description:
In
Standard(s):S1] PHY (9-12) 7: Describe properties of reflection, refraction, and diffraction. DM1 (9-12) 3: Use the recursive process and difference equations to create fractals, population growth models, sequences, series, and compound interest models. (Alabama)
Subject: Mathematics,Science Title: Shedding the Light Description: In Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 absolute |
What is PRECALCULUS HS MATHEMATICS UNIT 04 LESSON 01?
Subject Poster Date [20832] - [#GEDPLUSCurriculumGuide06final2.doc] - [Report 4] - "... college entrants who were prior year Florida high school ... community colleges, only 45.3% passed mathematics and 56 ... to get the gist of an entire chapter or unit
Mercedes High School; Departments; MATH; ... Unit 01: The purpose of the ... Possible Lesson 01 Students investigate terminology used to describe the behavior of functions. Initially, students share the vocabulary previously learned through give-and-take and card-matching |
Explore This Topic: What is the answer to algebra with pizzazz page 127? yours forever by? and The Incompetent Bullfighter by Gordon Bluddy. What is the answers to algebra with pizzazz worksheet page 155?
The answers to Middle School Math with Pizzazz Book PPB17 can be found in the teacher's edition. This allows teachers provide the most accurate information to students while helping them better understand the |
"... Abstract ..."
Abstracté inequalities. 1. Introduction and |
Product Description
The Algebra II book includes 220 activities that will challenge your students and give them the practice needed for confidence, competence, and mastery of algebra word problems at this level. Includes detailed solutions and practical hints based on the author's years of experience teaching algebra to students of all ages and abilities. Reproducible for single-classroom use. Foolproof problem-solving strategies, instruction, and guided practice |
The PPST Mathematics test measures those mathematical skills and concepts that an educated adult might need. Many of the problems require the integration of multiple skills to achieve a solution. This test covers several types of questions, and several types of math. Before you start reviewing math concepts, you should familiarize yourself with the test.
Order: These questions require an understanding of order among integers, fractions, and decimals.
Equivalence: These questions require an understanding that numbers can be represented in more than just one way.
Numeration and place value: These questions require an understanding of how numbers are named, place value, and order of value.
Number properties: These questions require an understanding of the properties of whole numbers.
Operation properties: These questions require an understanding of the properties (commutative, associative, and distributive) of the basic operations (addition, subtraction, multiplication, and division).
Computation: These questions require an ability to perform computations, change the result of a computation to fit the context of a problem, and recognize what is needed to solve a problem.
Estimation: These questions require an ability to estimate and to determine the validity of an estimate.
Ratio, proportion, and percent: These questions require an ability to solve problems dealing with ratio, proportion, and percent.
Numerical reasoning: These questions require the ability to interpret statements that use logical connectives or quantifiers, use reasoning to determine whether an argument is valid or invalid, and identify a generalization or an assumption.
Equations and inequalities: These questions require an ability to solve simple equations and inequalities and to guess the result of changing aspects of a problem.
Algorithmic thinking: These questions require an ability to understand an algorithmic view. In other words, you must follow procedure, understand different ways to solve a problem, identify or evaluate a procedure, and recognize patterns.
Patterns: These questions require an ability to understand patterns in data, including variation.
Algebraic representations: These questions require an ability to understand the relationship between verbal or symbolic expressions and graphical displays.
Algebraic reasoning: These questions require the ability to interpret statements that use logical connectives or quantifiers, use reasoning to determine whether an argument is valid or invalid, and identify a generalization or an assumption.
Geometric properties: These questions require an ability to use geometric properties and relationships in real-life applications.
The xy-coordinate plane: These questions require you to use coordinate geometry to represent geometric concepts.
Geometric reasoning: These questions require the ability to interpret statements that use logical connectives or quantifiers, use reasoning to determine whether an argument is valid or invalid, and identify a generalization or an assumption.
Systems of measurement: These questions require an ability to demonstrate basic understanding of the U.S. customary and metric systems of measurement. You should be able to convert from one unit to another and recognize correct units for making measurements.
Measurement: These questions require an ability to recognize the measurements needed to solve a problem. You must also be able to solve for area, volume, and length, including using formulas, estimation, and rates, and comparisons.
Data interpretation: These questions require an ability to read and interpret displays of information, including bar graphs, line graphs, pie charts, pictographs, tables, scatterplots, schedules, simple flowcharts, and diagrams. You must also have the ability to recognize relationships and understand statistics.
Data representation: These questions require an understanding of the correspondence between data sets and their graphical displays.
