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an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises. |
Basic College Mathematics - With CD - 3rd edition
ISBN13:978-0131868366 ISBN10: 0131868365 This edition has also been released as: ISBN13: 978-0131868359 ISBN10: 0131868357
Summary: The engaging Martin-Gay workbook series presents a user readers' perception of math by exposing them to real-life situations through graphs a...show morend applications and ensures that readers have an organized, integrated learning system at their fingertips. The integrated learning resources program features book-specific supplements including Martin-Gay's acclaimed tutorial videotapes, CD videos, and MathPro 5. This book covers topics such as multiplying and dividing fractions, decimals, ratios and proportion, percent, geometry, statistics and probability, as well as an introduction to algebra. For anyone who wishing to brush up on their basic mathematical skills. ...show less2.93 +$3.99 s/h
Acceptable
Blue Cloud Books Phoenix, AZ
Blue Cloud Books ??? Hot deals from the land of the sun.
$2.9393 |
Trevor Doyle
**REAL TEACHER TAUGHT LESSONS**
Algebra
This algebra course teaches basic number operations, variables and their applications. Gain a fundamental sense of equations, inequalities and their solutions. This course offers 11 full chapters with 6-8 lessons each chapter that present short easy to...
**REAL TEACHER TAUGHT LESSONS**
Pre-Algebra
This course teaches students to expand number sense to understand, perform operations, and solve problems with rational numbers. Pre-Algebra is taken by students as a first introduction to the concepts and skills needed to be successful in Algebra... |
The mission of Oak Mountain High School is to create an
atmosphere of excellence where all students are encouraged to achieve their academic,
creative, and physical potential through dynamic instructional methods,
extracurricular experiences, and relationships among students, staff,
parents, and the community.
Course Description:††††††††††††
††††††††††††††† Precalculus
is a college-preparatory course, which is required for the Advanced Academic
Diploma.† This course will prepare
students for future studies in calculus and college mathematics.† The textbook to be used is Precalculus-Enhanced with
Graphing Utilities by Prentice Hall Publishers.† Many topics introduced in Algebra II with
Trig are studied more extensively in precalculus.† There is emphasis on graphing functions and
relations from the equation, polynomial theory, conics, logarithms, vectors,
matrices, exponential equations, and limits.†
A more complete study of the unit circle and trigonometry is
undertaken as well as many topics from calculus.†
Supplies:
††††††††††††††† Three ring
binder, loose leaf paper, pencils, Scientific Calculator (TI-83 or TI-89)I
will not be providing any calculators for student use.† It is the responsibility of the student to
make sure that he or she brings a calculator on a daily basis to this
class.† If a student shows up to a test
without a calculator, he/she will not be provided one by the teacher.
Assessments:
††††††††††††††† Tests and quizzes:†
We will test each Friday and the concepts covered for the week. The
students will be told the topics to be covered on the test.† Tests will be given on either Wednesday or
Friday of each week.† Make-up sessions
for missed tests will be given when a student makes arrangements for the test
with me.† Tests can be completed from
3:00-4:00 in the afternoon or 7:00-7:30 during the mornings.†† It is the studentís responsibility to make
sure that any missed test is made up within the specified time limits.†
If a test is not made-up within
one week of the original test date, a zero will be given.†
††††††††††††††† Assignments:†
Student assignments will be graded for both completeness and
accuracy.† Homework is a necessity. The curriculum is challenging and
fast-paced.† This class is intended to
get students prepared for AP Calculus AB and BC.† Therefore, the workload in this class is
demanding.† Homework will be assigned
daily and the resulting practice is most important to success in the course.† Homework assignments will be discussed
before they are taken for a grade.†
Homework
must be completed on the same sheet with the studentís notes.† If homework is turned in without notes, no credit will be given for
the assignment.† Homework checks will
be done daily.† Any
assignment that is not turned in on the due date will result in a zero unless
it is excused through the office.† Sharing work
with another student or using another studentís work as his/her own will
result in a zero on the assignment and the reporting of the student to the
administration and necessary honor societies.
Attendance Policy:
††††††††††††††† Absences:†
Each student has two days to bring an excuse for days absent.† Students will have two days per absence to
complete missed work.† No work will be
made up for unexcused absences.†
Honors students will often be involved in
academic & extra-curricular field trips & school business
activities.† However, too many absences
of any type are detrimental to successful performance in honors classes where
the pace of the class is faster in order to prepare students for the next
level of demanding mathematics.†
Parents & students are asked to be selective in their requests for
absences & consider the following:
Any
class work missed must be made up to the teacherís specifications and timeline
Field
trips and school business activities can be separated into those
required by the curriculum (i.e. band & athletics) and non-essential
activities
Students
must take responsibility for their choices.† A
student should have gotten the notes from a fellow student and attempted
to understand the material when a lesson is missed before coming to get
help. Understand that when you make a decision to be absent that the
teacher does not become your personal tutor.† The teacher will assist you in getting
work made up within the same before or after school times afforded other
students.
Parents should encourage their children
to be balanced in their activities & academics and not become overly
committed
Class Procedures:
**Students will be expected to take notes and write down all
example problems presented on the board. Homework must be completed on the
same sheet with the studentís notes.†
If homework is turned in without notes, no credit will be given for
the assignment.†
Students will have opportunities to present problems from homework
assignments or work examples presented in class for extra credit points.† Students are responsible for retrieving
their graded assignments from the side counter on a daily basis.† The trays will be cleaned on a weekly
basis, and the teacher is not responsible for any assignments that the
student leaves in the trays, which may get discarded.† Major tests will not be placed in the
trays.† Students will receive these on
an individual basis.† Once the student
has had the opportunity to see his/her grade, the tests will then be
collected by the teacher and filed in the studentís personal file for future reference.
Bring Your Own
Device Policy:
Students will be allowed to bring electronic devices (ipad, phone,
etc.)† to honors precalculus to be used
for mathematical educational purposes (calculator, graphing app, notes...)
only.† Students will not be allowed to
use these devices in honors precalculus to work on assignments for other
classes or to use them for noneducational purposes (texting, phone calls,
emails, gaming, social networkingÖ).†
If a student becomes defiant about directives given concerning digital
use or uses the device for means other than mathematical educational
purposes, the consequences could range from a Class I to Class III violation.† ABSOLUTELY NO USE OF ELECTRONIC DEVICES ON TEST DAYS. †
Class Rules:
††††††††††††††† 1.† Be in class on time and
in your seat when the bell rings.†
††††††††††††††† 4.† BE RESPECTFUL AT ALL
TIMES.† You will be expected to do the
following:
†††† †††††††††††††††† †a. Do not disturb other students (this
includes talking at inappropriate times)
††††† ††††††††††††††† †b. Talk only with the teacher's permission -
only one person may talk at a time
††††† ††††††††††††††† †c. Raise your hand when wishing to ask a
question or make a comment
††††† ††††††††††††††† †d. Be attentive and on assigned task
††††† ††††††††††††††† †e. Be cooperative with your teacher and
classmates
††††† ††††††††††††††† †f.†
Refrain from sleeping (sleeping is head on desk or eyes closed)
††††† ††††††††††††††† †g. Listen and follow directions at all times
††††† ††††††††††††††† †h. Refrain from using foul language
††††††††††††††† 5.† ABSOLUTELY NO CHEATING IS ACCEPTABLE.† Cheating includes letting someone copy your
††††††††††††††††††††† work, as well as
copying someone else's work or sharing answers in any form.
††††††††††††††† 6.† Food, drinks, candy, gum, or backpacks are
not allowed in the classroom.
7.† Abide by all school and county rules.
*We will work from bell
to bell.† No
student is to gather around the door before the teacher dismisses the class. A detention will be assigned for
this behavior.
Consequences for
Inappropriate Behavior:
††††††††††††††† 1.† Verbal
warning
††††††††††††††† 2.† Written warning/conference and a parent
note sent home
This is the official web
site of the Shelby County Board of Education. Any other site that claims to
be affiliated with, represent or contain information about any Shelby
County School is not endorsed by the Shelby County Board of Education. If
you leave the official Shelby County Board of Education web site, the
Shelby County School District claims no responsibility for the content
beyond this point. |
First Steps for Math Olympians: Using the American Mathematics Competitions (Problem Books) (MAA Problem Book Series)
Book Description: Any high school student preparing for the American Mathematics Competitions should get their hands on a copy of this book! A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions (AMC) have been given for more than fifty years to millions of high school students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone taking the AMC exams or helping students prepare for them will find many useful ideas here. But people generally interested in logical problem solving should also find the problems and their solutions interesting. This book will promote interest in mathematics by providing students with the tools to attack problems that occur on mathematical problem-solving exams, and specifically to level the playing field for those who do not have access to the enrichment programs that are common at the top academic high schools. The book can be used either for self-study or to give people who want to help students prepare for mathematics exams easy access to topic-oriented material and samples of problems based on that material. This is useful for teachers who want to hold special sessions for students, but it is equally valuable for parents who have children with mathematical interest and ability. As students' problem solving abilities improve, they will be able to comprehend more difficult concepts requiring greater mathematical ingenuity. They will be taking their first steps towards becoming math Olympians! |
COMPLETE HOMESCHOOL KIT INTERMEDIATE MATH GRADE 3
Price:$103.50 Available Qty: 2
Qty:
COMPLETE HOMESCHOOL KIT INTERMEDIATE MATH GRADE 3 Written by Stephen Hake, author of the Saxon Middle Grades program, Math Intermediate 3 is ideal for students looking for a textbook approach that provides a smooth transition into Math 5/4. It is also helpful for students who are coming to Saxon from other programs. Math Intermediate 3 teaches mathematical concepts through informative lessons, helpful diagrams, and interactive activities and investigations. |
Enables teacher to add a question for which the numeric data in the question is selected randomly from a dataset generated by Moodle ISU.
Calculated multichoice
Similar to Calculated question type except that students have a correct solution to choose from in a list of options/possible answers. A formula can also be provided to calculate the correct result.
Calculated simple
A simple version of Calculated question type.
Embedded answers
Allows for the creation of a question with various answers within it, including multiple choice, short answers and numeric answers. Currently Moodle ISU does not have a graphical interface for creating Embedded question.
Essay
Essay question type allows students to enter short answers with multiple paragraphs.
Matching Question
The Matching question offers students a list of possibilities to select from.
Multiple Choice
Multiple choice allows selection of single or multiple responses to a question.
Numerical
Allows numerical responses with units. It also allows to set tolerances for the numerical answers.
Short answer
Allows student responses of a few words which can be matched to various possibilities. It allows usage of wildcards to do the comparisons.
True/False
Multiple choice question with answer containing boolean values.
Description
Not a question but description/instruction that appears as students move to different parts of the quiz.
Calculated
Calculated questions offer a way to create individual numerical questions by the use of wildcards that are substituted with individual values when the quiz is taken.
Calculated Multichoice
Calculated multichoice is similar to calculated question and the settings are similar. The main difference is that students have multiple choice for the answer. The answers could be embedded into the text that appears in the choices. For example, if the question is "What is the correct area of a triangle with base = {b} cm and height = {h} cm?" you could put in the choice text box which says …{={x}+..}... something like "The correct area is {=.5*{b}*{h}}". Moodle ISU 2 will generate random numbers from the dataset and substitute {b} and {h} with numbers; and for those values Moodle ISU 2 will generate correct answers in the multiple choice.
For explanation of the other settings available please refer to Calculated question type in this handout.
Simple Calculated Question
Simple calculated question is similar to Calculated question but has easier control for defining the dataset for Moodle ISU to generate numbers randomly.
Embedded Answers Question (Cloze)
Embedded answers question allows teachers to create questions within the body of the text itself. It allows multiple choice, short answers and numerical answers question. As of now, during the creation of this document, there is not any graphical interface to create embedded questions.
Numerical Embedded Questions
Numerical embedded questions allow students to enter their numerical answer in a text box. It is not much different from a short answer question from the student's view; it is different only in that it allows tolerance for answer.
eg.{1:NUMERICAL:=25.8:0.1#Correct~%50%25.8:1:#Close answer}
So if a student types 25.9 as the answer and submits the quiz then he gets full credit for the answer because the tolerance has been set to 0.1. But if he answers 26 then the student only gets half of the total credit. Any answer below 24.8 and above 26.8 does not get any credit.
Essay Question
Essay question allows students to type their response in a few lines. It could also be used for few paragraph responses however, ITRC does not recommend it for long essay questions due to user's login session related issues for security. Therefore, the better choice for longer responses might be to have the students submit a file in the Assignment tool.
Matching Question
Matching question can also be created with Embedded Question type, but Matching Question type is easy to configure if you do not like using wild-cards to create questions.
Multiple Choice
Offers a list of possible answers for students so that they can select one or more correct answers from the list.
Numerical Question
Numerical question allows students to enter numerical answers to questions with or without units. It is different from the calculated question in that it does not create questions on the fly but allows tolerance for numerical response.
Short Answer Question
Short answer question allows students to answer questions in words or phrases. ITRC recommends that the answer be as precise and short as possible. The answers from the students are matched against the possible answer models. In order for the answer to be correct there should be at least one match. The answer could be case sensitive or insensitive.
True/False
True/False question type allows student to select true if the statement proposed in question is valid and False if it is not.
Choose Wildcards Dataset Properties
Each wildcard needs to have a dataset from which it can take a value. In this section you will see all the wildcards used in your question.
Mandatory Wildcards Preset in Answers
This section consists of the wildcards you used in your formula to calculate the solution. Beside each wildcard is a drop down list that consists of two options.
will use the same existing private dataset as before: This option is present even if you create a calculated question for the first time. It just means that Moodle has created a possible dataset already for this question and it is private, i.e. not shared with other questions in the same category.
will use a new share dataset: This will create a dataset and share it with other questions in the category. It can save time if you have similar questions in the category. |
Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse
Ouellette shows how she learned to apply calculus to everything from gas mileage to dieting, proving that even the mathematically challenged can ...Show synopsisOuellette shows how she learned to apply calculus to everything from gas mileage to dieting, proving that even the mathematically challenged can learn the fundamentals of the universal language.Hide synopsis
Description:Very Good. 0143117378 Has some shelf wear, highlighting,...Very Good. 0143117378 |
In this calculus activity, 12th graders determine the areas bounded by curves and the volume of the solids of revolution. The two page activity contains a combination of ten multiple choice and free response questions and is to be used without a calculator. Solutions are not provided.
In this calculus worksheet, students solve functions using the derivatives. They calculate the volume where the graph is revolving around the x-axis, a line, the y-axis and where x=e. There are 28 questions.
In this calculus learning exercise, learners solve 17 multiple choice problems. Students find limits, summations, and derivatives of functions. Learners find the area of an enclosed region between two curves.
In this calculus worksheet, students observe the graph the function and identify the interval as increasing or decreasing. They identify the critical points and perform integration. There are 4 questions.
Here is a high-level, interractive presentation on calculus for your high schoolers. Parametric equations, derivatives, functions, and the Pythagorean Theorem are all part of this fine PowerPoint. Additionally, two interesting photographs of Mark Twain's homes begin the slideshow.
Students apply the Fundamental Theorem of Calculus. For this calculus lesson, students identify the graphical connections between functions and accumulation functions. They use a TI to represent the functions.
Students graph different functions and observe the slope of the tangent line. In this calculus lesson, students identify the slope and critical points on a graph. They use the TI calculator to provide a visual of the graph.
In this methods of applied mathematics worksheet, students solve 5 various types of problems that relate to variational calculus equations. First, they determine a second order differential equation for the geodesic. Then, students write down Euler Lagrange equations for 2 dependent variables, and then determine a system of first order differential equations describing motion of an object.
In this methods of applied mathematics worksheet, students solve 6 different types of problems related to variational calculus. First, they determine the first integrals of the Euler-Lagrange equations corresponding to the optimizations of each functional. Then, they determine the solution to a brachistochrone problem for bead moving between 2 different points and sketch their solution.
In this calculus practice exam, students select the best answer to 28 multiple choice questions. Questions cover information from the entire year of calculus. A suggested time limit of 55 minutes is included.
In this calculus worksheet, students are provided with a translation of a scene from the Simpsons in which the teacher solves a calculus problem. Students explain if her solution is correct. The one page worksheet contains two questions. Answers are not included.
For this calculus worksheet, students solve a variety of problems. They use trigonometric identities to solve problems, find the ratio of areas inscribed in polygons, solve functions, determine the graphs of functions, solve inequalities, and determine the equation of lines. This three-page worksheet contains 36 multi-step problems |
This course will not satisfy the general elective category for students who entered their program or study in or after the 2007 Fall semester.
Basic Algebra is considered a developmental course. A comprehensive departmental final examination is included in this course.
VI. Catalog Course Description
This is an introductory course in Algebra. Topics include operations with numerical and algebraic expressions, including rational and radical expressions, factoring, and graphing. Study skills are also emphasized.
VII. Required Course Content and Direction
Learning Goals:
Course Specific:
The student will be able to:
add, subtract, multiply, and divide signed numbers.
simplify algebraic expressions by distributive property and combining like terms.
solve linear equations and use linear equations to solve applications.
Planned Sequence of Topics and/or Learning Activities:
Solving of linear equations, inequalities, and quadratic equations by factoring
Properties and operations with radical expressions
Introduction to graphing of linear equations and slope concepts
Solving of applications using linear and quadratic equations
Assessment Methods for Core Learning Goals:
All Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.
Assessment Methods for Core Learning Goals:
Reference, Resource, or Learning Materials to be used by Students:
There is a departmentally selected textbook. Details on other materials provided by the instructor of each course section. See course format. Student notebook is required and a calculator is optional. |
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One of my favorite topics, matrix. This site is use full at giving the basics on how to multiply and the rules of...
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Comment:
One of my favorite topics, matrix. This site is use full at giving the basics on how to multiply and the rules of multiplying matrix's. I like how it highlights the equation inputs with the outputs making it easier to remember the steps to be taken. This method was used in the class with my Finite math professor. He was able to explain and illustrate this method and make it easy for us to re-identify it on our examinations.Technical Remarks:This site is very short. Easy to get to and definitely easy to use.
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After browsing the Merlot website for at least 30 minutes, I came across to this website. It educates us about Matrix...
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After browsing the Merlot website for at least 30 minutes, I came across to this website. It educates us about Matrix Multiplication that I have studied in my finite mathematics class. Multiplying matrices are really easy, but when u get the concept. It also can be tricky if you do not know how to solve it the right way. This website gives us more information on how to multiply matrices together. First, it tells us to multiply a row matrix with a column matrix of the same length. It also shows us an example on how to work through a matrices problem. I spent a few hours in understanding the material from this website and compared it to how I understood in my finite mathematics class. This is an excellent website because it has visuals, if you are not an English speaker you can still understand the concept by looking at the visuals. I think that Merlot has some great information that can educate us and help us understanding the material better. At last I would like to say that, this is a great resource for the students who have trouble understanding the concept of Matrix Multiplication.
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I spent about 15 minutes reviewing and testing my knowledge on this webpage and thought this was one of the better sites I've...
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I spent about 15 minutes reviewing and testing my knowledge on this webpage and thought this was one of the better sites I've discovered on MERLOT. The site is a brief introduction to multiplying matrices and the concepts were clear, easy to follow and the material is presented with simple explanations and excellent visuals. This site would have made my life a lot easier when I was learning matrix multiplication. This website would definitely be effective in enhancing a student's learning because it was interactive, making solving the application easy to follow and the visual highlights reinforce the material. First time users will find the software easy to use because its straightforward and very user-friendly.
Author:
Elaine Aguilar
(Student)
Date Added:
Apr 13, 2008 |
V63.0140.4: Linear Algebra
Linear algebra is an essential tool for every scientist, engineer, economist, statistician, and mathematician. It is also useful for computer scientists and countless other numerical sciences. Linear problems are often the simplest models of the natural world that can be made, and arise in literally thousands of applications. Complexity can arise because large numbers of variables can be involved. With the rise in electronic computing power, huge linear algebra problems can be solved, and these can be used to model very complicated situations in the real world. In fact, the desire to solve such problems has driven computing technology. In this course you will learn the language, concepts, and techniques, from the ground up. You will also learn how to visualize geometrically, and manipulate abstract ideas which may not be visualizable.
Lectures
SILV 507, Tuesday and Thursday, 6:20pm – 8:10pm. 110 mins, with 5–10 min break to get up and stretch! Attendance of lecture is important: there will often be activities such as worksheets which you will do in pairs or small groups. These will allow you to grapple with concepts and explain them to each other. For students lying on grade boundaries I will take lecture participation into account.
Required book
Linear Algebra and its Applications, 3rd Edition by David C. Lay, available at NYU Bookstore, Amazon, etc. (about $108). You may find the paperback Study Guide useful too. If the bookstore is sold out, or if you want to see what the Study Guide is like, you can get the first chapter for free at This website also has review notes.
Web-site
Check blackboard website.
Homework
11 problem sets, almost all from the book, to be handed in at start of Thursday lectures. Permission to hand in late must be obtained from me the previous week, and otherwise, unless you have a doctor's note or there are exceptional circumstances, late homework will not be counted in your grade. However you should still do HW even if late, since it forms an essential part of the learning process. Your lowest two HW scores will be dropped, so this allows you leeway.
Collaboration
I encourage you to study in groups. Get to know others in class. If you have no-one to study with, I can help you find someone. However you must write up homework in your own words, and understand what you write. Plagiarism (in homework or in exams) is a serious offense (see NYU CAS Academic Policies).
Exams and Grades
There will be 1 midterm and 1 final (dates given on below). There will also be about 4 quizzes, whose dates I will announce a week in advance, and which will happen during the last 30 minutes of lecture. Your lowest quiz grade will be dropped. Your overall grade will be determined using:
homework 25%, quizzes 20%, midterm 25%, final 30%.
The grades will not be curved. After the midterm I will settle on and announce a fixed grade boundary scheme.
Office Hours: Tuesday 4-5pm, and Wednesday 2-3pm (rm 926 WWH).
Tutoring
Free math help has historically been available 4 days a week on a drop-in basis at rm 704 WWH. Hours were 1pm–8pm Mon+Wed, 11am–8pm Tues+Thurs. Tutors may vary in their knowledge of linear algebra. However I don't know if the room has changed or if this is offered this year. Details to follow. . . |
The purpose of this course is develop mathematical content fundamental for success in Algebra and higher-level mathematics courses. The course will cover the five strands ( Algebraic Thinking; Data Analysis and Probability; Geometry and Spatial Sense; Measurement; Number Sense, Concepts, and Operations )of the Sunshine State Standards, the Pinellas County Schools Student Expectations and the Grade Level Expectations for mathematics.
My goal for this year is to help students realize through work and effort that they can be successful with learning Pre-Algebra. We will be using the Grencoe Pre-Algebra text, which is an excellent tool in learning the needed skills of Pre-Algebra. There will be DAILY assignments and it is REALLY important that students stay on schedule, that way students will understand classroom activities and assignments each day.
Expectations:
* When the bell rings be in your seat prepared to begin class with the necessary materials and homework out ready to grade and discuss, OTHER WISE. you will be considered TARDY. Start working on warm-up asssignment when posted in class.
* Pay attention in class. Raise your hand to be called upon to ask questions or make a comment. Do not shout out answers or comments in class without being prompted. Take notes as needed and concentrate during explanations of math skills. Do not talk or cause any disruptions that detract from other student's learning.
Hall Passes
Each student will receive two hall passes per marking period for my classroom. Bathroom/drink breaks will not be permitted during the first 10 minutes or the last 10 minutes of class; these needs should be addressed during passing time. Students must have their agenda signed and sign out on the room sign-out sheet prior to leaving the classroom.
* Use class time wisely. Stay on task, whether in group work or individual work. Sleeping, head on desk, eating, chewing gum, or drinks are not allowed.
*Teacher to parent/guardian communications with a "PS." (stamped or written) MUST be signed and returned the following day. Failure to do so will result in a detention.
* YOU ARE RESPONSIBLE FOR YOUR OWN LEARNING. You will have homework each night. Always ask questions and get help on materials you do not understand. Don't wait until you feel overwhelmed. When you are absent it is YOUR responsibility to make up homework. It is really difficult to catch up once you are behind. DON'T GET BEHIND!
REQUIRED SUPPLIES:
(6) Three pronged folders with two pockets to be used in Math class only. One for each marking period.
Agenda Math Folder (3 pronged folder for the correct marking period) which you will be required to keep neatly organized throughout each grading period. Paper Pencils DEAR reading book. (Students must have one in their backpacks at all times!)
Folder Organization
In the center in the page protector sheets you should have: a signed copy (signed and dated by student and parent) of the Course Information Sheet a signed copy of the class expectation sheet a signed copy of the math pledge
The first three items will be moved to the new folder each marking period. These items should always be found in the current math folder to receive credit towards your folder grade.
The front pocket is for class notes, class work and bell work. All work needs to be dated and put into date order.
The back pocket is for homework, tests, quizzes, and vocabulary. All work needs to be dated and filed by date order.
HOMEWORK:
1. Homework will be assigned almost every day and should be done in PENCIL only. 2. Parent's FULL signature should be in the UPPER LEFT corner of the homework and it will be randomly checked. PLEASE do not sign homework that is incomplete or does not have the proper heading with student's name at the right upper corner.
The following heading must be in the top right corner:
First and Last Name Period # Date Assigned Top line label with Page number & Problem #'s (or worksheet title)
3. Homework assignments will be (a) given verbally; (b) posted on the homework board by the end of the day and will remain there all week. 4. Homework will be checked daily for completeness. NO CREDIT will be given, and 2 demerits will be earned, unless there is EVIDENCE that ALL problems have been attempted and ALL work has been shown as modeled in class. 5. Homework must be turned in at the beginning of class to be counted as "on time." If for any reason a student does not have homework to turn in, they should write a note explaining why and turn it in instead of the assignment. Homework not turned in on time will receive two demerits. Homework that does not have a parent/guardian signature will receive one demerit. To get full credit you must turn it in when it is due and attempt/show work for all problems. Partial credit will not be given for homework. Late homework will not be accepted (unless an "excused" absence) for credit. You are expected to hand in the homework that is due the day you are absent on the day you return to school. You must make arrangements to stay after school within a week to take a test or quiz if you are absent on the day it is given to the class. 6. It is each student's responsibility to find out what was missed when absent and to make up that work in the time allotted in the student handbook. Students who miss class due to a prearranged trip, field trip, meeting, etc. are required to get all assignments PRIOR to the missed class or, if they are on campus, are expected to come by to check the homework board in the classroom. While students with an excused absence are entitled to extra days to have missed assignments completed and checked, it is advisable to use whatever means possible when absent to avoid falling behind. This policy does not apply to long-term projects. 7. Assignments with due dates and grades will be available on Parent Connect. Grades will be posted once the assignment has been reviewed. Most will be on a timely basis, but that could be a couple days up to a week. The turnaround on grades will vary depending on the assignment. Please be patient, I do not hand back papers until the entire class has handed in the work. If student's work is late so am I.
