text
stringlengths 8
1.01M
|
|---|
Math Software
Our CD
has
over 340 pages of self-paced instruction designed to make math fun.
Units covered include geometry, number theory, percent, integers,
pre-algebra, probability, statistics, logic and graphs. Downloads
of our software are available! |
UNLV Math Competitions
The mathematical competition activities at UNLV consist of a semester-long workshop on
problem solving, the Annual UNLV Mathematical Competition, and the William Lowell Putnam
Mathematical Competition. The local version of the Putnam exam is open to all undergraduate
students at UNLV. The competition is typically held during the fall term in October.
The William Lowell Putnam Mathematical Competition
The William Lowell Putnam
Mathematical Competition is the premier mathematical competition
for undergraduates in North America. This annual contest began in 1938 and is designed to
stimulate a healthful rivalry in mathematical studies in the colleges and universities in the
United States and Canada. It is administered by the
Mathematical Association of America
and attracts a large number of contestants from nearly 500 colleges and universities across North
America. It is usually held on the first Saturday of December and consists of two three-hour
sessions of six problems each. The problems are challenging and require considerable
ingenuity and insight, but little technical knowledge beyond calculus. In addition to
individual competition, the participating colleges are ranked based on the performance of
their three-member teams. |
Book Description: Offering students step-by-step mathematics progression through the GCSE Intermediate-tier examination topics, and presented in separate units of work, this book is designed to encourage and support the students whether they are new to GCSE or preparing to retake the exam. Worked exam questions with examples are accompanied by examiners' tips which show students how to gain marks, and advice is offered on the planning of a revision programme. |
Graphs and Functions
Graphs and Functions teaches an introduction to using a rectangular (Cartesian) coordinate system, and provides the help necessary to study the basics of graphing functions, including how to plot, identify quadrants and interpret graphs, determine whether a relation is a function and find its domain and range. |
Course 1- make sure you study the notes given today and the notes in your notebook. Know the formulas found on the KNOW THESE paper in your notebook. Practice doing some of the perimeter and area problems on the review sheet. You should also know about PEMDAS, exponents, and perfect squares. Don't forget to do your graphs.
Course 2- make sure you review all about central tendency. You should know all about stem and leaves, box and whiskers, and frequency tables. You should also know about exponents, PEMDAS, prime factorization, and gcf. |
Return here for REGISTRATION
Algebra 1 online Review is for the student that has already completed an Algebra 1 course in the recent past and needs to review the course before taking Algebra 2 or Geometry.
In this algebra class you will receive prompt replies (daily emails) to any algebra question you have, as well as,
receive a review of solving equations, multiplying and factoring polynomials, graphing lines, finding slopes of lines and creative ideas of solving word problems.
Each Lesson gives several examples and explanation of the math topic. Most have videos or games to use to help you learn the topic better. Each lesson has 1 or 2 assignments for you to complete and submit to me. I grade all assignments and tests the day that they are submitted to the classroom.
I answer email within 24 hours, but often it is in just a few hours.
The topics to be reviewed include solving linear equations, multiplying polynomials, factoring polynomials, money word problems, graphing lines, finding the slope of a line and finding the midpoint and length of a line segment.
You must already know how to add, subtract, multiply and divide integers and know how to use well the Order of Operations. -2+12(8-13) /20 =?
I answer email at least 350 days of the year.
The student must have a valid email address and must be able to easily check his emails and SAVE them in a folder on his computer.
Numbers 6: 24-26 |
Visual Mathematics is a highly interactive visualization software (containing -at least- 67 modules) addressed to High school, College and University students. This is a very powerful tool that helps to...
Advanced Mathematics Suite, or AMS for short, is a program which makes up for where TI left off when they developed the TI-83 Plus graphing calculator. It includes various useful utilities for work with...
Learning Mathematics can be a challenge for anyone. Math Flight can help you master it with three fun activities to choose from! With lots of graphics and sound effects, your interest in learning math should...
Create professional-quality Mathematics worksheets to provide students in grades K to 10 with the skills development and practice they need as part of a complete numeracy program. Over 60 Mathematics......
Undoubtedly, Mathematics is one of the most important subjects taught in school. It is thus unfortunate that some students lack elementary mathematical skills. An inadequate grasp of simple every-day...
Gartner states that 30% of helpdesk queries are related to password resets management and account lockout. With Jiji Self Service Password Reset(JSSPR), end-users now have the ability to securely reset their...
fMath Formula - GWT Widget provide a simple way to display equations or Mathematics formula on your GWT applications (Google Web Toolkit). It has more than 20000 symbols to display using MathML or in LaTeX....
Boost your math skill with cool and thrilling games. Our proven built-in learning engine does the rest for you. The package includes 10 games that train your math skill in addition up to 20, quick and...
SpeQ Mathematics (SpeQ Math) is a light, award-winning math program with intuitive interface that makes calculation tasks fun. It is aimed at engineers, students and anyone who needs to perform math...
Young Einstein Mathematics is a software for leaning Mathematics at a primary level. It is perfect for children who want to practice their mathematic skills in a very interactive way. A lot of drawings will...
Jiji self service password reset, In this the end-users can securely reset their own Active Directory passwords without having to involve highly technical helpdesk professionals. Gartner stated if a...
SimplexNumerica is an object-oriented numerical data analyzer, plot and presentation program. SimplexNumerica is proving to be extremely popular among scientists. Ergonomic programming using the newest... |
HOME
Welcome to MathFortress.com where you can "Fortify Your Math Knowledge". Here you will find unique Great Quality Videos and other resources for various mathematical disciplines all for FREE! You will need Adobe Flash Player to see the videos. This website is best viewed using Chrome or Firefox browsers. You can download any documents on this site for your own personal use either studying with them or incorporating them into your lesson plan if you are a teacher. Let everyone know about MathFortress.com
If you spot an error or typo on some of these resources or you would like to see resources on a specific topic feel free to email me: [email protected]
Website Updates
[June 16, 2013]
Added Families of Solutions (Level 3) in the DE section. This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 2 examples illustrating how to verify Implicit One-Parameter Family of solutions.
[June 9, 2013]
Added Families of Solutions (Level 2) in the DE section. This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 3 examples illustrating how to verify general solutions of ordinary differential equations.
[June 2, 2013]
Added Families of Solutions (Level 1) in the DE section. This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over families of solutions. In addition, particular solutions, general solutions, singular solutions, and piecewise-defined solutions are also presented.
[May 12, 2013]
Added Implicit Solutions (Level 1) in the DE section. This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over implicit solutions of differential equations. The concept of a formal solution is also presented.
[May 5, 2013]
Added Solutions (Level 4) in the DE section. This video introduces the basic concepts associated with solutions of partial differential equations. This video goes over 3 examples illustrating how to verify solutions to partial differential equations.
[April 28, 2013]
Added Solutions (Level 3) in the DE section.This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 3 slightly more challenging examples illustrating how to verify solutions to differential equations. In addition this video also covers how to determine an appropriate interval of definition.
[April 21, 2013]
Added Solutions (Level 2) in the DE section.This video introduces the basic concepts associated with solutions of ordinary differential equations. This video goes over 3 examples illustrating how to verify solutions to differential equations. In addition this video also covers how to determine an appropriate interval of definition.
[April 1, 2013]
Added Definitions and Terminology (Level 4) in the DE section.This video introduces the basic definitions and terminology of differential equations. This video goes over 8 examples covering how to classify Partial Differential Equations (PDE) by order and linearity.
[March 24, 2013]
Added Definitions and Terminology (Level 3) in the DE section.This video introduces the basic definitions and terminology of differential equations. This video goes over 6 examples covering how to classify ordinary differential equations by order and linearity.
[March 17, 2013]
Added Definitions and Terminology (Level 2) in the DE section.This video introduces the basic definitions and terminology of differential equations. This video goes over 4 basic examples covering how to classify ordinary differential equations by order and linearity.
[March 10, 2013]
Added Fractions (Part 5) in the GRE section.This video is a review of basic arithmetic for the purpose of solving problems on the quantitative reasoning section of the GRE revised General Test. This video covers the basics of fractions. Topics covered: Comparing Fractions, Comparing more then two Fractions, fractions with irrational Numbers, combination of operations with fractions.
[March 3, 2013]
Added Fractions (Part 4) in the GRE section.This video is a review of basic arithmetic for the purpose of solving problems on the quantitative reasoning section of the GRE revised General Test. This video covers the basics of fractions. Topic covered: division of fractions, complex fractions, and mixed numbers.
[February 24, 2013]
Added Fractions (Part 3) in the GRE section.This video is a review of basic arithmetic for the purpose of solving problems on the quantitative reasoning section of the GRE revised General Test. This video covers the basics of fractions. Topic covered: multiplication of fractions.
[February 17, 2013]
Added Fractions (Part 2) in the GRE section.This video is a review of basic arithmetic for the purpose of solving problems on the quantitative reasoning section of the GRE revised General Test. This video covers the basics of fractions. Topics covered include: addition and subtraction of fractions.
[February 10, 2013]
Added Fractions (Part 1) in the GRE section.This video is a review of basic arithmetic for the purpose of solving problems on the quantitative reasoning section of the GRE revised General Test. This video covers the basics of fractions. Topics covered include: The definition of a fraction and properties of fractions. |
Sections of the MAA
At present, the MAA has 29 sections, which are defined by ZIP or postal code. Sections are a vital component of the MAA, and a significant part of the Association's activity is centered on them. Each section holds at least one professional meeting per year, usually in the Spring.
Section meetings include, but not limited to:
Invited lectures
Contributed papers
Panel discussions
Other activities designed to promote and improve collegiate level mathematics
Programs of upcoming section meetings, if not available via the links below, may be obtained from the appropriate section secretary.
Many sections also conduct activities that involve both high school and college students. These include:
Sponsoring mathematics contests
Advising state departments of education on teacher certification in the mathematical sciences
Working with high schools and colleges on course content and curricula
Providing lecturers to colleges and high schools
Active MAA members who reside in the United States and Canada have the benefit of being affiliated with one of 29 sections.
Find My Section
Enter Zip Code or Canadian Postal Code
Borders for each section are roughly illustrated in the map below. Click map to see the full-sized version. |
Learn Basic Math, Algebra, and Geometry
Universal Class online courses will help you master the concepts in basic math, algebra, geometry, calculus and statistics quickly and easily. Our online classes are designed to give students the most flexibility and independence. These classes are appropriate for K-12 students, homeschoolers, college students and adult learners who need extra tutoring, test prep, review or just the enjoyment of learning math.
Our classes are self-paced and low-cost. You can enroll anytime, everything is online: lessons, assignments, and exams Mathematics |
Supporting Mathematics These range from entry level to level three.
The workshop also provides a place where students can go at any time of the college day to seek help and support with their learning in mathematics. They encourage self-learning and provides a supportive environment for students to work, full in the knowledge that help is nearby.
The project's aim is to provide appropriate part-time courses for students and offer easy access to support in order to keep them engaged in learning |
Hi math lovers, I heard that there are various programs that can help with us studying,like a teacher substitute. Is this really true? Is there a software that can assist me with math? I have never tried one before, but they are probably not hard to use I think. If anyone has such a program, I would really appreciate some more information about it. I'm in Remedial Algebra now, so I've been studying things like finding the sum and product of the quadratic equation and it's not easy at all.
You don't need to ask anyone to solve any sample questions for you; as a matter of fact all you need is Algebra Buster. I've tried many such algebra simulation software but Algebra Buster is way better than most of them. It'll solve any question that you have and it'll even explain each and every step involved in reaching that answer. You can try out as many examples as you would like to, and unlike us human beings, it won't ever say, Oh! I've had enough for the day! ;) I used to have some problems in solving questions on hyperbolas and rational expressions, but this software really helped me get over those.
Even I've been through that phase when I was trying to figure out a solution to certain type of questions pertaining to side-side-side similarity and point-slope. But then I found this piece of software and I felt as if I found a magic wand. In a flash it would solve even the most difficult problems for you. And the fact that it gives a detailed step-by-step explanation makes it even more handy. It's a must buy for every algebra student. |
Mathematics in Education
QuadEquations teaches the solution of quadratic equations by factorisation, by completing the squares and by formula. QuadEquations teaches the solution of quadratic equations by factorisation, by completing the squares and by formula. Special...
Quick and reliable knowledge of multiplication tables is an essential cornerstone of a student's mathematical ability. Quick and reliable knowledge of multiplication tables is an essential cornerstone of a student's mathematical ability.......
Ciclo VBelt Professional Edition is an advanced engineering tool that allows you create V-belt drive designs in a quick, accurate and reliable manner. Ciclo VBelt Professional Edition is an advanced engineering tool that allows you create V-belt...
Worksheet Generator lets you create own worksheets in seconds, in thousands of combinations. Worksheet Generator lets you create own worksheets in seconds, in thousands of combinations. Main Features : - Now you can create an endless supply of...
Math workpad is a programmable workpad for mathematics. Math workpad is a programmable workpad for mathematics. This widget lets you evaluate complex mathematical expressions. All results are displayed, and you can use the answer from the...
Math Quiz Creator is an educational application for Windows that lets educators quickly generate printable math quizzes with answer keys for students six to twelve years old. Math Quiz Creator is an educational application for Windows that lets...
The prime conversion software available for currency, metric and imperial, currently including the following 27 conversion groups and many subgroups:Acceleration, Angle, Area, Base, Consumption, Currency, Data Storage, Data Transfer, Density,...
CalcExp is designed as an alternative to the system build-in calculators. CalcExp is designed as an alternative to the system build-in calculators. CalcExp runs on Windows 2K/XP/Vista, MacOsX, Linux, and Solaris. The main features are:1....
A new OpenGL-based Software Package dedicated to Visual Psychophysics running on Mac OSX. A new OpenGL-based Software Package dedicated to Visual Psychophysics running on Mac OSX. It consists in a unique stand-alone application that does not...
Performs multivariate polynomial regression using the Least Squares method. Performs multivariate polynomial regression using the Least Squares method. The program determines the coefficients of the polynomial, the generalized correlation...
Selection, calculation and check of rolling bearings (inch versions). Application supports Imperial and Metric units, is based on SKF, ISO, ANSI, SAE standards and support many 2D and 3D CAD systems This module can be used for the selection,... The...
What is DC Proof? What is DC Proof? - Free, PC-based educational software - Logic-checking software provides instant feedback as you enter every line of proof - Includes interactive tutorial that introduces the standard methods of proof using...
AutoTRAX EDA LITE is a powerful integrated Electronic Design Suite for Electronic Engineers. AutoTRAX EDA LITE is a powerful integrated Electronic Design Suite for Electronic Engineers. It has all the features you expect and need to rapidly and...
A GPS mapping application for OS X. A GPS mapping application for OS X. All the essential functions of your GPS device are supported; all you need is a Mac, a GPS, and of course RouteBuddy.- Supports Garmin,TomTom, USGlobalSat, and NMEA Devices-...
If you are searching for a computer program that can plot simple graphs on your PC, GraphSight Junior is what you are looking for. If you are searching for a computer program that can plot simple graphs on your PC, GraphSight Junior is what you...
AlgoSim is a very intuitive and advanced mathematical software for numerical analysis and visualisation, and physical simulation. AlgoSim is a very intuitive and advanced mathematical software for numerical analysis and visualisation, and physical...
Selection, calculation and check of rolling bearings of the company FAG. Application supports Imperial and Metric units, is based on FAG, INA, ISO, ANSI, SAE standards and support many 2D and 3D CAD systems This calculation can be used for the...
Two programs for the tolerance analysis of linear, 2D and 3D dimensional chains (Worst case, Root Sum Squares, Monte Carlo...). Application is developed in MS Excel, is multi-language and supports Imperial and Metric units. Two programs for the...
Welcome to nTangle: Untangle a web of intersecting lines, from very easy to very hard. Welcome to nTangle: Untangle a web of intersecting lines, from very easy to very hard. A simple and relaxing way to pass your time. The program features more... The... |
10 Units 2000 Level Course
Available in 2013
Provides the essential mathematical techniques of Physical Science and Engineering. These are the methods of Multivariable Calculus and Differential Equations. Multivariable Calculus involves a study of the differential and integral calculus of functions of two or more variables. In particular it covers introductory material on the differential calculus of scalar and vector fields, and the integral calculus of scalar and vector functions. Differential Equations arise from mathematical models of physical processes. Also includes the study of the main analytical and numerical methods for obtaining solutions to first and second order differential equations. The course also introduces students to the use of mathematical software in the investigation of problems in multivariable calculus and differential equations.
Objectives
At the successful completion of this course students will have: 1. a sound grounding in the differentiation and integration of functions of several variables and in the methods of solution of ordinary differential equations.
2. skills in solving a range of mathematical problems involving functions of many variables.
3. basic skills in modelling real world problems involving multivariable calculus and ordinary differential equations, and in interpreting their solutions as they relate to the original problem.
4. skills in the application of computer software in the exploration of mathematical systems and in the solution of real-world problems relevant to the content of the course. |
MATH
131 – Linear Algebra I
Fall 2006
Text : Linear Algebra, 3rd Edition, by Fraleigh and Beauregard
Course
Meetings: The course lectures will be held in Sproul Hall 2340 on
Tuesdays and Thursdays at 2:10 pm-3:30 pm.Discussion sessions will be held on Wednesday with Ms. Rafizadeh (7:10
pm) or Mr. Kuang (8:10 am).You are
expected to attend both the lectures and the discussion sessions as per Math
Department decree.