Trends and inferences: These questions require an ability to recognize, compare, contrast, and predict based on given information and an ability to make conclusions or inferences from given data. |
terça-feira, 28 de maio de 2013
This book emanated primarily from concerns that the mathematical capabilities of young children continue to receive inadequate attention in both the research and instructional arenas. Research over many years has revealed that young children have sophisticated mathematical minds and a natural eagerness to engage in a range of mathematical activities. As the chapters in this book attest, current research is showing that young children are developing complex mathematical knowledge and abstract reasoning a good deal earlier than previously thought. A range of studies in prior to school and early school settings indicate that young learners do possess cognitive capacities which, with appropriately designed and implemented learning experiences, can enable forms of reasoning not typically seen in the early years. Although there is a large and coherent body of research on individual content domains such as counting and arithmetic, there have been remarkably few studies that have attempted to describe characteristics of structural development in young students' mathematics. Collectively, the chapters highlight the importance of providing more exciting, relevant, and challenging 21st century mathematics learning for our young students. The chapters provide a broad scope in their topics and approaches to advancing young children's mathematical learning. They incorporate studies that highlight the importance of pattern and structure across the curriculum, studies that target particular content such as statistics, early algebra, and beginning number, and studies that consider how technology and other tools can facilitate early mathematical development. Reconceptualising the professional learning of teachers in promoting young children's mathematics, including a consideration of the role of play, is also addressed.
sábado, 28 de julho de 2012
The Mathematical Collage has been written to meet an Associate Degree general education requirement of a mathematics course with a Beginning Algebra prerequisite. The text shows that mathematics is alive in today's world and helps students see the beauty and power of mathematics. Its contents consists of chapters on the lore of numbers, finance matters, measurement geometry and trigonometry, probability and statistics, and math in sports, It also includes Mathematical Excursions, short trips into various areas where mathematics is used, such as math and the tourist, math and the internet, math and voting, math and nursing, math and the automobile, math and cooking, math and the angler, math and the World Series of Poker.
quinta-feira, 26 de julho de 2012
It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.
This volume is concerned with the alignment between the way the mathematical performance of students is assessed and the reform agenda in school mathematics. The chapters in this book have been prepared to raise a set of issues that scholars are addressing during this period of transition from traditional schooling practices toward the reform vision of school mathematics. Chapters are: (1) "Issues Related to the Development of an Authentic Assessment System for School Mathematics" (T. A. Romberg and L. D. Wilson), (2) "A Framework for Authentic Assessment in Mathematics" (S. P. Lajoie), (3) "Sources of Assessment Information for Instructional Guidance in Mathematics" (E. A. Silver and P. A. Kenney), (4) "Assessment: No Change without Problems" (J. De Lange), (5) "The Invalidity of Standardized Testing for Measuring Mathematics Achievement" (R. E. Stake), (6) "Assessment Nets: An Alternative Approach to Assessment in Mathematics Achievement" (M. Wilson), and (7) "Connecting Visions of Authentic Assessment to the Realities of Educational Practice
Contents
Preface vii
1 Issues Related to the Development of an Authentic Assessment System for School Mathematics
THOMAS A. ROMBERG AND LINDA D. WILSON
This volume, a reprinting of a classic first published in 1952, presents detailed discussions of 26 curves or families of curves, and 17 analytic systems of curves. For each curve the author provides a historical note, a sketch or sketches, a description of the curve, a discussion of pertinent facts, and a bibliography. Depending upon the curve, the discussion may cover defining equations, relationships with other curves (identities, derivatives, integrals), series representations, metrical properties, properties of tangents and normals, applications of the curve in physical or statistical sciences, and other relevant information. The curves described range from the familiar conic sections and trigonometric functions through the less well known Deltoid, Kieroid and Witch of Agnesi. Curve related systems described include envelopes, evolutes and pedal curves. A section on curve sketching in the coordinate plane is included.
domingo, 1 de julho de 2012
A survey of math for liberal arts majors. This book is a survey of contemporary mathematical topics: voting theory, weighted voting, fair division, graph theory, scheduling, growth models, finance math, statistics, and historical counting systems. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation.
The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. |
Book Description: Aimed at effectively delivering the 2008 framework, the Pupil Books are packed with functional maths questions and spreads and ensure progression by providing differentiated material for each level. Year 8 Pupil Book 2 is fully levelled with built-in progression helping students to move easily from level 5 to level 6 and beyond. This Pupil Book: * Guarantees progression with colour-coded levelling and level boosters to help pupils work at the right level and progress with ease. * Enables pupils to develop vital functional skills and put maths into context with the help of the integrated functional maths questions and exciting real-world spreads. * Promotes personalised learning and self assessment using pupil-friendly learning objectives for every chapter. * Eases the class into understanding new concepts with worked examples. * Stretches and challenges the knowledge and skills of pupils using extension activities. * Provides rigorous maths practice with the hundreds of levelled questions. * Captures pupils' attention using the colourful design. * See the Teacher's Pack for more support and |
In this book we generate graphic images using the software Mathematica thus providing a gentle and enjoyable introduction to this rather technical software and its graphic capabilities. The programs we use for generating these graphics are easily adaptable to many variations. These graphic images are enhanced by introducing a variety of different... more...