8. Late Work /No Signature Passes
For the first and second six week marking all students will be given one late work pass and one no signature pass per marking period for my class. This does not excuse the assignment! On the day the homework is due, students opting to use the pass should hand it in with their name on it and the reason the assignment was not turned in on time. The assignment will earn full credit only if it is turned in the following school day. Students using a pass, who turn in the assignment the following day, will not earn demerits.
GRADING:
1. ALL GRADED ITEMS MUST BE RETURNED WITH A PARENT SIGNATURE THE FOLLOWING DAY AFTER THEY HAVE BEEN RETURNED TO THE STUDENT. FAILURE TO DO SO WILL RESULT IN A DEMERIT FOR EACH DAY UNTIL THE ITEM IS RETURNED WITH A PARENT SIGNATURE.
2. Quizzes may be given at regular intervals in each chapter and be announced in advance. Periodically, a quiz may be given without notice.
3. There will be a full period test at the end of each chapter/unit that will also include items in previous chapters that the classes had difficulty with and have been reviewed. Additional time will not be given unless arranged prior to test date.
4. Math folders will be collected periodically with advance notice given and will be worth 40 - 60 points.
5. Students MUST have their own calculator for use on quizzes and tests (with a few PREARRANGED exceptions). If a student does not have his or her own calculator to use, a 5 POINT PENALTY may be deducted from their final test score (2 points deducted from quiz grades).
6. There will be additional grades from in-class activities and projects.
7. Grades are figured on a weighted point system and include all graded items: tests, quizzes, class work, homework, projects, and group work.
8. The State of Florida/Pinellas County Grading Scale will be used:
A = 90 - 100 B = 80 - 89 C = 70 - 79 D = 60 - 69 F = below 60
CHEATING:
The submitting of work that is actually the work of another person is considered cheating and will be dealt with according to policy in the agenda. IF a student is unsure as to when collaboration is permitted on any given assignment, please see the teacher for clarification. The Madeira Beach Fundamental handbook is located in the front of the agenda.
I am looking forward to working with you and your parents. Please contact me if you have any questions or concerns regarding your child's progress in class. When you provide me with a parent email address I will send out notes regularly and I will also provide you with a breakdown on your student's progress. If anyone is interested in volunteering in our class please fill out a volunteer form and contact me as we can always use help in the classroom. The best way to reach me is by email -- my address: derolloy@pcsb.org Also, you may call the school and leave a message for me at 727-547-7697 and I will return your call as soon as I am able.
o What to bring to my math class o Where to find my assignments o How I am expected to do my homework o What to do if I get stuck on homework o How I am expected to behave in class o Where to go for help o That all fundamental guidelines apply (dress code, gum, tardiness, absences, grading, demerits…etc.)
As a parent I understand: o What my child needs to bring to school each day o How to check their homework o That my student will get demerits for incomplete work or no parent signatures on homework as well as detentions for unsigned parent communication o Where to find grades and class updates o The purpose behind Math Memos and that they are due each Monday o That all fundamental guidelines apply (dress code, gum, tardiness, absences, grading, demerits…etc.) |
v1 2Y01 Cambridge IGCSEMathematics (US) 0444 3 Syllabus ref Learning objectives Suggested teaching activities Learning resources particular case is about an area or a volume as the problems can be about 3D
v1 2Y01 Cambridge IGCSEMathematics (US) (0444) 3 Syllabus ref Learning objectives Suggested teaching activities Learning resources students to sort by a rule like all the statements where 'a' has a coefficient of
Instructions on IGCSE Examination Timetable JUNE 2013. ... books and notes, and they can talk to each other. However, they must not have any access to telephones, mobile phones, ... • Mathematics without Coursework Paper 12 - Core: 0580/12: 1h:
Edexcel IGCSEMathematics (4400) Grade Boundaries ... Notes '(R)' papers are 'International' papers, sat by overseas candidates. These are of the same standard as 'Home' papers and may be used for practice.
IGCSEMathematics is a fully examined course which encourages the development of mathematical knowledge as a key life skill, and as a basis for more advanced study. The syllabus aims to build students' confidence by helping them develop a feel
2 Cambridge IGCSE International Mathematics 0607. Examination in June and November 2013. 1. Introduction 1.1 Why choose Cambridge? University of Cambridge International Examinations (CIE) is the world's largest provider of international
Cambridge International Mathematics (IGCSE) syllabus is designed as a two-year course for examination at age 16-plus. The aims of this syllabus should enable students to: ... Core curriculum Notes Link within syllabus 3.1 Notation Domain and range Mapping diagrams domain is o unless stated
IGCSEMathematics – Statistics ... A teacher notes the number of correct answers given by a class on a multiple-chore test 10 20 30 40 41 50 Correct answers Frequency (i) Estimate the mean (iii) What is the modal class? Another class took the same test.
Notes: Postal address: You were enrolled by: Where did you hear about Brainline? ... Physical science (not accepted by universities on IGCSE) Mathematics Biology Biology Economics Geography History Mathematics (if taken with Biology) Accounting Business studies
IGCSE/GCSE /GCE EXAMINATIONS MAY/JUNE 2014 PLEASE OBSERVE STARTING TIME FOR EVERY EXAM EXAMS IN THE OLD HALL – SEE NOTES FOR EXCEPTIONS • Morning exams start 10:00 both for CIE and AQA if there are no other exams in the morning session; |
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics.
This lesson teaches students how to graph equations on the coordinate plane. The 'x' and 'y' coordinates are presented along with the concept of an ordered pair. This information is used to teach students how to set up a table of values to plot graphs of functions. Grades 8-12. 39 minutes on DVD.
Customer Reviews for Algebra 2 Tutor: Graphing Equations DVD
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Introductory Physics With Algebra Mastering Problem-solving
9780471762508
ISBN:
0471762504
Pub Date: 2006 Publisher: Wiley & Sons, Incorporated, John
Summary: Get a better grade in Physics! Physics may be challenging, but with training and practice you can come out of your physics class with the grade you want! With Stuart Loucks' Introductory Physics with Algebra as a Second Languagea?: Mastering Problem-Solving, you'll get the practice and training you need to better understand fundamental principles, build confidence, and solve problems. Here's how you can get a better ...grade in physics: Understand the basic language of physics Introductory Physics with Algebra as a Second Languagea? will help you make sense of your textbook and class notes so that you can use them more effectively. The text explains key topics in algebra-based physics in clear, easy-to-understand language. Break problems down into simple steps Introductory Physics with Algebra as a Second Languagea? teaches you to recognize details that tell you how to begin new problems. You will learn how to effectively organize the information, decide on the correct equations, and ultimately solve the problem. Learn how to tackle unfamiliar physics problems Stuart Loucks coaches you in the fundamental concepts and approaches needed to set up and solve the major problem types. As you learn how to deal with these kinds of problems, you will be better equipped to tackle problems you have never seen before. Improve your problem-solving skills You'll learn timesaving problem-solving strategies that will help you focus your efforts and avoid potential pitfalls.
Loucks, Stuart E. is the author of Introductory Physics With Algebra Mastering Problem-solving, published 2006 under ISBN 9780471762508 and 0471762504. Two hundred thirty five Introductory Physics With Algebra Mastering Problem-solving textbooks are available for sale on ValoreBooks.com, one hundred used from the cheapest price of $48.52, or buy new starting at $49.20 |
This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational... more...
The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be... more...
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the... more... |
Homework Helpers Pre-calculus
9781564149404
1564149404
Summary: The book pays particular attention to strategies for understanding and constructing logical arguments and proofs. Common patterns that reappear in many proofs are highlighted. In addition, geometry problems that review arithmetic and algebraic skills are presented and fully explained. Homework Helpers: Pre-Calculus is a straightforward, understandable, and thorough review of the topics in a typical pre-calculus class..., including: - Linear functions - Polynomials - Rational functions - Exponential functions - Logarithmic functions - Systems of equations
Szecsei, Denise is the author of Homework Helpers Pre-calculus, published 2007 under ISBN 9781564149404 and 1564149404. Two hundred twenty six Homework Helpers Pre-calculus textbooks are available for sale on ValoreBooks.com, one hundred seventeen used from the cheapest price of $0.01, or buy new starting at $8 |
Developmental Mathematics Basic Mathematics and Algebra
9780321506429
ISBN:
0321506421
Pub Date: 2007 Publisher: Pearson Addison Wesley
Summary: Lial's Developmental Mathematics gives students ...effective design with many exercises and applications to enhance comprehension of basic mathematics and algebra.
Lial, Margaret L. is the author of Developmental Mathematics Basic Mathematics and Algebra, published 2007 under ISBN 9780321506429 and 0321506421. Twenty six Developmental Mathematics Basic Mathematics and Algebra textbooks are available for sale on ValoreBooks.com, fourteen used from the cheapest price of $2.44, or buy new starting at $80.91 |
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Starting at $82 accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks. |
High School Pre-Calculus Tutor
9780878919109
ISBN:
0878919104
Publisher: Research & Education Assn
Summary: Algebra * Biology * Chemistry * Earth Science Geometry * Physics * Pre-Algebra * Pre-Calculus * Probability Trigonometry * Math Skills for SAT * Verbal Skills for SAT "With the Tutor Books, it's Easy to learn difficult subjects." The best help in preparing for homework and exams Includes every type of problem that may be assigned by your teacher or given on a test Guides you by working out problems in step-by-step de...tail Each "Tutor" helps you understand the subject fully, no matter which textbook you use.
Fogiel, M. is the author of High School Pre-Calculus Tutor, published under ISBN 9780878919109 and 0878919104. Twenty seven High School Pre-Calculus Tutor textbooks are available for sale on ValoreBooks.com, twenty five used from the cheapest price of $0.01, or buy new starting at $12.46Soft cover may have a little wear along edges and/or may have some indentations, slight creasing or corner curl, though the text pages are good to very good. Book is GOOD with [more]
Soft cover may have a little wear along edges and/or may have some indentations, slight creasing or corner curl, though the text pages are good to very good. Book is GOOD with average wear to cover and pages. We offer a no-hassle guarantee on all our items. Orders generally ship by the next business day. Default Text.[less] |
This course is designed to give students a mathematically sound introduction to algebra. The student is given the opportunity to develop fundamental algebraic skills and concepts based on the structure of the system of real numbers, such as equations, inequalities, problem solving, polynomials, factoring, graphs and functions, simultaneous equations, irrational numbers, square roots, relations, functions, and variations. Because graphing activities are integrated throughout classroom presentations and textbook activities, a graphing calculator is required for this course. The TI-83 or TI-83 Plus are the recommended calculators. |
This popular Physical Chemistry text book is now available in electronic format. We have preserved much of the material of the former hard copy editions, making changes to improve understanding of the concepts in addition to including some of the recent discoveries in physical chemistry. Many chapters have new sections and the coverage of several chapters has been greatly expanded. The chapter on statistical mechanics, 15, has been completely rewritten.
The eBook has also been divided into smaller modules that are appropriate for specific courses in Physical Chemistry.
Easy to use Clebsch-Gordan coefficient solver for adding two angular momentums in Quantum Mechanics. This tool is created for my Quantum Mechanics II course offered by Dr. Thompson in Summer of 2007.
[Instruction]
Execute "GUI.m" script by invoking "GUI".
Inspired by a discussion with my father on how to solve sudokus, I decided to implement a GUI for MATLAB and play around with automatic solving. The result can be found here: You can use the GUI just for playing sudoku and having an online check or you may turn on the solving aids: Display tooltips showing all valid numbers so far, or have a semiautomatic or a automatic solver which evaluates the logical constraints. On top of that, a branching algorithm is implemented, which solves any arbitrary sudoku very fast.
I set out to study ruby by creating a set of scripts, together called "Solver". Solver plays and creates sudoku puzzles. It uses a command line interface and reads or produces html files. It should be cross-platform (tested on MacOSX)..
Math Solver Free for Windows 8 is a handy tool for performing frequently used operations used for solving math problems. You can use this tool for solving quadratic equations or calculating the angles of a triangle.
The app also includes a unit converter and other useful tools for dealing with math problems by using your Windows 8 device.
Worksheet Generator for Chemistry is a handy and reliable software that helps you to easily and quickly create and customize your personal chemistry worksheets.
The application provides you with various exercise templates that allow you to adjust your worksheets. You are able to insert various chemistry exercises of different areas such as units and chemical formulae, thermochemistry, chemical kinetics, Redox reactions and organic chemistry. |
Nature of Problem Solving in Geometry and Probability - 04 edition
ISBN13:978-0534421489 ISBN10: 0534421482 This edition has also been released as: ISBN13: 978-0534421496 ISBN10: 0534421490
Summary: Liberal Arts mathematics books often cover much more material than can be addressed in a one-semester course. Karl Smith has created a solution to this problem with his new book: THE NATURE OF PROBLEM SOLVING IN GEOMETRY AND PROBABILITY. Loyal customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. Based on the successful NATURE OF MATHEMATICS text, this new book is designed to give ...show moreyou only the chapters and information you need, when you need it. Smith takes great care to provide insight into precisely what mathematics is--the nature of mathematics--what it can accomplish, and how it is pursued as a human enterprise. At the same time, Smith emphasizes Polya's problem-solving method throughout the text so students can take from the course an ability to estimate, calculate, and solve problems outside the classroom. Moreover, Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques.
Benefits:
The Book Companion Web site at includes section-by-section homework hints, projects, links to the World Wide Web, as well as a summary of essential ideas for that section.
"Group Research Projects" require collaborative research work and are suitable for larger-scale class projects.
Chapters are independent of one another and allow maximum teaching flexibility.
Chapter Summaries include important terms, types of problems, and a sample examination.
Historical Notes show mathematics as the result of both history and current research.
News Clips demonstrate mathematics in the media, and optional technology sections are included.
BCA Tutorial---Interactive tutorial software that's so sophisticated, it's simple! BCA Tutorial is browser-based, making it an intuitive mathematical guide even for students with little technological proficiency. BCA Tutorial allows students to work with real math notation in real time, providing instant analysis and feedback. The tracking program (built into the instructor's version) enables instructors to carefully monitor student progress.
In addition to robust tutorial services, your students also receive anytime, anywhere access to InfoTrac College Edition. This online library offers the full text of articles from almost 4000 scholarly and popular publications, updated daily and going back as much as 22 years. Both adopters and their students receive unlimited access for four months.
For your online and distance learning needs, WebTutor? Toolbox on WebCT and Blackboard can be packaged with this text! With WebTutor's text-specific, pre-formatted content and total flexibility, you can easily create and manage your own personal Web site!
Polya's method of problem solving is used throughout the text.
A chapter on set theory enables instructors the flexibility to cover this topic in more detail.
A chapter on networks and graph theory helps students see the applications of mathematics to logistical problems.
Sections on finite and infinite percents, binomial theorem, and binomial probabilities are included.
An innovative Prologue provides an overview of the history of mathematics. It asks the question, "Why study math?". An Epilogue shows how the material in the text relates to the natural sciences, social sciences, and the humanities. It also asks the question, "Why not study math?".
"In Your Own Words" problems provide students with practice in communicating the concepts they've learned.
Each chapter opener poses an "In the Real World" problem, and concludes with "Revisiting the Real World", which reviews a method for solving the problem. This structure motivates the chapter topic and provides a forum for review.
"Individual Research Projects" help students apply what they are learning to familiar situations. These projects require research or library work, further reinforcing the student's understanding of mathematical concepts in a variety of fields.
Euler Circuits and Hamiltonian Cycles. Trees and Minimum Spanning Trees. Topology and Fractals. Guest Essay: Chaos. Epilogue Why Not Math? Mathematics In The Natural Sciences, Social Sciences, And In The Humanities |
When You Purchase Thinkwell Video Math Courses Through the Co-op (for grades 6-12)
Introducing Thinkwell's Acclaimed Video Instruction
The Homeschool Buyers Co-op is pleased to present a the BEST DEAL ON THE PLANET for online video math courses from Thinkwell - the next-generation textbook. Put aside your boring textbooks and learn online from one of the best teachers in the country using Thinkwell's acclaimed online multimedia instruction!
Bring A Great Teacher math presenter is Dr. Edward Burger of Williams College, a top-ranked U.S. college. Dr. Burger is one of the great communicators in his field. HisChapter practice tests and chapter exams.
Worked out solutions to exercises with instant feedback.
Tracking of homework and chapter test results.
Website access of 12 months.
All Thinkwell math courses meet national standards and are in fact used in many accredited schools.
We have a limited number of subscriptions available, so tell your friends. If they buy, you'll earn BONUS SmartPoints:
Thinkwell's 6th grade math course is the perfect solution for any homeschool curriculum. It has thousands of interactive 6th grade math problems, but at the heart of it are our fun and effective video lessons.
Edward Burger is an award-winning teacher with a passion for teaching math, and he makes 6th grade math easy for every homeschool student. Created to work with any learning style, his homeschool video lessons are both fun and effective.
Thinkwell's 6's 7th grade math course is the perfect solution for any homeschool curriculum. It has thousands of interactive 7th grade math problems, but at the heart of it are our fun and effective video lessons.
Edward Burger is an award-winning teacher with a passion for teaching math, and he makes 67h grade math easy for every homeschool student. Created to work with any learning style, his homeschool video lessons are both fun and effective.
Thinkwell's 7 has built their Prealgebra course around hundreds of offerNote: Thinkwell says their Prealgebra course is "a college survey course suitable for students who have been through traditional 6th/7th/8th grade math courses but are still unprepared for Alegbra 1. The Thinkwell 6th/7th/8th grade course offered on this page provide a more detailed preparation for Algebra 1 for middle school students.
Students regularly complain that algebra has no bearing on their lives outside of class. Thinkwell's Algebra 1 (formerly "Intermediate Algebra") features video lectures that apply the material of the course to real-world problems and events, including determining the future value of investments or the duration of thunderstorms Algebra 2 (formerly "College Algebra") is built around a series of 261 include This version of this course does NOT include the "Test Bank,""Custom Website" or "Course Management Tools" features described in Thinkwell marketing materials. See Thinkwell FAQs for more information.
Thinkwell's Geometry course contains all of the geometry help your homeschool student needs. This complete online Geometry course is fun and easy to use; enjoyable and effective multimedia videos are the heart of the course. After watching a geometry video lesson, your students will review and practice with automatically graded exercises that give you an instant way to assess their progress, as well as with printable geometry worksheets with answer keys.
Videos feature award-winning teacher Edward Burger, whose multimedia video lessons have been created to work with any learning style. The course includes automatically graded exercises and tests, geometry practice worksheets, a geometry glossary (geometry dictionary) of geometry terms, at-a-glance grades and progress review, and our fun and interesting animated InteractivitiesNote: The Homeschool version of this course does NOT include the "Test Bank", "Custom Website" or "Course Management Tools" features described in Thinkwell marketing materials. See Thinkwell FAQs for more information.
About Thinkwell's Trigonometry Course: Thinkwell's Trigonometry is crafted around a series of 187 Calculus is built around a series of 277We asked Thinkwell what is the difference between "Thinkwell Calculus" and "Thinkwell Calculus compatible with AP", and they said, in a nutshell, "If you are going to take the AP exam, buy the AP version; otherwise, you are fine with the regular version."
We asked Thinkwell what is the difference between "Thinkwell Calculus" and "Thinkwell Calculus compatible with AP," and they said, in a nutshell, "If you are going to take the AP exam, buy the AP version; otherwise, you are fine with the regular version."We've used Thinkwell for a number of years now, starting with Pre-Algebra and going up to Algebra 2. We all love watching Professor Burger's video lectures. They are long enough to explain things well, and he is not only a great teacher but also very entertaining, which is a huge benefit when trying to learn topics such as linear functions! The content is very rich. My oldest son has just transitioned to our local Running Start program and is having no difficulty in math with this background. Because each course is created online, there isn't a...(more)
Becky, Co-op Member
I purchased Thinkwell College Algebra for my daughter to use this year and she has loved it! Ed Burger is a fun and engaging professor. The price of the course is less than purchasing a textbook, test booklet, and answer key for some of the more popular texts available, and Thinkwell includes a great teacher! We will definitely be purchasing more products from Thinkwell!
Stephanie B., Co-op Member
We were doing K12 prealgebra straight out of the textbook and my son hated it. We got Thinkwell's prealgebra and found the mini lectures and demos so useful. A good teacher showing the steps and explaining them clearly just works better for my son (and me!) than reading dry text from a book. We love thinkwell and it's quick assessments--all online so no CDs to mess with either. I tell everybody who asks about math programs on all my homeschooler lists.
R Hill, Co-op Member
For three years, our two sons have used Thinkwell's online math courses (Algebra I & II and Geometry). We absolutely love Thinkwell's math programs! Great teaching and instruction are contained in the videos as well as application of the various methods and formulas. The professor keeps the students engaged and challenged. Thinkwell's math programs allow my husband and I to keep our sons challenged in their math as they have now exceeded our level of learning in this area. The customer support for parents is outstanding as well. Thinkwell cont...(more)
Cindy Mc, Co-op Member
Since I started homeschooling 3 years ago, I felt I was killing my daughter's love of Math (she is gifted, while her sister is special needs, so I've left her to figure out Singapore Math on her own, which she managed well, but without any enthusiasm). Thinkwell is clear and interesting to her, she goes at her own pace. I check to see how she's doing and that she's completed it. For the placement, she was between 2 levels- if she weren't gifted I'd have gone to the easier level, but we went up instead, and its been a good challenge. She no l...(more)
Sarah Cavenaugh, Co-op Member
My son used Thinkwell math 7 this year. He appreciated being able to listening to a lecture with each lesson. Thinkwell has been an effective teaching tool for him. We will be using it again next year.
W. Miller, Co-op Member
Thinkwell Math is the best product out there for students headed into a math or science field in college. My son used Thinkwell Calculus, took the AP Calculus BC test, and scored a 5, allowing him to go directly into Calculus III in college. He loved Dr. Burger and learned so much from the course! My other children will be using it as well.
Linda in FL, Co-op Member
We have used Thinkwell Math for YEARS for the upper level maths and now use it from 6th grade to Calculus BC. Prof. Burger is hilarious and able to clearly teach concepts from the very simple to the absurdly complex. He adds little songs, funny demonstrations, and all kinds of interesting examples to make math fun. My kids who have taken the AP math tests have scored 5's, and Thinkwell has been excellent at preparing them for the tests. We are die-hard Thinkwell Math fans and have been happy to tell anyone looking for a math program to look ...(more)
Diana SEach lecture is clear, concise, and presented in an interesting and fun way. These engaging and thorough lectures help my son to learn to be much more attentive to details. The immediate grading of assignments, practice tests, tests, and exams provides my son with clear insight to how well he has learned the material.
My son used Thinkwell Pre-Calc last year, and is using Calc I & II this year. I believe this independent approach will equip my son for the demands of college. I have recommended this to others, and they are as well pleased. |
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Calculators in the Math Classroom Hello Fellow Math Teachers,
I have another survey question for you:
Do you allow calculators in your math class and why ?
I was shocked to see …
Math Notebooks Hello Fellow Math Teachers,
I have a survey question for you:
Do you require your students to maintain a math notebook and why?
I have taught …
Algebra Review I teach Algebra 1 in a middle school and I am looking for different ideas on how to review for a chapter test. My students need a lot of repetition and …
Assigning Variables to an Equation Not rated yet I teach Algebra I (Prentice Hall Text) and have a question. When you assess your students, do you require that that define variables before writing an … |
designed for grades 3–5 instruction and provides step-by-step mathematics lessons that incorporate the use of the TI-15 calculator throughout the learning process. The 30 lessons included present mathematics in a real-world context and cover each of the five strands: number and operations, geometry, algebra, measurement, and data analysis and probability. 248pp. plus Teacher Resource CD |
...
Show More standards as outlined in Crossroads in Mathematics. BEGINNING AND INTERMEDIATE ALGEBRA: THE LANGUAGE AND SYMBOLISM OF MATHEMATICS is oriented toward recent reforms in college level mathematics curricula |
Honors Geometry
Mr. Hartzer (Ms. Khalil) / Western International High School
Materials
Students are expected to maintain a binder for this class. The binder shall consist of five clearly separated and labeled sections: Warm-up activities, class notes, homework, quizzes/tests, and group/in-class work. This binder will be collected on a regular basis for review.
Students will be provided a calculator for in-class use. For this course, students will need access to a scientific calculator that provides basic trigonometric functions; during class, an appropriate calculator will be provided. For homework, students should note that such calculators are readily available online or as free cell phone apps, if an actual dedicated calculator is not available to them.
Students have been assigned books for use in both class and home, and are responsible for these books. |
Algebra Blocks This items very briefly describes the concept of factorization. Author(s): No creator set
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Health Assessment and Promotion This course focuses on the complete health assessment, the nursing process, and its relationship to the prevention and early detection of disease in clients across the life span. This course introduces processes of health assessment: interviewing, history-taking, and physical assessment. Dominant models, theories and perspectives are used to explain health behavior are considered in relation to evidence-based health promotion and health education strategies. Students are also expected to identif Author(s): No creator set
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Subtracting Integers The video explains three different models you can use to show why subtraction of integers works: 1) number line jumps; 2) concept of difference; 3) positive/negative counters. Teacher and a white board but this may help a student that doesn't get it, .