Tips for
Success: * Come to class!It is
amazing how much you can learn by being attentive in class. *
Collaborative learning is encouraged but remember only YOU will be taking the
quizzes and exams... * Like all mathematics, linear algebra is not a
spectator sport; you will learn only by doing! You will find that a
consistent effort will be rewarded. * Be organized. Have a notebook
or binder for Linear Algebra alone to keep your class notes, homework, quizzes
and exams in order. * No question you have should be left
unanswered. Ask your questions in class, discussion session or take
advantage of office hours.
Homework
(100 points): Homework will be assigned daily and the starred problems
will be collected during the next week's discussion session.No late
homework will be accepted.Homework will not be graded unless it is written
in order and labeled appropriately.An answer alone will get 0 points.Make sure to justify every answer.Your lowest homework score will be dropped
and the remaining homework will be averaged to get a score out of 100.
Quizzes
(100 points): There will be a short quiz given at the beginning of each
lecture testing you on the definitions and theory that you learned from last
class.You may use your notes.Quizzes will only last 5 minutes so make sure
that your notes are organized and that you arrive on time for class.There may also be a quiz at the end of
discussion with one problem similar to the homework problems assigned during
the previous week.You may not use your
notes for this quiz.The daily quizzes
will be worth 3 points each, the lowest two will be dropped giving a total of
50 points.The discussion quizzes will
be worth 10 points each, there will be at least 6, and I will keep only the top
5 scores for a total of 50 points.
Exams (300
points): I will give one midterm (100 points) and a final (200
points). Please bring your ID to each exam.There
are no make up exams. If a test is missed, notify me
as soon as
possibleon
the day of the exam. For the midterms only, if you have a legitimate and documented
excuse, your grade will be recalculated without that test.The Midterm is tentatively scheduled on
Thursday, October 26.The Final is on
Tuesday, December 15, from 11:30 am-2:30 pm.
Grades: General
guidelines for letter grades (subject to change; but they
won't get any more strict): 90-100% - A; 80-89% - B; 70-79% - C; 60-69% - D;
below 60% - F. In assigning Final Grades for the course, I will compare
your grade on all course work (including the Final)and your grade on the Final Exam.You will receive the better of the two
grades.
Calculator
Policy: It is the Math Department's policy to forbid the use of
calculators on both exams and quizzes. |
Number Theory and Geometry
This module runs in alternate years: 2012-13, 2014-15 and so on.
EMMS093S6 (30 credits)
Aims
This is a two-part course aiming to provide you with an introduction to two important areas of pure mathematics, number theory and geometry -- topics which every pure mathematician will find of interest.
The number theory section will cover types of numbers such as polygonal numbers and perfect numbers, followed by number theoretic functions, including Euler's φ function. We will prove Fermat's little theorem and study quadratic congruences as well as Pythagorean triples and sums of squares.
The section on geometry will devote time to vector geometry, affine geometry and Euclidean geometry. Curves arising from conic sections, such as the ellipse and the hyperbola, will also be studied and their properties derived from first principles, with some applications and generalisations. Finally there will be a look at the geometry of the complex plane assignment. The examination in the Summer Term has three sections. Section A (worth 40%) consists of compulsory short questions. Sections B and C (worth 20% each) contain several longer questions. You must answer one from Section B and one from Section C. |
Product Description
A beautifully-sequenced review of transformational geometry with the MIRA™, starting at a 7th grade level and moving upward. Includes plenty of activities for junior high students. Topics include properties of perpendicular lines, reflection, symmetry, and motion. 87 pages. Grade 7 and up.
Prices listed are U.S. Domestic prices only and apply to orders shipped within the United States. Orders from outside the
United States may be charged additional distributor, customs, and shipping charges. |
Exploring Algebra VHS Introduce middle school students to more advanced properties of functions and algebra.
3 - 5
VHS
$39.95
Statistics and Data Analysis in Sports VHS Using only a calculator, a stat book, and some custom equations, a new generation of baseball statisticians believes it's possible to accurately predict a player's true value to his team. |
{"itemData":[{"priceBreaksMAP":null,"buyingPrice":40,"ASIN":"0262510375","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":17.89,"ASIN":"0465046746","isPreorder":0}],"shippingId":"0262510375::RJG1e3lwrMpx2rJBMSl3zLgax%2BczYCRvV0TswIQEKm2QjoEGTtjkRNXYxTKuxmVlhBQnrz4KjZ1WVwF%2FOPlzAHasCnLhyYcOykrQOaevTFo%3D,0465046746::EMDfIdQlPWEa66NSjBhw5J9EEh7crEr7TbGc6yCSWD2egcQepj1qfLdb1OxTmyukCGefdSdLatuKirb0ifj09OurgFVdc5LZb7SQuKGn7 college-level math text for serious mathematicians and fans of recreational mathematics. This book proves that turtle graphics is not just kid stuff." Popular Computing
"Reading this book with the help of a good graphics computer system, you are sure to discover new and interesting math... an excellent textbook or self-study guide." W. Lloyd Milligan , Byte
About the Author
Andrea diSessa is Chancellor's Professor in the Graduate School of Education at the University of California, Berkeley, and a member of the National Academy of Education. He is the coauthor of Turtle Geometry: The Computer as a Medium for Exploring Mathematics (MIT Press, 1981).
I discovered this little gem of a book while exploring the stacks in the library when I was attending a local junior college back in the 80's. The author uses Logo's turtle graphics as a way of exploring the properties of geometric space. From very simple beginnings drawing regular polygons and other simple shapes, the book gradually works its way to more and more complicated scenarios. After exploring the properties of ordinary turtle graphics, turtle graphics are tried on the surfaces of spheres and cubes, then on more complicated surfaces. Little by little, concepts of non-Euclidean geometry are introduced, until the final chapters in which the turtle is used to demonstrate the geometric nature of gravity in Einstein's general theory of relativity.
I strongly recommend this book to anyone with interests in computer programming, geometry and physics. The unusual approach this book takes to the understanding of curved space is deceptively simple and surprisingly powerful.
Turtle Geometry teaches mathematics and physics via the computer and the Logo programming language. The mathematics covered is pretty advanced, including topology, and general relativity. Yet, through the use of turtle geometry this advanced math and physics becomes accessible to the layperson. Although all of the examples are in the Logo programming language there are listings of Basic routines in the back of the book. With the help of the Basic routines I was able to easily translate the Logo/Basic code to the Python programming language which I choose to use for reading this book. The reviewers of this book mention it as the beginnning of a revolution in mathematics education. It seems though, that this revolution did not come about as computers are still not used very effectively in the classroom. I think this is very sad as the teaching approach used in Turtle Geometry could be very successful in the classroom.
Anyone interested in logo from beginners to advanced users will benefit from reading this book. It has very easy and simple to understand examples, along with a review, and questions at the end of every chapter. Some solutions are provided at the end of the book, (and their even correct, as opposed to many other text books I've read). The pace of the book gets gradually more difficulst, yet more interesting as you reach the climax at the end. A must read for anyone interested in Mathematics. |
Chemistry Maths 2 teaches Maths from a "chemical" perspective and is the second of a three part series of texts taken during a first-year university course. It is the Maths required by a Chemist, or Chemical Engineer, Chemical Physicist, Molecular Biologist, Biochemist or Biologist. Tutorial questions with fully worked solutions structured on a weekly basis to help the students to... |
Tired of struggling with algebra homework assigned by your teacher?Your parents or friends can't help you? See what other people do when they need algebra help!
Tami Garleff of Grand Blanc, Michigan, ordered the Algebra Professor™late one night when she was unable to give her daughter enough help with her honors algebra class.Our algebra software was able to provide that assistance. This is what she said:
"After we ordered your algebra software, she was able to see step-by-step howto solve the problems. Your software definitely saved the day."
This is only one of the hundreds of real-life testimonials received from parents, students,and algebra teachers. Our algebra software is used in many schools and has been featured as great algebrahelp in educational publications such as T.H.E. Journal and Mathematics Teacher.
The Algebra Professor™ Puts Students in Control of their Learning.
It's one of the most powerful algebra software packages. It enables you to solve actual problemsfrom your algebra textbook — not just a limited set of computer generated examples.
It's an alternative to your algebra teacher. You don't just get the answers. TheAlgebra Professor teaches you how to solve algebra problems step-by-step,using the same methods that your algebra teacher uses in the classroom.
You get algebra help by observing andasking for explanations, which are only a click away.
It's like a 24/7 algebra tutor. Youfind out how algebra rules are applied in your particular problem.
It provides all the algebra help you will ever need: algebra expression simplification,algebra equation and inequality solution, graphing of algebraic curves, andcomplex numbers.
"It really helped me with my homework.I was stuck on some problems and your algebra software walked me step by step through the process. It not only shows you the answer, it shows you how to do it." — Charles Sievert, student,Bardstown KY I also like how an explanation can be shown for each step. That helps learn the functions of each different method for solving." — Troy Green, student, Callahan, FL
"I bought 'The Algebra Professor' for my daughter to help her with her 10thGrade Advanced Algebra class. Like most kids, she was getting impatient with the evolution of equations (quadratic in particular)and making mistakes in her arithmetic. I very much like the step-by-step display of your product. I thinkit got my daughter a better grade in the past semester." — Tom Canty, parent,Phoenix, AZ
"The program helped my son do well on an algebra exam. It helped refresh my memory of a lot of things I forgot." — Colleen D. Lester, Chalfont, PA
Plus, many experts from all areas of education hail the Algebra Professor™, too!
"This algebra software has an exceptional ability to accommodate individual users. While offering help with algebra homework,it also forces the student to learn basic math. The algebra tutor part of the software provides easy to understand explanationsfor every step of algebra problem solution." — Miguel San Miguel-Gonzalez, Education Specialist Texas A&MInternational University, Laredo
"Algebra lessons are very easy to create because of template-based problem generation.Students can get context sensitive algebra help on any solution step by a single button click... an ideal software tolearn basic algebra" — James Spann, MathematicsTeacher, PSJA High, Pharr |
The TI-82
Teacher Learning System
The TI-82 Teacher Learning System (TI-82 TLS)
The Teacher Learning System for the TI-82 graphing calculator (TI-82 TLS)
has been developed to assist the secondary mathematics teacher with learning
about this technology as well as designing and managing instruction using
it appropriately in the delivery of the secondary mathematics curriculum.
This may seem like a monumental task at this point! We hope teachers will
find this is not the case and will approach this new challenge confidently
and enthusiastically.
The components of the TI-82 TLS are:
Independent Study Written Materials
Graphing Calculator Programs and Functions for Algebra/Statistics,
Trigonometry, and Calculus
Video Supplements: Learning to Use the TI-82; Using Algebra/Statistics,
Trigonometry, and Calculus Programs; Programming the TI-82; Suggestions
for Designing and Managing Instruction
Listings of Calculator Programs
Numerous papers have been written documenting the advantages of using graphing
calculators to teach and learn mathematics. Many of these papers have even
described specific methods for integrating graphing calculators into the
secondary mathematics curriculum. Two different positions seem to be common
among practicing mathematics teachers. Some regard integrating graphing
calculators into the mathematics curriculum as a sort of panacea for teaching
mathematics in the next century. In an idealistic way, they believe students
will be able to easily learn the procedural manipulations of the graphing
calculator when they are introduced (after all, graphing calculators are
"user-friendly!?"). And, students will be enthusiastically looking
forward to their next opportunity to use them!
Other teachers maintain a more cautious posture. To them, perhaps a more
realistic scenario would be the following. Because calculators are so powerful
and offer so many options, it is likely that many students will push the
wrong key at the wrong time thereby finding themselves locked into a mode
from which they have no earthly idea how to recover. Since the teacher may
not know how the students entered these modes, he or she may not be immediately
able to return them to the proper format to continue the lesson. By the
end of the class, most students will have their hands in the air begging
for help! The class has the potential to end in disaster where students
and teacher alike are frustrated and convinced that the graphing calculator
is more trouble than it is worth! There is also the very real question of
whether students are learning mathematics or learning a sequence of procedural
steps required to obtain an answer.
Using the Teacher Learning System
The TI-82 TLS has been developed to help you learn about the TI-82 graphing
calculator using written materials, programs, and a video supplement.
The initial portion of the video supplement sets the stage for learning
how to use the TI-82. It assumes you know nothing about the TI-82 and introduces
you to its organizational setup. If you are not familiar with the TI-82,
we suggest you view this segment without your calculator; then, watch it
again with your calculator in hand. Knowing how the TI-82 is organized will
prove essential to your continued learning.
The initial chapter of the written materials builds upon the video by introducing
you to some of the fundamental programs. A brief explanation of each program
is given together with some examples. You should work through each of the
programs in this chapter using your calculator. As you continue, you will
undoubtedly feel more confident in your own abilities and begin to understand
the simplicity (or "friendliness") of this powerful learning tool.
The second portion of the video supplement introduces and explains how to
use some of the host of algebra and statistics, trigonometry, and calculus
programs that have been written explicitly for your classroom use. The companion
chapters in the written materials are arranged according to algebra and
statistics, trigonometry, and calculus. The introduction to each of these
chapters describes the programs and functions included in it. A concise
explanation for each program or function shows how to execute it and is
followed by examples and exercises; try them! Because the programs and functions
relate directly to the topics in the secondary mathematics curriculum, integration
of the TI-82 should be relatively simple. A brief introduction to programming
the TI-82 is also included in this portion of the video supplement.
The final portion of the video supplement discusses various aspects of designing
and managing instruction that integrates the TI-82 and includes suggestions
for gaining school and district acceptance and support.
The final chapter of the written materials includes the statements of the
programs developed. This is a valuable resource for teachers desiring to
do their own programming, i.e., extending existing programs or developing
new programs.
Written Materials and Programs/Functions for the TI-82 Graphing Calculator
The content of the TI-82 TLS written materials is listed below. Clicking
on the desired topic will work. The page references for the topics in the
TI-82 TLS book are also given in parenthesis, e.g., (G-4), if you have access
to this source.
Credits. The Graphing Calculator: Teachers and Students Learning
Together is made possible through funding to Oklahoma State University
from the Office of Educational Research and Improvement, U.S. Department
of Education under grant number R203A40026 with assistance from the Southwest
Educational Development Laboratory.
Disclaimer. The project materials are based on work sponsored wholly,
or in part, by the Office of Educational Research and Improvement, U.S.
Department of Education under grant number R203A40026. The content of these
materials do not necessarily reflect the view of OERI, the Department, or
any other agency of the U.S. Government. |
Examines a Tractatus algorismi written in 1307 in Montpellier by Jacopo da Firenze. It is one of the earliest surviving "abbacus" treatises and the first to contain a presentation of algebra. This book includes the text in late medieval Italian with an English translation. It discusses the contents and its place within early abbacus culture. more...
The relation between mathematics and physics has a long history, in which the role of number theory and of other more abstract parts of mathematics has become prominent. This book focuses on the broader interface of number theory, geometry, and physics. It is presented in three parts: Conformal Field Theories, Discrete Groups, and Renormalization. more...
Given its abstract nature and the highly syntactical competence required by the use of symbolic algebra, research on its teaching and learning must rely on approaches that include semiotic concepts and analyses that recall the history of algebraic ideas, among others. Educational Algebra: A Theoretical and Empirical Approach deals with a theoretical... more...
With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results. more...
If you think algebra has to be boring, confusing and unrelated to anything in the real world, think again! Written in a humorous, conversational style, this book gently nudges students toward success in pre-algebra and Algebra I. With its engaging question/answer format and helpful practice problems, glossary and index, it is ideal for homeschoolers,... more...
Cl... more...
This first book in the series will describe the Net Generation as visual learners who thrive when surrounded with new technologies and whose needs can be met with the technological innovations. These new learners seek novel ways of studying, such as collaborating with peers, multitasking, as well as use of multimedia, the Internet, and other Information... more... |
New GCSE Maths Linked Pair - AQA GCSE In Methods in Mathematics and Applications of Mathematics: Student Book
Find the extra content for Methods and Applications of Maths, all in one place, to teach the AQA Linked Pair GCSE Maths Pilot. Use with Collins New GCSE Maths AQA Scheme to provide full coverage for the Linked Pair. Students will discover that maths can be challenging and fun, combining maths problem solving with essential tools for work and life.
About this resource
• Covers both Foundation and Higher levels in one book. Higher level questions are clearly indicated. |
Get the confidence and the skills you need to master differential equations!
Need to know how to solve differential equations? This easy-to-follow, hands-on workbook helps you master the basic concepts and work through the types of problems you'll encounter in your coursework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every equation. You'll also memorize the most-common types of differential equations, see how to avoid common mistakes, get tips and tricks for advanced problems, improve your exam scores, and much more!
The Dummies Workbook Way
Quick refresher explanations
Step-by-step procedures
Hands-on practice exercises
Ample workspace to work out problems
Tear-out Cheat Sheet
A dash of humor and fun
Go to Dummies.com®for videos, step-by-step photos, how-to articles, or to shop the store!
More than 100 problems!