Presents an introduction to MuPAD - a modern Computer Algebra System. This book shows how we can use it in various areas of mathematics. It devotes a chapter to the graphical visualization of mathematical concepts. It is a resource for conducting workshops on using Computer Algebra Systems to explore and visualize mathematical concepts. more...
Introduces the reader to Mathematica's various approximate numbers, their arithmetic and the common numerical analysis operations such as numerical integration, root-finding, equation solving, minimization, and differential equation solving. This resource is useful for practitioners, professionals, and researchers. more...
The presentation of this book is on the comprehensible application of techniques for the approximation of the mathematical problems that are frequently observed in physical sciences, engineering technology and mathematical physics. The acceptance of the technique for the solution has been justified from mathematical point of view. The Software required... more...
This multi-author contributed proceedings volume contains recent advances in several areas of Computational and Applied Mathematics. Each review is written by well known leaders of Computational and Applied Mathematics. The book gives a comprehensive account of a variety of topics including - Efficient Global Methods for the Numerical Solution of Nonlinear... more...
The principal aim of this book is to introduce university level
mathematics both algebra and calculus. The text is suitable for
first and second year students. It treats the material in depth, and
thus can also be of interest to beginning graduate students. more...
Maple... more... |
This course follows on from FE & RM Part I. We will consider portfolio optimization, risk management and some advanced examples of derivatives pricing that draw from structured credit, real options and energy derivatives. We will also cast a critical eye on how financial models are used in practice.
In this course you will simulate prices of financial assets, use the Black-Scholes model to price European or Asian options, compute the Value-at-Risk of a bank and model financial time series with GARCH processes. The approach is hands-on with a strong emphasis on practical simulations that you will program, run and explore in your own computer.
"Monte Carlo methods in finance" will be offered on Iversity, starting 20 January 2014..
Mathematical Methods for Quantitative Finance covers topics from calculus and linear algebra that are fundamental for the study of mathematical finance. Students successfully completing this course will be mathematically well prepared to study quantitative finance at the graduate level.
The course will give you the tools with which to understand and predict market phenomena. A large dose of real-world applications will be provided along the way. These applications illustrate the power and relevance of underlying microeconomic theory while providing you a valuable opportunity to put the theory into practice. |
'Many students find that the obligatory Statistics course comes as a shock. The set textbook is difficult, the curriculum is...
see more
' applet displays boxplots of independent random samples drawn from 4 populations and an ANOVA table for the comparison of...
see more
This applet displays boxplots of independent random samples drawn from 4 populations and an ANOVA table for the comparison of the population means. The user can adjust sliders to change the means and standard deviations of the populations. As this happens, new samples are chosen and the boxplots and ANOVA table are updated. The applet includes a pie graph that shows the proportions of within and between group variation and a graph of the F distribution displaying the area corresponding to the p-value. These are also updated as the samples change is a free textbook from BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is suitable for...
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This is a free textbook from BookBoon.'Blast into Math! A fun and rigorous introduction to pure mathematics, is suitable for both students and a general audience interested in learning what pure mathematics is all about. Pure mathematics is presented in a friendly, accessible, and nonetheless rigorous style. Definitions, theorems, and proofs are accompanied by creative analogies and illustrations to convey the meaning and intuition behind the abstract math. The key to reading and understanding this book is doing the exercises. You don't need much background for the first few chapters, but the material builds upon itself, and if you don't do the exercises, eventually you'll have trouble understanding. The book begins by introducing fundamental concepts in logic and continues on to set theory and basic topics in number theory. The sixth chapter shows how we can change our mathematical perspective by writing numbers in bases other than the usual base 10. The last chapter introduces analysis. Readers will be both challenged and encouraged. A parallel is drawn between the process of working through the book and the process of mathematics research. If you read this book and do all the exercises, you will not only learn how to prove theorems, you'll also experience what mathematics research is like: exciting, challenging, and fun!' |
Math 155 is a liberal arts mathematics
class that is intellectually challenging without being too technical. This
course is designed for students NOT planning to major in the sciences or
a technical field.
Prerequisite:
None
Objective:
To explore the mathematical ideas and
their applications.
Description:
This course covers a variety of traditional
and nontraditional topics in mathematics. Historical development,
generalizations to mathematical theory and applications to real life are
components of each topic. Typically a course covers four to five
of the following topics: mathematics of finance, probability and
statistics, geometry, logic, set theory, number systems, algebraic modeling,
and problem solving.
Typical Text:
Using and Understanding Mathematics
* by Bennett and Briggs *Check with instructor before
purchasing text.