Author: Maria Miller Author(s): No creator set
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Engineering Statics Statics is a sophomore level engineering course, offered in all mechanical and civil engineering programs. Statics forms the essential pre-requisite to a number of follow-on courses, such as dynamics and mechanics of materials, and lays the foundation for design of mechanical systems. In most institutions, Statics is taught in a traditional way with an emphasis on the mathematical operations that are useful in its implementation, but without enough emphasis on modeling the interactions between r Author(s): No creator set
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Digital Roman Forum The purpose of the modeling project was to spatialize information and theories about how the Forum looked on June 21, 400 A.D., which was more or less the height of its development as Rome as a civic and cultural center. The digital model includes over twenty features (buildings and major monuments) filling up the western zone of the Roman Forum from the Temple of Vesta and Temple of Antoninus and Faustina on the east to the Tabularium facing the western slope of the Capitoline Hill. Author(s): No creator set
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Educational Technologies in Learning Theories Educational Technologies can be utilized in conjunction with multiple learning theories in order to target different learning styles. This course is an overview of what and how Educational Technologies can be utilized in various learning theories. Author(s): Leah MacVie
Bulletin of the Institute for Antiquity and Christianity, Volume IX, Issue 4 CONTENTS:
Calendar of Events,
Cover Illustration Description,
Schenke in Claremont,
Seminars of the Institute for Antiquity and Christianity: "Jews in Egypt Exhibit," "IAC Tour of Greece Planned," "Jews in Egypt: Ancient Roots of a Modern Community," "The Origins of Christmas: Ancient Traditions About the Birth of Jesus," "Understanding Paul," "The Glory That was Greece," "The City of David: Recent Excavations of Ancient Jerusalem," "The Royal Palace of EBLA," "Rome, The Eternal City," "Manuscri Author(s): The Institute for Antiquity and Christianity
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Behavior of steel members with trapezoidally corrugated webs and tubular flanges under static loadin Engineers have long realized that corrugated webs enormously increase steel girdersâ stability against buckling and can result in very economical design. Recently, the new idea of combining the tubular flanges with corrugated webs brought new issues of research. The objective of the research presented in this thesis is to investigate the behavior of steel members with corrugated webs and tubular flanges subjected to shear, bending, and axial compression. Relative buckling modes are also disco Author(s): Wang, Xiaobo
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"Topics in Philosophy: David Lewis, Spring 2008" " This course is a seminar on the history of institutions and institutional change in American cities from roughly 1850 to the present. Among the institutions to be looked at are political machines, police departments, courts, schools, prisons, public authorities, and universities. The focus of the course is on readings and discussions." Author(s): Rayo, Agust?n
Northwest Auburn Village Center Plan, Auburn, Alabama This document is a city plan for the Norwest Auburn Village Center in Auburn, Ala. dated November 8, 2004. Title on PDF: City of Auburn, Interim Specific Plan, Norwest Auburn Village CenterIraq and the Law: what went wrong? Rabinder Singh QC, a barrister at Matrix Chambers and Visiting Professor of Law at the LSE, has been involved in some of the leading cases of the last five years raising legal issues arising out of the war against Iraq. In this lecture he will for the first time in a public forum give an account of that work, which includes: the legality of the UK's participation in the invasion in 2003; attempts to get a public inquiry into the circumstances leading to the invasion; the applicability of the Hum Author(s): No creator set
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The West in a New World: what future for transatlantic relations? The world has changed dramatically since the end of the Cold War, but the transatlantic relationship has yet to be reviewed. The time has come to rethink it, along with the concept of the West. Pierre Hassner is an emeritus senior research fellow at CERI-Sciences Po. Author(s): No creator set
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LSE Literary Festival - Jekyll and Hyde: Law, Science, Psychology Editors note: We apologise for the poor audio quality of this podcast. Robert Louis Stevenson's Jekyll and Hyde develops an extraordinarily rich intersection between literary fiction, legal norms and the scientific imagination. This panel discussion brings together legal academics, psychoanalytical theorists and specialists in nineteenth-century literature in a conversation focused on the historical and cultural significance themes in the novel. The discussion will span the emergence of the ne Author(s): No creator set
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Does the Electric Car have the Juice? Fierce price competition, painstaking cost-cutting, and widespread volatility is making life in the auto industry incredibly challenging. How has Renault adapted, and where does it see the auto industry heading? As a fledgling technology (and one of the great hopes for reducing global carbon emissions) can any electric car concept overcome such an inhospitable environment? Renault Group Commercial Director Len Curran and Electric Vehicles chief Andrew Heiron will both be offering their insights Author(s): No creator set |
Modify Your Results
History is filled with people, events, facts, and details. Sometimes you can get lost in all the details. This is why the most important strategy to remember as you read a history textbook is to form the "big picture" of history.
The Remediation Book offers remediation for the skills and concepts in California Math Course 1, Course 2, and Algebra 1 and in Algebra Readiness. The Remediation Book is subdivided into the following strands: Whole Numbers, Decimals, and Integers; Fractions; Ratio, Proportion, and Percent; Geometry; Measurement; Algebra Concepts; Coordinate Graphs; Polynomials and Rational Expressions; Probability; and Statistics. Each strand is subdivided into 9 to 30 two-page lessons. Lessons provide examples, helpful hints, and a variety of exercises. |
Beginning Algebra With Applications
9780618803590
ISBN:
0618803599
Pub Date: 2007 Publisher: Houghton Mifflin
Summary: Intended for developmental math courses in beginning algebra, this text retains the hallmark features that have made the Aufmann texts market leaders: an interactive approach in an objective-based framework: a clear writing style, and an emphasis on problem-solving strategies. The acclaimed Aufmann Interactive Method, allows students to try a skill as it is introduced with matched-pair examples, offering students imm...ediate feedback, reinforcing the concept, identifying problem areas, and, overall, promoting student success."New!" "Interactive Exercises" appear at the beginning of an objective's exercise set (when appropriate), and provide students with guided practice on some of the objective's underlying principles."New!" "Think About It" Exercises are conceptual in nature and appear near the end of an objective's exercise set. They ask the students to think about the objective's concepts, make generalizations, and apply them to more abstract problems. The focus is on mental mathematics, not calculation or computation, and help students synthesize concepts."New!" "Important Points" have been highlighted to capture students' attention. With these signposts, students are able to recognize what is most important and to study more efficiently."New!" A Concepts of Geometry section has been added to Chapter 1."New!" Coverage of operations on fractions has been changed in Section 1.3 so that multiplication and division of rational numbers are presented first, followed by addition and subtraction"New!" A Complex Numbers section has been added to Chapter 11, "Quadratic Equations.""New Media!" Two key components have been added to the technology package: HM Testing (powered by Diploma) and, as part of the Eduspace course management tool, HM Assess, an online diagnostic assessment tool.
Aufmann, Richard N. is the author of Beginning Algebra With Applications, published 2007 under ISBN 9780618803590 and 0618803599. Three hundred three Beginning Algebra With Applications textbooks are available for sale on ValoreBooks.com, one hundred twenty eight used from the cheapest price of $3.32, or buy new starting at $51.03 [moreGlued binding. Paper over boards. 664 p. Contains: Illustrations, black & white, Illustrations, color. Intended for a young adult/teenage audience. This book has a light amount of wear to the pages, cover and binding. Blue Cloud Books-Hot deals from the land of the sun.[less]
Glued binding. Paper over boards. 664 p. Contains: Illustrations, black & white, Illustrations, color. Intended for a young adult/teenage audience. Very good condition book with only light signs of previous use. Sail the Seas of Value.[less]
BRAND NEW BOOK(never been opened).Might contain minor shelf ware or remainder marks.100% satisfaction guaranteed or your money back.Thank you for your support.WE SHIP NEXT BUSINESS DAY IN BUBBLE MAILER WITH TRACKING NUMBER.i1[less]
BRAND NEW BOOK(never been opened). Might contain minor shelf ware or remainder marks.100% satisfaction guaranteed or your money back. Thank you for your support. WE SHIP NEXT BUSINESS DAY IN BUBBLE MAILER WITH TRACKING NUMBER. i1. [less] |
This applet demonstrates a logistic growth model which plots population P_i for i = 1 to i = 600 given user input for the initial population P_0, growth rate G and carrying capacity CC. The difference... More: lessons, discussions, ratings, reviews,...
Enter a set of data points and a function or multiple functions, then manipulate those functions to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each co... More: lessons, discussions, ratings, reviews,...
The NA_WorkSheet Demo (beta version) is a collective aggregation of algorithms coded in Java that implements various Numerical Analysis solutions/techniques in one easy to use open source tool. The to... More: lessons, discussions, ratings, reviews,...
Choose a function from a list or enter your own, and see the way its equation changes as the function is translated horizontally and vertically, reflected over various lines, stretched, and compressed... More: lessons, discussions, ratings, reviews,...
On this online calculator calculate mathematical expressions and complex numbers. You can do matrix algebra and solve linear systems of equations and graph all 2D graph types. You can also calculate z... More: lessons, discussions, ratings, reviews,...
Discussion of polynomials, including properties of linear and quadratic polynomials. Investigate the way the roots and graph of a quadratic polynomial ax^2 + bx + c changes as a and the square root |
A Right Triangle Approach
Beecher, Penna, and Bittinger's Precalculus: A Right Triangle Approach is known for enabling students to "see the math" through its focus on ...Show synopsisBeecher, Penna, and Bittinger's Precalculus: A Right Triangle Approach is known for enabling students to "see the math" through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively. Mid-chapter Mixed Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Guide summaries provide built-in tools to help them prepare for tests. MyMathLab has been expanded so that the online content is even more integrated with the text's approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Mixed Review exercises from the text, as well as example-based videos created169397616941Fine. Hardcover. Instructor Edition: Same as student edition...Fine. Hardcover. Instructor Edition: Same as student edition with additional notes or answers. Almost new condition. SKU: 97803216941Hardcover. Instructor Edition: Same as student edition with...Hardcover. Instructor Edition: Same as student edition with additional notes or answers. New Condition. SKU: 97803216941 in very good dust jacket. Glued binding. Paper over...Very good in very good dust jacket. Glued binding. Paper over boards. 990 p. Contains: Illustrations. Audience: General/trade. PLEASE READ INSTRUCTOR'S REVIEW COPY SAME AS STUDENT EDITION MAY HAVE ADDITIONAL NOTES AND ANSWERS
Description:New annotated teacher edition; Textbook. Huge heavy copy,...New annotated teacher edition; Textbook. Huge heavy copy, oversized; Includes all answers; annotated teacher textbook; no labs, nothing else; textbook is brandnew; 990pp of text +74pp more of IA, that is instructor answers (and part solutions); check you work; very heavy book: order it bookrateMEDIA mail; it will be more expensive to expedite; USA sales only on account of book weight and size;1725769257 |
The UW Math Circle is full for the year and is not admitting new students. Our other events – Math Hour and the Math Hour Open Olympiad – are open to everyone. If you are interested in joining the circle next Fall, consider coming to the Olympiad in June.
To receive up-to-date information about this and related events that we organize, please join our mailing list here.
We also invite you to check out the UW Math Hour for some fun mathematics in the spring!
What is UW Math Circle?
The UW Math Circle is intended for Seattle-area middle school and junior-high school students, and it is being offered at no cost. The program is aimed at 7th, 8th, and 9th graders with mathematical minds, with the intent of continuing their development in this direction.
The students meet weekly in the Math Circle to engage in a variety of activities. Here, we develop many areas of mathematics, including (but definitely not limited to) logic, graph theory, combinatorics, and geometry. Follow the links at the top of the page for a more detailed breakdown of what's being covered in each meeting.
To reinforce the lessons learned at each Math Circle, weekly homework assignments are given at the end of the meetings. The students are encouraged to delve even further than the problem statement, in order to really get a feel for the solution. To reinforce this behavior, the first hour of each meeting is spent by the students explaining their solutions and methods to their peers, with the listening students free to critique the solutions and offer help when things get confusing.
The last half of the meeting is spent covering new material. We introduce the concepts to the students with a major emphasis on hands-on activities. For the students, this means that much of their time is spent actively engaging in problem-solving, with ample time to ask probing questions to their colleagues and the instructors. |
From the Publisher: Clearly written and comprehensive, the eleventh edition of Gustafson and Hughes' popular book, COLLEGE ALGEBRA, provides in-depth and precise coverage, incorporated into a framework of tested teaching strategy. The authors combine carefully selected pedagogical features and patient explanations to give readers a book that preserves the integrity of mathematics, yet does not discourage them with material that is confusing or too rigorous. Long respected for its ability to help learners quickly master difficult problems, this book also helps them develop the skills they'll need in future courses and in everyday life. Retaining the mathematical precision instructors have come to expect, the authors have focused on making this new edition more modern to better illustrate the importance of math in our world.
Description:
This college algebra text is written in a friendly and
an easy to understand manner in order to help students understand the concept presented. This feature combined with ample examples, various types of exercises, and well thought out, real ... |
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Starting at $106Precalculus,the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology. They have created a book that is designed for instructors and written for students making this the most effective precalculus text available today. Contents: P. Prerequisites 1. Functions and Graphs 2. Polynomial, Power, and Rational Functions 3. Exponential, Logistic, and Logarithmic Functions 4. Trigonometric Functions 5. Analytic Trigonometry 6. Applications of Trigonometry 7. Systems and Matrices 8. Analytic Geometry in Two and Three Dimensions 9. Discrete Mathematics 10. An Introduction to Calculus: Limits, Derivatives, and Integrals Appendix A: Algebra Review Appendix B: Key Formulas Appendix C: Logic |
Solving the Algebra Problem
Money available to fund "the gateway course"
Our society constantly strives to emerge through barriers confronting it, and each effort has led to another frontier to be challenged. St. Louis was the gateway to the West, and the Arch attests to that quest. The Statue of Liberty and Ellis Island were gateways to long-sought-after freedoms for early immigrants. The World Wide Web is the gateway to cyberspace, and NASA is the gateway to the stars.
In that same spirit of enthusiasm, we must seek support for the gateway course essential to a successful journey through education. Education leaders have identified that gateway course as algebra, which – alongside science and technology – constitutes the path of the future.
Bertrand Russell stated that, "Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform." Most recent research indicates those who study for degrees in fields associated with mathematical success will fill the jobs of the future.
The need to prepare future generations
Efforts are in place to double the number of mathematics graduates with bachelor degrees by 2015. In order to accomplish that objective, a serious effort must be exerted at the lower levels of education to prepare future generations of students to reach those proposed goals.
Former New York Mayor Rudolph Giuliani stated we must "do a better job of having the ladder of success there for everyone," and mathematics is the ladder that will make available an effective entry into the complicated fields attendant with science and technology.
Arizona Governor Janet Napolitano urges an improvement in these areas to engineer a talented workforce in the emerging occupations of the future. Secretary of Education Margaret Spelling stated at a recent news conference, "The field of math is ever more critical and a field that will be in demand. Unfortunately we're not doing well enough today."
Synergistic Algebra Modules
Armed with this knowledge and the need for an improved delivery and continuum, Pitsco provides a gateway through which these demands can be reached. Pre-Algebra Modules are laced with real-world, multi-level studies relevant to a student's future educational travels. Everything from probability and statistics to light and lasers to bioengineering is embedded in the curriculum.
Thus, a student is exposed to a gamut of mathematical knowledge and utilization to carry them on to higher development of the knowledge and skills so vital to the future of our national and personal existence. To seek this curriculum may necessitate the pursuance of grant or Title funds. Title I, Title II, and Title V grants may be utilized to direct the advancement of algebraic goals.
Consider these grant opportunities:
Federal Grants
Enhanced Assessment Grants
These programs are designed to assist in the administering of and development of accountability measures with mathematics as a chief ingredient.
Perkins Vocational Technology Act
Funds may be used for vocational and technology education activities plus professional development opportunities for teachers and counselors.
Innovative Education State Grants
This formula grant under Title V stimulates educational innovation by encouraging broad-based reform efforts. The funds may be used for technology, math, professional development software, or curricular materials.
National Science Foundation
NSF promotes and advances scientific programs in the United States and advances grants for science, math, and engineering research in education.
Private and Foundational Grants
Abington Foundation
This foundation provides gifts for educational programs, particularly for development of those programs that stress math readiness.
Frey Foundation
Frey supports math programs that encourage self-sufficiency and lead children to handle the challenges they will face later in life.
Intel
Intel has an ongoing grant program that can be accessed by schools in Arizona, California, Colorado, Massachusetts, New Jersey, New Mexico, Oregon, Texas, Utah, and Washington.
State Farm Foundation
This foundation is concerned with efforts to attain educational excellence, particularly in math.
Westinghouse Science and Math Grants
This grant source places special emphasis on math and science programs in elementary and secondary schools.
These grant areas support the ruminations of such eloquent spokespersons as Carl Sandburg, who said, "Arithmetic is where the answer is right and everything is nice and you can look out of the window and see the blue sky – or the answer is wrong and you have to start over and try again and see how it comes out this time." |
Mathematics Overview
Mathematics Overview
Mathematics is a major achievement of the human mind, a subject with its own structure and elegance, worthy of pursuit for its own sake. On the other hand, mathematics has always been used to help us understand the world and the society in which we live, and with the development of the computer, applications of the mathematical methods of thought have become even more prominent.
At Beloit we respect and teach both aspects of mathematics. The structure and intellectual appeal of mathematical ideas is central to our courses and curriculum. We stress the relationship of mathematical thinking to other fields of intellectual and practical endeavor. We emphasize the importance of clear and careful expression to mathematical reasoning; our courses involve practice in writing, giving oral presentations, and working on projects as part of a team.
THE MAJOR
Most students begin their mathematics course of study with calculus—the quantitative study of change and the mathematical ideas for describing it. Calculus is the cornerstone of further explorations in mathematics. In addition to teaching the fundamental concepts and technical aspects of the subject, we pay particular attention to its historical dimension, to those who developed the subject, and why it mattered to them.
The sophomore year is designed to give students a sense of contemporary mathematics. Normally one course in each term will be chosen from linear algebra, discrete mathematics, differential equations, vector calculus, and probability and statistics. During the junior and senior years, students continue to broaden their mathematical knowledge while pursuing some advanced topics in depth.
Mathematics majors participate in the department's weekly mathematics colloquium, an event that begins with informal interaction between faculty and students and is followed by a mathematical lecture given by a visitor, faculty member, or advanced student. Apart from regularly offered courses, students also have the options of independent study or supervised research in areas of faculty expertise in which we do not usually offer courses.
PROFESSIONAL EXPLORATION
CAREERS
The faculty of the mathematics department make a special effort to develop internship opportunities for mathematics majors and to encourage students to take advantage of such opportunities. Notable opportunities of this sort have included government-sponsored undergraduate research at national laboratories, software conversion, oceanographic research, statistical quality control, database programming, and management training.
Mathematics majors go in many different directions after leaving Beloit. Some go on to graduate school in mathematics; those who have a second major often continue in that field, given advantage by their work in mathematics. Universities entered by recent graduates include Chicago, Duke, Iowa, Michigan, Purdue, SUNY at Stony Brook, and Wisconsin, as well as the University of Chicago for business; Johns Hopkins University for astronomy; and UCLA for anthropology.
Other recent graduates have taken jobs in utility and insurance rate-making, operations research for a trucking firm, household energy modeling for the National Bureau of Standards, engineering flight simulators for the U.S. Air Force, high school and grade school teaching, and all kinds of computer work. |
MTHS 658
The Algebra and Geometry of Complex Numbers
Mulvey,Irene
06/25/2007 - 08/03/2007
Tuesday & Thursday 09:30 AM - 12:00 PM
Science Tower 139
Not every polynomial has a root in the real numbers; for example, the equation (x^2+1=0) has no solution in the real numbers. But, every polynomial has a root in the complex numbers. This indicates a fundamental algebraic difference between the set of real numbers and the set of complex numbers. The result that every polynomial has a root in the complex numbers is known as the Fundamental Theorem of Algebra and it was proved by Karl Friedrich Gauss in his doctoral thesis in 1799. (Now, there are reportedly over 100 proofs of this theorem and Gauss is said to have found four or five different proofs himself.) The name of the theorem is misleading--although the theorem is a statement about the algebra of complex numbers, many of the proofs rely upon sophisticated ideas from complex analysis, geometry, and topology.
A high point of this course will be understanding a couple of different proofs of the Fundamental Theorem of Algebra, but the real content will be working through the algebra and geometry of the complex numbers and the theory of analytic functions that are needed to understand the proofs. Students should leave the course with a thorough understanding of complex numbers and functions of a complex variable.
Grades will be based on regularly assigned problem sets that will be a mixture of computational problems and theoretical problems.
There are no specific prerequisites for the course; all the essential topics will be introduced in the course itself, and the course should be accessible to any student with a modest background in mathematics.
Irene Mulvey (B.A., Stonehill College; Ph.D., Wesleyan University) is professor of mathematics at Fairfield University. Her recent publications include "Symbolic Representation for a Class of Unimodal Cycles," Topology and Its Applications (2002), and "Multi-modal Cycles with Linear Map Having Exactly One Fixed Point," International Journal of Mathematics and Mathematical Sciences (2001). Click here for more information about Irene Mulvey James Ward Brown, COMPLEX VARIABLES AND APPLICATIONS (McGraw-Hill), Hardcover |
Home Math Workbook 57 1. How much water can you save if you have a 3 minute shower using the low-flow shower head? _____ 2. How much water can you save if you have a 6 minute shower using the low-flow shower head? _____ Part 2: How efficient is your ...
1 Program Components Introduction ... The Honors Gold Series helps students develop a deep understanding of mathematics through thinking, reasoning, ... This workbook contains daily lesson support with Think About a Plan, Practice, and
Grade 10 TAKS Mathematics—Objective 1 Understanding functional relationshipsis critical for algebra and geometry. Students need to understand that functions represent pairs of numbers in which the value of one number is dependent |
You like to collect puzzles and twist your brain? Then this book is definitely for you. It's one of the biggest collections of various puzzles based on probability, numbers, algebra… and so much more! Having about 500 illustrations and written in merry style, this book will make you happy and funny for many-many hours and take one of the best places in your collection.
This book is a perfect example of classic scientific masterpiece. The textbook is crystal clear, well organized, and thorough. "A Course of Pure Mathematics" is great for teaching yourself mathematics. Hardy is a sincerely elegant, fine, incisive thinker, and his unbounded enthusiasm for his subject, duly controlled by British understatement, shines through every page. He conveys the irresistible, almost addictive quality of math. This book is a little quaint. The terminology used by the author is a bit out of date, e.g. 'sequences' are 'functions of a positive integral variable'. But that's the thing that makes "A Course of Pure Mathematics" so charming. The book contains a lot of examples. This is a great book for teachers, tutors, and certainly students |
Functions Modeling Change -Text Only (Cloth) - 2nd edition
Summary: This fai...show morelure rates. A large number of real-world examples and problems enable students to create mathematical models that will help them understand the world in which they live.
The focus is on those topics that are essential to the study of calculus and these topics are treated in depth.
Linear, exponential, power, and periodic functions are introduced before polynomial and rational functions to take advantage of their use to model physical phenomena.
Building on the Consortium's Rule of Four: Each function is represented symbolically, numerically, graphically, and verbally where appropriate |
ALEX Lesson Plans
Title: Web 2.0 Mastering Polynomials Review
Description:
This Web 2.0 Mastering Polynomials Review Description: This
Title: Polynomial Subtraction
Description:
Students Polynomial Subtraction Description: Students
Title: Conquering Polynomials
Description:
In Conquering Polynomials Description: In
Title: What are You - Prime or Composite?
Description:
ThisStandard(s): [MA2013] (6) 7: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. [6-NS4 What are You - Prime or Composite? Description: This
Title: Polynomials Divided by Monomials
Description:
Investigation of division of polynomials by mononials.
This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project Business, Management, and Administration (9 - 12), or Mathematics (9 - 12) Title: What's The Real Cost of That Car? Description: This is a Commerce and Information Technology lesson plan. A project requiring research, critical thinking and complex decision-making about factoring all the costs of purchasing a large ticket item... a car.
Title: Show Me The Money - Saving and Investing
Description:
Students will learn how to analyze several savings products from various financial institutions. They will also demonstrate the ability to discuss the role of saving and investment products. This a Commerce and Information Technology lesson plan 37: Distinguish between situations that can be modeled with linear functions and with exponential functions. [F-LE1
Subject: Information Literacy (K - 12), or Mathematics (7 - 12) Title: Show Me The Money - Saving and Investing Description: Students will learn how to analyze several savings products from various financial institutions. They will also demonstrate the ability to discuss the role of saving and investment products. This a Commerce and Information Technology lesson plan.
Title: "Like Terms", I Add Them
Description:
Students2 (9-12) 158) 9: Solve linear equations in one variable. [8-EE7]
Subject: Mathematics (8 - 12) Title: "Like Terms", I Add Them Description: Students
Title: Fortune Properties
Description:
ThisStandard(s): [CE] (0-12) 8: Cooperation [CE] (0-12) 21: Patience [CE] (0-12) 8: Cooperation [CE] (0-12) 21: Patience 16: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. [A-REI1]
Subject: Character Education (K - 12), or Mathematics (9 - 12) Title: Fortune Properties Description: This
Title: Multiplying Polynomials
Description:
Students Multiplying Polynomials Description: Students
Title: Color this Polynomial Simplified
Description:
ThisStandard(s): [AED] VA1 (7-12) 1: Create original works of art from direct observationMA2013] (7) 7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. [7-EE Arts Education (7 - 12), or Mathematics (7 - 12), or Technology Education (9 - 12) Title: Color this Polynomial Simplified Description: This
Thinkfinity Learning Activities
Title: A Geometric Investigation of (a + b)2
Description:
This
Standard(s): [MA2013] AL1 (9-12) 10: Understand that polynomials form a system analogous to the integers; namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. [A-APR1]
Subject: Mathematics Title: A Geometric Investigation of (a + b)2 Description: This Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12 |
15 STATE NORMAL SCHOOL
ALGEBRA.-This course includes a thorough treatment of the fundamental operations; use of brackets; simple equations, factoring; highest common factor; lowest common multiple; simple and complex fractions; involution and evolution; the theory of indices, with applications, surds (radicals ), simple and compound, imaginary quantities; quadratic equations; equations in quadratic form; simultaneous quadratic equations; theory of quadratic equations; indeterminate equations of the first degree; inequalities; ratio, proportion, and variation; arithmetical, geometrical, harmonical progressions.
Hall and Knight's Elementary Algebra is the text-book used.
(a) Required of first-year Normal students.
2 hours per week, first half-year; 3 hours per week, second half-year.
(b) Required of second-year Normal students.
2 hours per week throughout the year.
PLANE GEOMETRY.-This course includes the general properties of regular polygons, their construction, perimeters, and areas; regular polygons and circles, with problems of construction; maxima and minima, and methods for determining the ratio of the circumference to the diameter. The first five books of Wentworth's New Plane and Solid Geometry.
Required of all second-year Normal students.
2 hours per week throughout the year.
ENGLISH.-(a) This course consists of a thorough study of the more advanced principles of English Grammar. It also includes elementary instruction in literature with abundant practice in simple composition.
Required of all first-year Normal students.
4 hours per week throughout the year.
(b) This course consists of instruction in the elementary principles of rhetoric together with much practice in composition. Many simple pieces of literature class are also studied.
Required of all second-year Normal students.
3 hours per week throughout the year.
(c) The work of this course is essentially the same as that of course (b) but is of much higher grade. Among the pieces studied are the more difficult ones prescribed for entrance to the Freshman class.
Required of all third-year Normal students.
2 hours per week throughout the year. |
The use of a calculator
For anyone who knows about Worthington Scranton, do they allow you to use calculators for math 140 and 141? Does it depend on the teacher or is it just a department made thing? Since the 8th grade, all of my classes allowed the use of a calculator so its going to be a big change for me if I have to start dividing and multiplying in my head.
Replies to: The use of a calculator
I think with penn state in general they're big on no-calculators, at least for 140-141. I took 140 [if that's calc 1] at berks one summer and they wouldn't let you use them at all. My friend goes to UP, and for both calc 1 and 2 they didnt allow it there. |
Modify Your Results
This world-class math program comes to you from the country of Singapore, the author made sure that you will enjoy learning math with the interesting lessons you will find in this textbook. The textbook is divided into 2 semesters. Chapters 1-6 are in Book A, Chapters 7-11 are in Book B.