Detailed, fully worked-out solutions to problems
The inside scoop on first, second, and higher order differential equations
A wealth of advanced techniques, including power series
Customer Reviews:
Review of Differential Equations Workbook For Dummies
By B. Heller - October 2, 2009
The work book is fine, but it is keyed to the Differential Equations for Dummies book written by the same author. The exercises are generally of ordinary difficulty, and there are some topics that are not covered. The book doesn't touch on Green Functions, but unfortunately that is true of most American texts on ordinary differential equations. There should have been more variety displayed in the application of ordinary differential equations, especially in solving problems in dynamics, ciruit analysis, fluid dynamics and perhaps even for basic problems in astronomy. For me the real value of ordinary differential equations is in its use in unlocking solutions to all kinds of practical problems. But overall, this book is a good review and well worth having in your mathematics library.
Very nice format to learn or review differential equations
By Leeber Cohen - June 21, 2010
This workbook requires that you have a knowledge of basic trigonometry and calculus. The workbooks in this series are wonderful because they provide short summaries with example problems. There then follows multiple problems for each subject with detailed solutions. This is the sbsolute key for individuals trying to review this subject or learn it on their own. In comparison to the Schaum's 3000 solved problems there is much less theory and many of the problems are easier to solve. The Schaum's series is aimed more at college and graduate students. There are a few unfortunate mistakes in the solved answers in this Dummies workbook which is slightly annoying. (That is why I took one star off) Does anyone know if the publisher has a website with the errata? If not I would suggest that the publisher should provide a website with corrections. For the money this book is a very good deal and Dr. Holzner should be congratulated. If you need to brush up on your linear algebra and... read more
Great Supplement to class
By Josh - November 3, 2011
I bought this book to supplement my current Diff Eq class, and it worked wonders. I had literally skipped or been doing other work in class for a few weeks and this book brought me back up to speed in no time. I would not expect someone with little to no math background to pick it up and understand everything that is going on in the book, but if you don't have a reasonable understanding of calculus your probably not worried about Diff Eq anyway.
AutoCAD 2007 features a new 3D rendering engine that greatly enhances the program's 3D functionality-and makes this industry-standard drafting program even more difficult to master, even for veteran ... |
MP Basic College Mathematics (Softcover)
Basic College Mathematics offers a refreshing approach to the traditional content of the course. Presented in worktext format, Basic College ...Show synopsisBasic College Mathematics offers a refreshing approach to the traditional content of the course. Presented in worktext format, Basic College Mathematics focuses on basic number skills: operations and problem-solving with whole numbers, fractions, and decimals. Other topics include geometry, measurement, ratios, proportions, percents, and the real number system (with an introduction to algebra). The text reflects the compassion and insight of its experienced author team with features developed to address the specific needs of developmental level students |
Inequality3
This is the third program about inequalities. It is suitable for advanced course in algebra. It discusses solutions of three or more inequalities in two-dimension space. It also includes discussion on characteristics of the unshaded region of xy-plane. Finally it teaches the student how to solve quadratic inequalities in a long step-by-step approach. |
Maugansville ACT classes at the university level for over 15 years, including several courses with discrete mathematics. These courses include sets and functions, relations, logic, proofs of mathematical induction, probability, basics of trees and graphs. combinations, permutations and |
Portland State University
The purpose of this survey is to explore attitudes students have towards
math and its relevance outside of the classroom.
Remember that this is an anonymous survey and that you are under no obligation
to answer these questions.
Please answer the questions to the best of your ability and knowledge.
Please give only one answer to each question.
In addition to your opinion about your program, we would like your feedback
about the wording of the items or the format of the survey. Please write any
comments you have about the questions next to the question or on the back of
the survey.
Quantitative Literacy: Mathematical skills that students use in
the context of communicating ideas, either receiving information, providing
information or making and communicating conclusions from data.Quantitative literacy is important to my major.
1.
2.
3.
4.
5.
2
I understand what quantitative literacy means.
1.
2.
3.
4.
5.
3
QL is important in my daily activities.
1.
2.
3.
4.
5.
4
I find myself applying QL in courses outside of my major.
1.
2.
3.
4.
5.
5
Having QL skills is important for my career.
1.
2.
3.
4.
5.
6
I have a good attitude towards math.
1.
2.
3.
4.
5.
Section B: Confidence with Mathematics:
Please indicate the extent to which you agree or disagree with each of
the following statements by checking the box corresponding to your answer.
Strongly Disagree
Disagree
Neutral
Agree
Strongly Agree
1
I am comfortable taking math classes.
1.
2.
3.
4.
5.
2
Math scares me.
1.
2.
3.
4.
5.
3
I can use math as a communication tool.
1.
2.
3.
4.
5.
4
I recognize that math skills are important outside of "math classes."
1.
2.
3.
4.
5.
5
I routinely use mental estimates to interpret information.
1.
2.
3.
4.
5.
6
I enjoy math.
1.
2.
3.
4.
5.
7
I often take courses that contain a lot of Math.
1.
2.
3.
4.
5.
8
I am comfortable with quantitative ideas.
1.
2.
3.
4.
5.
9
I am at ease in applying quantitative methods.
1.
2.
3.
4.
5.
10
I have good intuition about the meaning of numbers.
1.
2.
3.
4.
5.
11
I am confident about my estimating skills.
1.
2.
3.
4.
5.
Section C: Cultural AppreciationMath is important.
1.
2.
3.
4.
5.
2
Math plays an important role in science.
1.
2.
3.
4.
5.
3
Math plays an important role in technology.
1.
2.
3.
4.
5.
4
Math helps me to make sense of current events.
1.
2.
3.
4.
5.
5
I am aware of the origins of mathematics.
1.
2.
3.
4.
5.
Section D: Logical Thinking and ReasoningI am comfortable reading graphs.
1.
2.
3.
4.
5.
2
I am comfortable reading maps.
1.
2.
3.
4.
5.
3
I often use math to evaluate statistical information.
1.
2.
3.
4.
5.
4
I use math to evaluate the validity of poll results (e.g., political
polls). |
Summary
Widely known for incorporating interesting, relevant, and realistic applications, this text offers many real applications citing current data sources. There are a wide variety of opportunities for use of technology, allowing for increased visualization and a better understanding of difficult concepts. MyMathLab, a complete online course, will be available with this text. For the first time, a comprehensive series of lectures on video will be available.
Table of Contents
R. Algebra Reference
Polynomials
Factoring
Rational Expressions
Equations
Inequalities
Exponents
Radicals
Linear Functions
Slope and Equations of a Line
Linear Functions
Linear Mathematical Models
Constructing a Mathematical Model
Review Exercises
Extended Application: Using Marginal Cost to Estimate the Cost of Educating Immigrants |
Many schools now require calculators. This site is
not the place for a discussion of the problems (financial and otherwise) that this can cause, or
of the "philosophy" on which these policies are often based. If you are interested in
the politically-incorrect side of this issue, visit Mathematically Correct.
(And for an interesting discussion of the value of a broken calculator, try here.)
But if you are wondering which calculator to buy,
the following is my advice.
Scientific, business, etc, calculators
If you are looking for a "scientific"
or "business" or "statistics" calculator, then there are many affordable options
available to you. You can find cheap calculators at office-supply stores, discount department stores,
and electronics stores, among other places. I have only one specific recommendation: make sure
that the calculator has a fraction key; it usually looks something like this:
This is a very
helpful key, and will speed up fraction addition, simplification, and conversion.
Graphing calculators: Texas Instruments
If you are supposed to get a "Texas Instruments
graphing utility", then you would probably want one of the calculators from their line of
TI-84 models. The TI-84 is an update of their TI-83 which incorporates additional capabilities
(increased memory, computer connectivity, default apps, etc) but which is backwards compatible
with the TI-83. That is to say, the TI-84 will allow you to do more, while still remaining largely
keystroke compatible with the TI-83 that your teacher is using.If you are supposed to get a TI-83,
you might want to look at spending a little more to get the TI-84.
ADVERTISEMENT
(Note: There are some slight differences in the
models. For information, try here.)
However, the TI-84 seems to assume that you have
reliable access to a newer computer. Much of the manual is accessible only through the CD that
comes with the calculator, calculator-to-computer connectivity relies on USB ports, and you may
need to download and install at 23-meg Micro$oft program (.NET Framework) to get the computer side
of the calculator to work. You may also need to upgrade your browser, since the TI-84 appears to
require Internet Explorer 6 or newer. So I would recommend the TI-84 (over the TI-83) for the updated
capabilities, but only if you have ready access to an updated computer and a good Internet connection.
(Note: I have heard, from experienced users, that installation and use is not always problematic.
The above warnings reflect my personal experience. As they say, "your mileage may vary.")
Do NOT get a TI-92, nor its update, the Voyage 200,
unless you have verified that your school allows them; many schools are banning them. For some
reason, though the TI-89 has many of the same capabilities that are getting the TI-92 / Voyage
200 banned, the TI-89 is generally allowed. However, it would still be a good idea to check first.
Note that many (most?) instructors, especially at the high-school level, don't know how to use
the TI-86, -89, or -92, or the Voyage 200, so you'll be on your own when it comes to learning how
to use them. And their owners manuals tend to be the size of small textbooks.
If the only specification is that you are to get
"a graphing utility", then the choice is up to you. Many companies produce perfectly
nice calculators, but textbooks and teachers usually push the Texas Instruments TI-83 or -84. If
you're willing and able to read the manual for yourself, then get whatever calculator you like.
Otherwise, stick with Texas Instruments.
If you do get a TI-8X calculator, learn where the
"convert to fraction" menu item is (this varies from model to model; check your manual).
The command looks like this:
This command will convert the last value to its
fractional form, if possible. It's a very handy command. If you have the "Custom" menu
option, you might want to install the "convert to fraction" command on your custom menu,
for convenience sake.
(By the way, if you already have a TI-85, and would
like to have the "TABLE" feature that the TI-82, TI-83, and TI-86 have, use my "Table"
program. The page in the preceding link contains the program as a text file; you'll have to type
the program into your calculator yourself.)
Graphing calculators: Final thoughts....
If you are thinking of getting a Hewlett-Packard
(HP) calculator (graphing or otherwise), see if you can find a friend or a fellow student who will
let you borrow one. In my experience, people either love HPs or they really, really,hate them,
and it would be a shame to spend a couple hundred dollars just to learn that you're one of the
folks who hates 'em. They slice, they dice, they whistle "Dixie", but they might not
be your cup of tea. Take a good look first.
In "real life", any of the scientific
(or business or statistical, etc) calculators will serve most needs. Unless you're going into courses
where graphing calculators are expected, a cheap calculator that has trigonometric keys (the "sin",
"cos", and "tan" keys) should have just about anything you'll need. But graphing
calculators can be nice, even in "real life", for much the same reason that some of us
old-timers liked adding machines with a printout: the screen on a graphing calculator can display
more information and, in particular, can make it easier to find one's mistakes. So, for instance,
I tend to use a graphing calculator to balance my checkbook.
There is one other consideration: If there is no
specification regarding which calculator you should get (or if you are given a list of models from
which to choose), and you are planning on entering a scientific field of study at your college
or university (math, engineering, or physics, for instance, as opposed to Poly-Sci or French Lit),
then you might want to contact the appropriate departments to see if those departments have their
own preferences. Be forewarned: It is entirely possible that you will be required to buy multiple
calculators: one for the math department, another for the physics department, and yet-another for
the engineering department. Calculators are very trendy, but the trend-oids don't often think about
the real-world implications of their policies.
There; now ya know: I'm politically incorrect.
If you have lost the manual to your Texas Instruments
graphing calculator, look into downloading a new copy from the Texas Instruments' site.
The guidebooks are Adobe Acrobat documents, and fairly large ones at that, so you might want to
download the manual one chapter at a time if you have a slow or twitchy connection. |
The WUHS Mathematics Department strives to provide rich mathematical learning experiences, and the skills that support them, to a wide variety of students. All courses of study integrate technology with pencil-and-paper calculations so that students at every level can become proficient problem solvers. We view the study of algebraic concepts as the critical tool for secondary mathematics, thus algebra is included in all introductory courses.
Our Math Courses
Monday, 26 July 2010 06:28
2210/ ALGEBRA I (meets daily*) Grades 9-12 Level III 1 credit Students who have succeeded in Algebra I have earned a final grade of at least 75 in high school Pre-Algebra or middle school Math 8. This course is designed to introduce students to the concepts and terminology of algebra. The course approach combines lecture, large and small group work, projects, individual work, and appropriate use of technology. The course will cover the relationship of real numbers, problem-solving, graphing on the Cartesian plane, solving equations in one or two variables, the study of radicals and exponents, simplifying polynomials, solving equations using factoring and the quadratic formula, and the study of sets. Students who succeed in this course are prepared for Geometry. At the end of this course, students who have obtained grades from 60 to 79 will be subsequently enrolled in Intermediate Algebra. |
In answer to your other questions
>>Anyways, must I learn the analytic geometry if I just want to make simple programs that resemble something of 3d, but maybe not 100% accurate?
No, you can write very simple programs without understanding the maths. But that's all you'll be able to do. If you learn a little more, you'll be able to go much further. And you'll be able to make more sense of the maths on Wikipedia.
>>They don't teach any useful math at school and they aren't any time soon so I don't know where to start learning
Don't forget that it's more important to a teacher that the dull students aren't left behind, than the bright students get ahead. Maybe you can find a teacher who is willing to explain something to you outside of class. Or maybe a parent or relative of yours could help.
At my school there was a maths society where we explored topics outside of the curriculum...
Having a good teacher is probably the best way to learn this sort of stuff, but failing that a good book might be helpful. Check your library for something that's at the right level for you.
>>And I don't what this type of stuff means:
>>sin^2 (x) <<????
Basically, computer programmers need to make sure the computer understands them. Mathematicians need to make sure that other mathematicians understand them. So while programming languages tend to be fairly simple and consistent, mathematical notation is much less so.
Also remember that mathematics until recently was nearly always written by hand, and even today much is written by hand. A notation that's easier to read in slightly messy writing is a winner.
There are many areas of mathematics where there are a few different notations in popular usage. Often say Europe will use one notation and the US will use another.
Anyway, this is one case where "everybody knows" that sin^2(x) means sin(x)*sin(x). Just learn it.
>>$variable = new variabletype();
This is to do with object oriented programming, a big topic that I don't think you should worry about just yet. PHP does not require you to use it. |
The Grading System: Instructor Notes
The grading scheme from the student guide is reproduced below.
There are three components to the student's grade.
As the instructor, you are responsible for the determining the
section component and how you will
use it to adjust the student's final course grade.
Evaluating the section component. Since we consider cooperative
learning to be an essential feature of the introductory program, we
require that team homework count for at least 40% of the section component.
Aside from that, it is up to you how to determine the section component
of the grade. For example, you may choose to give weekly individual or
group quizzes and/or
daily reading quizzes; you may choose to collect individual homework;
you may choose to give credit for in-class work, presentations, extra
credit, good team evaluations, etc. It helps to choose a system
that encourages study habits that you believe will contribute to
student learning.
Informing the students.
It is important that you explain your system for evaluating the section component clearly
and carefully in your first day handout
so that your students know how they will be evaluated.
It is also important to ensure that the feedback you give students on their
section work accurately reflects the impact it will have on their
grade. There are many simple ways to achieve this. One is to
grade section work with a median of approximately 70%. If that does
not suit your class, or your grading, an alternative is
to announce the median score each time you return graded work.
The Grading System: Reproduced from the Student Guide
Grades in this math course.
All sections of this course use the same grading guidelines
to standardize the evaluation process.
Your final letter grade in the course will be based on three components:
The uniform component.
The section component.
The gateway component.
Your uniform component will determine your baseline letter
grade for the course. Your baseline grade will be adjusted by the
section and gateway components as described below to determine your
course letter grade.
1. The uniform component.
There are two uniform midterm exams and a uniform final exam.
Each of these exams will be taken by all students
in all sections at the same time, and are graded by all the instructors
working together.
Your uniform component score will be determined from your scores on each exam as follows:
Midterm Exam 1
25% of uniform component score
Midterm Exam 2
35% of uniform component score
Final Exam
40% of uniform component score
After each exam, a letter grade will be assigned to your uniform component score using
a scale determined
by the course director specifically for that exam.
We do not use the "10-point scale" often seen in high school
courses in which scores in the 90's get an A,
in the 80's get a B, and so forth;
the level of difficulty of the exams will be considered.
The scale for the uniform component score will apply to all students in all sections.
2. The section component. To help you learn the material,
you will be given a variety of reading assignments, team homework,
individual homework, quizzes and other in-class activities. Your instructor will decide how the section component is determined for your particular section and grade the section work to determine your section score.
The section component has the potential to increase your final grade above the baseline grade by one third of a letter grade (e.g., from a B+ to an A-, etc.); and, assuming that the assigned work is completed, this component cannot lower your final grade below the baseline grade by more than one third of a letter grade. So, if you are keeping up with the course and doing well
in your section work,
it will not only help you to do well in the uniform exams, but may also
add to your baseline grade. Similarly, if you
fall behind in your section work, it may reduce your baseline grade.
3. The gateway component. There will be one or two (depending
on the course you are taking)
online basic skills gateway test(s) which you need to pass by the
deadline announced in the course schedule. These routine tests are repeatable,
and in general do not pose a problem for students who are keeping up with the course work.