Availability:
Multiple sections of this class are taught
in the fall and spring. One section is also taught in the summer. |
The =EQUALS= club
library includes short booklets 36-72 pages, with explanations, worked examples,
the logic (and ill-logic) of the critical thinking behind the subject.
Help videos accompany the booklets (and programming) and yes, most importantly,
the spreadsheet work is included for each booklet. The spreadsheet not
only includes worked examples, but instructions on how to do the work yourself,
at your own pace.
The math profession
is inundated with the mandate, "Make things relevant". It's not as easy as
it sounds - and at the same time, it's very easy. Take a topic like
mortgage payments. There's actually an incredible amount of math involved
here. But as important is learning how to set up the logic of the
situation. And in doing so, you come upon a situation, "How do I find the
answer to this?" In one example, it's a geometric series that confronts
you. And rather than learn how to find the sum of a geometric sequence,
and then figure out where to apply it, the application gives rise to the need!
Of course, there
are many times this is good - and many times, it's good to have all that
knowledge in one's back pocket!
And more are in the
works. Electricity. Magnetism. The Pendulum.
Buoyancy. Flight. Radar. Colors. Temperature.
Electron Orbits. Steamships.
If you - or your company - is
interested, let's talk about creating a booklet on what you do. Trust me, it
does not matter what it is, we can use Excel to create a very interesting,
educational, fun booklet! But don't take my word for it. If you're at all
interested, let's talk! |
Elementary Algebra - 5th edition
Summary: Algebra can be like a foreign language, but ELEMENTARY ALGEBRA, 5E, gives you the tools and practice you need to fully understand the language of algebra and the ''why'' behind problem solving. Using Strategy and Why explanations in worked examples and a six-step problem solving strategy, ELEMENTARY ALGEBRA, 5E, will guide you through an integrated learning process that will expand your reasoning abilities as it teaches you how to read, write, and think mathematically. Feel confident...show more about your skills through additional practice in the text and Enhanced WebAssign. With ELEMENTARY ALGEBRA, 5E, algebra will make sense because it is not just about the x...it's also about the WHY |
Objectives: This course provides a comprehensive introduction to
the standard numerical techniques commonly used in obtaining solutions to
engineering problems. The availability of powerful software packages which
provide convenient implementations of these methods does not eliminate the
need for a thorough understanding of principles and practice. An informed
choice of method is often required to match a particular application at
hand, and it is sometimes useful to be able to customize methods. While
it is obviously possible to use a software package without knowledge of
its technical basis, this is a risky business with numerical methods since
unexpected and seemingly inexpicable problems can, and do, occur. Acquiring
an in-depth working knowledge of numerical computation using Matlab software
is a secondary objective of the course.
This book is useful unless you are already a Matlab guru or hate learning
software from a text, rather than on the fly [a personal choice].
Access to Matlab software is essential.
Two options are possible (one cheap and one expensive). Matlab is available
on campus unix servers and may be accessed by dial-in from home after installing
XWindows software, a licence for which can be purchased
from the CHIP (cost $20). Alternatively Matlab software may be purchased
from Mathworks,
or various other sources, but it is expensive. A student
version of Matlab is available to purchase for $99US. Further information
about on campus resources can be found on the IST matlab site.
Calculator
Some kind of calculator [NO RESTRICTION] is required for doing tests and
the exam.
Outline: Most
of the topics are covered in the text, with some re-arrangement and omission
according to time constraints. Lecture notes will also be provided throughout
the course as well as being posted in pdf format on the website for reference.
After some preliminary material on numerical computation, errors, precision,
and matlab, the five main course units will be: I. Linear algebra II. Root-finding
and non-linear systems III. Curve-fitting and interpolation IV. Numerical
differentiation and quadrature V. Integration of differential equations.
Within this general outline we may adjust the detailed topics as we go along.
Details and text references will be provided on the course webpage. Continuous
feedback during the course is particularly welcome and helpful. By the way....if
you're a little rusty on linear algebra you might like to get up to speed
by reviewing it asap, before we start Unit I.
Grading Scheme: Assignments (0%) + Tests (3@15%) + Final exam (55%)
Assignments. Suggested problems will be assigned and posted on
this site. You can get help with these in the tutorials, from TAs, or from
me. The first line for efficient communication is email, and especially
the course listserv which is a great resource for communal discussion. Solutions
can be handed in at any time to a TA to get feedback. Solutions to all homework
problems will be posted on the course webpage at appropriate times. Try
them before looking at the solutions!