Math Triumphs is an intensive intervention resource for students who are two or more years below grade level. The series accompanies Glencoe Algebra 1,Geometry, and Algebra 2 and provides step-by-step intervention, vocabulary support, and data-driven decision making to help students succeed in high school mathematics.
Mathematical Connections is a bridge that will take you from where you are in your study of mathematics to algebra and geometry. Since topics in mathematics are connected, this course will also lead you to data analysis and probability.
Matilda Bone is a 180 page historical novel for children and interested adults written by Karen Cushman, the critically acclaimed writer of children's books and author of the Newbery medal novel The Midwife's Apprentice and the Newbery Honor novel Catherine, Called Birdy. Thorndike provides the following summary:
In Blood and Bone Alley, where she has come to serve Red Peg the Bonesetter, Matilda finds she is alone in her belief that prayer and devotion are the only worthy pursuits. Here she has to go to market, tend the fire, mix plasters and poultices, and help treat patients. Surrounded by people who laugh and joke and eat sausages, while she herself seeks higher things, Matilda feels alone and misunderstood. How she yearns for her former life at the manor, where she was instructed by Father Leufredus and her most difficult task was to find her way to the privy in the dark! With the fascinating and pungent world of medieval medicine as a backdrop, Matilda Bone is the compelling, comic story of a girl learning to live contentedly in this world. "A fascinating glimpse into the colorful life and times of the 14th century." - School Library Journal
From the Book jacket:
AN ATTACK ON THE VERY SOUL OF REDWALL
Slagar the Fox is determined to vanquish peaceable Redwall. Gathering his mercenary band of
rats, stoats, and weasels, he advances upon the Abbey with a cunning scheme. There will be no heroics, no courageous battle plans. He knows too well the power of the legendary Redwall sword. Instead, he will steal the children of Redwall from under their parents' very noses. And his prize captive will be Mattimeo, the headstrong young son of the fearless mouse warrior Matthias!
When a TV game show comes to Bayport, a crime wave begins. As Frank and Joe fight a grudge match with the current team champions, they are also trying to discover who on the staff of the show is the mastermind behind burglaries that seem to follow the traveling show.
Algebra 2 brings math to life with many real-life applications. Circling the globe are three key aspects of Algebra 2--the equations, graphs, and applications that you will use in this course. They will help you understand how mathematics relates to the world. As you explore the applications presented in the book, try to make your own connections between mathematics and the world around you!
This textbook serves as the centerpiece of the new McDougal Littell Biology program. Through graphic photos and illustrations, memorable connections, and lab activities in every chapter, McDougal Littell brings Biology into the world of a student. It provides students with a structured framework of key concepts and main ideas upon which to build their knowledge of biology. Critical thinking and problem solving activities help to teach students how to think in a scientific way.
Geometry, like much of mathematics and science, developed when people began recognizing and describing patterns. In this course, you will study many amazing patterns that were discovered by people throughout history and all around the world. You will also learn to recognize and describe patterns of your own. Sometimes, patterns allow you to make accurate predictions.
Research is about satisfying curiosity, about finding some¬thing you are interested in, exploring it, and making discoveries. Research is about extending the range of what you know. It is like sailing off the edge of the map into unknown territory. Research is an exciting adventure, but this adventure requires no fancy equipment. All you really need is curiosity, a desire to find out who, what, where, when, why, and how.
This textbook is closely aligned to the Michigan High School Content Expectations for English Language Arts. Every time you learn new information or practice a skill, you are mastering one of the expectations. Each unit, each reading selection, and each workshop in this textbook connects to at least one of the expectations. The expectations covered in each section of a unit are listed on the opening page of the section.
Scientists are curious. Since ancient times, they have been asking and answering questions about the world around them. Scientists are also very suspicious of the answers they get. They carefully collect evidence and test their answers many times before accepting an idea as correct |
hands to explore and build proficiency and eventually to replicate... I've previously taken regular calculus classes with engineers and won... This is not the same at all. We were solving real problems every day...Students work through problems using an online interactive textbook D...When teams become stuck on a problem Chiel or a teaching assistant m...
hands, to explore and build proficiency, and, eventually, to replicate and build on recent math models used in the biological sciences. The course is cross-listed as both a biology and biomedical engineering class.
"I've previously taken regular calculus classes with engineers and wondered what would the classes ever be useful for," said Kate Coyle, a biology major who completed the Dynamics class and graduated this semester. "Labs I've had in biology and physics show you the protocol and the expected result.
"This is not the same, at all. We were solving real problems every day."
Students work through problems using an online interactive textbook, Dynamics of Biological Systems: A Modeling Manual Chiel wrote and the computer programming language Mathematica, which scientists worldwide rely on to build mathematical models of complex systems. Chiel's book is available free to students as well as teachers who may want to use it as is or as a model for their own classes.
When teams become stuck on a problem, ,Chiel or a teaching assistant makes suggestions, gives clues and tries to coax out the answer. After success, teachers quiz individuals about how they found the solution and what they'd learned.
The class of 30 is spread out among hexagonal tables. Teams power up their laptops and go to work. Each day the teachers rotate to a different group of students, and after each class they compare notes on who has mastered the skills and who needs extra help, Gill said.
When the second half of the semester begins, teams choose a mathematical model that was recently published in a scientific journal, begin reconstructing and analyzing it and then writing in detail what they learn. The students then extend the model to answer new questions that they ask themselves, and write up results as if they were writing for a scientific journal.
Coyle and her teammates Valencia Williams and Joshua DeRivera focused on a pa |
This course builds on students' previous experience with functions
and their developing understanding of rates of change.
Students will solve problems involving geometric and
algebraic representations of vectors and representations of lines
and planes in three-dimensional space; bro ...
More
High-quality learning of mathematics is rooted in both formal and informal reasoning and critical thinking skills of children. Such a connection influences their thinking, achievement, decisions, and attitudes about studying mathematics in later years.
Geometry is not the science of visual graphs and shapes, rather is a subject of reasoning and proof. Kids should begin looking at geometry as a reasoning subject from the early stage. Therefore, the learning content for geometry should be developed with such a demand in mind.
This is a great source of fresh and content-rich hands-on activities for all early learners with all types of learning styles and capabilities. These activities give students rich opportunities to understand the essence of numbers and numerical operations as measuring tools for quantities.
http ...
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In this webinar material, the student gets familiar with the ideal simple and basic power cycles and combustion and their T - s, p - V and h - T diagrams, operation and major performance trends when air, argon, helium and nitrogen are considered as the working fluid.
Performance Objectives: ...
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Take charge of your career with the NAPR e-learning program. This highly interactive program is skill-focused with your personal and professional development as the end goal. Review the program contents to see what courses are yours for only $129.95! By enrolling in this program, you agree that t ...
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About Coggno
Coggno is an Intuitive Web-Based Learning Software, Aggregator and Syndicator of Training Curriculum. Learn more >> |
CMATH for Delphi 7 5.2.4 description
CMATH is a comprehensive library for complex-number arithmetics and mathematics.
The following features make CMATH an ideal replacement for the unit Complex coming with Delphi:
1. High-performance implementation in machine code leads to superior speed.
2. Accuracy and safety are greatly enhanced.
3. Each of the floating-point accuracies (complex(float), complex(double), and complex(extended)) is given its own, individually optimized treatment.
4. Polar coordinates (magnitude;angle) are supported in addition to the usual cartesian coordinates (real;imaginary).
The Shareware edition is optimized for PentiumXX, while maintaining compatibility with AMD processors (Athlon) and down to 486DX.
This version is for Delphi 7.
CMATH for Delphi 7 5.2.4
CMATH is a comprehensive library for complex-number arithmetics and mathematics, both in cartesian and polar format (single, double, and extended precision). The implementation in Assembly language ensures maximum speed, accuracy, and safety, far superior to the unit Complex coming with Delphi. CMATH is optimized for Pentium II-IV, but will also run on 486DX and Athlon. For Borland Delphi 2005. Free Download
CMATH is a comprehensive library for complex-number arithmetics and mathematics, both in cartesian and polar format (float, double, and extended precision). The implementation in Assembler ensures superior speed, accuracy, and safety, as compared to other available complex class libraries. All CMATH functions may be called from C or C++. For MS Visual C++ 5, 6, 2003, 2005, or 2008. Free Download
CMATH for Borland C/C++ makes fast complex-number math functions (cartesian and polar) available in three precisions. This comprehensive library was written in Assembler for superior speed and accuracy. All functions may be called from C or C++. Free Download |
Start reading Great Formulas Explained - Physics, Mathematics, Economics on your Kindle in under a minute. Don't have a Kindle? Get your Kindle here or start reading now with a free Kindle Reading App this book you will find some of the greatest and most useful formulas that the fields of physics, mathematics and economics have brought forth. Each formula is explained gently and in great detail, including a discussion of all the quanitites involved and examples that will make clear how and where to apply it. On top of that, there are plenty of illustrations that support the explanations and make the reading experience even more vivid.
I am enjoying the style of this book and its use of explanations plus worked examples but as with all text books on engineering watch out for mistakes. On location 634 at 38% there are numbers which are wrong viz: 24 x 6 =114, instead of 144. This mistake carries on to the next part of the example so is unlikely to be a typo. But overall it is good in my opinion, though not 5 stars
Probably aimed at those who don't come into much contact with maths,which is fair enough. A further book might want to dig a bit deeper to show what maths can do, possibly explaining why , for example, you cannot really eliminate risk from trading, an illusion which helped land the world's economy in the present mess!
Lots of interesting facts formulas and trivia that makes interesting light reading of what is usually considered complex subjects and their practical applications:Especially liked section on Quadratic Equations & one on Explosions.
This is indeed a compilation of great formula's, I myself being an economist find his selection for economics a bit odd but I enjoyed the physics bit of it, It took me back to high school. I'm uncertain who I would recommend this to, I would guess, one of the disciplines in the title, because it helps put into context what your discipline has that differs from the other. |
Extended Studies in Mathematics 1
10 Units
This course deepens students understanding of the principles and practices of teaching and learning Mathematics in secondary schools. Students will explore ways of differentiating curriculum to meet the diverse needs of learners in the Mathematics classroom. Specific attention will be given to the literacy and numeracy demands of Mathematics as an area of study; and the incorporation of technology into the teaching and learning of Mathematics. |
Glen Ridge, FL PrecalculusThe course also gives the students a thorough introduction of functions and quadratic equations. They will learn all the operations associated with the two, such as factoring and graphing. The end of the course takes the students? knowledge of algebra 1 one step further by introducing them to some basic concepts of geometry.
...Precalculus includes algebra, coordinate geometry, trigonometry, and most of all, functions---the general concept as well as specific functions. Students come to this course familiar with basic algebra and geometry. A precalculus course builds on all of their previous mathematical knowledge and experience to understand calculus that is essential to succeed in a college |
Now, as a Professor Emeritus, this highly experienced teacher has undertaken the gratifying project to publish a series of foundational textbooks covering the essentials of real analysis and algebra, thereby sharing both his rich experiences and his outstanding expertise with the mathematical community as a whole. In the new series "Cornerstones" of Birkhäuser Verlag, which is to be devoted to publishing fundamental textbooks in mathematics, his two companion volumes "basic real analysis" and "advanced real analysis" have already appeared in 2005 (see Zbl 1095.26001 and Zbl 1095.26002), and his two other companion volumes" "basic algebra" and "advanced algebra" are about to follow right away.
The book under review, is the first volume of Anthony W. Knapp's announced algebra text. Together with its companion volume "advanced algebra", which is to appear by September 2007 (see Zbl 1133.00001), it is designed to systematically develop those fundamental concepts and methods of modern abstract algebra that are indispensable for every active mathematician in our days. The author's main goal is to provide a global view of fundamental algebra, its various applications, and its ubiquitous role in contemporary mathematics. As the author points out in the preface to his book, the leading idea is to explain what the young mathematician needs to know about modern abstract algebra in order to communicate well with colleagues in all branches of mathematics and related sciences. In this vein, the primary audience of the two companion textbooks is students who encounter the material for the first time and who are planning a career in which advanced mathematics will play a predominant role.
As for the contents of the present volume "basic algebra", the book consists of ten chapters and six appendices. Much of the material covered here seems to correspond to standard course work, but most of the chapters include many further topics beyond that. This makes the entire text very flexible with regard to teaching or self-study likewise, and the reader has various choices to arrange her or his studies according to the respective needs.
Chapter 7 offers more advanced group theory, with the focus on free groups, free products, and group representations. Additional topics in this chapter are Burnside's theorem and the elements of group extensions.
Chapter 8 is devoted to the fundamental concepts and methods of commutative algebra. This chapter explains rings and modules, prime and maximal ideals, unique factorization domains, the structure of finitely generated modules over a principal ideal domain, noetherian rings, integral dependence, localization and local rings, and the structure of Dedekind domains.
Chapter 9 develops the general theory of field extensions and then goes on to study Galois groups and their various applications to algebraic equations and geometrical constructions.
The final Chapter 10 deals with the structure theory of modules over noncommutative rings, with special emphasis put on finiteness conditions and functorial properties of Hom and tensor products for such modules.
The set of six appendices, included for the convenience of the reader, compile some basic facts from set theory and number domains that are used throughout the text.
As a special feature, the text comes with numerous concrete examples and hundreds of selected exercises, and a separate 90-page section at the end of the book provides detailed hints or even complete solutions for most of the working problems. Each chapter comes with its own guiding abstract, and general instructions for using this textbook are given right after the thorough preface.
The key features of this outstanding algebra text can be summarized as follows:
(1) The basics of algebra are taught by stressing their close interrelations, and they are built on each other continually.
(2) The three prominent themes, namely the analogy between integers and polynomials, the interplay between linear algebra and group theory, and the interaction between number theory and geometry, recur and blend together frequently.
(3) Applications of abstract algebra to different areas of mathematics, natural sciences, and engineering appear repeatedly, often so in sequences of guided working problems (with solutions at the end of the book).
(4) The author presents the subject matter in a forward-looking way by taking its natural development into account and proceeding from the particular to the general, thereby setting high value on the didactic aspects of teaching modern abstract algebra.
(5) Computational methods are emphasized throughout the entire text in order to combine the abstract with the concrete tools.
Finally, the author's notorious masterly style of writing, which stands out by its high degree of clarity, elegance, refinement, and accuracy, also rules over this newest textbook of his, which is very likely to become one of the great standard texts in algebra for generations.
The author has already given an outlook to the contents of the forthcoming companion volume "advanced algebra", which will treat topics from modern number theory, Wedderburn-Artin ring theory, Brauer groups, homological algebra, infinite field extensions, basic algebraic geometry, and the arithmetic of algebraic curves. The mathematical community should be looking forward to the appearance of this second volume in the near future! |
Introduction to the Mathematics of Money: Saving and Investing - 07 edition
Summary: This is an undergraduate textbook on the basic aspects of personal savings and investing with a balanced mix of mathematical rigor and economic intuition. It uses routine financial calculations as the motivation and basis for tools of elementary real analysis rather than taking the latter as given. Proofs using induction recurrence relations and proofs by contradiction are covered. Inequalities such as the Arithmetic-Geometric Mean Inequality and the Cauchy-Schwarz Inequality are use...show mored. Basic topics in probability and statistics are presented. The student is introduced to elements of saving and investing that are of life-long practical use. These include savings and checking accounts certificates of deposit student loans credit cards mortgages buying and selling bonds and buying and selling stocks. The book is self contained and accessible. The authors follow a systematic pattern for each chapter including a variety of examples and exercises ensuring that the student deals with realities rather than theoretical idealizations. It is suitable for courses in mathematics investing banking financial engineering and related topics. ...show less
New Book from multilingual publisher. Shipped from UK within 4 to 14 business days. Please check language within??the description. Established seller since 200075.50 +$3.99 s/h
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My son uses it for his math and science classes in school. He says it's more than adequate to do the job for him. He's taking Algreba I and Chemistry. My daughter also uses one for her college courses. She's taking College Algrebra and Chemistry II. |
Trigonometry - 9th edition
Summary: Over the years, the text has been shaped and adapted to meet the changing needs of both students and educators. As always, special care was taken to respond to the specific suggestions of users and reviewers through enhanced discussions, new and updated examples and exercises, helpful features, and an extensive package of supplements and study aids. The result is an easy-to-use, comprehensive text that is the best edition yet.
1. The Trigonometric Functions. Angles. Angle Relationships and Similar Triangles. Trigonometric Functions. Using the Definitions of the Trigonometric Functions.
2. Acute Angles and Right Triangles. Trigonometric Functions of Acute Angles. Trigonometric Functions of Non-Acute Angles. Finding Trigonometric Function Values Using a Calculator. Solving Right Triangles. Further Applications of Right Triangles.
4. Graphs of the Circular Functions. Graphs of the Sine and Cosine Functions. Translations of the Graphs of the Sine and Cosine Functions. Graphs of the Tangent and Cotangent Functions. Graphs of the Secant and Cosecant Functions. Harmonic Motion1528859 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!!
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2008 Hardcover Good 0321528859. Ninth Edition. MathLab Code already used. This book is in good condition only. The book has some shelfwear, edgewear, corner wear. Inside pages are clean. Solid study...show more or reading copy but not for collectors.; 10.55 X 7.95 X 0.87 inches; 5 |
Vector algebra web assignment using an embedded Java applet by Vladimir Sorokin. Objective is to qualitatively understand the relationship between two summed vectors and their resultant vector. Links to helpful resources included. |
Intermediate Algebra - With CD - 6th edition
Summary: Key Message:TheTobey/Slater seriesbuilds essential skills one at a time by breaking the mathematics down into manageable pieces. This practical ''building block'' organization makes it easy for readers to understand each topic and gain confidence as they move through each section. The authors provide a ''How am I Doing?'' guide to give readers constant reinforcement and to ensure that they understand each concept before moving on to the next. With Tobey/Slater, readers have a tutor a...show morend study companion with them every step of the way. Key Topics:Basic Concepts; Linear Equations and Inequalities; Equations and Inequalities in Two Variables and Functions; Systems of Linear Equations and Inequalities; Polynomials; Rational Expressions and Equations; Rational Exponents and Radicals; Quadratic Equations and Inequalities; The Conic Sections; Additional Properties of Functions; Logarithmic and Exponential Functions Market:For all readers interested in basic college mathematics. ...show less
6 |
Elementary Linear Algebra : Applications Version - 10th edition
Summary: When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide ...show morea fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning200.07 +$3.99 s/h
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Mrs. Osborne is always seeking new tools for her toolbox. Not hammers, pliers and other physical tools, but mathematical principles and concepts. These tools are problem solving tools that can be applied in businesses and industries of all types. What can these mathematical tools do? They can allow a superstore to set lower prices than any other store, determine the best possible location for a new fire station, or design a box that holds a specific volume but uses the least material. They can schedule workers for a set of tasks, determine the best design for waiting lines in a bank, improve the quality of products through quality control and much more.
Can every problem be solved? This depends on what you mean by a solution. Sometimes we can accept an approximate answer as good enough rather than spend an enormous amount of time to obtain the exact solution. Occasionally, a problem can be particularly difficult to solve and, perhaps, it is even impossible to determine an exact answer. When this is the case, the applied mathematician can build a mathematical model and use technology such as computer simulations to find an acceptable solution. Computers can run the simulations hundreds and even thousands of times in a brief time frame. Using statistics, the simulations can give a very good estimated answer. Mathematics is an essential key in today's business and industries. Filling your toolbox with good mathematical concepts can put you ahead of others in the workforce. Of course, just like with physical tools, one must start with simple tools and work toward using "power" tools. So come and get started discovering a new set of tools for your toolbox!
Credentials:
Master of Operations Research: engineering, North Carolina State University.
Master of Arts: mathematics, Wake Forest University.
Bachelor of Science: mathematics and business administration/accounting, Averett University. |
Transformation Groups For Beginners
9780821836439
ISBN:
0821836439
Pub Date: 2004 Publisher: American Mathematical Society
Summary: The authors present an easy introduction of transformation groups in a way that will appeal to undergraduate students in mathematics, advanced undergraduates in physics and chemistry, and advanced mathematicians.
Duzhin, S. V. is the author of Transformation Groups For Beginners, published 2004 under ISBN 9780821836439 and 0821836439. Three hundred one Transformation Groups For Beginners textbooks are availa...ble for sale on ValoreBooks.com, two used from the cheapest price of $74.84, or buy new starting at $40.00.[read more]
Ships From:Multiple LocationsShipping:Standard, ExpeditedComments:RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). Brand new. We distribute directly for the publisher. The notion of symmetry is important in many... [more]RENTAL: Supplemental materials are not guaranteed (access codes, DVDs, workbooks). BrandBoonsboro, MDShipping:Standard, ExpeditedComments:Brand new. We distribute directly for the publisher. The notion of symmetry is important in many... [more][ The first two chapters provide a warm-up to the material with, for example, a discussion of algebraic operations on the points in the plane and rigid motions in the Euclidean plane. The notions of a transformation group and of an abstract group are then introduced. Group actions, orbits, and invariants are covered in the next chapter. The final chapter gives an elementary exposition of the basic ideas of Sophus Lie about symmetries of differential equations. Throughout the text, examples are drawn from many different areas of mathematics. Plenty of figures are included, and many exercises with hints and solutions will help readers master the material.[ |
Unit 4 Grade 10 Applied
Linear Systems
Lesson Outline
BIG PICTURE
Students will:
solve systems of two linear equations, and solve related problems that arise from realistic situations.
A summative task and paper and pencil assessment are included as a part of the unit. Teachers can decide to use one or
both assessments for the unit. If both assessments are used then the unit will last ten days.
The unit was written so that the use of CAS is integrated into every lesson. Although there are no examples showing
specific screen shots, it is expected that students will have it available to use for solving and checking whenever needed.
However, the materials in this unit can be used without CAS. A CAS user manual is included as well as video tutorials for
the skills outlined in the manual. The manual and videos include keystrokes for the commonly used skill sets needed for
linear systems such as solving for one variable or adding/subtracting two equations. This manual should be available to
students as they work through the concepts in the unit. To be able to see the keystrokes, the TI Nspire key fonts must be
installed on your computer. A guide to install the key fonts is included.
Day Lesson Title Math Learning Goals Expectations
1 Where Do We Meet? Identify/Solve problems that arise from realistic situations that ML1.02, ML 2.05
can be modelled by two linear relations. ML3.01, ML3.03
Determine graphically the point of intersection of two linear
equations. CGE 3c
Interpret the story the graph tells, including point of intersection
and what occurs before and after the intersection point.
2 What's the Point? Determine the coordinates of the points of intersection for pairs of ML2.05, ML3.01,
linear relations given their graphs and interpret the meaning of the ML3.03
point of intersection.
Solve a problem that arises from a realistic situation represented
by two linear relations.
3 Approximate or Discuss accuracy of solutions obtained through graphical means. ML1.01, ML1.03,
Accurate? Establish the need to isolate a variable in order to use the ML3.02
substitution method and practice the skill of isolating.
CGE 2c, 5b
Develop understanding of facility of solving systems using the
substitution method to improve the accuracy of a solution.
4 The SubMathiner Determine the conditions for which a linear relation application is ML3.02, ML3.03
preferred to the algebraic models by comparing the rate of change
and initial value of two linear relations making up a system of
equations.
Identify which variable is the most efficient for isolating and then
solve linear systems using the method substitution.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-1
Day Lesson Title Math Learning Goals Expectations
5 There Is Another Way! Identify situations where the solving by substitution is not ML3.02, ML3.03
efficient.
Identify necessary conditions or "look-fors" that make solving by CGE 4b, 7b
elimination possible.
Develop the algebraic method of solving a system by elimination.
6 There Is Another Way! Determine that an equation multiplied by a constant is equivalent ML3.02, ML3.03
- Part II to the original equation.
Develop a complete algorithm for the algebraic method of
elimination to solve a linear system.
Solve problems using the method of elimination that arise from
realistic situations described in words.
7 Which One is Best? Identify necessary conditions or "look-fors" in a system of ML1.01, ML1.03,
equations that make it best suited to be solved by graphing, ML3.01, ML3.02,
substitution or elimination. ML3.03
Solve a system of equations using two of the three methods.
CGE 3c, 4f, 5a, 5e
Solve a system of linear equations using the most appropriate
method.
8 Summative Task Create contextual linear systems problems, complete with ML1.01, ML1.03,
Evaluation – Day 1 solutions and graphs, and present them in a visual format e.g., ML3.01, ML3.02,
poster project or PowerPoint slideshow. ML3.03
This is available from
the members only CGE 5b
section of the OAME
web site
9 Summative Task Exchange problems created amongst them for others to solve, ML1.01, ML1.03,
Evaluation – Day 2 verify their solutions, and justify the selection of preferred ML3.01, ML3.02,
method of solution. ML3.03
Finalize their three linear-system problems, making necessary
changes based on input from peers. CGE 2c, 4f, 5e, 5g
10 Final Evaluation This is a one-day paper and pencil test that evaluates student ML3.01, ML3.02,
learning for the remaining overall expectations and math ML3.03
This is available from processes.
the members only Students will apply their knowledge to generic situations, as well
section of the OAME as real world contexts.
web site
Students will generate graphical and algebraic models from the
data calculated in tables of value.
11 Jazz Day
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-2
Nspire CAS Handheld Manual
Getting Started
When you turn on the handheld, press /N.
You will be asked whether you want to save the
document. Select No. To do this, use the large
circular "navpad" to move to the right, then press the
xbutton in the middle of the navpad.
Next select 1:Add Calculator. To do this, press the x button again.
You are now ready to use CAS on the handheld.
Some Helpful Shortcuts
If you make a mistake at any point that you want to undo, press /Z.
If you undo something that you want back again, press /Y.
How to Solve for a Variable: Example One
Say that you wish to solve the equation 6x – 2y = 16 in - 2y = 16. You will
see this result:
Continue solving the equation. You probably see that
to finally isolate the y variable, it is necessary to divide
the equation by -2 on both sides. Again, just start
typing the operation you want to perform. Press pv2.
The handheld will insert Ans for you. Press · to
calculate the result.
As you can see, the handheld reports that y = 3x - 8 .
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-3
Nspire CAS Handheld Manual (Continued)
How to Solve for a Variable: Example Two
Say that you wish to solve the equation 6x + 2y = 18 + 2y = 18. You will
see this result:
Continue solving the equation. You probably see that
to finally isolate the y variable, it is necessary to divide the equation by 2 on both sides. Again,
just start typing the operation you want to perform. Press p2. The handheld will insert Ans for
you. Press · to calculate the result.
As you can see, the handheld reports that
y = -3(x-3) .
Is this the result you expected?
Your teacher will discuss this with your class.
After the discussion, use the space below to write your
own explanation of what this means:
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-4
Nspire CAS Handheld Manual (Continued)
How to Check a Solution to a Linear System
Say that you have solved the following linear system:
4x + 2y = 24
8x - 6y = 18
9
and you believe the solution is , 3.