You may practice each test online
as many times as you like, and you may take
a test for a score as often as twice per day
until the deadline. The gateway tests do not have the potential to raise your baseline
grade, but if they are not passed by the deadline, the gateway component will
automatically reduce your final grade in the course. Deadlines and grade penalties
will be announced in your class. All sections of your course have the same deadlines
and penalties assigned to the gateway component.
Section averages.
Course policy is that a section's average final letter grade cannot differ
too much from that section's average baseline letter grades.
This means that the better your entire section does on the uniform exams,
the higher average letter grade your instructor can assign in your section.
It is therefore in your best interest to help your fellow students in
your section do well in this course.
In other words, cooperation counts!
Grades at the university.
Many students who come to the University of Michigan have to adjust
themselves to college grading standards.
The mean high school grade point average
(recalculated using only strictly academic classes)
of our entering students is around 3.6,
so many of you were accustomed to getting "straight A's"
in high school.
Students' first reaction to college grades is often,
"I've never gotten grades like these."
However, a grade of 15/20 on a team homework assignment
(which you might previously have converted to 75% - a high school C)
may well be a good score in a college math course.
Your own instructor is your best source of information on
your progress in the class.
Describing the grading system to students. You should state
explicitly how you plan to arrive at semester grades - what exams will be
given, approximately what weight they will have in the overall assessment of
the student's work, how team homework is counted, how much quizzes will
count, etc. The in-class component of the grade can be based on quiz
scores, individual homework, class participation, or whatever you find
appropriate. It is important to not to assign letter grades to the
in-class component of the grade because the grades you award at the end of
the term will have to be in alignment with the performance of your class on
the uniform exams.
Assigning final semester grades. The procedure for
calculating semester grades will be discussed in course meetings as the term
progresses.
Grade books and records. Keep a good, clear record of your
grades in a secure place. Don't lose it. Record all scores which
will count towards students' grades. Many grades complaints can be
prevented by keeping accurate records. It's easy to forget to record
grades before returning papers, so record everything, including all grade
changes, immediately. Students are very serious about their grades and
expect them to be treated as a strictly private matter. You do not
need to keep a record of students' attendance unless you choose to, however,
you may want to note any extended absences.
Complaints about your grading. From the point of view of
University of Michigan students, a great deal hinges on getting the high
grades they are accustomed to getting in high school. Many first term
freshman have never had a grade lower than an A! They will often
argue persistently over one or two points. This is not a sign that they
don't respect you. Of course, you should treat all student
complaints about grading mistakes or unfairness in a serious manner. |
Contents
The Jeff Tech Mathematics Team
The Jeff Tech Mathematics Team is a non-remedial excellence program that operates under an amalgamation of methodologies and learning strategies. One facet of the Jeff Tech Mathematics Team is collaborative seminars in which students work together to mathematically develop, compare, problem-solving strategies, and prepare for the various competitions that we participate in.
New Techniques
The Jeff Tech Mathematics Team teaches you not only "what to learn", but "how to learn". Participants discover how to apply study strategies to course topics and problems as they review content material, questioning techniques, and precise mathematical communication. The key to the program is developing student leaders who are presented as "model students of the subject". Above all else, students will develop critical thinking and problem solving skills.
Mission
The purpose of the Jeff Tech Mathematics Team is to promote the interest of mathematics at Jeff Tech, and to aid math students or anyone with an interest in mathematics, and also to promote interaction among students and faculty. |
books tagged "Calculus" [via]
George Thomas' clear, precise calculus text with superior applications defined the modern-day, three-semester or four-quarter calculus course. The ninth edition of this proven text has been carefully revised to give students the solid base of material they will need to succeed in math, science, and engineering programs. This edition includes recent innovations in teaching and learning that involve technology, projects, and group work. [via]
George Thomas' clear precise calculus text with superior applications defined the modern-day calculus course. This proven text gives students the solid base of material they will need to succeed in math, science, and engineering programs. [via]
This text embodies the broad principles of calculus reform-conceptual understanding motivated by real-world applications and the application of the "Rule of Four" in numerical, visual, algebraic, and verbal interpretations. At the same time, this book retains traditional calculus. The author emphasizes visualization and problem solving. [via]
Emphasizing conceptual understanding, this calculus text includes real world applications and stresses multiple representations - numerical, visual, algebraic, and verbal interpretations. The concept of derivative is covered before the rules of differentiation are developed. This approach gives students a conceptual understanding of and an opportunity to work with the derivative and before they are introduced to the "rules'" or formulas. The problems maintain a balance between algebraic skills and conceptual understanding. [via]
James Stewart has revised this calculus text, retaining the focus on problem solving, accuracy, explanations, and theThe new edition of Calculus continues to bring for those going into mathematics and those going into the sciences and engineering. This new text exhibits the same strengths from earlier editions including an emphasis on modeling and a flexible approach to technology understandingWritten by three giftedand funnyteachers, How to Ace Calculus provides humorous and readable explanations of the key topics of calculus without the technical details and fine print that would be found in a more formal text. Capturing the tone of students exchanging ideas among themselves, this unique guide also explains how calculus is taught, how to get the best teachers, what to study, and what is likely to be on examsall the tricks of the trade that will make learning the material of first-semester calculus a piece of cake. Funny, irreverent, and flexible, How to Ace Calculus shows why learning calculus can be not only a mind-expanding experience but also fantastic fun edition of James Stewart's best-selling calculus book has been revised with the consistent dedication to excellence that has characterized all his books. Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to reveal the beauty of calculus. Stewart's examples stand out because they are not just models for problem solving or a means of demonstrating techniques--they also encourage readers to develp an analytic view of the subject. This edition includes new problems, examples, and projects. [via]
James Stewart has revised this calculus text, retaining the focus on problem solving, accuracy, explanations and the carefullyJames Stewart's well-received SINGLE VARIABLE
[via]
Continues the outstanding tradition of earlier volumes with attention to detail, well-written explanations and a lively, accessible approach to learning. The size of this edition has been substantially reduced by rewriting major portions of the material for more efficient exposition and effective use of space. New material has been added on parametric representations of surfaces, Jacobians and Kepler's laws. Also includes new reference matter on complex numbers as well as biographies and historical notes which capture the personalities of the great mathematicians continuity. Charts and graphs throughout |
Abstract algebra
Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields.
The term "abstract algebra" is used to distinguish the field from "elementary algebra" or "high school algebra" which teaches the correct rules for manipulating formulas and algebraic expressions involving real and complex numbers.
Historically, algebraic structures usually arose first in some other field of mathematics, were specified axiomatically, and were then studied in their own right in abstract algebra. Because of this, abstract algebra has numerous fruitful connections to all other branches of mathematics.
In universal algebra, all those definitions and facts are collected that apply to all algebraic structures alike. All the above classes of objects, together with the proper notion of homomorphism, form categories, and category theory frequently provides the formalism for translating between and comparing different algebraic structures |
A Level Mathematics for Edexcel (series)
Suitable for: Post 16/A Level
A new and more inspiring way to teach Edexcel A Level and AS Level maths!
Why not replace your current, old, A Level Edexcel maths texts with new and more inspiring materials? This A Level maths series, endorsed by Edexcel, will help greater numbers of your students achieve success at AS Level and A Level maths. Order an inspection copy to see for yourself how unique and inspiring these new materials are!
"Makes last minute revision the night before an exam effortless...points are easy to identify. The format is very clear and concise, so much so that it is 'readable'...uncomplicated explanations and definitions...definitely worth consideration." - Mathematics in |
Lula, GA ACT believe that this allows the student to understand how science works, and understanding the process allows them to more easily see where the answers that they might have formerly memorized are coming from. As a research scientist, I use Microsoft Excel extensively to analyze data. I routinely use statistical and logical functions and data plots in my data analysis.
...Therefore, the integers are a natural tool of study in the field of discrete math.)
EXPERIENCE:
I have extensive experience in subjects which may fall under the umbrella of discrete math, as approximately half of my mathematical training has revolved around subjects such as topology, algebra, an... |
Mathematics: Sound smarter without trying harder
Buy ePub
List price:
$3.49
Our price:
$2.99
You save: $0.50 (14%)
Do have trouble figuring out a restaurant tip? Does the thought of algebra still give you nightmares? Fear not! The Very Lazy Intellectual: Mathematics introduces you to quantitative calculation and logical reasoning. Unlock the mysteries (or at least the basics) of algebra, calculus, geometry, and trigonometry! |
Many firefighter exams include mathematical problems pertaining to the job of firefighting. Knowledge of basic arithmetic, algebra, and geometry is necessary in the fire service. Measuring gas/oil mixtures that fuel portable power saws, mixing cleaning fluids with water during maintenance chores, determining the placement of a ladder for proper climbing angle, and monitoring gallons per minute (GPM) flowing through hose lines are just a few examples of how firefighters use numbers. The mathematics selected for this review includes the most common areas included in previous firefighter examinations.
Basic Terminology, Symbols, and Order of Operations
Terminology (The Language of Mathematics)
There are many terms used in mathematics that you should understand. A list of some of the more common terms and their definitions follows:
Integers: all positive and negative whole numbers, including zero, but not including fractions and decimals.
Example: -2,-1, 0, 1, 2, …
Fraction: part of a whole number.
Example:
Mixed Number: a whole number and a fraction.
Example:
Rational Numbers: all numbers that can be expressed as the ratio of two integers (fractions and integers).
Example:x/y where xand y are integers
Irrational Numbers: all numbers that cannot be expressed as the ratio of two integers.
Example: π (3.14) and many square roots, etc.
Term: a single number or the product of one or more numerical (number) coefficient and/or literal (letter) coefficient factors. Like terms have the same literal factor. Unlike terms do not have a common literal factor.
Example: (like terms): 2a and 3a.
Example: (unlike terms): 6, 3x, and yz
Factor: an individual number (numerical) or letter (literal) in a term.
Example: 2, A, and b are factors of the term 2ab
Algebraic Expression: two or more terms connected by plus or minus signs.
Example: 4k + 7
Algebraic Equation: a statement representing two things that are equal to one another.
Example: 12x – 8x = 4x
Mathematical Symbols and Corresponding Common Phrases
Order of Operations (Evaluating Expressions)
Many numerical expressions include two or more operations—for example, exponents, division, and addition. These operations must be performed in correct sequential order. The acronym PEMDAS helps in remembering what the correct sequence is.
When there are two or more Parentheses, grouping symbols, perform the innermost grouping symbol first. Exponents should be worked on next. Multiplication and Division, as well as Addition and Subtraction are grouped to denote that when these operations are next to each other, just perform the math from left to right.
PEMDAS is used when evaluating formulas, solving equations, solving algebraic expressions, and working with monomials and polynomials.
Arithmetic Sequences
An ordered list of terms in which the difference between consecutive terms is constant is called an arithmetic sequence. If you subtract any two consecutive terms of the sequence you will obtain the same difference, known as the constant interval between the terms.
Inequalities
A statement that one expression is greater than or less than another expression is called an inequality.
Several symbols are used in statements and word problems involving inequalities. A list of these symbols and their meaning follows: |
Algebra
Welcome to the Algebra portion of the site! On this and the following pages, we'll try to clear up some common
problems people have with algebra (a subject that has been stumping everyone from seventh graders to college students
throughout the ages). Everything from the basics of solving equations to exponents, and from graphing to word
problems (which people seem to absolutely love) will be covered.
After each section, there is an optional (though highly recommended) quiz that you can take to see if you've fully
mastered the concepts. And don't forget to visit the message board
and the formula database.
Follow any of the links below to go to the section you need help with. |
The Developmental Mathematics Department
is committed to student success by creating a supportive learning
environment in which students can improve mathematical skills, gain
mathematical confidence, and build a foundation for success.
Department Overview
Collin College has a long
history of offering basic mathematics and algebraic skills courses to enable students to acquire a solid foundation for successful performance in college level
mathematics. Among the courses offered to promote success are
Math 0302, 0305 and 0310.
Students must take the assessment (at the
Collin Testing Center) for placement purposes. Once placed in a course, many support services are provided to enable students to succeed. Among the services are the Math Lab, videos of lectures on specific topics, tutoring, study skills seminars, and scheduled review sessions. |
The trick to doing well in a differential equations class is learning how to classify problems by the means that we learn to solve them. Once you can recognize what kind of problem you have, you go through that process to solve it and you're done. I really enjoyed my differential equations course, and I think other people would have enjoyed it more if they could have recognized the patterns. |
Numerical methods and analysis
Numerical methods and analysis
This is a standard two-semester text for a first course in numerical analysis at the advanced undergraduate level, offering unique coverage of numerical approximation/interpolation, graphics, and parallel computing. A portion of the programs are written in Turbo Pascal. The remainder are pseudocode or generalized algorithms. Because other texts use FORTRAN or just pseudocode, the Turbo Pascal flavor of the Buchanan/Turner text sets it apart and makes it particularly appropriate for the typical undergraduate with Pascal programming skills and access to a personal computer. |
MTH/HMTH212 Numerical Methods
Duration :1 semester
Core Course for Major, minor
24 lectures
Aim:
The course introduces simple techniques in each of the basic areas of
numerical mathematics, with the exception of "Optimization" which is
treated separately in the course HMT221.
The aim is to give an understanding, intuitive, geometric, of
numerical methods
together with some analysis in order to
explain relative merits. All the methods are
computer based, so part of the course provides an introduction to
computing
and experience of a simple programming language. It is intended that as a
result of the
course students can apply numerical methods to problems which they meet in
Mathematics and other subjects in their degree studies. The MATLAB software
is chosen for the course as it has a fairly standard language structure and
incorporates
powerful
mathematical functions and good graphics. Some tutorials and assignments
are set aside to develop programming skills.
Course Outline:
Computers: programming and errors.
Programming with MATLAB. Rounding errors and their effect. Stability
4
Numerical solution of a system of linear equations:
Gaussian elimination
with partial pivoting. Gauss-Jordan and a consideration of efficiency.
L-U decomposition and the inverse matrix.
4
Roots of non-linear equations:
The bisection, Newton's and the secant method for a single equation.
Newton's method for set of non-linear equations.
4
Curve fitting:
Least squares fitting of polynomials and general
functions. Polynomial interpolation
with the error formula. Splines as design curves.
4
Numerical differentiation and integration:
Numerical differentiation with the truncation and rounding errors
The trapezoidal and Simpson's rules extended to composite form.
4
Numerical solution of ordinary differential equations:
First order problems, Euler, Taylor and Runge-Kutta methods. Systems
of first order equations and second
order
initial value problems. The shooting method and finite
differences for boundary value problems. |
Posts in category Number
Casio Education have videos which clearly explain how to use their graphics calculator for the most popular applications in the General Mathematics course in NSW. There is are 2 PDFs that go with each video that can be printed and distributed to students.
While students need to be proficient at performing calculations without the graphics calculator function (as these are increasingly being included in HSC examinations), they should be familiar with using their graphics calculator to quickly perform the calculation.
When using a graphics calculator, the focus changes for mere computation to understanding of the question and problem solving. Students do not have to be concerned with the automated process of calculation getting in the way of them understanding and learning.
Topics include:
Financial Mathematics
Compound Interest
Present Value
Future Value (no video, just PDF at time of post)
Algebraic Modelling
Developing a model
Using a model
Refining a model
Verifying a model
There are many more class activites and dowloads that can be found here. |
Math 150 is an introduction to the theory and practice of mathematics with a focus on the role of creativity, experimentation and imagination. The course is intended to be accessible to anyone with three and one half years of high school mathematics. |
Lula, GA ACT believe that this allows the student to understand how science works, and understanding the process allows them to more easily see where the answers that they might have formerly memorized are coming from. As a research scientist, I use Microsoft Excel extensively to analyze data. I routinely use statistical and logical functions and data plots in my data analysis.
...Therefore, the integers are a natural tool of study in the field of discrete math.)
EXPERIENCE:
I have extensive experience in subjects which may fall under the umbrella of discrete math, as approximately half of my mathematical training has revolved around subjects such as topology, algebra, an... |
Mathematics: Sound smarter without trying harder
Buy ePub
List price:
$3.49
Our price:
$2.99
You save: $0.50 (14%)
Do have trouble figuring out a restaurant tip? Does the thought of algebra still give you nightmares? Fear not! The Very Lazy Intellectual: Mathematics introduces you to quantitative calculation and logical reasoning. Unlock the mysteries (or at least the basics) of algebra, calculus, geometry, and trigonometry! |
Fundamental Concepts of Abstract Algebra
MAA Review
[Reviewed by Allen Stenger, on 09/13/2012]
This is a competent but uninspiring first course in abstract algebra, concentrating on groups, rings, and fields; but with an extensive coverage of vector spaces, much more than is needed to explain extension fields. It is an unaltered reprint of a 1991 work published by PWS-Kent.