Tests. Questions will: (i) test your knowledge of the material
presented in the lectures or assigned text topics, with an emphasis on understanding
the concepts, not formal proofs; (ii) test your mastery of the techniques,
as required to solve the assignment problems (at least one test problem
will be very similar, if not the same as an assigned problem). Sophisticated
Matlab syntax and programming will not be tested, but a good basic working
knowledge of Matlab as you should acquire from doing the assignments will
be assumed in the tests. Consequently, it is in your interest
to make absolutely sure you understand and can do all the assigned problems
and get help if you are having trouble. Learning this material is an experiential
process and cramming for tests is definitely not a feasible numerical method
for success. [Your benefit in terms of marks for assignments is indirect
since you should do better on the tests if you can do them.] Test solutions
will be posted.
Final Exam. The exam will include questions based on all course
units (0 to V). As for the tests, problems will focus on: (a) theoretical
knowledge - understanding of the methods and issues etc. (b) calculation
skills - [limited] application of the methods in hand-solution, and (c)
practical problems - homework assignments, practical implementation of algorithms,
knowledge of Matlab use, and so on. |
Problem Solving Approach to Mathematics for Elementary School Teachers, A (11th Edition)
9780321756664
ISBN:
0321756665
Edition: 11 Pub Date: 2012 Publisher: Addison Wesley
Summary: This is the leading textbook for students learning how to teach mathematics to elementary school students, focusing on problem solving. It remains current with its discussion of standards in teaching today and it teaches students the value of professional development for their future careers. It encourages active learning and provides many exercises, study tools and opportunities for active learning. Students will ga...in valuable insight into how they can apply their mathematics and teaching knowledge in the classroom. We offer many high quality discounted mathematics textbooks to buy or rent by semester.
Rick Billstein is the author of Problem Solving Approach to Mathematics for Elementary School Teachers, A (11th Edition), published 2012 under ISBN 9780321756664 and 0321756665. Four hundred seventy nine Problem Solving Approach to Mathematics for Elementary School Teachers, A (11th Edition) textbooks are available for sale on ValoreBooks.com, one hundred seventeen used from the cheapest price of $86.41 2nd day shipping available, ships same or next business day. Get bombed!!This is the U.S. stud [more]
ALTERNATE EDITION: This is a loose-leaf edition text book (same content, just cheaper!!). 2nd day shipping available, ships same or next business day. Get bombed!!This is the U.S. student edition as pictured. [less] |
iLearn Math
iPASS stands for an "Individual Prescription for Achieving State Standards," which reflects two of its most important features:
It is prescriptive at a very detailed level. Instruction is matched to the specific concept and skill deficits of individual students.
It is mastery-based. Students achieve mastery of each standard as a prerequisite for progress through the program.
It is a fully automated, web-based math curriculum and instruction system that provides individualized instruction to meet the identified needs of each student while freeing up the teacher to monitor and facilitate learning on a one-to-one basis. It provides the following functions without requiring teacher intervention:
All pre- and post-assessment
Placement
Original instruction
Systematic practice
Review
In addition, iPass incorporates course management, progress reporting, and teacher support in a tightly integrated system aligned with state standards.
The curriculum is designed for Math Intervention in Grades 3 through High School. It provides an efficient yet comprehensive coverage of content in Grades 1 through Algebra II. It is highly aligned with the NCTM Focal Points and the recommendations of the National Math Advisory Panel and covers all the core concepts necessary for success in elementary grades, middle grades as well as Algebra or Integrated Math in High School. |
Introductory Calculus
Revised: November 2006
Course Description
Main topics include derivatives of functions of one variable; an introduction to integration
of functions of one variable; and applications of derivatives and integrals. Calculator:
A TI-83 or TI-83+ graphing calculator is required for this course.
Objectives
1. To provide students with a working knowledge of the fundamental concepts and
techniques of differential and integral calculus of algebraic functions of one variable. 2. To provide students experience with applications of these techniques and use
of technology in solving real world problems. 3. To enhance student's problem solving skills; 4. To emphasize algebraic, numerical, geometric, and verbal approaches to calculus
concepts. |
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for which problem would u like to prefer laplace transfprm over differential equation? |
Introductory and Intermediate Algebra for College Students - With 2 CDS - 3rd edition
Summary: TheBlitzer Algebra Seriescombines Equations and Inequ...show morealities in One Variable; Linear Equations in Two Variables; Systems of Linear Equations; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Basics of Functions; Inequalities and Problem Solving. MARKET: for all readers interested in20.21 +$3.99 s/h
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TrigonometryALCULATE THIS: TRIGONOMETRY JUST GOT A LOT EASIER TO LEARN!Now anyone with an interest in basic, practical trigonometry can master it -- without formal training, unlimited time, or a genius IQ. In "Trigonometry Demystified, best-selling author Stan Gibilisco provides a fun, effective, and totally painless way to learn the fundamentals and general concepts of trigonometry. With "Trigonometry Demystified you master the subject one simple step at a time -- at your own speed. Unlike most books on trigonometry, this book uses prose and illustration... MOREs to describe the concepts where others leave you pondering abstract symbology. This unique self-teaching guide offers questions at the end of each chapter and section to pinpoint weaknesses, and a 100-question final exam to reinforce the entire book. Simple enough for beginners but challenging enough for professional enrichment, "Trigonometry Demystified is your direct route to learning or brushing up on trigonometry. Learn all aspects of trigonometry: * How angles are expressed * The relationships between angles and distances * Calculating distances based on parallax * Coordinate systems and navigation * And much more! Text provides a totally painless way to learn the fundamentals and general concepts of trigonometry. Uses prose and illustrations to describe the concepts, offers questions at the end of each chapter and section, and includes a 100-question self-test. Softcover.