2
This would be tedious to check by pencil and paper, but it is quick to check with the handheld.
Here is how to do it. First be certain that you are on a Calculator page. If you need help with
this, see the Getting Started section from earlier in this manual.
You are going to press the following keys to check the solution against the first equation:
4X+2Y=24*X=9p2_AND_Y=3
9
This means: "Check this equation such that x and y 3 ."
2
Don't forget to press the _ key (lower-right corner of keypad) before and after the AND.
Here is what it will look like on your handheld screen:
To have the handheld check the solution, press the ·
key. If the solution is correct, the handheld will return
the result "true". If the solution is not correct, the
handheld will report "false".
9
You should find that the handheld reports that , 3 is a correct solution for the first equation.
2
Remember, it is necessary to check the solution in the second equation as well.
It works the same way as before, but you can save
some typing! Use the circular "navpad" and press up
twice. The first command you entered is highlighted.
Now press the · key. The handheld copies the
command down to the line you are working on. You
can now use the navpad to move left until the cursor
is behind the * symbol. It looks like this:
Press the . key to erase the first equation, then type the second equation. Then press ·.
9
As you can see, , 3 is a correct solution for the
2
second equation as well.
Since the solution is correct for both equations from the linear system, we know it must be the
right answer.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-5
Nspire CAS Handheld Manual (Continued)
How to Add or Subtract Two Equations
The elimination method for solving a linear system involves adding or subtracting the given
equations.
Say that you are considering the following linear system:
3x + 2y = 16
5x - 2y = 8
You probably agree that if we add these two equations, the y variable will be eliminated.
Here is how to do this on a handheld. First be certain that you are on a Calculator page. If you
need help with this, see the Getting Started section from earlier in this manual.
When you type in the equations, be certain to enclose them in brackets. Remember that we
decided to add the equations. Here are the keys you should press:
(3X+2Y=16)+(5X-2Y=8)
It will look like this on your handheld:
Press the · key. The handheld will display the result:
You have eliminated the y variable.
Subtracting two equations works the same way as adding two equations. The key is to
remember that you must enclose each equation in brackets when you type it into the handheld.
How to Multiply to Find an Equivalent Equation
Consider the following linear system:
2x - 5y = 7
6x + 3y = 3
If we immediately add or subtract the equations, neither the x or the y variable is eliminated.
Instead, we must multiply one of the equations by an integer so that the coefficients match.
Then, if we subtract the equations, a variable will be eliminated.
Let's multiply the first equation by 3. Remember that all terms on both sides of the equation
must be multiplied by 3, so that the equation stays balanced.
Here is how to do this on a handheld. First be certain that you are on a Calculator page. If you
need help with this, see the Getting Started section from earlier in this manual. Press the
following keys: 3r2X+3r-5Y=3r7
What you have typed should look like this:
Press the · key. The handheld will display
the result:
Now we have a system that we 6x - 15y = 21
can begin to solve by subtracting
6x + 3y = 3
the equations:
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-6
Grade 10
Unit 4 Day 1: Where Do We Meet? Applied
Installing TI-Nspire CAS Key Fonts - Teacher
In order to have the keys shown in your Word documents you need to download and
install the Nspire Keys font on your computer. Here's how:
Download the fonts:
1. Go to
2. Select Downloads from the top of the screen.
3. Go to the Key Fonts section and select TI-Nspire Key Fonts from the drop down box (you
may have to scroll to the bottom).
4. Click on the Download button.
5. Click on TI-Nspire(tm) Key fonts for Windows(r). Make sure you know where you are saving
the fonts (i.e. Desktop, My Documents, etc.).
Install the fonts:
1. Go to the Control Panel on your computer. Most computers just require you to click
on the start button and the control panel folder should be visible from the start menu.
2. Open the Fonts folder by double-clicking on it.
3. Go to the File Menu and Install New Font…
4. You will now need to find the TINspireKeys font file. Once you find it, select it from
the List of Fonts box and select OK.
5. An easier way: Minimize all windows except the Fonts folder window. Reduce the
size of this window so you can see the TINspireKeys font file on your desktop or in a
folder and drag and drop it in the Fonts folder.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-7
Math Learning Goals Materials
Minds On: 15 Min. BLM 4.1.1-4.1.3
Identify/Solve problems that arise from realistic situations that can be
Chart paper
modelled by two linear relations. Computer Algebra
Action: 45 Min. Determine graphically the point of intersection of two linear equations. Systems (CAS)
Consolidate/ Interpret the story the graph tells, including point of intersection and what
Debrief: 15 Min occurs before and after the intersection point.
Total = 75 Min.
Assessment
Opportunities
Minds On… Small Groups Guided Exploration Divide class into
Introduce the idea of systems of equations by building on linear application homogeneous
groups of at most 4
problems from the previous unit (BLM 4.1.1). students per group.
Whole Class Discussion
Summarize the idea of a Point of Intersection, or Solution to a System.
Action! Pairs Worksheet
Utilizing Think, Pair, Share, students interpret the system of equations
application scenarios (BLM 4.1.2), connecting them to the appropriate
equations, then discuss with the class.
Whole Class Discussion
Ensure that all of the students have the scenarios and equations matched
properly. Review the parts of y = mx + b, and how the words in the scenario
matched the components of the equations. E.g., flat fee corresponds with 'b',
the y-intercept.
Small Groups Practice
Assign students a letter A through D, and then have them work in their letter
group, attempting the problem associated with their letter. Students practice
analyzing systems of linear equations, creating a table of values, plotting
points, finding the point of intersection, and interpreting the meaning in the
larger context of the problem (BLM 4.1.2). Afterwards they must recreate the
graph on a sheet of chart paper and summarize their findings along with the
questions.
Consolidate Whole Class Presentation
Debrief Chart paper
Each of the letter groups presents their findings and displays their chart paper presentations should
graph. be evaluated to be
aware of misguided
Whole Class Discussion understanding.
Discuss the similarities in the types of questions for Problems A, B, and C,
and what makes Problem D different.
Home Activity or Further Classroom Consolidation
Assign BLM 4.1.3 as home activity and ask students to complete the
Reflection following journal entry.
Skill Drill Journal: The equation of a vertical line is x = a and the equation of a
horizontal line is y = b. Where will these lines intersect? Support your answer
with an example that includes a graph.
4.1.1: Working on Commission
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-8
Nahid works at Euclid's Electronics. She is paid a salary of $200 per week plus a commission of
5% of her sales during the week.
The equation P 0.05s 200 , represents Nahid's pay for the week where P represents the
total pay for the week and s represents her total sales.
If Nahid earned $290 in a week use the
equation to algebraically determine how
much she sold.
Use your handheld to help you solve. Refer
Week's Pay ($)
to the user manual if you need to review
how to solve using the handheld.
Total Value of Sales ($)
Nahid is offered another job at Fermat's Footwear, where the pay is a salary of $100 per week
and 10% commission on all sales. The graph below represents the Pay vs. Sales for this job.
Which of the following equations do you think represents pay for one week at Fermat's
Footwear?
a) P 0.01s 100
b) P 0.10s 100
c) P 100s 10
Week's Pay ($)
d) P 0.05s 200
Provide a reason or justify why you selected
the equation that you chose. Refer back to
the equation for Euclid's Electronics for hints.
4.1.1: Working on Commission (Continued)Total Value of Sales ($)
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-9
Nahid needs help determining
which job she should keep.
She decides to look at them as a
system of equations when she
creates a graph comparing the
two equations at the same time.
Analyze the graph and complete
the questions below.
Week's Pay ($)
_____ Euclid's Electronics
.…….. Fermat's Footwear
Total Value of Sales($)
1. Where the two lines cross is called the point on intersection, or the solution to the
system. At what coordinates do the two lines cross?
2. What does this coordinate represent in terms of Nahid's sales, and pay for the week?
3. If Nahid usually makes $1500 worth of sales per week, which job should she take? Explain.
4. How does the graph help Nahid determine which is the better job?
5. What does the point (1000, 250) represent in the graph?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-10
4.1.2: What's My Equation?
You are given four problems below. Each problem will require two equations to solve it. The
equations that are needed to solve each problem appear at the bottom of the handout. Match
the equations with the problems and compare your answers with another student.
Note: There are more equations than problems and all the equations use x for the independent
variable and y for the dependent variable.
Problem A: Equations
Yasser is renting a car. Zeno Car Rental charges $45 for the rental of the car
and $0.15 per kilometre driven. Erdos Car Rental charges $35 for the rental of
the same car and $0.25 per kilometre driven. Which company should Yasser
choose to rent the car from?
Problem B: Equations
The school council is trying to determine where to hold the athletic banquet. The
Algebra Ballroom charges an $800 flat fee and $60 per person. The Geometry
Hall charges a $1000 flat fee and $55 per person. Which location should the
school council select for the athletic banquet?
Problem C: Equations
The yearbook club is considering two different companies to print the yearbook.
The Descartes Publishing Company charges a flat fee of $475 plus $4.50 per
book. School Memories charges a flat fee of $550 plus $4.25 per book. Which
company should the yearbook club select to print this year's yearbook?
Problem D: Equations
The school is putting on the play "Algebra: The Musical". Adult tickets were sold
at a cost of $8 and student tickets were sold at a cost of $5. A total of 220
tickets were sold to the premiere and a total of $1460 was collected from ticket
sales. How many adult and student tickets were sold to the premiere of the
musical?
EQUATIONS:
1. y = 4.50 + 475x 2. 60 + 800x = y 3. y = 1000 + 55x 4. x = 45 + 0.15x
5. y = 1000x + 55 6. y = 45 + 0.15x 7. x + y = 220 8. 5x + 8y = 220
9. y = 4.25x + 550 10. y = 550x + 4.25 11. y = 800 + 60x 12. x + y = 1460
13. y = 0.25x + 35 14. y = 4.50x + 475 15. y = 35x + 0.25 16. 5x + 8y = 1460
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-11
4.1.2: What's My Equation? (Continued)
Problem A:
Yasser is renting a car. Zeno Car Rental charges $45 for the rental of the car and $0.10 per
kilometre driven. Erdos Car Rental charges $35 for the rental of the same car and $0.25 per
kilometre driven. Which company should Yasser choose to rent the car from?
To solve the question, complete the table of values, and the graph.
Zeno Erdos
Distance Cost Distance Cost
(km) (km)
0 0
10 10
20 20
30 30
Cost ($)
40 40
50 50
60 60
70 70
80 80
90 90
100 100
Kilometers Driven
1. How can the car rental cost and the cost per kilometre be used to draw the graph?
2. What is the point of intersection of the two lines? What does it represent?
3. Under what conditions is it best to rent from Zeno Car Rental?
4. Under what conditions is it best to rent from Erdos Car Rental?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-12
4.1.2: What's My Equation? (Continued)
Problem B:
The school council is trying to determine where to hold the athletic banquet. The Algebra
Ballroom charges an $800 flat fee and $60 per person. The Geometry Hall charges a $1000 flat
fee and $55 per person.
Which location should the school council select for the athletic banquet?
To solve the question, complete the table of values, and the graph.
Algebra Ballroom Geometry Hall Algebra Ballroom vs. Geometry Hall
Number Number
of Cost of Cost
People People
0 0
10 10
20 20 Cost ($)
30 30
40 40
50 50
60 60
70 70
80 80
90 90
100 100
Number of People
1. How can the flat fee and the per person cost be used to draw the graph?
2. What is the point of intersection of the two lines? What does it represent?
3. Under what conditions is it best to go with Algebra Ballroom?
4. Under what conditions is it best to go with Geometry Hall?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-13
4.1.2: What's My Equation? (Continued)
Problem C:
The yearbook club is considering two different companies to print the yearbook. The Descartes
Publishing Company charges a flat fee of $475 plus $4.50 per book. School Memories charges
a flat fee of $550 plus $4.25 per book. Which company should the yearbook club select to print
this year's yearbook?
To solve the question complete the table of values, and the graph.
Descartes School Memories
Number Number
of Books Cost of Books Cost
0 0
50 50
100 100
150 150 Cost ($)
200 200
250 250
300 300
350 350
400 400
450 450
500 500
Number of Books
1. How can the flat fee and the cost per book be used to draw the graph?
2. What is the point of intersection of the two lines? What does it represent?
3. Under what conditions is it best to go with Descartes Publishing?
4. Under what conditions is it best to go with School Memories?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-14
4.1.2: What's My Equation? (Continued)
Problem D:
The school is putting on the play "Algebra: The Musical". Adult tickets were sold at a cost of $8
and student tickets were sold at a cost of $5. A total of 220 tickets were sold to the premiere and
a total of $1460 was collected from ticket sales.
How many adult and student tickets were sold to the premiere of the musical?
To solve the question complete the table of values, and the graph.
Let x represent the # of student tickets sold
Let y represent the # of adult tickets sold
Number of Adult Tickets
x y x y
0 0
40 40
80 80
120 120
160 160
200 200
Number of Student Tickets
1. What is the approximate point of intersection of the two lines? What does it represent?
2. Does the rest of the graph (other than the POI) give us any information about the number of
tickets sold?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-15
4.1.3: Meaning of the Point of Intersection
1. Your family wants to rent a car for a weekend trip. Cars R Us charges $60.00 per weekend
for a midsize car plus $0.20 per km. Travel With Us charges $0.50 per km.
a. Graph both options on the grid and
determine the number of kilometres
where both companies will cost the
same amount.
b. Explain what this means for your
weekend trip.
2. Anthony and Anne are bicycling at a Provincial Park. Anthony travels at the rate of 10 km/hr
and begins 2 km from the park entrance. Anne begins at the park entrance and travels at a
rate of 15 km/hr. They both travel at a constant rate towards the Outdoor Education Centre.
Graph both routes on the grid and
determine the meaning of the point
of intersection.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-16
4.1.3: Meaning of the Point of Intersection (Continued)
3. For a car wash fundraiser Team A washes 2 cars per hour starting a 7:00 a.m.
Team B begins washing cars at 9:00 a.m. and washes 3 cars per hour.
Graph the car washing progress of each team on the grid and determine the meaning of the
point of intersection, as well as the meaning of the points before and after the point of
intersection.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-17
Grade 10
Unit 4 Day 2: What's the Point? Applied
Math Learning Goals Materials
Minds On: 15 Min. BLM 4.2.1-4.2.5
Determine the coordinates of the points of intersection for pairs of linear
Computer Algebra
relations given their graphs and interpret the meaning of the point of Systems (CAS)
Action: 35 Min. intersection. Chart paper and
Consolidate/ Solve a problem that arises from a realistic situation represented by two markers
Debrief: 25 Min linear relations.
Total = 75 Min.
Assessment
Opportunities
Minds On… Pairs Worksheet
Utilizing Think, Pair, Share, students interpret the linear system (BLM 4.2.1),
then discuss with the class. Stress the point that the solution depends on the
conditions under consideration.
Action! Whole Class Guided Exploration
Represent graphically a situation that is modelled by a linear system.
Students should understand the meaning of specific parts of the graph. e.g.,
point of intersection.
Demonstrate the graphical method of solving a linear system (BLM 4.2.2).
Discuss the questions; emphasize the meaning of the point of intersection in
terms of the problem.
Individual Practice
Students practice analyzing systems of linear equations, finding the point of
intersection, and interpreting the meaning in the larger context of the problem
(BLM 4.2.3).
Consolidate Pairs Investigation
Debrief Through a series of graphing activities (BLM 4.2.4) student explore the point
of intersection from different perspectives.
Whole Class Discussion
As a class discuss the strategies used. Left Side Right Side verification is
discussed as an alternative tool to graphing all of the lines to solve Questions
1 and 2. Students brainstorm as a class about Questions 3 and 5.
Home Activity or Further Classroom Consolidation
Solve the system of equations problems (BLM 4.2.5).
Concept Practice
Exploration
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-18
4.2.1: A Visual Cell Phone Problem
Two cell phone companies charge a monthly flat fee plus an additional cost for each minute of
time used. The graph below shows the Time vs. Cost relationship, for one month.
____ Talk More
…… We Talk
Cost ($)
Time (minutes)
1. What is the Point of Intersection (POI), and what is the meaning of the POI in relation to the
cell phone plans?
2. Under what conditions is it best to use the Talk More cell phone plan?
3. Under what conditions is it best to use the We Talk cell phone plan?
4. How does the graph help you to determine which cell phone plan is the most appropriate at
any given time?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-19
4.2.2: Music is My Best Friend
iTones and Music Mine are two online music providers. Each company charges a monthly
membership fee and then a per song download rate.
iTones charges $10 per month, and $1 per song C n 10
Music Mine charges $7 per month and $1.50 per song. C 1.5n 7
Where C represents the total cost for one month and n represents the number of songs
purchased.
Create a table of values showing the total charges for up to 8 songs purchased.
Graph the lines on the same graph below.
iTones Music Mine
n C n C
0 0
1 1
Cost ($)
Number of Songs
1. If Lulu plans to purchase 7 songs this month, which is the best plan for her? Explain.
2. Which plan is cheaper if you only plan to buy 4 songs per month? How do you know from the
graph?
3. Which cell phone plan would you choose and why? Relate your answer back to the POI.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-20
4.2.3: Where Do We Meet?
For each of the following situations, find the point of intersection and describe the meaning of
this point. Describe which company or service you would choose under what circumstances. A
template has been provided for the first situations.
A B
Point of intersection:_____________
Interpretation of the point:
Cost ($)
If the job lasts less than _____ hours,
choose ______. If the job lasts more
than ______ hours, choose _______.
If the job lasts _______ hours,
choose either company and the cost
is______
Time (hours)
Point of intersection:_____________
Interpretation of the point:
Cost ($)
If the kilometers driven is less than
A _____, choose ______. If the
B kilometers driven is more than
______, choose _______.
If the kilometers driven is _______,
choose either company and the cost
is______
Kilometers Driven
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-21
4.2.3: Where Do We Meet? (Continued)
For each of the following situations, find the point of intersection and describe the meaning of
this point. Refer back to the template provided for the first situations.
A
B Point of intersection:_____________
Interpretation of the point:
Cost ($)
Time (hours)
Point of intersection:_____________
C
Interpretation of the point:
B
Cost ($)
A
Talking Time (hours)
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-22
4.2.4: Does This Line Cross?
From the list of relations below, determine which lines cross through the point (2,3).
You may use the graph to assist you.
1. y 2 x 3
2. y x 1
3. y 2 x 7
4. y 3
5. x 2
6. y 2
Questions:
1. Which of the lines passes through the point (2,3)?
2. Is there another way to determine if the line passes through the point, other than graphing?
Explain.
3. Without graphing, how can you quickly determine if a horizontal or vertical line passes
through a point?
4. Other than the point (2, 3), what are the other points of intersection on your graph?
5. Is it possible for two lines to have more than one point of intersection with each other?
Discuss this with your partner.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-23
4.2.5: Is this Accurate?
1. Find the point of intersection. (Solve the system using graphical method.)
a) y = 2x + 1 b) y = -x -2
y = 3x – 2 y = 2x + 7
Point of intersection is :_______________ Point of intersection is:________________
c) y = 2x + 1 d) y = -5
y = 4x – 4 y = -3x+2
Point of intersection is :_______________ Point of intersection is :_______________
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-24
Grade 10
Unit 4 Day 3: Approximate or Accurate? Applied
Math Learning Goals Materials
Minds On: 15 Min. BLM 4.3.1-4.3.5
Discuss accuracy of solutions obtained through graphical means. Computer Algebra
Establish the need to isolate a variable in order to use the substitution Systems (CAS)
Action: 50 Min. method and practice the skill of isolating. Overhead
Consolidate/ Develop understanding of facility of solving systems using the projector
Debrief: 10 Min BLM 4.3.3
substitution method to improve the accuracy of a solution.
transparency or
computer with
LCD projector
and FLV video
Total = 75 Min. player
Assessment
Opportunities
Minds On… Pairs Investigation Students are
Distribute BLM 4.3.1 to each student. Students are to work in pairs. One student in encouraged to use
CAS to check their
each pair is to solve one of the problems. Students are to then exchange solutions and
solutions. They will
provide feedback to each other regarding their solution. Write the heading "System A" probably get a
and "System B" on the board chart paper or overhead transparency. Students are to "false" statement
write their solution to each system under the appropriate heading. returned which
Whole Class Discussion should reinforce the
Discuss the solutions provided to each system. Ask for reasons as to why their approximate nature
solutions are not exactly the same. The goal is to draw out the approximate nature of of their solution.
the solutions and that this is one of the disadvantages of solving systems graphically.
Students can use
Action! Individual Worksheet CAS to solve their
Distribute BLM 4.3.2 to each student. Students are to solve these "simple" systems equations using an
algebraically and note which equation they solve first in each equation and why they explicit method (not
chose that equation. The goal is to stress that they can only solve equations that are using the SOLVE
expressed in a single unknown. command).
Whole Class Demonstration If an overhead
Using BLM 4.3.3, display the first system on an overhead projector. Ask the class to projector is not
identify what is different about the system they see on the overhead projector from the available, use scrap
ones that they were able to solve on BLM 4.3.2. Stress student responses that highlight paper with the
individual pieces of
the fact that both equations now have two unknowns. Note: The first system is one of
both equations
the systems they solved in the Minds On (BLM 4.3.1 System B). written on each
To solve the system, lead the class in demonstrating the method of substitution by piece of paper and
cutting the overhead along the dotted lines and physically replacing the "y" in the post on the board or
second equation with the expression "2x + 7" from the first equation. Ask students use the movie file
why this is correct mathematically. "Method of
Sub_Intro" that
Distribute BLM 4.3.3 (Student Worksheet) and ask students to solve the resulting demonstrates the
equation. Repeat this process using the second system on BLM 4.3.3. Note that in the process. Note: The
second system we could isolate either x or y. process is narrated
in the file.
Small Groups Worksheet
Using BLM 4.3.4, in groups of three, each student solves one of three systems. The Students are to
point of intersection for each is: System A (-4, 8); System B (0, -4); System C (2, -10). identify which is
The three points are collinear. The students are to determine the equation of the line cheaper before the
connecting all three. The correct equation is y = -3x – 4. point of intersection
(lower flat fee) and
Consolidate Small Groups Worksheet which is cheaper
Debrief Distribute BLM 4.3.5 to students. Each group is to divide the three problems among after (lower rate of
the group members and solve them using substitution and then complete the questions change).
on the reverse of the handout. The goal is to identify for what types of problems the
method of substitution is preferable to solving by graphing (i.e. approximate solutions
and/or values for graphing are to large for practical solution).
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-25
Home Activity or Further Classroom Consolidation
Journal: Dillon was absent for today's lesson. Explain to him how to find the point of
Concept Practice
intersection between 4x - y = 7 and 6x + y = 13. Provide a detailed explanation of
Reflection
each step.
Assign concept practice questions.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-26
4.3.1: What's my POI?
Each one of you will solve one of the systems of equations given below.
Once you have solved the system you were assigned, trade with your partner and check
their solution. Share your feedback with your partner.
Once you have shared your feedback and are confident in the solutions to the systems,
post your point of intersection under the appropriate heading on the class list.
System A System B
1 y 2x 7
y x 1
2 y 3 x 4
y 3 x 4
Point of Intersection: ( , ) Point of Intersection: ( , )
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-27
4.3.2: A Better Way
Solve the following systems of equations algebraically. Use your CAS handheld to solve and
check if needed.
1. Equation 1: y + 2 = 10 and Equation 2: x + y = 12
Point of intersection: (____, ____)
2. Equation 1: 3x + 2y =33 and Equation 2: 2x = x + 7
Point of intersection: (____, ____)
In each of the systems you solved above, which equation did you choose
to solve first? Why did you select that equation in each case?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-28
4.3.3: Putting the Pieces Together – Teacher Demonstration
y = 2x + 7 and y = -3x + 4
-2x + y = 0 and x - y = 12
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-29
4.3.3: Putting the Pieces Together – Student Worksheet
System 1: y = 2x + 7 and y = -3x + 4System 2: -2x + y = 0 and x - y = 12TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-30
4.3.4: The "Sub" Way
In groups of three, have each person in the group solve one of the systems below.
Use your CAS handheld to help you solve and check your system.
Share your solutions with each person in the group.
System A System B
y = 4x + 24 and y = -5x – 12 13x + y = – 4 and 5x + y + 4 = 0
System C Challenge
y = -x – 8 and y = -5x CHALLENGE: Plot each of the POI's from
Systems A, B, and C and find the equation of
the line that connects the three points.
Equation of Line:_____________________
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-31
4.3.5: What's My Equation? - Part 2
Part A
Let's return to our application problems that we solved graphically earlier in the unit.
Assign each person in your group one of the three problems to solve. Solve these
application problems using the method of substitution introduced today. Use the CAS
handheld to help you solve.
Problem A:
Equations
Yasser is renting a car. Zeno Car Rental charges $45 for the rental
of the car and $0.15 per kilometre driven. Erdos Car Rental charges
y = 45 + 0.15x
$35 for the rental of the same car and $0.25 per kilometre driven.
For what distance do the two rental companies charge the same
y = 35 + 0.25x
amount?
Problem B:
Equations
The school council is trying to determine where to hold the athletic
banquet. The Algebra Ballroom charges an $800 flat fee and $60
y = 60x + 800
per person. The Geometry Hall charges a $1000 flat fee and $55
per person. For what amount of guests do the two banquet halls
y = 55x + 1000
charge the same amount?
Problem C:
Equations
The yearbook club is considering two different companies to print
the yearbook. The Descartes Publishing Company charges a flat fee
y = 475 + 4.50x
of $475 plus $4.50 per book. School Memories charges a flat fee of
$550 plus $4.25 per book. For what amount of books do the two
y = 550 + 4.25x
companies charge the same amount?
____________________________________________________________________________
I am solving problem ___:
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-32
4.3.5: What's My Equation? - Part 2 (Continued)
Part B
Discuss the following questions with your group members.
1. Looking at your problem, how can you tell from the equation which company is cheaper
before the point of intersection (where the costs are equal)?
2. Looking at your problem, how can you tell from the equation which company is cheaper after
the point of intersection (where the costs are equal)?
3. Is this true for all problems?
4. Now that you've solved the problems using two different methods, which method do you
prefer? Why?
5. When do you think solving by substitution would be preferable to solving by graphing?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-33
Grade 10
Unit 4: Day 4: The SubMathiner Applied
Math Learning Goals: Materials
BLM 4.4.1-4.4.4
Minds On: 10 Determine the conditions for which a linear relation application is preferred to Scissors
the algebraic models by comparing the rate of change and initial value of two
Glue
linear relations making up a system of equations.
Action: 55 Identify which variable is the most efficient for isolating and then solve linear Computer Algebra
Systems (CAS)
systems using the method substitution.