The book includes a large number of exercises, most of moderate difficulty. A novel feature is that each problem section starts with a set of easy true-false questions to test the student's understanding; for example, an exercise on p. 188 is "the polynomial x4 + 3x3 + 9x2 + 9x + 18 is irreducible over the rational field", and an exercise on p. 332 is "a regular 680-gon is constructible". |
600 MANUALLY SELECTED MATH SOFTWARE RESOURCES600 MANUALLY SELECTED MATH SOFTWARE RESOURCES:600 MANUALLY SELECTED MATH SOFTWARE RESOURCES: 1/12/2009 10:23600 MANUALLY SELECTED MATH SOFTWARE RESOURCES: 11/2/2006 2:58600 MANUALLY SELECTED MATH SOFTWARE RESOURCES: 4/30/2007 1:42 |
Introduction to MapleMaple is a very powerful Computer Algebra system that can do many of the calculations that you might encounter in many branches of mathematics, science and engineering. We'll look at some of its capabilities. Maple has two modes: "Document Mode", which can be used to make fancy-looking documents, and "Worksheet Mode", which is what we'll use. So when you have a choice of Worksheet or Document, choose Worksheet. You can also make Worksheet the default format for new files under Tools, Options, Interface.We're looking at a Maple worksheet. Worksheets can have text, such as this, as well as Maple input and Maple output. Here is some Maple input and output.The multiplication sign in Maple is the asterisk *. The division sign is /. For powers we use ^5HRiQ2JFEiM0SSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJ4RicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiNGSi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictRjM2LVEiO0YnRi9GNi9GOkZmbkY7Rj1GP0ZBRkNGUC9GSVEsMC4yNzc3Nzc4ZW1GJw==LCYiIiQiIiIqJiIiJUYkKUkieEc2IkYmRiRGJA==This input was in "2D input". Some of the older material posted online uses "Maple notation". In the next example we input an expression from the menu on the left hand 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IyIiIiIiJA==When you click on a Maple input region and press Enter, Maple performs whatever command you gave it, prints whatever it will print, and goes on to the next region (or makes a new input region if there's no next one). You can also insert a new input region in the middle of your worksheet by clicking on [> on the tool bar or a new text region by clicking on the T beside it. 3+5;IiIpNote the ";" at the end of the command. After you press Enter, Maple computes and prints the result and gives you another promptLVEiOkYnRi9GNkY5RjtGPUY/RkFGQy9GRlEsMC4yNzc3Nzc4ZW1GJy9GSUZRThis time I used ":" instead of ";". This tells Maple to compute the result, but not print itM0YRiw2JFEiNEYnRi8=IiM5Maple uses the standard algebraic precedence rules , so this is interpreted as 2+(3*4), not (2+3)*4. Maple can act as a calculator, but there are several key differences. The following is an integer that would be too large for your calculator to 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Maple writes fractions as fractions (automatically reducing them to lowest terms), without resorting to decimal approximationsmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjNGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2Iy1GLzYkUSI5w==IyIiIiIiJA==If you do want to see this as a decimal, you can use the "evalf" command. As with almost every Maple command, the input to "evalf" is enclosed in parenthesesidGQQ==JCIrTExMTEwhIzU=The default (what Maple does unless otherwise specified) is to use 10 significant digits. This can be changed, using a variable called "Digits". Let's see this number to 25 digits instead of 10MyNURiM2Iy1JI21uR0YkNiRRIjFGJy9GM1Enbm9ybWFsRictRiM2Iy1GQDYkUSIzRidGQy8lLmxpbmV0aGlja25lc3NHRkIvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGTi8lKWJldmVsbGVkR1EmZmFsc2VGJ0ZDLUkjbW9HRiQ2LVEiO0YnRkMvJSZmZW5jZUdGUTExMTExMTExMTExMJCEjRA==Maple is case-sensitive. "Digits" is not the same as "digits" or "DIGITS". Those wouldn't affect the number of digits Maple uses.":=" is the assignment sign in Maple. It means "assign the value on the right to the variable on the left". This is different from "=" which makes an equation.Once "Digits" has been set, Maple uses this setting every time it computes a decimal result until you change "Digits" again. If you want to change the number of digits for one "evalf" command only, you can specify this as a second input to "evalf". The inputs are separated by a commaictSSNtb0dGJDYtUSIsRidGQS8lJmZlbmNlR0ZRLyUqc2VwYXJhdG9yR0YxLy+NiRRIzQwRidGQUZBJCJJTExMTExMTExMTExMTExMTExMTEwhI1MIMxMEM1Maple can do lots of symbolic calculations. For example, it knows thisiNEYnRjIvksvJSliZXZlbGxlZEdGMUYyLCQqJiMiIiIiIiNGJSlGJkYkRiVGJQ==It doesn't have a symbolic value for the next one, so it just returns unevaluatedjMzFGJ0YyLLyUpYmV2ZWxsZWRHRjFGMg==LUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComIyIiIiIjSkYsSSNQaUdGJUYsRiw=Again, if you want a numerical value, you can get one with "evalf". You can use "%" to refer to the previous maple resultGLDYlUSIlRidGL0YyL0YzUSdub3JtYWxGJw==JCI6Mi8neXhAVigpPktvNjUhI0QRzaW5GJy9GMFEmZmFsc2VGJy9GM1Enbm9ybWFsRictRjY2JC1GIzYjLUkmbWZyYWNHRiQ2KC1GLDYlUSNQaUYnRj1GPy1GIzYjLUkjbW5HRiQ2JFEjMzFGJ0Y/WLyUpYmV2ZWxsZWRHRj5GP0Y/LUkjbW9HRiQ2LVEiO0YnRj8vJSZmZW5jZUdGPi8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4Mi8neXhAVigpPktvNjUhI0Q=Maple can do almost any computational task that might arise in undergraduate mathematics. It doesn't do proofs, but it can be used to help with proofs by exploring what might or might not be true.Maple is incredibly powerful, but to learn to use it effectively takes some effort. One thing to remember: Maple has absolutely no intelligence. It will try to do exactly what you tell it to do, no more and no less.Unfortunately, what you tell it to do is not always the same as what you thought you were telling it to do, or what you wanted it to do. It has no idea of what you want to do, or why you want to do it. It can't read your mind. So to get it to do something, you have to know what command would make it do that, and how to use that command. This is a common theme in all programming languages and software packages. Maple has thousands of functions and commands. Probably no one person knows all the details of all of them. Fortunately, Maple has an extensive help system. To get help on a particular command, you can enter a question mark followed by the name of the command9HRiQ2LVEiPwwLjExMTExMTFlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEmZXZhbGZGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljOr you can use the Table of Contents, or Topic Search or Text Search from the Help menu.Roots of Functions, Differentiation and Plotting: Part IMany problems of scientific interest involve finding the root or roots of a function. That is, finding the value or values of x for which f(x) = 0 where f is a given function. In real applications, it is unlikely that the Example 1 Find the roots of f(x) = x^5 - x^3 + 2*x^2 + 1First, let's plot the function to get an idea of how many roots there are and where they are 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It looks like there is one real root somewhere near x = -1.5. Let's suppose that this is the root of interest to our application problem and see how we can get a more accurate value using the solve command. First, let's try it out on a quadratic equationLS1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiMtSSNtbkdGJDYkUSIyKCZtaW51cztRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmpuLUZDNiRRIjNGJ0ZGLUZMNi1RIn5GJ0ZGRk9GUkZURlZGWEZaRmZuL0ZpblEmMC4wZW1GJy9GXG9GZG9GPS1GTDYtUSIrRidGRkZPRlJGVEZWRlhGWkZmbkZobkZbb0ZCLUZMNi1RIj1GJ0ZGRk9GUkZURlZGWEZaRmZuL0ZpblEsMC4yNzc3Nzc4ZW1GJy9GXG9GXXAtRkM2JEZKRkYtRkw2LVEiLEYnRkZGTy9GU0YxRlRGVkZYRlpGZm5GY28vRlxvUSwwLjMzMzMzMzNlbUYnRj1GRi1GTDYtUSI7RidGRkZPRmRwRlRGVkZYRlpGZm5GY29GXnA=NiQiIiMiIiILi1JJW1zdXBHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiMtSSNtbkdGJDYkUSI1In5HRmpuLUZMNi1RKiZ1bWludXMwO0YnRkZGT0ZSRlRGVkZYRlpGZm4vRmluUSwwLjIyMjIyMjJlbUYnL0Zcb0Zhb0ZLLUY7NiVGPS1GIzYjLUZDNiRRIjNGJ0ZGRkhGSy1GTDYtUSIrRidGRkZPRlJGVEZWRlhGWkZmbkZgb0Ziby1GQzYkUSIyRidGRkZLLUY7NiVGPS1GIzYjRl1wRkhGam8tRkM2JFEiMUYnRkZGRi1GTDYtUSI7RidGRkZPL0ZTRjFGVEZWRlhGWkZmbkZobi9GXG9RLDAuMjc3Nzc3OGVtRicMaple cannot make progress on this problem analytically, so leaves the five roots unsolved in an array. This array is assigned to a variable below. Then we look through the roots, evaluating them until we find the real 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Polynomials have a lot of structure that general functions do not have. For example, Maple knows that a fifth order polynomial has five (possibly repeated) roots and has built-in methods to evaluate them accurately. For general functions, we can use the fslove command to find roots in given intervals. QyQ+SSJmRzYiLCoqJEkieEdGJSIiJiIiIiokRigiIiQhIiIqJEYoIiIjRi9GKkYqRio=LCoqJEkieEc2IiIiJiIiIiokRiQiIiQhIiIqJEYkIiIjRixGJ0YnQyQtSSdmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JC9JImZHRigiIiEvSSJ4R0YoOyEiI0YsIiIiJCErIT1uXmUiISIqMaple objects introduced in this lesson: ;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
:
+
-
*
/
^
evalf % ?
Digits sin Pi plot solve fsolve |
Mathematics
Middlesex Community College libraries offer students in Mathematics and related disciplines access to numerous resources. Use the tabs below to locate books, websites, tutoring services and citation help. (bc)
Quick Guides
Troubleshooting
If you have problems accessing MCC databases take a look at these adjustments that may need to be made to your computer. A library card is NOT required to access library databases. Please look at these suggestions if you are prompted for your library card number. A library card is only necessary to check out or renew books. |
Materials Needed for Class:
1. Notebook (3 ring binder with paper)
2. Pencil for quizzes/tests (pen may be used for notes)
3. Textbook - book must be covered with paper cover
4. Scientific calculator or better (TI-30XS MultiView or TI-30xIIs is recommended)
The website, has practice problems and extra help related specifically to the textbook used in Algebra. The textbook is Algebra 1 2007 |
Discussion on:
Technology is not a fundamental
That's the sort of stupid cop out that gives people a general science course.
Baisc arithmetic , followed by early maths is a fundemantal, because those tools will be required which ever branch of mathematics you choose to branch into and mathematics is a widely applicable tool in everyday life.
The fundmamentals of mathematics are very narrow, and apply to a very small domain of objects, numbers basically.
Technology, however has an enormous scope, from the basics of electronics, to logic, to methods and it's impact on society.
On top of that you'll never be able to learn it without the three R's. |
Introductory Algebra through Applications 2nd Edition
0321518020
9780321518026 KEY TOPICS: Whole Numbers; Fractions; Decimals; Basic Algebra: Solving Simple Equations; Ratio and Proportion; Percents; Signed Numbers; Basic Statistics; More on Algebra; Measurement and Units; Basic Geometry MARKET: for all readers interested in introductory algebra. «Show less... Show more»
Rent Introductory Algebra through Applications 2nd Edition |
Mathematics - Pre-Algebra
Intended Learning Outcomes
The main intent of mathematics instruction at the secondary level is for students to develop mathematical proficiency that will enable them to efficiently use mathematics to make sense of and improve the world around them.
The Intended Learning Outcomes (ILOs) describe the skills and attitudes students should acquire as a result of successful mathematics instruction. They are an essential part of the Mathematics Core Curriculum and provide teachers with a standard for student learning in mathematics.
The ILOs for mathematics at the secondary level are:
Develop positive attitudes toward mathematics, including the confidence, creativity, enjoyment, and perseverance that come from achievement.
Course Description
The goal of Prealgebra is to develop fluency with rational numbers and proportional relationships. Students will extend their elementary skills and begin to learn algebra concepts that serve as a transition into formal Algebra and Geometry. Students will learn to think flexibly about relationships among fractions, decimals, and percents. Students will learn to recognize and generate equivalent expressions and solve single-variable equations and inequalities. Students will investigate and explore mathematical ideas and develop multiple strategies for analyzing complex situations. Students will analyze situations verbally, numerically, graphically, and symbolically. Students will apply mathematical skills and make meaningful connections to life's experiences.
Order rational numbers in various forms, including scientific notation (positive and negative exponents), and place numbers on a number line.
Predict the effect of operating with fractions, decimals, percents, and integers as an increase or a decrease of the original value.
Recognize and use the identity properties of addition and multiplication, the multiplicative property of zero, the commutative and associative properties of addition and multiplication, and the distributive property of multiplication over addition.
Recognize and use the inverse operations of adding and subtracting a fixed number, multiplying and dividing by a fixed number, and computing squares of whole numbers and taking square roots of perfect squares.
Derive formulas for and calculate surface area and volume of right prisms and cylinders using appropriate units.
Explain that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related and the cube of the scale factor describes how corresponding volumes are related.
Find lengths, areas, and volumes of similar figures, using the scale factor.
Select appropriate two- and three-dimensional figures to model real-world objects, and solve a variety of problems involving surface areas and volumes of cylinders and prisms |
Discrete Mathematics 1st Edition
1441980466
9781441980465
Discrete Mathematics: This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs. «Show less
Discrete Mathematics: This books gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal... Show more»
Rent Discrete Mathematics 1st Edition today, or search our site for other Gallier |
Understandable and convenient interface:
A flexible work area lets you type in your equations directly. It is as simple as a regular text editor. Annotate, edit and repeat your calculations in the work area. You can also paste your equations into the editor panel.
Example of mathematical expression:
5.44E-4 * (x - 187) + (2 * x) + square(x) + sin(x/deg) + logbaseN(6;2.77)
History of all calculations done during a session can be viewed. Print your work for later use. Comprehensive online help is easily accessed within the program.
2)
Factor Calculator 5.6.2
Calculate the factors of any number with a single click. Small application window allows simultaneous use with Word, Outlook, Excel, etc.. Recommended on The Math Forum @ Drexel (University) for Middle School, High School and College, ages 6+. 99ΒΆ License:Shareware,
$0.99 to buy Size:
2592KB
7)
Kids Abacus 2.0 License:Shareware,
$ to buy Size:
2901KB
8)
Machinist MathGuru 1.0.90
Solve common trade maths problems in a whiz with Machinist's Math Guru software.
This inexpensive, easy to use utility is designed primarily for students, machinists, toolmakers and CNC programmers. License:Shareware,
$37.00 to buy Size:
3462KB
9)
ASCII Art Generator 3.2.4.6
ASCII Art Generator is an amazing graphics art to text art solution, which converts digital pictures into full color text-based images, and makes them eye-catching with a very cool and readable texture, composed of letters and digits. License:Shareware,
$29.95 to buy Size:
668KB
1) Math Game 1.1
Time that children spend on computer games has not been decreasing. In this new age, parents and teachers can find ways to use the entertainment industry to educate and enlighten our youth. License:Shareware,
$9.95 to buy Size:
8292KB
2)
FindGraph 2.22
FindGraph is a graphing, curve-fitting, and digitizing tool for engineers, scientists and business. Discover the model that best describes your data. License:Shareware,
$79.95 to buy Size:
3370KB
5) Multivariable Calculator - SimplexCalc 4.1.4
SimplexCalc is a multivariable desktop calculator for Windows. It is small and simple to use but with much power and versatility underneath. It can be used as an enhanced elementary, scientific, financial or expression calculator. License:Shareware,
$15.00 to buy Size:
1060KB
6) Multipurpose Calculator - MultiplexCalc 5.4.4
MultiplexCalc is a multipurpose and comprehensive desktop calculator for Windows. It can be used as an enhanced elementary, scientific, financial or expression calculator. License:Shareware,
$15.00 to buy Size:
1184KB |
Which Graphing Calculator to buy?
Which Graphing Calculator to buy?
I'm sorry if this topic appears to be in the wrong section, I was not sure what this would go under... if a moderator would be so kind as to move it to the correct sub-forum, I would be glad =)
I'm going into Grade 12 this year, and will need a graphing calculator obviously not only for next year's work but for University as well. I'm not going to be majoring in math (shiver), but of course I will be taking some higher level math courses. (calc, data, al-geo, etc...)
My question is, which graphing calculator should I buy? I live in Toronto, Canada, and had my eye on the Ti-89's, as they are the newest that I am aware of... I am under the impression the titanium version of the 89 is better? ... price is likely not an issue.
I would recommend the TI-83 plus. It is a wonderful peice of hardware that is simple to use. The TI-89 is way too complicated to use unless you have someone teach you how to use it or have hours to waste figuring that thing out. The TI-83 is still extremely powerful if you know how to use it. It is also not as expensive. Honestly, in college you will probably not use your graphing calculator much, maybe just to add and subtract, do some simple trig, and other scientific calculations. In college if you use any computing devices in your math course it will most likely be an actual computer. You will probably use maple or some other math program. I would definitely recommend the TI-83 over the TI-89 simply because it is cheaper and easier to use. But like you said money really isn't the main issue.
I would say either are a good choice (the 89+ or 83+) However, keep in mind that some teachers may not allow, or at least want, you to use an 89, not that there is anything that they could do anyway. Also, I agree with gravenewworld in that an 83 is very simple and easy to use, the 89 is much more formal, and gets mad if you use the wrong syntax (for example, not closing parenthesis).