Stan Gibilisco is one of McGraw-Hillís most diverse and best-selling authors. His clear, friendly, easy-to-read writing style makes his electronics titles accessible to a wide audience and his background in mathematics and research make him an ideal handbook editor. He is the author of The TAB Encyclopedia of Electronics for Technicians and Hobbyists Teach Yourself Electricity and Electronics, and The Illustrated Dictionary of Electronics. Booklist named his book, The McGraw-Hill Encyclopedia of Personal Computing, one of the Best References of 1996. |
Addendum to Course Description
Intended Outcomes for the course
Upon the successful completion of this course students will be able to:
Formulate, interpret, and apply mathematical concepts especially, techniques for computing sets, graphs and trees, recursive definitions, and discrete probability in real world contexts.
Use analytical problem solving strategies to solve problems using multiple approaches and to interpret the results in practical terms.
Utilize those techniques in discrete mathematics and logic that are used in the study and practice of computer science.
Be successful in subsequent coursework in the mathematical foundation of Computer Science.
Course Activities and Design
Outcome Assessment Strategies
Assessment must include:
1. At least two in-class proctored examinations, one of which may be the final exam, and
2. At least two of the following additional measures, where at least one includes writing:
Course Content (Themes, Concepts, Issues and Skills)
Perform traversals of graphs and trees; construct simple functions by composition of known functions; determine whether simple functions are injective, surjective, or bijective; and classify simple functions by rate of growth.
Describe the concepts of countable and uncountable sets, and apply the diagonalization method to construct elements that are not in certain countable sets.
Construct inductive definitions for sets, construct grammars for languages (sets of strings), and construct recursive definitions for functions and procedures.
Determine whether a binary relation is reflexive, symmetric, or transitive and construct closures with respect to these properties.
Construct a topological sort of a partially ordered set and determine whether a partially ordered set is well-founded.
Use elementary counting techniques to count simple finite structures that are either ordered or unordered, to count the worst case number of comparisons and, with discrete probability, to count the average number of comparisons for simple decision trees.
Find closed form solutions for simple recurrences using the techniques of substitution, cancellation, and generating functions.
Demonstrate standard proof techniques and the technique of inductive proof by writing short informal proofs about simple properties of numbers, sets, and ordered structures. |
Practice the math skills you'll need for success in other college courses and in your daily life with COLLEGE ALGEBRA, the textbook that has helped hundreds of thousands of students excel in the algebra course. Over 400 worked examples include authors' notes, which explain the steps involved in the problem-solving process. Review Exercises, Chapter Summaries, and Chapter Tests help you assess your strengths and weaknesses and prepare for quizzes and exams. Chapter 9, "The Mathematics of Finance," is especially helpful for business majors, with its coverage of present value, sinking funds, simple and compound interest, and amortization. Icons in COLLEGE ALGEBRA guide you to CengageNOW, an effective online tool that diagnoses areas were you need extra help and provides you with a Personalized Study plan. Need more help? A live online tutor with a copy of your textbook is just a click away232.95
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Think Without Ink% - Delhi
Features of this book Important arithmetic terms and definitions Lucid explanation of terminologies Glossary of arithmetic numbers Comparative study o ...
Features of this book Important arithmetic terms and definitions Lucid explanation of terminologies Glossary of arithmetic numbers Comparative study of mathematical properties Understanding explanation of basic arithmetic A guide for preparing competitive examinations Clearly an enchanting arithmetic book for further studies Mathematics is an important subject without which we cannot imagine the modern world of science and technology. In mathematics, arithmetic is the back bone of mathematical sciences. Here we deal with some basic concepts of arithmetic and their applications which you will also feel enchanting and make more interesting to read a lot. written by K. Venkataraman |
When you apply to grad school, recommendation letters are the most important. It doesn't really matter whether those courses are official, as long as you learn what you need and leave a good impression to your professors.
I used to think that that there was something that happened in a classroom that could never be replicated by reading a book. However, I find that I was wrong. I really do enjoy talking to the professors and other people who like math, but at the end of the day I just want to learn.
A book and the internet is all you need to learn really
user19161
5:26 AM
@Eric Yes, I learn most things by myself. The lectures were a waste of time.