Consolidate:10
Total=75 min
Assessment
Opportunities
Minds On… Individual Worksheet Refer back to the
graphical solution of
Distribute BLM 4.4.1 to each student. Students are to complete the solution to
this problem and
the contextual problem as a review of solving by substitution. connect the
Optional: Discuss the home activity assigned in yesterday's class to consolidate appropriate region of
the graph with the
the algorithm for solving by substitution. appropriate part of
the solution.
Action! Pairs Kinesthetic Activity
Students will need
Distribute BLM 4.4.2 and a blank piece of paper to each pair of students. scissors and glue for
Students are to cut the boxes necessary for the solution of the system at the top of this portion of the
the handout and glue them on the blank piece of paper. Once they have lesson.
completed their solution, they are to compare their solution with another pair of
students.
Whole Class Discussion
Ask students what is different in solving this system from the systems they were
solving the previous day. Highlight the need to distribute once they have
substituted in the expression.
Small Groups Investigation
Distribute BLM 4.4.3 to each student. After students respond to #1, highlight the
importance of identifying which variable it is easiest to isolate for when using
substitution. Students will complete the solution to one of the three systems
provided. The solution to all three systems is (-1, 2). Check to see that students
understand that as long as a system has values that follow an arithmetic
progression, the solution to the system will be (-1,2). Discuss as a class the
second equations created in question #7 to ensure that everyone has the correct
systems as these will be assigned for students to complete for their home activity.
Consolidate Pairs Worksheet
Debrief Distribute BLM 4.4.4 to each student. Students are to write the algorithm for
solving by substitution using the text boxes provided and then solve the system
as model of solving by substitution.
Whole Class Discussion
Discuss correct order of steps for solving by substitution.
Home Activity or Further Classroom Consolidation
Complete the systems created in question #7 from BLM 4.4.3.
Skill Practice
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-34
4.4.1: The Lowdown on Downloads
Let's return to our music downloading problem. Here's the problem again.
iTones and Music Mine are two online music providers. Each company charges a
monthly membership fee and then a per song download rate.
iTones charges $10 per month, and $1 per song C x 10
Music Mine charges $7 per month and $1.50 per song. C 1.5x 7
1. Find the number of songs that I would need to download where the costs are the same for
the two music providers.
2. Paris solved the problem and then made the following conclusion:
If you download less than 6 songs per month than choose iTones
since the cost per song is less. If you download more than 6
songs per month than choose Music Mine since the fixed cost is
less. If you download exactly 6 songs per month, choose either
music provider.
Is the conclusion that Paris made correct? If not, underline the part(s) of her conclusion that are
incorrect and then rewrite it so that it is correct.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-35
4.4.2: Putting the Pieces Together
Solve the system: y = 10 – 2x and x – 2y = 10
The solution to this system is given in the pieces below. Cut the pieces out and glue
them in the correct order on a separate piece of paper. Use the handheld to help you.
Hint: There are 10 steps in the complete solution.
x – 2(10 – 2x) = 10 –x = 20
x=6 Point of Intersection: (6,-2)
x – 20 – 4x = 10 y = 10 – 12
y = 14 x – 10 – 2x = 10
y = -2 y = 10 – 2(6)
5x = 10 + 20 x = 30/5
–x = 10 + 10 5x = 30
x = -20 x – 20 + 4x = 10
x = -2 Point of Intersection: (-2,6)
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-36
4.4.2: Putting the Pieces Together – Solution (Teacher)
Solve the system: y = 10 – 2x and x – 2y = 10
The solution to this system is given in the pieces below. Cut the pieces out and glue them in the
correct order on a separate piece of paper. Use the handheld to help you. Hint: There are 10
steps in the complete solution.
x – 2(10 – 2x) = 10
x – 20 + 4x = 10
5x = 10 + 20
5x = 30
x = 30/5
x=6
y = 10 – 2(6)
y = 10 – 12
y = -2
Point of Intersection: (6,-2)
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-37
4.4.3: An Interesting Problem
Consider the following three systems of equations:
System A System B System C
x + 2y = 3 and 4x + 5y = 6 -2x + y = 4 and 7x + 10y = 13 -5x – 3y = -1 and x + 3y = 5
1. In order to solve these systems by substitution, we need to first isolate one variable in one
equation. Circle the variable in each system that would require just one step to isolate.
Compare your choice with a neighbour.
2. Using your handheld to help you, isolate the variable you selected in #1 for each system.
System A System B System C
3. Assign each system to one person in your group and solve the system assigned to
you in the space below. Use your handheld to help solve and check.
I am solving system _____:
Point of Intersection (_____, _____)
4. Compare your solution to the rest of the group. What do you notice?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-38
4.4.3: An Interesting Problem (Continued)
5. The chart below lists out only the numbers that appear in each system. What do you
notice about the numbers in each system?
System A System B System C
1, 2, 3, 4, 5, 6 -2, 1, 4, 7, 10, 13 -5, -3, -1, 1, 3 , 5
6. Let's see if this works with more systems. Each system below has only one equation
given. Assign each system to one person in the group and create a second equation
that will give the solution (-1, 2) when solved.
System A System B System C
Equation 1: x + 6y = 11 Equation 1: -14x – 9y = -4 Equation 1: 9x + 7y = 5
Equation 2: ____________ Equation 2: ____________ Equation 2: ____________
7. Share your equation with everyone in the group and copy down the equations from
the rest of the group. Review the equations created and make sure they follow the
rule that you noted in #5. You will solve these three systems as a part of your home
activity.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-39
4.4.4: The Sub Steps
Solving using the method of substitution requires five steps. The steps are given below in the
text boxes. Discuss with your partner what you think the correct order is for the steps and then
write the steps in the space provided. Solve the system in the chart as model of solving by
substitution. Check using your handheld.
State the point of intersection. Solve the resulting equation.
Substitute the isolated expression into Substitute your solution into an original
the other equation. equation to solve for the other variable.
Isolate for a variable. The easiest variable
to isolate for has a coefficient of 1.
Example: Solve
Steps for Solving by Substitution
4x + y = 6 and 2x – 3y = 10
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-40
Grade 10
Unit 4 Day 5: There Is Another Way! Applied
Math Learning Goals Materials
Minds On: 15 Min. BLM 4.5.1- 4.5.4.
Identify situations where the solving by substitution is not efficient.
Computer Algebra
Identify necessary conditions or "look-fors" that make solving by Systems (CAS)
Action: 45 Min. elimination possible. BLM 4.5.4 cut out
Consolidate/ Develop the algebraic method of solving a system by elimination. (1 eqn/student)
Debrief: 15 Min
Total = 75 Min.
Assessment
Opportunities
Minds On… Pairs > Investigation
Students are given a contextual problem (BLM 4.5.1) to be solved by
substitution, using Think, Pair, Share. Discuss issues that occur when they
try to solve the problem. Lead students to the conclusion that we need a
better way to solve this system.
Action! Pairs > Worksheet
Distribute BLM 4.5.2. Students add and subtract equations in a given set of
linear systems. Identification of what operation (+/-) will eliminate a
variable. Develop necessary conditions for elimination.
Whole Class > Guided Example
Reinforce the elimination algorithm for students using BLM 4.5.3.
Whole Class > Kinesthetic Activity
Using BLM 4.5.4, students find their 'elimination partner' who has an
equation suitable for eliminating a variable by addition or subtraction. Each
equation will have only one suitable match. Checks for student understanding
of the conditions necessary for elimination.
Consolidate Individual > Practice
Debrief
Students return to the contextual problem discussed in the Minds On (BLM
4.5.1) and solve by elimination. Students to check their solution using CAS.
Whole Class > Discussion
Compare ideas on conditions necessary for elimination.
Home Activity or Further Classroom Consolidation
Students create three sets of equations in which one variable could be
eliminated.
Reflection
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-41
4.5.1: A Trip to Jim Hortons – Teacher Notes
In question 1, encourage students to develop equations to represent the context given.
This will help students prepare for the summative task in this unit.
The linear system that describes the context:
5s 7e 14.95
3s 7e 12.75
… is designed to be problematic when solved by substitution, but simple to solve by elimination.
When solving by substitution, students will note that upon re-arranging to solve for a variable,
fractional coefficients and/or repeating decimals are encountered.
4.5.2: An Elimination Introduction – Notes to Teacher
After discussing the introduction to this section, you may wish to have your students go through
the "How to Add or Subtract Two Equations" section of the CAS manual included at the
beginning of this unit file.
The purpose of this exercise is for students to understand that adding and subtracting equations
can eliminate a variable. After completing the exercise students should be able to identify what
conditions are necessary for elimination to occur when adding, and what conditions are
necessary for elimination to occur when subtracting.
The use of the CAS on the handheld is encouraged to allow a student to complete this exercise
even if their algebra skills are not at grade level.
4.5.3: Solving a Linear System by Elimination – Teacher
Notes
Guide students to a solution for the system. Use of CAS is encouraged so that students with
algebra skills that are below grade level are still able to learn the elimination algorithm.
Students to describe in their own words the steps required to solve a linear system by
elimination after guided example. Show students how to check a solution to a linear system
using CAS on the handheld (see CAS manual at the beginning of the unit file).
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-42
4.5.1: A Trip to Jim Hortons
It's summer vacation. Ah, sweet freedom. The only problem is that you're the designated
coffee gopher at the office where you have a summer job. On Monday, you were sent out to
Jimmies to pick up five small coffees and seven extra large coffees. You remember that the
total cost was $14.95, including tax. On Tuesday, you were sent out to get three small coffees
and seven medium coffees. You recall that the total came to $12.75, with tax.
It's Wednesday morning and your coffee crazy co-workers are calling for their cup o' joe.
Unfortunately, since the morning fix hasn't arrived yet, no one can remember how much a small
or extra large coffee costs, including yourself. You need to find out how much each size costs
to collect the correct amount of money for the Wednesday coffee run.
1. Let s be the number of small coffees ordered on a single day.
Let e be the number of extra large coffees ordered on a single day.
As a class, can we decide on an equation to represent the purchases made on Monday,
and an equation to represent the purchases made on Tuesday?
Monday's equation: ___________________________________________________
Tuesday's equation: ___________________________________________________
2. Now we have a linear system. Take a few minutes to solve the linear system using
substitution in the space below. Then pair with another student to discuss your solution.
3. What problems, if any, did you encounter?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-43
4.5.2: An Elimination Introduction
You know that two integers can be added, or subtracted:
5 15
7 6
12 9
In the same way, equations can be added, or subtracted:
3x 2y 19 10x 20y 80
10x + 15y 25
5x 2y 5
8x = 24 5y = 55
Notice that by adding the equations in the first linear system, the y variable was eliminated
(there were 0y), which makes it possible to solve for x .
By subtracting the equations in the second linear system, the x variable was eliminated (there
were 0x), which makes it possible to solve for y .
1. Work in pairs to consider the following linear systems. Decide what operation – addition or
subtraction – would result in the elimination of a variable. You may use CAS on the
handheld to help you decide.
9x + y = 4 3x - y = 50 -7x - 6y = 338
14x + y = -1 12x + y = 115 9x + 6y = -366
18x - 5y = 454 19x + 2y = 102 17x - 8y = 323
12x - 5y = 316 19x - 2y = 50 6x + 8y = 114
9x - 4y = 235 7x - 16y = 441 5x - 3y = 188
15x + 2y = 409 7x - 17y = 476 6x - 11y = 344
2.
What needs to be true about a linear system so that a variable is eliminated when the
equations are added or subtracted?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-44
4.5.3: Solving a Linear System by Elimination
1. How would you begin solving this linear system? Addition or Subtraction?
5x + 4y = 7
3x - 4y = 17
2. Solve the system.
3. In your own words, describe what you must do to solve a linear system by elimination.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-45
4.5.4: Find Your Elimination Partner - Set of Systems
(Teacher)
Give each student in your class an equation. Matching equations are organized here beside
each other. Students to move around room and find their elimination partner, then solve the
system together and check the solution using CAS on the handheld. Solutions for teacher
reference included at right. Each equation works only with it's partner as shown in the table
below. Once they have found their partner, have them work together to solve. They may use
CAS to check the solution.
6x + 4y = 12 6x − 9y = 51 (4,-3)
4x – 3y = -10 2x + 3y = 22 (2,6)
5x + 2y = -11 x + 2y = -7 (-1, -3)
7x + 13y = 72 7x – y = -194 (-25, 19)
18x - 11y = 360 13x - 11y = 315 (9,-18)
11x + 15y = 204 8x + 15y = 222 (-6,18)
9x + 5y = 173 2x + 5y = -86 (37,-32)
10x + 30y = 60 -10x + 20y = 40 (0, 2)
12x + 18y = 36 12x + 12y = -36 (-15, 12)
48x + 16y = 48 16x + 16y = -16 (2, -3)
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-46
Grade 10
Unit 4 Day 6: There Is Another Way! – Part II Applied
Math Learning Goals Materials
Minds On: 15 Min. BLM 4.6.1-4.6.6
Determine that an equation multiplied by a constant is equivalent to the
Computer Algebra
original equation. Systems (CAS)
Action: 45 Min. Develop a complete algorithm for the algebraic method of elimination to Six overhead
Consolidate/ solve a linear system. marker; multiple
Debrief: 15 Min Solve problems using the method of elimination that arise from realistic colours suggested.
situations described in words. Overhead
projector and 5
copies of BLM
Total = 75 Min. 4.6.1 transparency
Assessment
Opportunities
Minds On… Small Groups > Guided Exploration Make five copies of
BLM 4.6.1 on an
Divide class into groups of four students. Display graph of points from the overhead
equation x + 2y = 6 on an overhead. Each group is then given a constant to transparency. Select
multiply this equation by. Groups create a table of values for their new constants from the
group 2, 4, 8, 12,
equation, and plot the points on an overhead copy of BLM 4.6.1. Each and 20.
group's sheet is then placed over the original plot shown. Students will see
that their "new" equations are equivalent to the original. Ask students to
comment on what they observe as each group places their graph over the
original transparency.
Action! Whole Class > Guided Example
Distribute BLM 4.6.2. Students use what they have observed from the Minds
On to modify a linear system such that a variable will be eliminated by
addition or subtraction.
Pairs > Worksheet
Distribute BLM 4.6.3. Using Think, Pair, Share, return to an earlier example
from this unit and solve by elimination. One half of class instructed to
eliminate x variable, the other half instructed to eliminate y variable. Discuss
why the decision to eliminate one variable first as opposed to another does
not change the solution.
Individual Practice > Worksheet
Using BLM 4.6.4, students solve two linear systems based on contextual
examples.
Consolidate Pairs > Reflection
Debrief
Distribute BLM 4.6.5. Given a question, students are asked to write a
summary of the steps necessary to solve by elimination.
Whole Class > Discussion
Introduce the performance task to students. Students will be asked to develop
a context, include a linear system that describes the context, and then solve
the linear system, by graphing, and by the students' choice of substitution or
elimination.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-47
Home Activity or Further Classroom Consolidation
Using BLM 4.6.6, provide practice with questions that have parallel and
coincidental solutions.
Concept Practice
Skill Drill
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-48
4.6.1: What's the difference?
Original equation: x 2y 6
Multiply the equation by the constant ______. The new equation is _____________________.
Complete the table of values for your equation and plot the values on the grid provided.
x -4 -2 0 2 4
y
10
8
6
4
2
-10 -8 -6 -4 -2 2 4 6 8 10
-2
-4
-6
-8
-10
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-49
4.6.2: Elimination Preparation
1. Consider the following linear system:
3k 15m 15
k m 1
If you add or subtract the equations, will a variable be eliminated? Explain.
2. What could be done to create the conditions necessary for elimination?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-50
4.6.3: Algebra, the Musical, Redux
Recall that in the first lesson of this unit, you solved the following problem by graphing:
The school is putting on the play "Algebra: The Musical". Adult tickets were sold
at a cost of $8 and student tickets were sold at a cost of $5. A total of 220 tickets
were sold to the premiere and a total of $1460 was collected from ticket sales.
How many adult and student tickets were sold to the premiere of the musical?
If x represents the number of student tickets sold, and y represents the number of adult
tickets sold, then the equations that model this problem are:
(from cost of tickets) 5x 8y 1460
(from number of tickets sold) x y 220
You probably remember that this problem took a while to solve by graphing, and the answer you
found was not necessarily very accurate, since you read the point of intersection off of the
graph.
You will work with a partner now to solve this problem using the method of elimination.
1. Since you have been asked to eliminate the x or y variable (circle one) first, what will be
the first step you take to create the conditions necessary for elimination?
2. Solve the linear system now. You may use CAS to help find the answer and check the
solution. Use the space below for rough work.
3. Does it matter which variable is eliminated first? That is, does it change the final answer?
4. Think back to when you solved this problem by graphing. Do you find the method of
elimination easier or harder? Explain.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-51
4.6.4: Two for You
Try solving the following questions using the method of elimination. You may use CAS on the
handhelds to help solve the questions and check your solutions.
1. A fitness club charges an annual fee and an hourly fee. In a single year, member A worked
out for 76 hours and paid $277 in total. Member B worked out for 49 hours and paid $223
in total. What is the annual fee? What is the hourly fee?
HINT: Start by writing "let" statements to define the variables you will use. For example:
Let a represent the amount of the annual fee.
Let h represent the amount of the hourly fee.
2. This past summer, you ran a food booth at a local festival. You sold hotdogs for
$1 each and samosas for $2.50 each. From 205 purchases, you made $400 in total. To
help plan purchases for next year's festival, you'd like to know how many hotdogs and
samosas were sold. Unfortunately, you forgot to keep track of this when selling the food.
Can you determine how many hotdogs and samosas were sold?
NOTE: Assume one hotdog or one samosa per purchase.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-52
4.6.5: Help an Absent Friend
Consider the following linear system:
2x 3y 1
3x y 7
How would you solve it? Write in words a description of the steps you would take.
To help you understand what to write, pretend for a moment that you are writing the instructions
for a friend who is not in class today. What steps would you need to describe?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-53
4.6.6: "Here's To The Crazy Ones"
1. Solve the following linear system by elimination:
4x 2y 12
8x 4y 32
2. Did you encounter any results that are unusual? Explain what is different compared to
questions you have already solved.
3. Re-arrange each equation from the linear system into y mx b form, then graph.
For example, here is how the first equation can
be re-arranged: 10
8
4x 2y 12
2y 4x 12 6
2y 4x 12 4
2 2 2 2
y 2x 6
-10 -8 -6 -4 -2 2 4 6 8 10
-2
-4
-6
-8
-10
4. What do you notice about the slope in each equation that you re-arranged? What do you
notice about how the two lines visually relate to each other? Is there a solution to this linear
system?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-54
4.6.6: "Here's To The Crazy Ones" (Continued)
5. Solve the following linear system by elimination:
6x 2y 2
12x 4y 4
6. Did you encounter any results that are unusual? Explain what is different compared to
questions you have already solved.
7. Re-arrange each equation from the linear system into y mx b form, then graph.
10
8
6
4
2
-10 -8 -6 -4 -2 2 4 6 8 10
-2
-4
-6
-8
-10
8. What do you notice about the slope and y-intercept in each equation that you re-arranged?
What do you notice about how the two lines visually relate to each other? Is there a
solution to this linear system? If so, how many?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-55
Grade 10
Unit 4 Day 7: Which One is Best? Applied
Math Learning Goals Materials
Minds On: 20 Min. Identify necessary conditions or "look-fors" in a system of equations that BLM 4.7.1-4.7.5
Computer Algebra
make it best suited to be solved by graphing, substitution or elimination. Systems (CAS)
Action: 35 Min. Solve a system of equations using two of the three methods. Overhead
Consolidate/ Solve a system of linear equations using the most appropriate method. projector and
Debrief: 20 Min BLM 4.7.2
transparency and
signs of BLM
Total = 75 Min. 4.7.1
Assessment
Opportunities
Minds On… Whole Class Kinesthetic Activity
Teacher explains the 4 Corners activity and indicates that signs are in each
corner representing the methods of Graphing, Substitution, Elimination, and
Not Sure (BLM 4.7.1). The teacher then puts up the overhead (BLM 4.7.2)
displaying the first set of equations. Students must go to the corner with the
method that they believe is the best method for solving. Each corner must
justify their method choice. Work through the three sets of equations.
Whole Class Discussion
The overhead displaying all of the 4 Corners questions is displayed.
Students are asked to match the three sets up with one of the methods, and
they can only use each method once. E.g, System 1 is best suited to
elimination. System 3 could be graphing or substitution, but substitution is
best used for System 2, therefore System 3 is graphing. Discuss what aspects
make a system of equations best suited to a certain method.
Action! Pairs Worksheet
Utilizing Think, Pair, Share, students must solve the three sets of equations,
choosing one of them to solve using two methods (BLM 4.7.3).
Whole Class Guided Exploration
Take up the three sets of questions by having students put their solutions on
the board using as many methods as are appropriate. Discuss the key aspects
again for selecting a method.
Consolidate Small Groups Model Making Assign Frayer model
as an assignment to
Debrief Students work in groups of three to complete a Frayer Model (BLM 4.7.4) on be submitted next
one of the Graphing, Substitution, or Elimination methods. class
Home Activity or Further Classroom Consolidation
Students practice solving using multiple methods, and identifying the best
Application method (BLM 4.7.5)
Concept Practice Remind students to start thinking about ideas for summative, where they must
create their own 'real-life' question with systems of equations.
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-56
4.7.1: Four Corners
NOT
SURE
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-57
4.7.1: Four Corners (continued)
GRAPHING
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-58
4.7.1: Four Corners (continued)
SUBSTITUTION
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-59
4.7.1: Four Corners (continued)
ELIMINATION
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-60
4.7.2: Which Method?
2 x 3 y 10 System A
4x 5 y 2
____________________________________________________
y x2 System B
x 5 y 4
______________________________________________
y 2x 7 System C
y 4 x 5
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-61
4.7.3: Which Method? (Continued)
Graphing:
For System A determine if you
can solve the system using
each of the three methods you
have learned, and if you can,
then solve.
2 x 3 y 10
4x 5 y 2
Justification:
Justify why you can or cannot
solve using this method.
Substitution: Elimination:
Justification: Justification:
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-62
4.7.3: Which Method? (Continued)
Graphing:
For System B determine if you
can solve the system using
each of the three methods you
have learned, and if you can,
then solve.
y x2
x 5 y 463
4.7.3: Which Method? (Continued)
Graphing:
For System C determine if you
can solve the system using
each of the three methods you
have learned, and if you can,
then solve.
y 2x 7
y 4 x 564
4.7.4: The Frayer Model
Definition Facts/Characteristics
Examples Non-Examples
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-65
4.7.5: 3 Ways
Two catering companies provide food and the banquet hall for weddings, proms and
anniversaries. Nick and Heather are getting married in September and they have two
catering companies to choose from:
Cookie's Frugal Gourmet
Catering Minestrone
Cesaer Salad Soup
Chicken Picatta Mixed green
Roasted salad
Potatoes Prime Rib
Steamed Garlic Mashed
Vegetables Potatoes
Sherbert Asparagus
Coffee or Tea Apple Pie
Coffee or Tea
The cost(C) for the different menu options Solve the system using the graphing
includes the cost of the hall rental and method:
price per person(n).
Cookie's Catering: C= 40n+500
Frugal Gourmet: C=45n+350
Cookie's Catering Frugal Gourmet
Point of intersection:_________________
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-66
4.7.5: 3 Ways (Continued)
Solve the system using substitution Solve the system using elimination
Point of intersection:_______________ Point of intersection:_________________
What does the point of intersection mean You used 3 different methods to solve the
in this catering problem? system, what did you notice about the
points of intersection? Does this surprise
you?
Nick and Heather have invited 80 people Heather prefers the Frugal Gourmet menu
to their wedding. How much will it cost for to Cookie's Catering. How much more will
each menu? she pay for her preference?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-67
4.7.5: 3 Ways (Continued)
The student council is providing lunch and music for the grade 10 class. They have two quotes
from Lunch Express and Let's Do Lunch. The costs for each were given as follow:
Lunch Express: If 100 students attend, it will cost $1 000. If 200 students attend, it will cost $1
500.
Let's Do Lunch: If 50 students attend, it will cost $700. If 150 students attend, it will cost $1
350.
Solve the system using the three different methods.
Equations for the companies:
Lunch Express:_____________ Let's Do Lunch:__________________________
Lunch Express Let's Do Lunch
Graphing Method Substitution Method
Point of intersection:_________________ Point of intersection:_________________
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4-68
4.7.5: 3 Ways (Continued)
Elimination Method The student council has $1 800 in their budget
for the lunch. They prefer Let's Do Lunch,
what is the greatest number of grade 10
students they can have at the lunch?
Point of intersection:____________________
What does the ordered pair (25,750) mean on the Lunch Express line?
TIPS4RM Grade 10 Applied: Unit 4 – Linear Systems (August 2008) 4- |
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science.
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid's Elements.
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. |
Math labs help students nail challenging topics"We launched the session on Graphing Equations first because, according to the math instructors we polled, that was the most challenging concept for students to grasp," says Michael Rasmussen, CME project lead.
Interested math students may visit the CME to sign up for complimentary labs facilitated by math instructors who interact with the students via WebEx® web conferencing software and a telephone line.
"During the lab, faculty members field questions from students," Rasmussen says. "Either the faculty member or the student can work on the problem, sharing work with the group."
The Graphing Equations lab has been offered since March, he notes, but other popular topics will go live this month, including Order of Operations, Variables and Simple Equations.
Each session lasts an hour. Students are welcome to stay as long as they want and return throughout the week. This is especially beneficial, Rasmussen points out, for those who want extra reinforcement.
He says the feedback so far has been "phenomenal." "Students go into the session really confused, and then the ones who get it often stick around for the second session and volunteer to help those who are still stuck." |
Find a Litchfield, NH Algebra 1
...In these studies, mathematics is an indispensible tool to deconvolute and understand the experimental results. Math is also used to model and evaluate possible mechanisms of the reaction pathway. Truly, math is the queen of the sciences as well as a necessity in everyday life. |
Modify Your Results
As a high school student in Alabama, you know that passing the Alabama High School Graduation Exam (AHSGE) is required for graduation. The eight Countdown Tests in this book will help you prepare for the Reading Comprehension and Language areas of the test. Each multiple-choice test item relates to an AHSGE Reading Comprehension Objective or Language Objective. There are additional practice tests at the end of each unit.
Designed to meet the needs of today's classroom, Glencoe Literature has been developed with careful attention to instructional planning for teachers, strategic reading support, and universal access that meets the learning needs of all students.
This book offers sequential language instruction along with extensive drill and practice in grammar, usage, and mechanics. This important tool includes a handbook as well as vocabulary, spelling, and composition lessonsA flexible program with the solid content students need, Glencoe Algebra 1 strengthens student understanding and provides the tools students need to succeed--from the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests.