Which Graphing Calculator to buy?
ti 89 all the way, I can't stand to use 83's after getting my 89, they are easy to use and are worth the money just because they can integrate and do derivatives. Also, it is much easier to use for large equations or fractions because when you enter it it gets printed out just like you would write it on paper would get the TI-89 Titanium. I have a TI-86 and a TI-89 and I prefer the 89. It's just alot nicer. The manual that comes with it is pretty good. It solves differential equations also, which is useful because you can do the even problems in most textbooks and check yourself.
Some teachers may not let you use the 89, but I still think it's worth getting. Just get another cheap calculator that has cos(), sin() etc if that is the case. Or, you could just wait, and see what is and isn't allowed, and then make your choice wouldn't go that far. I couldn't use my 89(or any other calculator) on any tests but it was nice to check homework when I didnt have Mathematica handy, I think it in some ways helped to be honest. Also as posted above I thought the 83 could only do definate integrals. Either way, the 89 has more power, isn't that much more expensive and I can't stress enough how GREAT the textbook print is.
When you have a big physics or math problem with fractions and powers it is infinitely awesome, if I didnt make myself clear this basically puts fractions on two lines as you would see them in a book, powers as superscripts and any symbols you enter come up just you would see in a book. If you have the money go for the 89 no questions asked I would sayI have used the TI models before and none of them compare with the hp-46gx. Yes it takes a little getting used to but it is worth it. It can do indfinite intergls, diff eqs, prob, stats and more. the graphing featre is unmatched. It also has a solve application, and an equation library.
I'm in love with my TI-86. Plenty of power, and a layout that I like much better than the 83/4/+/whatever, while still being allowed in most undergrad math courses. I have the 89 as well, but I really haven't had a chance to use it much, as it is restricted in all math courses at my University. It's a very cool calculator, but you need to make sure that you can use it at your school.
Having used a TI-83 in high school and a TI-89 in college after I dropped my '83 on a hard floor, I'd say you'll much rather want to use Mathematica/Maple at any given opportunity. That said, for the purpose of 'graphing calculator', the TI-89 is much better at graphing (should you want to do that), it has the ability to do parametric and polar graphs, and find integral curves for derivative fields (really cool!). Also, it's far more user-friendly, in particular something like
Which version would you rather check for errors? Obviously the '89's formatting makes doing things a lot faster and with fewer errors. For those reasons, I recommend the '89 over the '83. It's not even much more expensive.
One more thing - both have a very big advantage over plain scientific calculators in test-taking, namely that long numerical expressions can be entered in one line using parantheses, which saves very much time.
edit: The HP calculators might be even better than the TI's, I don't know anything about them except that you can use Reverse Polish Notation on them. Although no one I know uses them, so you'll have more trouble communicating with other students about calculator issues.
for 89T, you need to know the basic programming knowledge, arguement input technique and etc. i was using TI 83 throughout my whole high school year until the last month b4 AP tests. My third 83s broke down....... so i got a 89t and used it to passed all AP math test and science test this year. 83+ is good enough until cal1 and cal2, but 89 can be used upto D.E+.
But the point is...... ti 89 is hard to use, i barely figure it out (with 2 years experience of mathematica) the month b4 AP test, good luck with thatThe TI-83 only lets you take a derivative at a point, it doesn't actually find f'(x). The 89 can actually find the derivative or antiderivative of a function. I myself only have an 83. I know some people who have the 89 and they use it sometimes to do integrals really quick on tests and it really helps them, but after a couple of years now, I can do most integrals on paper and they can't. I would say, if you can afford the 89, go for it and use it on tests, but don't do homework with it or you won't know how to integrate by hand.
I remember now the 83 can take the derivative of the function and plot it. Im not sure there is a way to explicitly get what the exact derivative is. For example if you put in sin (x) in y1 slot and plot it and put nderiv(sin(x),x,x) in y2 slot, ti 83 will also plot the cos(x). There really is no point in getting a TI-89 in college, most universities will insist that you learn computer programs like maple, mathematica, etc. At any decent school you should even have even have access to the programs in your dorm room/off campuss so you can still use them to do homework. |
think I know why...because the teacher couldn't come up with an example
of
where calculus would be used, at least not one that he student would think
"Yeah, I can see that...cool!".
Our world is constantly changing. Algebra assumes that "x" is always a
given number. Calculus helps us to keep track of "x" as it changes due to
time, energy, and other factors.
Mathematics is the study of patterns. These patterns occur in nature; math
allows us to descibe these patterns and predict future behavior based on
these patterns.
Mathematics is the science of making the "unseen" visible. For example,
everyone knows that an object weighing many tons cannot float; yet
mathematics describes how it is possible for airplanes to fly. Why does a
large building stand? Why does an apple fall to the ground? Why are my
eyes brown? Calculus lets us explore and answer these questions. |
Question on the Boas Math Methods book.
For a rigorous acount with no exercises, try hilbert's and courant's 2volume text, if you need just to know how to solve it without understanding why, then Arfken is better than Boas, for example in the green functions area Boas' book is lacking it just gives examples without concrete algorithm of how to solve green functions problems, Arfken gives it. |
Specification
Aims
To develop understanding of functional analysis. To establish existence and uniqueness of solutions for a number of important mathematical models. To derive numerical algorithms for PDEs and prove rigorous error estimates. To understand integral equations and their numerical properties.
Brief Description of the unit
This course unit introduces fundamental tools from functional analysis and uses them to develop a theory of existence and uniqueness for some important PDEs from mathematical physics with an emphasis on numerical approximations. We start with fundamental concepts from functional analysis involving Banach and Hilbert spaces, compactness and linear operators. We then apply these tools to develop the right framework to show existence and uniqueness of some important PDEs. Galerkin methods are discussed to approximate them. We go on to some advanced topics involving Fourier transforms in Lebeque spaces, spectral theory and integral equations of the first and second kind. A strong emphasis throughout the whole course is put on the numerical implementation of the discussed techniques.
Learning Outcomes
On successful completion of this course unit students will
understand the concept of Banach and Hilbert spaces and some of
their theory;
understand the concepts of weak derivatives and Sobolov spaces
understand the importance of existence and uniqueness theory and how it is developed for the Poisson equation, the heat equation and the Helmholtz equation.
be able to understand the finite difference and finite element approximations and prove error estimates
understand fundamental results about the spectral theory of linear operators
understand examples of integral equations of the first and second kind and their different numerical behaviour |
Extension Y7 AUTUMN TERM
UNIT: Algebra 1 - Sequences and Functions
TIME ALLOCATION: 6 Hours
PRIOR KNOWLEDGE KEY WORDS STARTER
Recognise and extend Sequence, term, nth term, 30 starters (subtangent)
number sequences, such as consecutive, predict, rule,
the sequence of square generate, continue, finite, STARTER OF THE DAY –
numbers, or the sequence infinite, ascending, substitution
of triangular numbers. descending, symbol,
expression, algebra, STARTER OF THE DAY – make
Read and plot coordinates substitute, trial and a connection
in all four quadrants. improvement, plot, quadratic
SUM OF THE SIGNS
Understand and use the
relationships between the
four operations, and
principles of the arithmetic
laws. Use brackets.
LEARNING OBJECTIVES LEARNING OUTCOMES
Level 5
To be able to generate and describe a Know that a sequence can have a finite or
sequence infinite number of terms
The sequence of counting numbers 1, 2, 3, … is
To be able to use letter symbols to
infinite and the sequence of 2 digit numbers
represent unknown numbers and
(where both digits are the same) is finite
variables
To be able to write down first 5 terms and 10th
term, given the nth term of sequences such as:
5n + 4
100 - 10n
3n – 0.1
105 – 5n
n x 0.1
Use a spreadsheet or graphical calculator to
find particular terms such as
The 24th multiple of 13 in the sequence
The 100th multiple of 27
The nth mutliple of 18
To be able to generate a sequence Use a spreadsheet to generate tables of values
when given the position-to-term rule. and explore term-to-term and position-to-
term linear relationships
To represent mappings expressed
algebraically
Level 6
To begin to use linear expressions to Find the first few terms of the sequence and
describe the nth term of an arithmetic describe how it continues using a term-to-
sequence, justifying its form by term rule
referring to the activity or practical Describe the general (nth) term and justify
context from which it was generated. the generalisation by referring to the context
Example – Growing triangles
This generates the sequence 3, 6, 9, …
Possible explanations
'We add 3 each time because we add one more
dot to each side of the triangle to make the next
triangle'
'It's the 3 times table because we get'
To be able to generate sequences from
practical contexts
The nth term is 3n justification
'This follows because the 10th term would be 3
lots of 10.'
Develop an expression for the nth term for
sequences such as
To begin to use linear expressions to 7, 12, 17, 22, … 5n + 2
describe the nth term of an 100, 115, 130, 145, … 15n + 85
arithmetic sequence 2.5, 4.5, 6.5, 8.5, … (4n +1)/2
-12, -7, -2, 3, … 5n – 17
4, -2, -8, -14, … -6n + 10
LEVEL 7
To be able to generate a sequence Find the first few terms in the sequence,
using position-to-term definition of describe how it continues using a term-to-term
the sequence rule
To be able to describe in symbols the
rule for the next term or nth term in a
sequence (Quadratic)
n2 2n2 + 2 n2 – 3
ACTIVITIES ICT RESOURCES
Exploring primes activities: MATHSNET algebra topics
Numbers of factors; factors Mymaths
Square number sequence
of square numbers; Mersenne Algebra, sequences
Squares in Rectangles
primes; LCM sequence;
Goldbach's theorem; n² and Nth term generator
(n + 1)²; n² and n² + n; n² + 1; Match up
n! + 1; n! – 1; Quadratic Generator
~ Venn diagrams for HCF / (with answers)
LCM Sequences (slide bars)
Taria (Matchup) will need to
download software (free)
KS3 Y8 Intervention
~ Lesson 8N1.1 Solving
number problems 2
FUNCTIONAL SKILLS and MPA OPPORTUNITIES
Cuisenaire Rods – Interactive Using only 2 rods make all cuisenaire rods
Cross-curricular links with music – sequences generated by beats and rhythm
Rich Learning Task: Swimming Pool
PLENARIES AND KEY QUESTIONS
What did you look for in your sequence to help you find the nth term?
How does this link to ... ? (Use the context that generated the sequence.)
Probe further to get pupils to justify specific parts of the generalisation – e.g. explain why
'multiply by 4' is part of your nth term.
The term-to-term rule for a sequence is 'previous term + 2'. What does that tell you about
the position-to-term rule? Do you have enough information to find the rule for the nth term?
Why?
What do you look for in a sequence to help you to find the position-to-term (nth term) rule?
How would you go about finding the position-to-term (nth term) rule for this information on a
sequence:
Position 3 5 10
Term 11 19 39
Compare a linear to a quadratic sequence. What do you notice about the differences between
succeeding terms?
What clues do you look for when deciding whether a sequence is quadratic?
What can you say about the nth term for a quadratic sequence?
What strategies do you use to find the nth term for a quadratic sequence? |
p. 3
sped 601 course description this course focuses on principles and guidelines for teaching mathematics to students with disabilities grades 7-12 including number and operations algebra functions geometry measurement mathematical modeling data analysis and probability and trigonometry national council of teachers of mathematics nctm standards common core state standards for mathematics and council for exceptional children cec standards instructional approaches in developmental context effective instructional strategies for enhancing the academic performance of students with learning disabilities and application of mathematical and scientific concepts and skills in real life settings 3 credits a touro course resource web page has been created specifically for this course which may include an updated bibliography current articles videos and links to resources common assignments and more all touro course resource pages may be located on this specific course resource web page can accessed directly http schools.webhop.org/touroresources601 this syllabus may contain links to external internet addresses that may move with time student learning outcomes sped 601 students will be able to 1 describe and appropriately refer to common core state standards for mathematics for grades 7-12 and cec common core knowledge and skills essential for all beginning special education teachers 2 give an account of nctm math standards 3 explain the connections between math education and real life experiences including literacy use 4 describe principles of differentiated instruction response to intervention rti and instructional supports for learning based on principles of universal design for learning udl 5 describe approaches to teaching problem solving reasoning and critical thinking in the context of mathematics 6 give an account of curriculum development and instructional approaches in developmental context with attention to adaptations and modifications to meet the needs of students with disabilities and reference to cec standards 7 describe instructional strategies in the areas of number and quantity algebra functions geometry mathematical modeling statistics and probability and trigonometry for implementation within special education population 8 give an account of and use basic techniques in the construction and implementation of performancebased assessment 9 give an account of and use of assistive technology and math resources on the web 10 utilize a collaborative model with other professionals in mathematics instruction 11 describe and engage in appropriate teacher self-reflection back to top suggested topical outline sped 601 mathematics and theories of learning adolescents and school mathematical proficiency cognitive education and mathematics instruction strategic and adaptive mathematical thinking sped 601 page 3 graduate programs in education and special education
p. 4
learning disabilities and their effect on mathematics performance nctm s agenda for action http nctm standards common core state standards for mathematics o http the role of the mathematics teacher creating a safe supportive environment in mathematics classroom universal design for learning/lesson plans http and http lessonbuilder.cast.org the role of manipulatives and hands-on activities mastering basic number facts focusing on algebraic thinking building generalizations from arithmetic and quantitative reasoning generalizing patterns toward the idea of function curriculum focal points for geometry and spatial thinking statistical and probability thinking frameworks collaborative model in mathematics classrooms differentiated instruction teaching tools and resources accommodating students with disabilities improving instruction by improving questioning technology in the math class problem solving the role of homework testing and evaluating formative and summative assessments alternative assessment back to top suggested assignments sped 601 papers are to be typed double-spaced and written in accordance with apa style 1 review the article garnett kate november 1998 math learning disabilities division for learning disabilities journal of cec http support or disagree with underlying principles presenting valid support and documentation in four five pages using a minimum of three articles published within the last five years in scholarly journals slo 2 3 6 9 2 a four to five page summary of one of the following topics include a minimum of three articles published within the last five years in scholarly journals slo 2 4 5 6 7 8 9 the following site http scholar.google.com may prove helpful mathematics curriculum and common core standards planning for mathematics instruction for special needs learners the art of questioning in mathematics problem solving and reasoning what it means to meet student needs understanding by design data driven instruction in mathematics for special needs learners project based learning in mathematics http pbl-online.org 3 create a video reaction or lead a class discussion on one of the following videos from conrad wolfram or stephen wolfram as he speaks on ted talks http graduate programs in education and special education sped 601 page 4
p. 5
conrad wolfram teaching kids real math with computers http with_computers.html stephen wolfram computing a theory of everything http everything.html 4 create a math lesson for presentation in class for a specific grade 712 in any sub-division of math e.g number and operations algebra functions geometry mathematical modeling data analysis and probability and trigonometry show how it is adapted to special needs children slo 1 3 5 6 7 8 9 10 5 create a word document or a web page with 20-40 internet math resources websites and share them with your professor and classmates write a brief description of what will be found on each resource site and how it may be used by math teachers and their students common assignments sped 601 design a unit plan for a mathematics topic in the common core standards grades 7-12 develop lesson plans in udl format and a sample student assessment e.g worksheet create a presentation on a mathematics topic in common core standards and an adaptation of that lesson for one or more students with disability classifications create a series of youtube videos on mathematics and share the links with your instructor and classmates requesting feedback suggested technology sped 601 the use of technology as a mode of teaching and learning is encouraged particularly as a model for potential teachers to use technology in their own instruction blackboard for posting of assignments announcements discussion groups use of power point where appropriate both for teaching of content and presentations by students use of video where appropriate for representation of course material use of internet-based topics and discussions where appropriate during class time use interactive white boards e.g smartboards use of microsoft excel with formulas updating of e-portfolios suggested methods sped 601 class will be conducted in lecture format with small-group discussions and activities using case studies monographs and probing questions students may be asked to create lesson plan create and demonstrate mathematics lessons and instruction and develop methods for assessment back to top graduate programs in education and special education sped 601 page 5
p. 7
the following are relevant standards for this course and its objectives from new york state and the council for exceptional children program mission in education special education the mission of the program is to educate train and graduate individuals who embody and promote excellence in education we accomplish this through aiding in students development of the tools of effective thinking and learning focused through essential components of the theory and practice of teaching we hold that the primary goal of learning is to develop the skills and passion for further learning the mission of this program therefore includes fostering in students the means and desire to seek ongoing professional development through independent learning opportunities as well as through formal education all persons are capable of developing their intellectual potential to higher levels our mission is to nurture this development in our students and provide them with the means and encouragement to do the same with their students we accomplish this through fostering interaction with strong theoretical knowledge and then facilitating experiential development through students putting this knowledge into practice in authentic classroom situations interwoven into students learning and practice experiences is a dedication to multiculturalism diversity and global awareness we instill in our graduates a commitment to bring the benefits of education to all children adolescents and adults regardless of individual differences or special needs to facilitate these goals we foster technological literacy in our students towards the purpose of them empowering their own students with these skills program goals and student learning outcomes goal one theory and research students will explore theoretical and conceptual frameworks such as philosophy and social theory that inform a modern understanding of education students will go on to critically analyze these areas and integrate them into a larger understanding of educational practice students will be able to explain principles of effective instruction present effective lessons drawing on both theoretical knowledge and knowledge of standards and requirements analyze and discuss basic principles of cognitive education as they relate to child development and learning apply knowledge of child development and learning to creation of developmentally appropriate and effective instructional tools create and present effective lessons that reflect a synthesis of theoretical and content knowledge analyze texts for validity of reasoning and drawing of inferences analyze and use research literature in the field of education and related disciplines combine varied elements of their course of study to produce a final culminating practicum project conduct internet research using information literacy skills goal two multiculturalism globalism and diversity students will appreciate the implications of living in a global society further students will demonstrate knowledge and competency in issues of diversity related to culture gender and ability within america students will encourage such interest and appreciation in the learners with whom they work students will relate globalism diversity and multiculturalism to their professional role and explore these areas both within an academic context and through the real-life situations of teaching back to top graduate programs in education and special education sped 601 page 7
p. 8
students will be able to interpret multiple perspectives held by different cultures on ways of understanding the world and themselves demonstrate through writing and discussion appreciation for cultures that differ in important respects from the student s own culture encourage the exploration of global diversity and multicultural issues among their peers and students analyze and critique the implications for teaching and learning within diverse and culturally varied school settings apply multicultural and diversity training to the creation of strategies for class environment management pedagogy and course planning reflect on and analyze their thinking and professional awareness for biases and prejudices in the context of what they learn about other cultures within field experience and practicum courses apply enhanced knowledge of global diversity and multicultural issues in real classroom situations goal three learners with special needs students will appreciate issues and concerns specific to learners with special needs this encompasses special education gifted and at-risk learners further students will apply this knowledge to develop plans of action for meeting the needs of these students that are in alignment with federal state and local standards and requirements as well as current accepted theory students will be able to explain the relationship of special education theories such as differentiation of instruction and evidence-based instruction to fundamental areas of pedagogy such as instructional planning classroom management and the act of teaching analyze the effectiveness of specific tools such as life-space interviews and behavior contracts in effectively addressing problem behavior of individual children synthesize theory with specific mandates such as nysed alternate assessment performance indicators to formulate strategies for addressing special learners needs describe and evaluate the relationship between principles of special education and general principles of education such as cognitive theory formulate robust goal-oriented pedagogical practices for students based on effective use of iep s demonstrate knowledge of critical legislation such as idea http nichcy.org/laws/idea and section 504 and the impact of concomitant concepts such as fape and lre apply relevant local state and national standards such as council for exceptional children cec standards to developing strategies in key areas such as assessment classroom management and lesson planning apply common core standards http to the learning environment describe transition services http goal four technological literacy students will achieve technological literacy towards the purpose of effectively implementing technology in instructional practices and related areas back to top students will be able to demonstrate knowledge and use of technology for instructional purposes e.g interactive white boards student e-portfolios apply technology in academic research planning and organization describe the nature and use of appropriate assistive technology in meeting the needs of special education students graduate programs in education and special education sped 601 page 8