@JasonBourne Ok well can you at least answer this: What is the official language of the country you live in? If the place you live in is not recognized as it's own country, the what is the language used in daily life of the are you live in?
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields.Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.
that book is basically undergrad topology with a lean towards manifolds
I think I understand the expansion/contraction part here, but the explanations of how Cl measures failure of UF seems way too crude (namely: if |Cl|=1, then UFD, if |Cl|>1, then not UFD; this test measures only the bare minimum there is to say about failure of UF), or unsatisfactorily indirect (diophantine equation solutions).
@Eric Since you ask me so much about books, I will give you the list I think is the best. Read Cohn's Classic Algebra, Basic Algebra, and Further Algebra; Rudin's Mathematical Analysis, Real and Complex Analysis, and Functional Analysis; Lee's Topological Manifolds, Smooth Manifolds, and Riemannian Manifolds. That is a total of 9 books to last all the way from first year undergrad to second year grad.
Most of the math courses I am currently taking in university are packed with students from China, Hong Kong and Korea. They do seem to be extremely hard working and disciplined, and seem indeed to be good with doing fast calculations. I also met a Chinese woman recently doing her master's degree ...
Generally, the asians who have migrated to US/Europe are the ones who have been largely successful in their home country. So, when Americans see the Asian population, they mainly see the hand-picked lot so to say. Its ridiculous to compare a good hand-picked lot as opposed to random lot.
@JasonBourne I don't care what people do with Terence Tao as long as people do not ping him and bother him too much.
user19161
First, race is largely a cultural instead of biological classification.
@skullpatrol Intelligence in a conventional setting is a very complex symptom of genetics, upbringing, exposure, health during infancy and pre-infancy etc. Relegating it to only genes is an insult to all the other factors that have contributed to it.
I have a quick question: Is $A\neq B$ considered to be the negation of $A=B$? As in, does it mean "A is not equal to B in at least one case"? Or does it mean "A is never ever ever not equal to B"? Here, A and B can be functions of some variable.
like if A=5 and B=3, then we have $5 \neq 3$. But if A and B are functions of time t, say .. then there only needs to be one moment, e.g. t=3 when $A(3) \neq B(3)$ - they could be equal everywhere else - for $A \neq B$ to hold |
Product Details
A Guide to Advanced Linear Algebra by Steven H. Weintraub
This book provides a rigourous and thorough development of linear algebra at an advanced level, and is directed at graduate students and professional mathematicians. It approaches linear algebra from an algebraic point of view, but its selection of topics is governed not only for their importance in linear lagebra itself, but also for their applications throughout mathematics. Students in algebra, analysis, and topology will find much of interest and use to them. The careful treatment and breadth of subject matter will make this book a valuable reference for mathematicians throughout their professional lives. |
Its unique programmed approach patiently presents the mathematics in a step-by-step fashion together with a wealth of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. Both students and professionals alike will find this book a very effective learning tool and reference.
Partial Differentiation
Application of Partial Differentiation
Polar Coordinates
Double and Triple Integrals
Differentials and Line Integrals
Vector Integration
Curvilinear Coordinates
Surface and Volume Integrals
Vectors
Vector Differentiation |
Creating interactive models in Mathematica allows students to explore hard-to-understand concepts, test theories, and quickly gain a deeper understanding of the materials being taught firsthand. This screencast shows you how get started creating interactive models in Mathematica. Includes Chinese audio.
When working in Mathematica, you will often find it useful to view groups of functions that relate to a specific subject area or set of tasks. The Documentation Center includes guide pages and the function navigator for this purpose. Learn more in this "How to" screencast. Includes Japanese audio.
Mathematica provides several convenient ways to find information about functions. In addition to searching the documentation or navigating the guide pages, you can access documentation on functions directly from within your notebook. Learn more in this "How to" screencast. Includes Japanese audio.
Mathematica can run its calculations on other computers that have Mathematica installed. Passing computations to other, potentially more powerful, machines can increase the efficiency of your work. Learn more in this "How to" screencast. Includes Japanese audio.
Mathematica offers great flexibility for adding text to graphics; you can add text interactively using the Drawing Tools palette or programmatically using various graphics primitives. Learn more in this "How to" screencast. Includes Japanese audio.
Palettes give you immediate access to many features built into Mathematica, from creating syntactically complete expressions and inserting special characters to building up charts and slide shows, all through a convenient point-and-click interface. Learn more in this "How to" screencast. Includes Japanese audio.
Mathematica allows Greek letters to be integrated into symbol names, strings, graphics, and text. You can input Greek letters by using palettes or keyboard shortcuts. Learn more in this "How to" screencast. Includes Japanese audio.
You may want to export data from Mathematica to a spreadsheet. Excel is one example of a common spreadsheet format that Mathematica supports. Learn more in this "How to" screencast. Includes Japanese audio.