The book's design is up-to-date as it underlines the real-world applications of Maths as well as its connections to other subjects like science, history and music. The Chapter Projects, Hands-On Labs, and Interdisciplinary Investigations makes the book very useful and interesting to the students.
This textbook of Glencoe Mathematics Course 1 has unit lessons on Number, Operations, and Statistics, Number and Operations: Decimals and Fractions, Patterns, Relationships, and Algebraic Thinking, Measurement and Geometry, Number, Operations, and Algebraic Thinking.
This book is talked about The Texas Prairies and Lakes region offers a wide range of attractions. Among them is the States Fair of Texas. Located in Dallas, it boasts the 212-foot Texas Star-the tallest Ferris wheel in North America. As with all circles, the ratio of the circumference of the Texas Star to its diameter is a constant, π. You'll learn more about ratios in Chapter 7 and circumference in Chapter 12.
Mathematics: Applications and Concepts is a three-course Middle School series intended to bridge the gap from Elementary Mathematics to Algebra 1"Mathematics: Applications and Concepts is |
Mathematics is beautiful. Despite being the product of man's purest intellectual pursuit, mathematics is, nonetheless, a very human topic as demonstrated by the beauty we perceive in a nautilus shell or the image of the Vitruvian man. We humans have taken the exact and perfect rules of mathematics as the basis for contributions to everything from science and art to economics and music.
Because many of the other courses depend on the mastery of quantitative analysis, we highly recommend that students complete their quantitative problem solving requirement in their first year at Stony Brook.
Standards for "Master Quantitative Problem Solving" 1. A certified course shall teach a well-defined area of mathematics such as university-level geometry, statistics, or calculus. The course will address at least four of the above Outcomes. 2. MAP courses will not be considered for certification in Mastering Quantitative Problem Solving
As of December 2013, the courses below have been certified as meeting the learning objectives and standards for the QPS category. |
Books
Matrices
An engaging introduction to vectors and matrices and the algorithms that operate on them, intended for the student who knows how to program. Mathematical concepts and computational problems are motivated by applications in computer science. The reader learns by doing, writing programs to implement the mathematical concepts and using them to carry out tasks and explore the applications. Examples include: error-correcting codes, transformations in graphics, face detection, encryption and secret-sharing, integer factoring, removing perspective from an image, PageRank (Google's ranking algorithm), and cancer detection from cell features. A companion web site,
codingthematrix.com
provides data and support code. Most of the assignments can be auto-graded online. Over two hundred illustrations, including a selection of relevant xkcd comics.
Chapters: The Function, The Field, The Vector, The Vector Space, The Matrix, The Basis, Dimension, Gaussian Elimination, The Inner Product, Special Bases, The Singular Value Decomposition, The Eigenvector, The Linear Program
The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool.
This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems
Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.
Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This new edition of the acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme, and demonstrates their importance in a variety of applications. The authors have thoroughly revised, updated, and expanded on the first edition. The book opens with an extended summary of useful concepts and facts and includes numerous new topics and features, such as: - New sections on the singular value and CS decompositions - New applications of the Jordan canonical form - A new section on the Weyr canonical form - Expanded treatments of inverse problems and of block matrices - A central role for the Von Neumann trace theorem - A new appendix with a modern list of canonical forms for a pair of Hermitian matrices and for a symmetric-skew symmetric pair - Expanded index with more than 3,500 entries for easy reference - More than 1,100 problems and exercises, many with hints, to reinforce understanding and develop auxiliary themes such as finite-dimensional quantum systems, the compound and adjugate matrices, and the Loewner ellipsoid - A new appendix provides a collection of problem-solving hints.
"Comprehensive . . . an excellent introduction to the subject." — Electronic Engineer's Design Magazine. This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first seven chapters, which require only a first course in calculus and analytic geometry, deal with matrices and linear systems, vector spaces, determinants, linear transformations, similarity, polynomials, and polynomial matrices. Chapters 8 and 9, parts of which require the student to have completed the normal course sequence in calculus and differential equations, provide introductions to matrix analysis and numerical linear algebra, respectively. Among the key features are coverage of spectral decomposition, the Jordan canonical form, the solution of the matrix equation AX = XB, and over 375 problems, many with answers.
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects. Today, they are used in applications as various as describing the geometry of spacetime, guiding the Space Shuttle, and developing computer applications in virtual reality. In this book, J. B. Kuipers introduces quaternions for scientists and engineers who have not encountered them before and shows how they can be used in a variety of practical situations.
The book is primarily an exposition of the quaternion, a 4-tuple, and its primary application in a rotation operator. But Kuipers also presents the more conventional and familiar 3 x 3 (9-element) matrix rotation operator. These parallel presentations allow the reader to judge which approaches are preferable for specific applications. The volume is divided into three main parts. The opening chapters present introductory material and establish the book's terminology and notation. The next part presents the mathematical properties of quaternions, including quaternion algebra and geometry. It includes more advanced special topics in spherical trigonometry, along with an introduction to quaternion calculus and perturbation theory, required in many situations involving dynamics and kinematics. In the final section, Kuipers discusses state-of-the-art applications. He presents a six degree-of-freedom electromagnetic position and orientation transducer and concludes by discussing the computer graphics necessary for the development of applications in virtual reality.
Lie groups, Lie algebras, and representation theory are the main focus of this text. In order to keep the prerequisites to a minimum, the author restricts attention to matrix Lie groups and Lie algebras. This approach keeps the discussion concrete, allows the reader to get to the heart of the subject quickly, and covers all of the most interesting examples. The book also introduces the often-intimidating machinery of roots and the Weyl group in a gradual way, using examples and representation theory as motivation. The text is divided into two parts. The first covers Lie groups and Lie algebras and the relationship between them, along with basic representation theory. The second part covers the theory of semisimple Lie groups and Lie algebras, beginning with a detailed analysis of the representations of SU(3). The author illustrates the general theory with numerous images pertaining to Lie algebras of rank two and rank three, including images of root systems, lattices of dominant integral weights, and weight diagrams. This book is sure to become a standard textbook for graduate students in mathematics and physics with little or no prior exposure to Lie theory. Brian Hall is an Associate Professor of Mathematics at the University of Notre Dame.
Retaining the accessible and hands-on style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work.
Along with new and updated examples, the Third Edition features:
A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm
Application of classical Gram-Schmidt with reorthogonalization
A revised approach to the derivation of the Golub-Reinsch SVD algorithm
New coverage on solving product eigenvalue problems
Expanded treatment of the Jacobi-Davidson method
A new discussion on stopping criteria for iterative methods for solving linear equations
Throughout the book, numerous new and updated exercises—ranging from routine computations and verifications to challenging programming and proofs—are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.
Fundamentals of Matrix Computations, Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upper-undergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations.This is the first book of its kind which teaches matrix algebra, allowing the student to learn the material by actually working with matrix objects in modern computer environment of R. Instead of a calculator, R is a vastly more powerful free software and graphics system. The book provides a comprehensive overview of matrix theory without being bogged down in proofs or tedium. The reader can check each matrix result with numerical examples of exactly what they mean and understand their implications. The book does not shy away from advanced topics, especially the ones with practical applications.
Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. |
Environmental science is an integrated, interdisciplinary field that combines the study of ecology, physics, chemistry, biology, soil science, geology, atmospheric science, and geography. It is among the top 10 most popular Advanced Placement examinations taken by high school seniors in an effort to receive postsecondary college credit.
Idiot's... more...
Mathematical craftwork has become extremely popular, and mathematicians and crafters alike are fascinated by the relationship between their crafts. The focus of this book, written for mathematicians, needleworkers, and teachers of mathematics, is on the relationship between mathematics and the fiber arts (including knitting, crocheting, cross-stitch,... more...
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains. Containing basic theory and a wealth of new views and results, it will become an essential resource for graduate... more...
Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly... more... |
Tour of the Calculus
This text breathes life in to the core mathematical principles and process of calculus, in its largest aspect a celestial measuring tape and man's ...Show synopsisThis text breathes life in to the core mathematical principles and process of calculus, in its largest aspect a celestial measuring tape and man's attempt to represent the world in time and space. Using clear, instructive explanations, this book explains more than a mathematical system, it also explores an instrument commensurate with humankind's limitless capacity to question and theorize about it's place in the universe |
Starting from first principles, this book covers all of the foundational material needed to develop a clear understanding of the Mathematica language, with a practical emphasis on solving problems. Concrete examples throughout the text demonstrate how Mathematica can be used to solve problems in science, engineering, economics/finance, computational linguistics, geoscience, bioinformatics, and a range of other fields. The book will appeal to students, researchers and programmers wishing to further their understanding of Mathematica. Designed to suit users of any ability, it assumes no formal knowledge of programming so it is ideal for self-study. Over 290 exercises are provided to challenge the reader's understanding of the material covered and these provide ample opportunity to practice using the language. Mathematica notebooks containing examples, programs and solutions to exercises are available from less |
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Description
Algebra II Daily Activities:
1)Students
will have class work nearly every day.All class work, unless otherwise instructed, is due at the end of the
class period and will be graded (completed or not). When students enter the
classroom, they are to:
a)Start
on board work (do not wait for bell).
b)Have
homework due that class period out on their desk. Graded homework, quizzes and
tests will be distributed.
2)The
beginning of each class will be devoted to homework questions and selected
students will be asked to work selected homework problems on the board.
Homework will be due two class periods after it was assigned.Late work will receive a 30 point
deduction.
3)After
homework questions are answered, instruction on new material will be given and
examples worked in class.Students
will be expected to take notes in their loose-leaf notebook.Instruction this year will be
student-centered.The instructor
will present a problem and guidance, but the students are expected to work
toward the proper solution.
4)Please, do not be afraid to stop the
teacher at any time and ask a question if the material is not clear.Almost certainly, you are not the only
student who does not understand.There
are no stupid questions (except " Is this a stupid question?")!
5)Mistakes
and errors are an essential part of the learning process.When you make a mistake, first identify
the error, then find the proper method, and finally figure out how to avoid
making the same mistake again (these must be shown to receive credit for
corrected work).Everyone makes
mistakes, including your teacher.If you discover me making a mistake, stop me, identify the mistake,
explain the correct method or answer, and I will add 5 points to the next test.
6)Quizzes
will be open note, tests will be closed note (NO formula charts).Unless otherwise instructed, students
are expected to have all pertinent material in memory for tests.It is in your best interest to
initially attempt all quizzes without notes, and then use your notes to check
completed work and to work other problems.Make notes of what you were unable to work without help, and
devote more time to studying those topics.
7)Do
not put up material and get ready to leave class until instructed by the
teacher.
8)Do
not ask to go to the restroom unless it is an emergency.Go before or after class.No one will be permitted to go to the
restroom during instruction.
9)I
give partial credit, but you must show your work to receive any credit
for a problem.With very few
exceptions, all problems in this course will have intermediate steps.If you do not show your problem setup
and intermediate steps, I will give you NO partial credit for the problem.
10)Homework and
quizzes may be corrected and turned in by the next class period in order to get
half of the deducted points back, if all steps needed to solve the problem are
written down.Corrections must be
done on a separate sheet of paper from the initial assignment and the initial
assignment must be attached.Tests
may not be corrected.What you
make on the test initially is what you get.
11)Academic
dishonesty (cheating) will earn you a zero on an assignment or test.Academic dishonesty involves copying
somebody else's work and passing it off as your work.This is theft of somebody else's knowledge and ability.Academic dishonesty includes (but is
not limited to) copying off another student's quiz, test, or homework, copying
directly from published material (either in books or on the internet, known as
plagiarism), or intentionally allowing another student to copy your work and
pass it off as his or her own.
12)Quizzes and tests
must be made up within one class day of your return, or you will receive a
zero.You are responsible for scheduling the makeup and showing up.
You are responsible for learning the material
that was presented during your absence.DO NOT use the excuse "But I wasn't here and I didn't get it."Get help from me (before or after
school, not during class) or from a fellow student.I will NOT track you down to teach you the material.
How Parents Can Help
Please download or print the attached Fall schedule. This has all the classwork and homework for the entire semester. Please ensure that your student is doing work every night.
Requirements
Supplies Needed:
(Bring to class every day unless otherwise instructed)
1)3-hole
notebook and notebook paper
2)MacBook
computer
3)2
pencils and erasers
4)Graphing
calculators will be available for use in the classroom.
5)Personal
calculators are allowed unless prohibited by teacher.
Grading
Grades:
90% of each six-weeks grade will be based on the following
weights:
Homework:1 grade
Quizzes:2 grades
Tests:3 grades
The remaining 10% will be from the comprehensive six-weeks
exam.
Homework is due the next class day after it was assigned. Late work not pre-approved will have 30 points deducted.
Policies
General Course
Expectations and Rules:
1)Students
are expected to come to class every period prepared.
2)Students
are expected to be attentive and to not disrupt the class.
3)Students
are expected to show respect for anyone in the classroom.This includes other students, the
teacher, substitutes, and visitors.
4)Students
are expected to treat all property in the classroom (whether school-owned or
owned by the teacher or other students) with respect and ensure that all
borrowed material is returned in the original condition. |
Algebra and Trigonometry - 7th edition
Summary: For undergraduate courses in Algebra and Trigonometry with optional Graphing Calculator usage.
The Seventh Edition of this dependable text retains its best features -- accuracy, precision, depth, strong student support, and abundant exercises -- while substantially updating content and pedagogy. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engine...show moreering calculus. ...show less
Angles and Their Measure. Right Triangle Trigonometry. Computing the Values of Trigonometric Functions of Given Angles. Trigonometric Functions of General Angles. Unit Circle Approach; Properties of the Trigonometric Functions. Graphs of the Sine and Cosine Functions. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions. Phase Shift; Sinusoidal Curve Fitting |
from 100 providers and counting...
In the first six weeks of the course, we begin with an introduction to the parts of the upper limb and a discussion of the anatomic position, including the three-dimensional planes in which body movements are performed. Next, we cover the osteology of the upper limb by describing the bones of the extremity, how they articulate at synovial joints, and the movements that are possible at these joints. We explore the blood supply and innervation to the upper limb.
A revolution is underway in science classrooms. The demands of the new workplace and the ready access to information afforded by new technologies have radically changed the way we define a scientifically literate society.
More than ever teachers need professional development that provides them with the resources they need and empowers them to take the action required to build classrooms where the next generation of scientifically literate students will flourish.
Complex analysis is the study of functions that live in the complex plane, i.e. functions that have complex arguments and complex outputs. In order to study the behavior of such functions we'll need to first understand the basic objects involved, namely the complex numbers. We'll begin with some history: When and why were complex numbers invented? Was it the need for a solution of the equation x^2 = -1 that brought the field of complex analysis into being, or were there other reasons? |
Lessons:How do
you really
do this stuff? --
Purplemath's algebra lessons are written with the student in mind.
These lessons emphasize the practicalities rather than the technicalities,
demonstrating dependable techniques, warning of likely "trick"
questions, and pointing out common mistakes. The lessons are cross-referenced
to help you find related material, and a "search" box is on
every page to help you find what you're looking for. (Note: A few trigonometry
lessons have recently been added, with more lessons on the way. If you
have suggestions regarding topics, particularly within trigonometry, that
you would like to see added to Purplemath, please say
so. Thank
you!)
Learning
Forums:Helping
students gain understanding and self-confidence in algebra.
-- These forums exist in the hope of helping learners grow in mathematical
knowledge and inner strength. The forums are free-access and are "staffed"
by volunteers. For best success, don't wait until the last minute or until
you're "totally lost"; start asking questions as soon as you
find yourself feeling "stuck".
Site Reviews:
-- Tired of looking
through page after page of search-engine hits trying to find a site that
might have something useful? These categorized Internet links have
all been reviewed by Purplemath.
Only those sites
with something immediately useful (and free, or free-to-try) for algebra
students are listed. You won't find math jokes or recreational math sites here.
Instead, check these review for sites containing lessons, tutoring forums,
worksheets, articles on "how math is used in real life",
and more.
Homework
Guidelines: How
to suck up to your teacher.
-- English teachers tell students explicitly how to format their papers.
Math teachers, on the other hand, frequently just complain in the lounge
about how messy their students' work is. Neat homework can aid your
comprehension and might make your teacher like you better. These Homework
Guidelines for Mathematics will give you a leg up, explaining in clear
terms what your math teacher is looking for.
Study Skills
Self-Survey: Do
I have what it takes?
-- Much of your success or failure in algebra can be laid at the
feet of your study habits. Do you have good math study habits? Take
this survey and find out. |
The Academic Advantage
One-on-one instruction in the convenience of your own home that focuses on academic improvement and building confidence. Math topics tutored range from basic arithmetic to trigonometry, from pre-algebra to pre-calculus, from algebra to geometry, and also
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Academic Systems
Produces multimedia instruction software for mathematics and English. Interactive Mathematics includes integrated animation, graphics, audio, and video; individualized student programs; an array of help and support options; and an online reporting system
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Addison-Wesley Higher Education - Pearson Education
Publisher of programs and materials for primary and secondary school students and teachers; higher education textbooks and multimedia in major academic subjects for students and professors; books and multimedia for business professionals, practicing engineers,
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Aepryus Software
Aepryus is a developer of math, physics, and evolutionary biology software for Microsoft Windows computers. Download, purchase, or obtain information about programs such as Aepryus Graph, a function plotting application capable of 2D and 3D shaded plots
...more>>
AgentSheets - AgentSheets, Inc.
A combination of end-user programmable agents, spreadsheets and Java authoring tools. The new version of AgentSheets lets end-users build a wide range of applications that include interactive simulations, games, and intelligent web agents. Projects created
...more>>
Aha!Math - Learning.com
This K-5 curriculum package, aligned to state and Common Core standards, supports differentiated instruction with multiple instructional models. Aha!Math provides students with immediate feedback in interactive story settings. Freely sample games and
...more>>
AlgebraNet
Software for explanation and demonstration of elementary algebra techniques (reducing, simpifying, factoring, equations).Testing facilities. Free demo; fee for full version. In English or Dutch.
...more>>
Algebra Software - Algebra-net
Windows software that enables students to solve actual problems from algebra textbooks and not just a limited set of computer generated examples. Features, testimonials, and purchasing information available on the site.
...more>>
Algebrator
Key in mathematical expressions for this software to interpret and simplify or solve, one step at a time, with explanations along the way. Algebrator simplifies algebraic expressions; factors and expands expressions; finds LCM and GCF; rationalizes complex
...more>>
Algebra Vision - Sean Berry
Algebra software that lets you visually interact with algebraic expressions. Watch demos on the site, or sign up for a free trial. Individual and school-level licenses available.
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Alive Books - Sotirios Persidis
The site offers a free downloadable course on Calculus of a Single Variable, as well as a link to a modern new Mathematical Handbook is given. The Handbook is part printed matter and part online, and fully searchable even within mathematical expressions.
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All Ivy Tutoring
Phoenix-based tutoring service providing one-on-one, in-home tutoring, offering help in all math subjects from basic math through college level differential equations and linear algebra.
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All Star Tutoring
Professional one-on-one tutoring services in New York City's boroughs, including GED test preparation, city-wide exams, and Regents exam preparation.
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AMATH - AMATH Systems, Inc.
Software for Building and Reinforcing Foundation Mathematics. AMATH is a simple, self-paced, self grading, computer-aided workbook created to combat the math literacy problem in the U.S. It covers 103 modules of foundation mathematics
including: arithmetic,
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Amazing Math Tutor San Diego - Sam Mirs
One-on-one in-home tutoring for algebra, trigonometry, geometry, pre-calculus, calculus and college math students in San Diego county. Blog posts, which date back to January, 2013, have included "The 7 Steps to Succeed in Math Tests," "The 3 main Questions
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... and Math Tutoring - Stuart Raffeld
This one-on-one tutoring service meets tutees throughout California's West San Fernando Valley, and also tutors online, over-the-phone, and by e-mail. Posts in Stu's blog, which date back to February, 2011, have included "Ten Ways to Improve your SAT
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APlusStudent Online Learning
Interactive math lessons with graphics, animation, and audio, based on Micromedia Flash technology. Teacher-designed, standards-based lessons. Parents can monitor the progress of their children. There is also homework help and an online gallery where
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Arithmemouse - Tinman Learning, Inc.
Arithmemouse Times Tables is a multiplication game that facilitates teaching children multiplication facts--not just a drill. It is nonviolent, with light puzzles, and without life meters or punishment for failure. A free demo is available. Arithmemouse
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Ask Dr. Callahan - Dale Callahan
For the homeschooling parent who needs high school math and science training material: textbooks, videos for the parent and child, teaching guidelines, tests and test grading guides as well as support for the duration of the course. Courses in geometry,
...more>> |
Modify Your Results
From the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests, these programs strengthen student understanding and provide the tools students need to succeed.
"New York Algebra 2 with Trigonometry" is the third of three books in Glencoes New York High School Mathematics Series. This series offers complete coverage of New Yorks Mathematics standards, strands, and performance indicators. As students learn to integrate a comprehensive array of tools and strategies, they become proficient in mastering concepts and skills, solving problems, and communicating mathematically. This series of books helps your students identify and justify mathematical relationships; acquire and demonstrate mathematical reasoning ability when solving problems; use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes; and succeed on the Regents Examinations |
Synopses & Reviews
Please note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:
Updated to reflect questions and question types on recent tests, this workbook presents hundreds of math questions in both multiple-choice and grid-in formats with worked out solutions. These exercise with answers will hone studentsÂ' math skills and prepare them to excel when they take the actual SAT. The author also suggests special math strategies to help test takers approach and correctly answer question types that might be unfamiliar to them. Here is intensive preparation for the SATÂ's all-important Math section, and a valuable learning tool for college-bound students who need extra help in math.
Synopsis:
(back cover)
Exercises and practice tests to hone your math skills and prepare you to excel on the SAT
Detailed solutions for all problems
A systematic review of all SAT math topics
Special math strategies to help you approach and answer question types that you find most challenging |
This best-selling text by these well-known authors provides the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathem...show moreatica, and MATLAB. Its focus balances the traditional manual methods with the new computer-based methods that illuminate qualitative phenomena and make accessible a wider range of more realistic applications. Seldom-used topics have been trimmed and new topics added: it starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the text.
Features
NEW--Emphasis on new technology--Recognizes the need to instruct students in the new methods of computing differential equations.
Shows students the software systems tailored specifically to differential equations as well as the widely used Maple, Mathematica, and MATLAB.
Brings to life the symbolic solutions of differential equations through the visualizing of qualitative features.
NEW--Extensive expansion of figures to the Answers Section.
Emphasizes the qualitative features of problem solutions.
NEW--Application Modules--Follow key sections throughout the text; while many involve computational investigations, they are written in a technology-neutral manner. Technology-specific systems modules are available in the accompanying Applications Manual.
Actively engages students, providing facility and experience in the geometric visualization and qualitative interpretation that play a prominent role in contemporary differential equations.
NEW--Fresh numerical emphasis--Made possible by the early introduction of numerical solution techniques, mathematical modeling, stability and qualitative properties of differential equations. The text includes generic numerical algorithms that can be implemented in various technologies.
Gives students and instructors a choice when implementing which type of technology they can utilize, as well as provides an innovative combination of topics usually dispersed later in other texts.
NEW--Leaner and more streamlined coverage--Shaped by the availability of computational aids.
Allows students to learn traditional manual topics (like exact equations and variation of parameters) more easily.
Unusually flexible treatment of linear systems--Covers in Chapters 4 and 5 the necessary linear algebra followed by a substantial treatment of nonlinear systems and phenomena in Chapter 6. The use of matrix exponential methods plays an enhanced role in this edition.
Reflects the current trends in science and engineering education and practice2895 +$3.99 s/h
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Brockett Designs Emigrant, MT144 |
Editorial projects
Projects I have worked on in my capacity as a freelance copyeditor/editor. Dec 3
In all books before Algebra 1/2 (the equivalent of a Pre-Algebra book), the book is designed for the student to complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a varied number of problems which include what the students learned today and in select previous lessons—all for one day's class. This daily cycle is interrupted for tests and additional topics. In the Algebra 1/2 book and all higher books in the series, the mental math is dropped, and tests are given more frequently. The Saxon math program has a specific set of products to support homeschoolers, including solution keys and ready-made tests, which makes it popular among some homeschool families.
Saxon math
Saxon Phonics K
Saxon Phonics 1
Saxon Phonics 2
Flip to back Flip to front Listen Playing... Paused You're listening to a sample of the Audible audio edition. Learn more
When I bought this book, I knew it was to be used in conjunction with the whole Saxon Phonics Intervention program. However, it does have some super lists of vocabulary words, phonic rules, syllable division rules, spelling words, sight words, and irregular pattern words. I used Hooked On Phonics and Phonics Intervention when I home schooled my children. Both had learning difficulties, and phonics based reading helped. (They both have gone to college.) Now that I am a geezer, I work as a private tutor.
Phonics Intervention
Saxon Math 5/4
Saxon Math 6/5
Saxon Math 7/6
Saxon Math 8/7
Algebra 1: An Incremental Development
Saxon's 'Algebra 2' is the second in an integrated three books or three courses series comprised of 'Algebra 1', 'Algebra 2' and 'Advanced Mathematics' designed to prepare students for calculus. The 'Algebra 2' set covers topics that advanced math students are expected to master in 9th grade. While called a 'homeschool kit' it can be used quite effectively by parents 'after school' to supplement or enhance a child's math proficiency which is how we have been using Saxon (me and my 2 boys) ever since 4th grade.
Algebra 2: An Incremental Development
The Future of Human Spaceflight: Objectives and Policy Implications in a Global Context
United States Space Policy: Challenges and Opportunities Gone Astray
A European Approach to Space Security
A Place for One's Mat: China's Space Program, 1956–2003
Reconsidering the Rules for Space Security
Science and the Educated American
Nuclear Reactors: Generation to Generation
AAAS Bulletin
judicial independence
challenges of mass incarceration
challenges to public universities
the university and the city
future of research universities
what is missing in medical thinking
after the 2008 elections
science and technology policy problems
race in the age of Obama
the new pragmatism
election and its consequences
financial crisis and economic policy
education of an American dreamer
black humor
nanotechnology: novel applications
future of power
the nuclear future
on the future of energy
Humanities Indicators
Humanities Indicators Offering the latest information on the state of the humanities in schools, colleges, the workforce, scholarly research, and American life. Departmental Survey |
MA 210 Calculus and Analytic Geom I Ottum, Joseph with an examination of the real number system and the Cartesian plane. Additional topics to be considered include functions and their graphs, limits and differentiation techniques, the mean value theorem, applications of the derivative, indefinite integration, the trigonometric functions. 3:0:3 Prerequisite: MA131 and MA141 or MA150 or equivalents a mathematical limit and compute various limits
Define a continuous function
Recognize where continuity occurs and its consequences
Define the derivative in terms of a limit of a difference quotient and recognize its geometric applications and properties
Differentiate polynomials, trigonometric, and exponential functions
Utilize first and second derivatives to graph functions
Apply derivatives to optimization and related rates problems
Apply the power rule, the sum rule, the difference rule, the constant factor rule, the product rule, the quotient rule, the chain rule
Core Assessment:
Core Assessment for MA 210 Calculus and Analytic Geometry I
1. Define a mathematical limit and compute various limits.
2. Define a continuous function.
3. Recognize where continuity occurs and its consequences.
4. Define the derivative in terms of a limit of a difference quotient and recognize its geometric applications and properties
Grading: Two Tests 25% of final grade each Participation/Homework Notebook 25% of final grade Final Examination 25% of final grade Gades A:90-100 B:85-89 C:80-84 D:70-79
Late Submission of Course Materials: Assignments should be turned in on the specified due date.