p. 9
apply technology to developing strategies in essential areas of pedagogy such as instructional planning classroom management and the act of teaching understand and use technology including assistive technology for instruction and for assisting all children with gaining access to the curriculum comprehend the rapidly changing nature of technology and the need for ongoing learning to maintain technological literacy goal five application of professional learning students will integrate knowledge gained through their course work field experience and practicum into authentic teaching situations students will be able to enact effective lesson plans that accomplish lesson unit and course objectives develop educationally significant assignments and projects that facilitate the accomplishment and measurement of lesson unit and course objectives demonstrate principles of effective instruction within specific pedagogical content areas relate classroom practice and planning to relevant standards i.e cec nysed content naeyc and demonstrate alignment with standards apply educational and content-specific theories to advance key areas of pedagogy such as instructional planning classroom management and the act of teaching design and implement effective one-on-one intervention strategies with special needs and at-risk students relationship of learning outcomes to new york state learning standards http the standards relevant to the course are included here and are addressed within outcomes #1 above mathematics science and technology mathematics science and technology standard 3 math students will understand mathematics and become mathematically confident by communicating and reasoning mathematically by applying mathematics in real-world settings and by solving problems through the integrated study of number systems geometry algebra data analysis probability and trigonometry 1 students use mathematical reasoning to analyze mathematical situations make conjectures gather evidence and construct an argument apply a variety of reasoning strategies make and evaluate conjectures and arguments using appropriate language make conclusions based on inductive reasoning justify conclusions involving simple and compound i.e and/or statements 2 students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world the use of numbers to communicate mathematically and the use of numbers in the development of mathematical ideas understand represent and use numbers in a variety of equivalent forms integer fraction decimal percent exponential expanded and scientific notation understand and apply ratios proportions and percents through a wide variety of hands-on explorations develop an understanding of number theory primes factors and multiples recognize order relations for decimals integers and rational numbers graduate programs in education and special education sped 601 page 9
p. 10
3 students use mathematical operations and relationships among them to understand mathematics add subtract multiply and divide fractions decimals and integers explore and use the operations dealing with roots and powers use grouping symbols parentheses to clarify the intended order of operations apply the associative commutative distributive inverse and identity properties demonstrate an understanding of operational algorithms procedures for adding subtracting etc develop appropriate proficiency with facts and algorithms apply concepts of ratio and proportion to solve problems 4 students use mathematical modeling/multiple representation to provide a means of presenting interpreting communicating and connecting mathematical information and relationships visualize represent and transform two and three-dimensional shapes use maps and scale drawings to represent real objects or places use the coordinate plane to explore geometric ideas represent numerical relationships in one and two-dimensional graphs use variables to represent relationships use concrete materials and diagrams to describe the operation of real world processes and systems develop and explore models that do and do not rely on chance investigate both two and three-dimensional transformations use appropriate tools to construct and verify geometric relationships develop procedures for basic geometric constructions 5 students use measurement in both metric and english measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data estimate make and use measurements in real-world situations select appropriate standard and nonstandard measurement units and tools to measure to a desired degree of accuracy develop measurement skills and informally derive and apply formulas in direct measurement activities use statistical methods and measures of central tendencies to display describe and compare data explore and produce graphic representations of data using calculators/computers develop critical judgment for the reasonableness of measurement 6 students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations use estimation to check the reasonableness of results obtained by computation algorithms or the use of technology use estimation to solve problems for which exact answers are inappropriate estimate the probability of events use simulation techniques to estimate probabilities determine probabilities of independent and mutually exclusive events 7 students use patterns and functions to develop mathematical power appreciate the true beauty of mathematics and construct generalizations that describe patterns simply and efficiently recognize describe and generalize a wide variety of patterns and functions describe and represent patterns and functional relationships using tables charts and graphs algebraic expressions rules and verbal descriptions develop methods to solve basic linear and quadratic equations develop an understanding of functions and functional relationships that a change in one quantity variable results in change in another graduate programs in education and special education sped 601 page 10
p. 11
verify results of substituting variables apply the concept of similarity in relevant situations use properties of polygons to classify them explore relationships involving points lines angles and planes develop and apply the pythagorean principle in the solution of problems explore and develop basic concepts of right triangle trigonometry use patterns and functions to represent and solve problems language for information and understanding language for information and understanding standard 1 students will read write listen and speak for information and understanding as listeners and readers students will collect data facts and ideas discover relationships concepts and generalizations and use knowledge generated from oral written and electronically produced texts as speakers and writers they will use oral and written language to acquire interpret apply and transmit information interpret and analyze information from textbooks and nonfiction books for young adults as well as reference materials audio and media presentations oral interviews graphs charts diagrams and electronic data bases intended for a general audience compare and synthesize information from different sources use a wide variety of strategies for selecting organizing and categorizing information distinguish between relevant and irrelevant information and between fact and opinion relate new information to prior knowledge and experience understand and use the text features that make information accessible and usable such as format sequence level of diction and relevance of details 2 speaking and writing to acquire and transmit information requires asking probing and clarifying questions interpreting information in one s own words applying information from one context to another and presenting the information and interpretation clearly concisely and comprehensibly produce oral and written reports on topics related to all school subjects establish an authoritative stance on the subject and provide references to establish the validity and verifiability of the information presented organize information according to an identifiable structure such as compare/contrast or general to specific develop information with appropriate supporting material such as facts details illustrative examples or anecdotes and exclude extraneous material use the process of pre-writing drafting revising and proofreading the writing process to produce well-constructed informational texts use standard english for formal presentation of information selecting appropriate grammatical constructions standard 2 language for literary response and expression listening and reading for literary response involves comprehending interpreting and critiquing imaginative texts in every medium drawing on personal experiences and knowledge to understand the text and recognizing the social historical and cultural features of the text read and view texts and performances from a wide range of authors subjects and genres understand and identify the distinguishing features of the major genres and use them to aid their interpretation and discussion of literature identify significant literary elements including metaphor symbolism foreshadowing dialect rhyme meter irony climax and use those elements to interpret the work recognize different levels of meaning read aloud with expression conveying the meaning and mood of a work graduate programs in education and special education sped 601 page 11
p. 12
evaluate literary merit based on an understanding of the genre and the literary elements 2 speaking and writing for literary response involves presenting interpretations analyses and reactions to the content and language of a text speaking and writing for literary expression involves producing imaginative texts that use language and text structures that are inventive and often multilayered present responses to and interpretations of literature making reference to the literary elements found in the text and connections with their personal knowledge and experience produce interpretations of literary works that identify different levels of meaning and comment on their significance and effect write stories poems literary essays and plays that observe the conventions of the genre and contain interesting and effective language and voice use standard english effectively standard 3 language for critical analysis and evaluation listening and reading to analyze and evaluate experiences ideas information and issues requires using evaluative criteria from a variety of perspectives and recognizing the difference in evaluations based on different sets of criteria analyze interpret and evaluate information ideas organization and language from academic and nonacademic texts such as textbooks public documents book and movie reviews and editorials assess the quality of texts and presentations using criteria related to the genre the subject area and purpose e.g using the criteria of accuracy objectivity comprehensiveness and understanding of the game to evaluate a sports editorial understand that within any group there are many different points of view depending on the particular interests and values of the individual and recognize those differences in perspective in texts and presentations e.g in considering whether to let a new industry come into a community some community members might be enthusiastic about the additional jobs that will be created while others are concerned about the air and noise pollution that could result evaluate their own and others work based on a variety of criteria e.g logic clarity comprehensiveness conciseness originality conventionality and recognize the varying effectiveness of different approaches 2 speaking and writing for critical analysis and evaluation requires presenting opinions and judgments on experiences ideas information and issues clearly logically and persuasively with reference to specific criteria on which the opinion or judgment is based present in essays position papers speeches and debates clear analyses of issues ideas texts and experiences supporting their positions with well-developed arguments develop arguments with effective use of details and evidence that reflect a coherent set of criteria e.g reporting results of lab experiments to support a hypothesis monitor and adjust their own oral and written presentations according to the standards for a particular genre e.g defining key terms used in a formal debate use standard english precise vocabulary and presentational strategies effectively to influence an audience standard 4 language for social interaction oral communication in formal and informal settings requires the ability to talk with people of different ages genders and cultures to adapt presentations to different audiences and to reflect on how talk varies in different situations listen attentively to others and build on others ideas in conversations with peers and adults express ideas and concerns clearly and respectfully in conversations and group discussions learn some words and expressions in another language to communicate with a peer or adult who speaks that language graduate programs in education and special education sped 601 page 12
p. 13
use verbal and nonverbal skills to improve communication with others 2 written communication for social interaction requires using written messages to establish maintain and enhance personal relationships with others write social letters cards and electronic messages to friends relatives community acquaintances and other electronic network users use appropriate language and style for the situation and the audience and take into account the ideas and interests expressed by the person receiving the message read and discuss social communications and electronic communications of other writers and use some of the techniques of those writers in their own writing back to top social studies social studies standard 1 history of the united states and new york students will use a variety of intellectual skills to demonstrate their understanding of major ideas eras themes developments and turning points in the history of the united states and new york 1 the study of new york state and united states history requires an analysis of the development of american culture its diversity and multicultural context and the ways people are unified by many values practices and traditions explore the meaning of american culture by identifying the key ideas beliefs and patterns of behavior and traditions that help define it and unite all americans interpret the ideas values and beliefs contained in the declaration of independence and the new york state constitution and united states constitution bill of rights and other important historical documents 2 important ideas social and cultural values beliefs and traditions from new york state and united states history illustrate the connections and interactions of people and events across time and from a variety of perspectives describe the reasons for periodizing history in different ways investigate key turning points in new york state and united states history and explain why these events or developments are significant understand the relationship between the relative importance of united states domestic and foreign policies over time analyze the role played by the united states in international politics past and present 3 study about the major social political economic cultural and religious developments in new york state and united states history involves learning about the important roles and contributions of individuals and groups complete well-documented and historically accurate case studies about individuals and groups who represent different ethnic national and religious groups including native american indians in new york state and the united states at different times and in different locations gather and organize information about the important achievements and contributions of individuals and groups living in new york state and the united states describe how ordinary people and famous historic figures in the local community state and the united states have advanced the fundamental democratic values beliefs and traditions expressed in the declaration of independence the new york state and united states constitutions the bill of rights and other important historic documents classify major developments into categories such as social political economic geographic technological scientific cultural or religious graduate programs in education and special education sped 601 page 13
p. 14
4 the skills of historical analysis include the ability to explain the significance of historical evidence weigh the importance reliability and validity of evidence understand the concept of multiple causation understand the importance of changing and competing interpretations of different historical developments consider the sources of historic documents narratives or artifacts and evaluate their reliability understand how different experiences beliefs values traditions and motives cause individuals and groups to interpret historic events and issues from different perspectives compare and contrast different interpretations of key events and issues in new york state and united states history and explain reasons for these different accounts describe historic events through the eyes and experiences of those who were there taken from national standards for history for grades k-4 social studies standard 2 world history students will use a variety of intellectual skills to demonstrate their understanding of major ideas eras themes developments and turning points in world history and examine the broad sweep of history from a variety of perspectives 1 the study of world history requires an understanding of world cultures and civilizations including an analysis of important ideas social and cultural values beliefs and traditions this study also examines the human condition and the connections and interactions of people across time and space and the ways different people view the same event or issue from a variety of perspectives know the social and economic characteristics such as customs traditions child-rearing practices ways of making a living education and socialization practices gender roles foods and religious and spiritual beliefs that distinguish different cultures and civilizations know some important historic events and developments of past civilizations interpret and analyze documents and artifacts related to significant developments and events in world history 2 establishing timeframes exploring different periodizations examining themes across time and within cultures and focusing on important turning points in world history help organize the study of world cultures and civilizations develop timelines by placing important events and developments in world history in their correct chronological order measure time periods by years decades centuries and millennia study about major turning points in world history by investigating the causes and other factors that brought about change and the results of these changes 3 study of the major social political cultural and religious developments in world history involves learning about the important roles and contributions of individuals and groups investigate the roles and contributions of individuals and groups in relation to key social political cultural and religious practices throughout world history interpret and analyze documents and artifacts related to significant developments and events in world history classify historic information according to the type of activity or practice social/cultural political economic geographic scientific technological and historic 4 the skills of historical analysis include the ability to investigate differing and competing interpretations of the theories of history hypothesize about why interpretations change over time explain the importance of historical evidence and understand the concepts of change and continuity over time explain the literal meaning of a historical passage or primary source document identifying who was involved what happened where it happened what events led up to these developments and what consequences or outcomes followed taken from national standards for world history graduate programs in education and special education sped 601 page 14
p. 15
analyze different interpretations of important events and themes in world history and explain the various frames of reference expressed by different historians view history through the eyes of those who witnessed key events and developments in world history by analyzing their literature diary accounts letters artifacts art music architectural drawings and other documents investigate important events and developments in world history by posing analytical questions selecting relevant data distinguishing fact from opinion hypothesizing cause-and-effect relationships testing these hypotheses and forming conclusions standard 3 geography geography can be divided into six essential elements which can be used to analyze important historic geographic economic and environmental questions and issues these six elements include the world in spatial terms places and regions physical settings including natural resources human systems environment and society and the use of geography adapted from the national geography standards 1994 geography for life 1 students will use a variety of intellectual skills to demonstrate their understanding of the geography of the interdependent world in which we live local national and global including the distribution of people places and environments over the earth s surface map information about people places and environments understand the characteristics functions and applications of maps globes aerial and other photographs satellite-produced images and models taken from national geography standards 1994 investigate why people and places are located where they are located and what patterns can be perceived in these locations describe the relationships between people and environments and the connections between people and places 2 geography requires the development and application of the skills of asking and answering geographic questions analyzing theories of geography and acquiring organizing and analyzing geographic information adapted from the national geography standards 1994:geography for life formulate geographic questions and define geographic issues and problems use a number of research skills e.g computer databases periodicals census reports maps standard reference works interviews surveys to locate and gather geographical information about issues and problems adapted from national geography standards 1994 present geographic information in a variety of formats including maps tables graphs charts diagrams and computer-generated models interpret geographic information by synthesizing data and developing conclusions and generalizations about geographic issues and problem standard 4 economics students will use a variety of intellectual skills to demonstrate their understanding of how the united states and other societies develop economic systems and associated institutions to allocate scarce resources how major decision-making units function in the u.s and other national economies and how an economy solves the scarcity problem through market and nonmarket mechanisms 1 the study of economics requires an understanding of major economic concepts and systems the principles of economic decision making and the interdependence of economies and economic systems throughout the world explain how societies and nations attempt to satisfy their basic needs and wants by utilizing scarce capital natural and human resources define basic economic concepts such as scarcity supply and demand markets opportunity costs resources productivity economic growth and systems graduate programs in education and special education sped 601 page 15 |
This textbook gives a thorough introduction into the programming environment MATLAB in combination with Simulink, a tool for the numerical and symbolical treatment of simple and complex technical systems and the visualization of results. The book has roughly three parts, the first one giving an introduction into MATLAB, the second one focussing on the associated tools Simulink, Stateflow and SimMechanics, and the last one presenting eight projects mostly very detailed. The first part comprising chapters 1 to 3 gives a detailed overview of the language of MATLAB. Commands are always introduced in connection with applications, mathematical concepts are given, but the reader should be acquainted with the mathematical background. This is not a substitute for the MATLAB handbook, but it is possible to immediately apply MATLAB commands. Special topics are animation of 2D and 3D models, symbolic algebra, programming with MATLAB and code acceleration. Chapter 2 introduces into analytical and synthetical modeling of kinematic systems, the methods of Newton/Euler and Lagrange and linearization. Chapter 3 is about vibration models. The mathematical theory of self-oscillations and eigenvalues is outlined, emphasizing different approaches. The next four chapters handle in a comparable way tools associated to MATLAB, namely Simulink, Stateflow and SimMechanics. Emphasis for Simulink is on mathematical methods, choice of approach especially for stiff differential equations and algebraic loops in dynamic models. Chapter 5 concentrates on the use of MATLAB programs for simulations with emphasis on differential-algebraic equations, discontinuities and boundary value problems. Chapters 6 and 7 treat Stateflow, which allows the simulation of event-triggered models, and SimMechanics, which provides special elements for mechanical many-body systems. This third edition of the book has the balancing roboter as a new project in part three. This part is abundant with graphics and results for several interesting models, but relies heavily on access to the books website, where the complete code for the projects can be found. Presumably the book is no easy reading because of the concise exposition and the necessary presupposed knowledge in e.g. control theory, but the many examples allow for immediate implementation of own models. Questions of choice of appropriate method, numerical instability, choice of step size and many more are introduced and treated within the numerous examples.