Geophysics professor Frank Scherbaum walks through an example of how he used Mathematica to develop an integrated system for students, teachers, and researchers to use in their probabilistic seismic hazard analysis work. Includes Spanish audio.
Geophysics professor Frank Scherbaum walks through an example of how he used Mathematica to develop an integrated system for students, teachers, and researchers to use in their probabilistic seismic hazard analysis work. Includes Japanese audio.
This screencast helps you get started using Mathematica by introducing some of the most basic concepts, including entering input, understanding the anatomy of functions, working with data and matrix operations, and finding functions. Includes Spanish audio.
Mathematica gives students the power to manipulate interactive graphics and develop complex data models. High-school teacher Abby Brown shares the success she experiences by using Mathematica in her classroom. Includes Spanish audio.
William Meyer, the vice president of technology at Scattering Solutions, LLC, describes an example of using Mathematica's data-analysis capabilities to save time and money on drug screening. Includes Japanese audio.
This video features John Kiehl, co-owner of Soundtrack Recording Studio, who shares an example of Mathematica using powerful set theory and pattern-matching capabilities to make and produce music. Includes Japanese audio. |
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Fundamental Number Theory with Applications
Edition:
2
Publisher:
Chapman & Hall/CRC
Number of Pages:
368
Price:
94.95
ISBN:
9781420066593
Number theory has an important role in many branches of mathematics and in computer science, and even appears at times in physics and chemistry. Having a fundamental knowledge in this area will be fruitful for scientists in above mentioned areas. The book under review tries to provide such fundamental knowledge of number theory with its applications, mainly in computer science.
All chapters of the book have lots of boxed parts including bibliographies related to the mathematical subjects, which this makes the book very interesting for studying. These bibliographies are very useful, particularly for the historical background.
The first chapter includes fundamental topics like finite continued fractions and Fibonacci numbers, and basic theorems like Wilson's theorem, Fermat's theorem and the Chinese remainder theorem. The author introduces and proves these facts in terms of divisibility (without using the notion of congruence). The chapter also covers Lamé's theorem and Thue's theorem, which are seldom seen them in other texts on fundamental number theory. Following this process, in chapter two, which deals with congruences, Mollin studies some primality tests and gives an introduction in cryptography. The third chapter, on primitive roots, includes an introduction to the interesting topic of random number generation and discusses further topics in cryptography. In chapter four, on quadratic residues, Mollin also discusses algorithms for factoring.
Chapter five is about simple continued fractions and uses them to analyze rational approximations of irrational numbers. The author goes briefly back to factoring in this chapter again. Then he studies Pell's equation, which is a Diophantine equation; a more precise study of these equations is the subject of last chapter.
The author tries to indicate some recent improvements briefly, in appendixes at the end of book. He focuses especially on the ABC conjecture, which has some consequences for Diophantine equations, and he studies the AKS algorithm, which is a primality test with polynomial running time. I think these are very useful for students to make them familiar with recent advances.
All of the chapters have good exercises, both numerical and theorical; and the reader will find the solutions of the odd-numbered ones at the end of book.
The book under review is a good text for undergraduates, suitable for a course in one semester or an extended course for two semesters, and it can be used in some courses in computer science as well.
Mehdi Hassani is a co-tutelle Ph.D. student in Mathematics in the Institute for Advanced Studies in Basic Science in Zanjan, Iran, and the Université de Bordeaux I, under supervision of the professors M.M. Shahshahani and J-M. Deshouillers. |
Hi All, I am in need of aid on factoring, graphing parabolas, matrices and graphing circles. Since I am a beginner to College Algebra, I really want to learn the bedrocks of Algebra 2 completely. Can anyone recommend the best resource with which I can begin reading the basics? I have a midterm next week.
I understand your problem because I had the same issues when I went to high school. I was very weak in math, especially in vertex calculator and my grades were bad confident that you will find it helpful too.
I have tried out quite a lot of software. I would without any doubt say that Algebrator has assisted me to come to grips with my difficulties on graphing function, relations and binomials. All I did was to just key in the problem. The response showed up almost instantaneously showing all the steps to the result. It was quite simple to follow. I have relied on this for my algebra classes to figure out Intermediate algebra and Basic Math. I would highly recommend you to try out Algebrator.
I am so pleased to hear that there is hope for me. I really appreciate it. Why did I not think about this? I would like to start on this immediately . How can I purchase this program? Please give me the particulars of where and how I can get this program.
I remember having often faced problems with solving a triangle, logarithms and powers. A truly great piece of math program is Algebrator software. By simply typing in a problem from workbook a step by step solution would appear by a click on Solve. I have used it through many algebra classes – Basic Math, Basic Math and Algebra 2. I greatly recommend the program. |
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