Classroom Rules of Conduct: Students are expected to participate fully in class learning activities. Phones and beepers are to be placed on "vibrate" or turned off. Students are required to exercise courteous behavior between themselves and with the instructor.
The Definite Integral. Area Under a Curve, The Fundamental Theorem of Calculus.
15
M
12/10
Review
16
W
12/12Can solve 5 out of 5 problems involving limits
Can solve 4 out of 5 problems involving limits
Can solve 3 or fewer out of 5 problems involving limits
Makes no attempt to solve any limit problem
Synthesis Outcomes 4, 5
Can find the derivative of 5 out of 5 functions
Can find the derivative of 4 out of 5 functions
Can find the derivative of 3 or fewer out of 5 functions
Makes no attempt to solve any derivative problem
Analysis Outcomes 2, 3
Can solve 5 out of 5 problems correctly concerning continuity
Can solve 4 out of 5 problems correctly concerning continuity
Can solve 3 or fewer out of 5 problems correctly concerning continuity
Makes no attempt to solve any problem concerning continuity
Application Outcomes 5, 8
Apply the power rule, the sum rule, the constant factor rule, the product rule, and the chain rule to 5 out of 5 problems correctly
Apply the power rule, the sum rule, the constant factor rule, the product rule, and the chain rule to 4 out of 5 problems correctly
Apply the power rule, the sum rule, the constant factor rule, the product rule, and the chain rule to 3 or fewer out of 5 problems correctly
Makes no attempt to provide any application
Content of Communication Outcomes 1, 2
Can define what a limit is with perfect accuracy. Can define what a continuous function is with perfect accuracy
Can define what a limit is with substantially complete accuracy. Can define what a continuous function is with substantially complete accuracy
Can define what a limit is with incomplete accuracy. Can define what a continuous function is with incomplete accuracy.
Makes no attempt to define any concept
Technical skill in communication Outcomes 4
Can define a derivative in terms of the limit of a difference quotient with perfect accuracy
Can define a derivative in terms of the limit of a difference quotient with substantially complete accuracy
Can define a derivative in terms of the limit of a difference quotient with incomplete accuracy
Makes no attempt to define any concept
Graphing functions using calculus Outcomes 6
Can utilize first and second derivatives to graph a function with greater than 80% accuracy.
Can utilize first and second derivatives to graph a function with 80% accuracy.
Can utilize first and second derivatives to graph a function with less than 80% accuracy.
Makes no attempt to graph any function
Solving optimiztion and related rates problems Outcomes 7
Can apply derivatives to solve 5 out of 5 problems of optimization or related rates
Can apply derivatives to solve 4 out of 5 problems of optimization or related rates
Can apply derivatives to solve 3 or fewer out of 5 problems of optimization or related rates
Makes no attempt to solve any optimization or related rates problem
Copyright:
This material is protected by copyright and can not be reused without author permission. |
Synopses & Reviews
Publisher Comments:
While the mathematics of classical engineering and science is primarily "continuous, " the mathematics of computer science is primarily "discrete" or "combinatorial." This volume provides a useful guide to combinatorial mathematics for computer scientists and applied mathematicians. Based on a beginning graduate-level course taught by the author, it covers the two major subdivisions of combinatorics, enumeration and graph theory, with emphasis on the conceptual needs of computer science. Each part is divided into a "basic concepts" chapter that emphasizes the intuitive ideas of the subject, followed by four "topics" chapters that explore these ideas in depth. Given the rapid and continued growth of computer science today, this accessible, well-written volume will be an invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics.
Book News Annotation:
A textbook for a beginning graduate course for students majoring in mathematics or computer science. It uses combinatorial mathematics to teach basic techniques of proof. The 1985 edition was published by Computer Science Press, Rockville, Maryland. Annotation c. Book News, Inc., Portland, OR (booknews.com)"Synopsis"
by Firebrand, |
Twelfth graders explore integral calculus. In this Calculus lesson, 12th graders use the tools of integral calculus to investigate the motion of a free falling objet which is governed by both gravity and air resistance.
Students explore the Fundamental Theorem of Calculus. In the Calculus activity, students investigate indefinite and definite integrals and the relationship between the two, which leads to the discovery of the Fundamental Theorem of Calculus.
Students integrate integrals. In this integrating integrals lesson, students integrate definite and indefinite integrals. Students use their Ti-89 to find the integrals of cubic, inverse, and trigonometric function graphs on a given interval.
In this plasma torus learning exercise, students solve 5 problems including finding the dimensions of the Io torus, determining the formula for the volume of a torus, finding the actual volume of the Ion torus and finding the amount of sodium atoms in the torus. Students are given an integral calculus problem where they use the 'washer method' to find the formula for the volume of a torusTwelfth graders solve first order differential equations using the separation of variables technique. For this calculus lesson, 12th graders explain the connection between math and engineering. They brainstorm what engineers do in real life.
Students explore the area under the curve using the TI InterActive! document. In this calculus instructional activity, students input various functions and create tables. They answer questions based on their results.
Students explore the concept of definite integrals. In this definite integrals lesson, students find the area between two curves. Students use the Ti-Nspire to find the definite integrals of curves such as sine and cosine.
Students investigate integral calculus. In this calculus lesson, students investigate the relationship between the area above and below the curve using integral calculus. Students look for a general rule for area above: area below.
Students investigate integral calculus. In this calculus lesson, students explore an application of integrations through a leaking hot tub problem. The activity emphasizes using the integral of a rate of change to give the accumulated change.
Students explore integral calculus. In this calculus lesson, students explore the relationship between the area under the graph of a functions and the integral of the function. Students also discover the rule for the integral of f(x)=ax^n use a graphing calculator to do calculations and edit their calculations using script. In this graphing calculator lesson, students compute the length of intervals given in parametric form. Students verify the results for specific given functions and define the critical points where the first derivative is found.
Learners explore the concept of approximating integrals. In this approximating integrals lesson, students approximate integrals by finding the area of rectangles. Learners use a graphing calculator to find the left, right, and midpoint riemann sums.
Students practice calculating and analyzing Riemann sums and illustrate when Riemann sums will over/under-approximate a definite integral. They view how the convergence of Riemann sums as the number of subintervals get larger. |
STELLA - isee systems
A model building and simulation software package. Read about STELLA-based materials such as Lessons in Mathematics: A Dynamic Approach. Get help with STELLA training, seek live support building a model, see tutorials, purchase supporting books and videos,
...more>>
Stella: Polyhedron Navigator - Robert Webb
"Small Stella" is a program for viewing polyhedra and printing their nets so you can build your own. It has over 150 built-in models, plus their duals. Models include Platonic solids, Archimedean, Kepler-Poinsot, Johnson solids, "Near Misses," and Stewart
STEM Sheets
Makers of printable flash cards. Choose number ranges, and whether or not to include answers, before freely downloading PDFs of addition, subtraction, multiplication, or division problems.
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Stephan Kaufmann
A site with information about Stephan Kaufmann's Mathematica books, notebooks and packages, including A Crash Course in Mathematica.
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Steve Fulling's Home Page - Stephen A. Fulling
Courses in Foundation Coalition Freshman Calculus, linearity, and other subjects offer objectives, assignments, solutions and reports, exams, and supporting documentation such as books (.pdf, .ps, and .dvi formats). The site also includes access to the
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Steven Strogatz
Research, teaching, publications and more by Strogatz, Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. Best known in the academia for his 1998 Nature paper on "small-world" networks, which he co-authored with his former student
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Steven Strogatz - The New York Times Company
Mathematics from an adult perspective -- from the basics of math to the baffling -- by Steven Strogatz, a professor of applied mathematics at Cornell University. This New York Times series is not meant to be remedial, but rather to give readers a better
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Steve's Math Site
"Mathematic memorabilia" by a Phoenix, Arizona high school student: binary numbers, factorials, calculations of 2^x from x=1 to x=200+, hand calculations of pi, logarithms and one radian, 3^x from x=1 to x=100+, and more.
...more>>
Steve's Words - Steve Lee
Mathematics-related articles by a student at UCLA include brief reviews of books on chaos theory and an article on the connection between game theory and nuclear strategy.
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Stickets - Wanderlands
A puzzle game for iPhone "that forgot Tetris existed": drag tri-colored L-shaped blocks onto a grid and tap contiguous, similarly colored areas comprised of three or more squares in an ongoing quest to preserve space on the grid. The app also challenges
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The Stock Market Game - woodydrn
Create a company, hire its staff, build its board, and see how it does in the marketplace. If you can convert your companies to a business park, you may win the game.
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Stock Options - The Animated Tutorial - Jerry Marlow
A fast and easy way to teach and to learn about stock options, option prices, stock-market volatility, and Black-Scholes options pricing theory. CD and Book $39.95. The theory provides a sophisticated way of analyzing and understanding the relations among
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Stock-Trak - Stock-Trak
Stock-Trak is a virtual stock exchange simulator and fantasy stock market game. It allows its users to practice online stock trading within all of the major securities. Browse the site for information on stock investing research and fantasy stock market
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The Storybook of Geometry - ThinkQuest 1996
Learn the basics of geometry and see how they relate to real world situations. Explore and read stories that help to uncover the mysteries of geometry. Story problems (with answers): The Great Space Ace; The Pharoah's Pyramid; The Ice Cream Cone; Filling
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The Story of Mathematics - Luke Mastin
Summary of major mathematicians and developments of mathematical thought over the centuries, "from its roots in ancient Mespotamia, Egypt and Greece to the abstraction of the modern era.... without getting too technical or getting bogged down in too much
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Real Analysis: A First Course, 2nd Edition
9780201437270
ISBN:
0201437279
Edition: 2nd Pub Date: 2001 Publisher: Pearson
Summary: Real Analysis, 2/e is a carefully worded narrative that presents the ideas of elementary real analysis while keeping the perspective of a student in mind. The order and flow of topics has been preserved, but the sections have been reorganized somewhat so that related ideas are grouped together better. A few additional topics have been added; most notably, functions of bounded variation, convex function, numerical met...hods of integration, and metric spaces. The biggest change is the number of exercises; there are now more than 1600 exercises in the text |
Abstract. There are a number of software packages available which solve a wide variety of problems. Unfortunately, the average computer user is not making full use of these packages because they are typically quite large and complex. By buildingThe purpose of this handbook is to help students of applied analysis to organize the necessary resources for the successful completion of independent study projects. The nature of these projects is somewhat novel for mathematics classes- the... |
Trigonometry: A Complete Introduction is the most comprehensive yet easy-to-use introduction to Trigonometry. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge. The book covers all areas of trigonometry including the theory and equations of tangent,... more...
500 Ways to Achieve Your Best Grades
We want you to succeed on your college algebra and trigonometry midterm and final exams. That's why we've selected these 500 questions to help you study more effectively, use your preparation time wisely, and get
your best grades. These questions and answers are similar to the ones you'll find on a typical... more...
Trigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosine,... more...
Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing... 20 detailed videos featuring Math instructors who explain how to solve the most commonly... more...
Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.
The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical t more...
From the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings. Beautifully illustrated, the book explores the milestones in elementary mathematics that enliven the understanding of these buildings and combines... more... |
are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers.
From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
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"It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." The Mathematical Gazette
From the reviews of the second edition:
"If I had to recommend one book on the subject to a student – or even to a fully grown mathematician who had never played with p-adic numbers before – it would still be this book. … Gouvêa has succeeded admirably in taking a topic that is not standard in the undergraduate mathematics curriculum and writing a book accessible to undergraduates that allows its reader to play with some intriguing mathematics and explore a topic which is both fun and important." (Darren Glass, The Mathematical Association of America, January, 2011)
Most Helpful Customer Reviews
This book really grabbed me on a number of points. First, in addressing a rather abstract topic (often not included in a basic undergraduate curriculum) it does a good job trying to compute concrete examples. It stays broad, as not to lose the reader on the messy details of any particular part of the theory. Hence the book is good even for students who are a little weak on their background. It is well-organized and exposed for an introductory-level text. In particular, its proofs are rather clear, concise, and meaningful. There are only a couple points where Gouvea uses trickery (a la Rudin) to prove things, and he is honest enough to warn before they come. Indeed, the footnotes are quite entertaining, especially for one who has read enough math books to catch his jokes. Overall, the read is casual. It is good for independent reading. The problems in the book are also worthy of praise. They are interspersed after proofs and in the middle of exposition, as ways to make sure the reader is following. Indeed, they are always pertinent and carefully planned. In addition, they point out ways in which mathematics authors often skip over details which the reader should actually verify for him/herself. Specifically, they perpare a student for reading graduate-level texts (which are notoriously full of this occurrence). Pedagogically, therefore, this is a very important tool, and useful book for a budding math student. Finally, for the graduate student who wants to go down the path of p-adics, Gouvea does a good job of pointing the reader in the several different directions the literature can guide him/her. He gives references to other texts, giving just a taste of their contents, throughout. His eye towards further study is keen.Read more ›
This is the best introduction-level mathematics textbook I have ever read, and I have read (and own) many. Every theorem and definition is well-motivated, and problems for the reader are interspersed within the text to make sure that every subtle nuance of the exposition is understood. Though introductory, Gouvea manages to incorporate some relatively advanced topics, (as far as undergraduate mathematics goes) such as the Weierstrass Preparation Theorem, local rings, and analysis in C_p. All this and the topic at hand is fascinating to boot. p-adic numbers are perfect for anyone wishing to pick up an amazingly interesting topic not found in most undergraduate or graduate courses. In conclusion, I recommend this book to the set of people interested in p-adic numbers, and its complement.
You're curious about beautifull topics in math, but reading a classical texbook, browsing through a list of lemma and therorems just get you sleep ? Read this one. The idea behind theorems, and why and how they came alive are so nicely exposed that this book can replace your favorite bed time one. |
Help your child build Math skills with fun and engaging activities. Packed with lessons and exercises from Elementary School to High School, each designed to prepare students for success in state standards testing. Build fundamental skills with Basic Math, including addition, subtraction, multiplication and division. Expand your horizons with Pre-Algebra, Algebra and Geometry.
AmericanHeadway, Second Edition is the world's
Is it more efficient to rent a car or take taxis while on vacation? How do coupons change demand? MICROECONOMICS: AN INTUITIVE APPROACH WITH CALCULUS explains the economic theory underlying day-to-day choices. The A sections of each chapter introduce concepts using intuition, a conversational writing style, everyday examples, and graphs. The B sections cover the same concepts with accessible mathematical analyses. Each copy includes access to online LiveGraphs -- a suite of interactive, animated graphs that allows you to view dimensional graphs and functions illustrated in the book, as well as some additional graphs that are not in the printed text. LiveGraphs and the Study Guide are accessible through the accesscode that is included with the purchase of a new text.
Code in the Cloud ( Ryushare - Uploaded - Rapidgator user's desktop computer. Instead, they're building services on the network that can be used by thousands of users at the same time.
Entity Framework is Microsoft's Data Access platform for .NET development. This course will introduce you to the key concepts and behaviours of using the Entity Framework from designing models, writing data accesscode and integrating Entity Framework into your software solutions. If you have never used Entity Framework, start here with Visual Studio 2012 and Entity Framework 5. Developers with experience with earlier versions of EF can find useful information throughout about new designer features introduced in Visual Studio 2012 as well new modeling capabilities and API features provided in Entity Framework 5.
Code in the Cloud ( Rapidgator - Uploaded users desktop computer. Instead, theyre building services on the network that can be used by thousands of users at the same time.
Q: Skills for Success is a six-level series with two strands, Reading and Writing and Listening and Speaking. The series provides students with: Clearly identi?ed learning outcomes that focus students on the goal of instruction; Thought-provoking unit questions that provide a critical thinking framework for each unit; Explicit skills instruction that builds students language pro?ciency; All new content and practice activities for every unit, approximately 20 hours of practice per strand, with Q Online PracticeThis book is for the career developer who wants to take his or her skill set and/or project to the next level. If you are a professional software developer with 3-4 years of experience looking to bring a higher level of discipline to your project, or to learn the skills that will help you transition from software engineer to technical lead, then this book is for you.
The Handbook of Research on Hybrid Learning Models: Advanced Tools, Technologies, and Applications collects emerging research and pedagogies related to the convergence of teaching and learning methods. This significant resource provides access to the latest knowledge related to hybrid learning, discovered and written by an international gathering of e-learning experts.
American Headway 1 Student BookAmerican Headway 1 Workbookcode control units in vehicles BMW Group. |
I am going to study computer science next year. I am afraid I can't handle the mathematics in the university because I only know some basic mathematics, such as set theory, simple probability, simple matrix operation and I don't know calculus.
1 Answer
I'd suggest getting a good handle on Discrete Mathematics, first and foremost, though I'd never discourage anyone from studying calculus and linear algebra, if they desire to do so. Of more immediate use, however, would be studying Discrete Mathematics. Unfortunately, most textbooks in discrete mathematics are somewhat expensive.
One great choice, for a "beginner" (in that it presumes very little in the way of a mathematics background), is Susanna S. Epp's Discrete Mathematics with Applications. This text, however, is very expensive.
Another text which is excellent is Edward R. Scheinerman's Mathematics: A Discrete Introduction, though it is geared more for math majors than for computer science majors. I think it's less expensive than Epp's text, so I'd suggest taking a look at it, as well.
If cost is an issue, there are some well known notes that are freely accessible and free. For example, see
See also this earlier post, where the question posted sought recommendations for a great text in discrete mathematics. The "leading" answer there recommends Concrete Mathematics by Knuth and company, which is a phenomenal text, but some students may find it difficult to tackle without a more solid foundation in mathematics, including at least some Calculus. But do please do take a look at the text. If you hope to be a computer scientist, Concrete Mathematics will be, either now or later, a "must read" text book. (It is also considerably less expensive than many introductory Discrete Mathematics textbooks!)
I don't agree. I'd read Concrete Mathematics in high school, it was very friendly and the only part I would skip was about hypergeometric functions (it was tedious). True, explanations are concise, but there are many helpful examples and almost everything is done from the very basics. I would definitely recommend this book! (+1 for the other books.)
–
dtldarekJul 21 '13 at 18:53
@dtldarek I wasn't sure on that one. It's one of my "faves"! I rewrote my post to describe it more accurately.
–
amWhyJul 21 '13 at 19:00 |
We will begin with a brief review of (systems of) linear equations. Then, we will learn how to solve linear systems using Gauss-Jordan elimination. We sill discuss matrix algebra with applications to input-output analysis and Markov processes Input-output analysis is used to determine how interdependent producers should behave. Markov processes are used to predict long term values of interdependent quantities that vary probabilistically.
Next, we will talk about linear programming (LP) problems. An LP problem is on in which you seek to maximize a linear function—profit, for example—subject to certain linear constraints, such as budgetary or workforce limitations. You will learn to solve LP problems geometrically, using the simplex method, and by computer.
Integer and 0-1 programming problems, which are closely related to LP problems, are too labor-intensive to solve by hand. We will learn how to solve them using Excel. We will touch briefly on the subject of computational complexity.
We will take a look at game theory, the study of strategic interactions between competing interests. We will explore the connection between game theory and LP problems.
Finally, we will look at the mathematics of finance. Here we study how different forms of interest can affect loans and investments.
Description:
This syllabus was submitted to the Rhodes College Office of Academic Affairs by the course instructor. |
CORD Applied
Mathematics teaches algebra and geometry concepts in the context of
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The course materials engage students in cooperative teams, allowing
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9780534495015
ISBN:
053449501X
Pub Date: 2005 Publisher: Brooks/Cole
Summary: An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems. Based on their teaching experiences, the authors offer an accessible text that emphasizes the fundamentals of discrete mathematics and its advanced topics. This text shows how to express precise ideas in clear mathematical language. Students discover the importance of discrete ma...thematics in describing computer science structures and problem solving. They also learn how mastering discrete mathematics will help them develop important reasoning skills that will continue to be useful throughout their careers.
Schlipf, John is the author of Discrete Mathematics For Computer Science With Student Solutions Manual on CDROM, published 2005 under ISBN 9780534495015 and 053449501X. Six hundred sixteen Discrete Mathematics For Computer Science With Student Solutions Manual on CDROM textbooks are available for sale on ValoreBooks.com, one hundred forty eight used from the cheapest price of $4.91, or buy new starting at $32.70.[read more |
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This introductory text explores the translation of geometric concepts into the language of numbers in order to define the position of a point in space (the orbit of a satellite, for example). The two-part treatment begins with discussions of the coordinates of points on a line, coordinates of points in a plane, and the coordinates of points in space. Part 2 examines geometry as an aid to calculation and the necessity and peculiarities of four-dimensional space. Written for systematic study, it features a helpful series of "road signs" in the margins, alerting students to passages requiring particular attention, and an abundance of ingenious problems — with solutions, answers, and hints — promote habits of independent work
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"All through both volumes ['Functions & Graphs' and 'The Methods of Coordinates'], one finds a careful description of the step-by-step thinking process that leads up to the correct definition of a concept or to an argument that clinches in the proof of a theorem. We are ... very fortunate that an account of this caliber has finally made it to printed pages... Anyone who has taken this guided tour will never be intimidated ever again... High school students (or teachers) reading through these two books would learn an enormous amount of good mathematics. More importantly, they would also get a glimpse of how mathematics is done."
—- H. Wu, The Mathematical Intelligencer
"This book is a concise and compact treatment of the essential ideas of coordinate geometry. The authors demonstrate powerfully how geomtric ides may be communicated and studied effectively without the aid of pictures. Graphics are of course of vital importance int he methods of Euclidean geometry. However, the methods of coordinate geometry are able to transform pure geometric ideas into algebraic manipulations where the meaning is very clear once the formalism is learnt. In particular the book demonstrates the value of conveying information in the form of images embedded in formulas. This is very useful in the transmission of information by electronic means. . . This book is a valuable tool for teaching the redimentary concepts of analytical geometry. It contains a number of excellent examples and exercises which go further than a mere introductory programme. the exercises, while not numerous, are very thought-provoking and are bound to pose a serious challenge to the interested student |
Excellent value - immediate shipping - wrapped with care. 90807. Hardcover - no dustjacket. Outside glossy covers have light wear/smudges. 623 pages - 1993 - 4th edition - ...plus appendix, answers and index. Notations and highlights on less than 5% of pages - estimated. Still very readable. Otherwise, rest of book is clean and free of any other writing. Feel at home - buy NOW with CONFIDENCE! Size is 8" x 9-1/4".Read moreShow Less
Reading, MA, U.S.A. 1993 Hard Cover 4th Edition Near Fine 8vo-over 7?"-9?" tall. Older Edition (4th Ed. ), HB/none, NF, 623 pp. + Appendix. Review Copy. Book has name neatly ...written on inside of rear free endpaper, otherwise fine, almost new looking. College Level. Prospective users include students majoring in liberal arts, elementary education, the social sciences, business, and nursing and the allied health fields. The writers' primary goal in writing this book was to give students a text that they can read, understand, and enjoy while learning mathmatics.Read moreShow Less
Ships from: Stonington, IL sixth edition of this best-selling text balances solid mathematical coverage with a comprehensive overview of mathematical ideas as they relate to varied disciplines. This book provides an appreciation of mathematics, highlighting mathematical history, applications of mathematics to the arts and sciences across cultures, and introduces students to the uses of technology in mathematics. Exercise sets are now organized into Concept/Writing, Practice the Skills, Problem Solving, Challenge Problems/Group Activities, Research Activities. An updated Consumer Math section including updated material on sources of credit and mutual funds. Motivational, chapter-opening material demonstrates connections between math and various other disciplines. KEY MARKET For those who require a general overview of mathematics, especially in the fields of elementary education, the social sciences, business, nursing and allied health fields.
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Meet the Author
Allen Angel received his BS and MS in mathematics from SUNY at New Paltz. He completed additional graduate work at Rutgers University. He taught at Sullivan County Community College and Monroe Community College, where he served as chairperson of the Mathematics Department. He served as Assistant Director of the National Science Foundation at Rutgers University for the summers of 1967 - 1970. He was President of The New York State Mathematics Association of Two Year Colleges (NYSMATYC). He also served as Northeast Vice President of the American Mathematics Association of Two Year Colleges (AMATYC). Allen lives in Palm Harbor, Florida but spends his summers in Penfield, New York. He enjoys playing tennis and watching sports. He also enjoys traveling with his wife Kathy.
Christine Abbott received her undergraduate degree in mathematics from SUNY Brockport and her graduate degree in mathematics education from Syracuse University. Since then she has taught mathematics at Monroe Community College and has recently chaired the department. In her spare time she enjoys watching sporting events, particularly baseball, college basketball, college football, and the NFL. She also enjoys spending time with her family, traveling, and reading
Dennis Runde has a BS degree and an MS degree in Mathematics from the University of Wisconsin--Platteville and Milwaukee respectively. He has a PhD in Mathematics Education from the University of South Florida. He has been teaching for more than fifteen years at State College of Florida–Manatee-Sarasota and for almost ten years at Saint Stephen's Episcopal School. Besides coaching little league baseball, his other interests include history, politics, fishing, canoeing, and cooking. He and his wife Kristin stay busy keeping up with their three sons--Alex, Nick, and Max |
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MATH 003
Basic Skills (3) Natural numbers; integers; rational numbers; decimals; ratio, proportion; percent; graphs; applications. Students who have passed MATH 001 may not schedule this course for credit. This course may not be used to satisfy the basic minimum requirements for graduation in any baccalaureate degree program |
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Intermediate Algebra: Connecting Concepts through Applications
9780534496364
ISBN:
0534496369
Edition: 1 Pub Date: 2011 Publisher: Brooks Cole
Summary: INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate so...lutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, INTERMEDIATE ALGEBRA: CONNECTING CONCEPTS THROUGH APPLICATIONS takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and skills.
Clark, Mark is the author of Intermediate Algebra: Connecting Concepts through Applications, published 2011 under ISBN 9780534496364 and 0534496369. Seven hundred eighty seven Intermediate Algebra: Connecting Concepts through Applications textbooks are available for sale on ValoreBooks.com, one hundred ninety seven used from the cheapest price of $43.63, or buy new starting at $167534496371 |
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