Reviewer:
Dieter Riebesehl (Lüneburg) |
Helpful illustrations and exercises included throughout this lucid coverage of group theory, Galois theory and classical ideal theory stressing proof of important theorems. Includes many historical notes. Mathematical proof is emphasized. Includes 24 tables and figures. Reprint of the 1971 edition.This survey of fundamental algebraic structures employs techniques applicable to mathematics, physics, engineering, and computer science. Topics include relations between groups and sets, the fundamental theorem of Galois theory, and the results and methods of abstract algebra in terms of number theory, geometry, and noncommutative and homological algebra. Solutions. 2006 edition.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Dr. Carleen Eaton continues on to Algebra 2, and brings with her 10 years of experience in teaching math and science. This course meets or exceeds all state standards and is essential to those having trouble with Algebra in high school or college. With her clear explanations and examples of commonly seen problems, Dr. Eaton will make sure you understand all the confusing concepts in Algebra 2, ranging from Quadratic Inequalities to Matrices and Conic Sections. Dr. Carleen Eaton has an M.D. from the UCLA School of Medicine and in her teaching career has won numerous "Teacher of the Year" awards. She is also continually ranked as one of the top instructors in California.
Dr. Carleen Eaton guides you through Algebra 1 with captivating lessons honed from teaching math and science for over 10 years. This course meets or exceeds all state standards and is essential to those having trouble with Algebra in high school or college. Carleen's upbeat teaching style and real world examples will keep you engaged while learning. She covers everything in Algebra 1 from Linear Expressions to Systems of Equations and Rational Expressions. Along the way she has received multiple "Teacher of the Year" awards and rankings as one of the top instructors in California. Dr. Eaton received her M.D. from the UCLA School of Medicine.
The author defines "Geometric Algebra Computing" as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry.
Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'.
There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises.
This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools.
Algebra can be like a foreign language, but INTERMEDIATE ALGEBRA, 5E, gives you the tools and practice you need to fully understand the language of algebra and the "why" behind problem solving. Using Strategy and Why explanations in worked examples and a six-step problem solving strategy, INTERMEDIATE INTERMEDIATE ALGEBRA, 5E, algebra will make sense because it is not just about the x...it's also about the WHY. |
We are committed to helping students succeed in mathematics by offering a virtual math lab for individual and home school math students. We have created comprehensive, multimedia, video lessons using a step-by-step approach so students can understand each concept.
On our virtual algebra and geometry site, students can read about the company, find out what a math lesson actually covers (objectives), browse lessons by category, and purchase the lesson they choose (using PayPal).
With our virtual algebra and online geometry, we include a worksheet and answer key (the answer key shows all steps in the completion of each problem) for each lesson. Each lesson covers multiple levels of understanding so every student can learn.
We understand that with the cost and lack of availability for private tutoring and local learning centers, there needs to be an alternative and affordable way for parents to help their students succeed in math. Our service is very reasonable in cost. Our lessons cost between $1.00 and $3.00. The low cost of our lessons doesn't compromise the quality of our lessons. We are dedicated to providing the best math lessons possible for our students.
Our target audience is parents who want their students to succeed in math. They either do not have access to or cannot afford tutoring and learning centers. Also, home school students and anyone that wants quality math help for their students.
What sets our products apart from our competition is that we do not just show students how to "do" a particular problem. We teach concepts for understanding. We present our lessons with multiple examples, "Try These" problems, and a lesson worksheet with an answer key (with all of the steps needed to solve each problem - not just the answer). We also provide a list of lesson objectives so you know the lesson you pick is the lesson you need. Click for Lesson Objectives.
We are continually updating and adding new lessons. Lessons are added and modified based on our strict quality assurance and your direct feed-back. |
Overview
Mathematics is at the core of human civilization and is the cornerstone of all modern science and technology. The Mathematics Program has three main functions: to provide students in the program with the opportunity to study the primary areas of contemporary mathematics, to provide physical and social science majors with the necessary mathematical tools for work in their disciplines, and to introduce all students to serious and interesting mathematical ideas and their applications.
Requirements
The program requirements are flexible enough to allow a student to prepare for graduate study in mathematics, professional schools (such as medical or law), or employment in the public or private sector. Students in the program are expected to follow the standard divisional procedure for Moderation and to fulfill the collegewide distribution and First-Year Seminar requirements.
By the time of Moderation a student in the program should have taken (or be taking) these courses or their equivalents: Mathematics 141, Calculus I; Mathematics 142, Calculus II; Mathematics 212, Calculus III; and Mathematics 261, Proofs and Fundamentals. By graduation, a student must have completed: Mathematics 242, Elementary Linear Algebra; Mathematics 332, Abstract Algebra; Mathematics 361, Real Analysis; at least two other mathematics courses numbered 300 or above; a computer science course, preferably before beginning the Senior Project; and the Senior Project.
Recent Senior Projects in Mathematics
"A Structure Theorem for Plesken Lie Algebras over Finite Fields"
"Classification of Adinkra Graphs"
"Enumerating faces of Zonohedra"
"Modeling Origami Folding with Thick Paper"
"Voronoi Diagrams with Non-Linear Bisectors"
Courses
In addition to the core and elective courses, the Mathematics Program offers tutorials in advanced topics.
Mathematics and Politics Mathematics 106 This course considers applications of mathematics to political science. Five major topics are covered: a model of escalatory behavior, game-theoretic models of international conflict, yes-no voting systems, political power, and social choice. The implications of each model presented, as well as the limitations of the model, are discussed. There is no mathematical prerequisite, but the course includes some algebraic computations and discussion of deductive proofs of the main results.
Introduction to Mathematical Modeling Mathematics 109 Mathematical modeling is the process of using mathematics to describe and solve problems about real-world scenarios. A mathematical model is a representation of a particular phenomenon using structures such as graphs, equations, or algorithms. This course presents the skills used in creating, interpreting, and using mathematical models to solve real-world problems. Precise writing as well as careful use of algebraic manipulations is stressed.
Precalculus Mathematics Mathematics 110 For students who intend to take calculus and need to acquire the necessary skills in algebra and trigonometry. The concept of function is stressed, with particular attention to linear, quadratic, general polynomial, trigonometric, exponential, and logarithmic functions. Graphing in the Cartesian plane and developing the trigonometric functions as circular functions are included. Prerequisites: eligibility for Q courses and satisfactory performance on the precalculus entrance exam.
Chance Mathematics 119 The mathematical theory of probability is useful for quantifying the uncertainty in everyday life. This course introduces basic ideas in discrete probability and explores a wide range of practical applications such as evaluating medical diagnostic tests, courtroom evidence, and data from surveys. The course uses algebra as a problem-solving tool. Prerequisite: passing score on Part I of the Mathematics Diagnostic. Communications (and Miscommunications) Using Math Mathematics 122 This course introduces the math behind everyday communications, from mass media to cell phones. Topics covered include cryptography, as used in secure websites; and elements of sound and image analysis used in MP3 players and digital cameras. Prerequisite: Mathematics 110 or the equivalent.
Statistics for Everyday Life Mathematics 123 Statistics is used in the stock market, weather forecasting, medical studies by insurance companies, and quality testing. This course introduces core ideas in statistical reasoning to enable students to make sense of the statistics they encounter in the media, in their classes, and in everyday life. Prerequisite: precalculus or the equivalent.
Exploration in Number Theory Mathematics 131 An overview of one of the oldest areas of mathematics that is designed for any student who wants a taste of mathematics outside the calculus sequence. Topics include number puzzles, prime numbers, congruences, quadratic reciprocity, sums of squares, Diophantine equations, cryptography, coding theory, and continued fractions. Prerequisite: Mathematics 110 or permission of the instructor.
Game Theory Mathematics 135 Game theory is a mathematical approach to modeling situations of conflict, whether real or theoretical. Using algebra and some analytical geometry, students explore the mathematical foundations of game theory. At the same time, they encounter a wide range of applications of the theory of games. Topics include zero-sum games, nonzero-sum games, pure and mixed strategies, von Neumann's minimax theorem, Nash equilibria, and cooperative games. Prerequisite: Mathematics 110 or permission of the instructor.
Calculus I Mathematics 141 An introduction to the basic ideas of differentiation and integration of functions of one variable. Topics include limits, techniques of differentiation, definite integrals, the fundamental theorem of calculus, and applications. Prerequisite: Mathematics 110 or the equivalent.
String Theory Mathematics 191 An introduction to the mathematical ideas underlying string theory, a theory of particle physics that supposes the fundamental constituents of matter and energy are not points, but rather tiny strings or loops. No prior background in physics is required. Prerequisite: Mathematics 141 or the equivalent.
Mathematical Models in Biology Mathematics 209 An introduction to common approaches for dynamic modeling in biology, including difference equations, matrix algebra, and simulation. The main focus is on population and disease models, but there is some flexibility to explore other types of biological examples. Students learn the mathematical ideas involved in constructing and analyzing the models, and conduct computer simulations using Matlab. Prerequisite: one year of calculus.
Introduction to Differential Equations Mathematics 211 cross-listed: mbb Topics include the classification of differential equations; determining the existence and uniqueness of ordinary differential equations; and solving first- and second-order differential equations using a variety of mathematical tools, such as integrating factors, Laplace transforms, and power series. Prerequisites: Mathematics 141 and 142, or permission of the instructor.
Linear Algebra with Ordinary Differential Equations Mathematics 213 Topics in linear algebra include n-dimensional Euclidean space, vectors, matrices, systems of linear equations, determinants, eigenvalues and eigenvectors; topics in ordinary differential equations include graphical methods, separable differential equations, higher order linear differential equations, systems of linear differential equations and applications. Prerequisites: Mathematics 142 or the equivalent. Elementary Linear Algebra Mathematics 242 This course covers the basics of linear algebra in n-dimensional Euclidean space, including vectors, matrices, systems of linear equations, determinants, and eigenvalues and eigenvectors, as well as applications of these concepts to the natural, physical, and social sciences. Equal time is given to computational, applied, and theoretical aspects of the course material. Prerequisite: Mathematics 141 or permission of the instructor.
Proofs and Fundamentals Mathematics 261 An introduction to the methodology of the mathematical proof. The logic of compound and quantified statements; mathematical induction; and basic set theory, including functions and cardinality, are covered. Topics from foundational mathematics are developed to provide students with an opportunity to apply proof techniques. Prerequisite: Mathematics 142 or permission of the instructor.
Problem Solving Mathematics 299 The course focuses on solving difficult problems stated in terms of elementary combinatorics, geometry, algebra, and calculus. Each class combines a lecture describing the common tricks and techniques used in a particular field with a problem session in which students work together using those techniques to tackle some particularly challenging problems. Prerequisite: any 200-level mathematics course or permission of the instructor.
Computational Geometry Mathematics 303 / Computer Science 303 The focus of this class is on the computational complexity of the algorithms presented and appropriate data structures. Topics may include Voronoi diagrams, convex hull calculations, and line-segment intersections. Prerequisites: Mathematics 212 and 242, and some programming knowledge.
Advanced Calculus Mathematics 312 This course treats the differential and integral calculus of several variables from an advanced perspective. Students are expected to be familiar with the fundamentals of multivariate calculus from Mathematics 212. Topics include curvilinear coordinates, change of variables for multiple integrals, Stokes' theorem, divergence theorem, Fourier series and transform, and applications to probability and the physical sciences. Prerequisite: Mathematics 212 or permission of the instructor.
Data Analysis: Getting the Extra Rigor Mathematics 313 This course provides the computational, algebraic, and statistical tools needed to understand and make contributions in empirical science. The main focus is multidimensional data—data that typically are a function of space and time. After a solid linear algebra review, topics covered comprise covariance and cross-covariance functions and matrices, spanning sets, spectral representations and truncations, discrete vs. continuous spectra and the real number continuum, singular value decomposition, and Monte Carlo techniques. Prerequisites: Mathematics 212 and 242.
Combinatorics Mathematics 316 Combinatorial mathematics is the study of how to combine objects into finite arrangements. Topics covered in this course are chosen from enumeration and generating functions, graph theory, matching and optimization theory, combinatorial designs, ordered sets, and coding theory. Prerequisite: Mathematics 261 or permission of the instructor.
Graph Theory Mathematics 317 Graph theory is a branch of mathematics that has applications in areas ranging from operations research to biology. Topics discussed include connectivity, trees, Hamiltonian and Eulerian paths and cycles; isomorphism and reconstructability; planarity, coloring, color-critical graphs, and the four-color theorem; intersection graphs and vertex and edge domination; matchings and network flows; matroids and their relationship with optimization; and random graphs. Prerequisite: Mathematics 261 or permission of the instructor.
Probability and Statistics Mathematics 319 cross-listed: economics Every day we make decisions based on numerical data in the face of uncertainty. We do so while reading the latest political polls, playing a card game, or analyzing a scientific experiment. Probabilistic models and statistical methods help us think through such decisions in a precise mathematical fashion. This course provides a calculus-based introduction to the techniques and applications of probability and statistics. Applications are selected from the natural and social sciences. Prerequisite: Mathematics 142 or the equivalent.
Partial Differential Equations Mathematics 321 The primary focus is the derivation and solutions of the main examples in the subject rather than on the existence and uniqueness theorems and higher analysis. Topics include hyperbolic and elliptic equations in several variables, Dirichlet problems, the Fourier and Laplace transform, and Green's functions.
Operations Research Mathematics 322 The study of techniques for finding optimal solutions to complex decision-making problems. The course tries to answer questions such as how to schedule classes with a limited number of classrooms on campus, how to determine a diet that is both rich in nutrients and low in calories, or how to create an investment portfolio that meets investment needs. Techniques covered include linear programming, network flows, integer/combinatorial optimization, and nonlinear programming. Prerequisites: Mathematics 212 and 242. Dynamical Systems Mathematics 323 An introduction to the theory of discrete dynamical systems. Topics covered include iterated functions, bifurcations, chaos, fractals and fractal dimension, complex functions, Julia sets, and the Mandelbrot set. The class makes extensive use of computers to model the behavior of dynamical systems. Prerequisite: Mathematics 261 or permission of the instructor.
Fourier Analysis and Wavelets Mathematics 324 Recently, signal processing has gone through a mathematical revolution. Traditionally, it was built on the Fourier transform, a tool used to express signals as superpositions of pure sinusoidal functions. While the Fourier transform is suited to understanding physical phenomena, such as waves, it lacks the flexibility to analyze more complicated functions. A new tool, the wavelet transform, has become the staple of many signal processing tasks. This course introduces the mathematical foundations of the Fourier and the wavelet transforms, with excursions into signal processing. Prerequisites: Mathematics 212 and Mathematics 213 or Mathematics 242. Abstract Algebra Mathematics 332 An introduction to modern abstract algebraic systems. The structures of groups, rings, and fields are studied, together with the homomorphisms of these objects. Topics include equivalence relations, finite groups, group actions, integral domains, polynomial rings, and finite fields. Prerequisite: Mathematics 261 or permission of the instructor.
Advanced Linear Algebra Mathematics 335 This course starts with a discussion of dual spaces, direct sums, quotients, tensor products, spaces of homomorphisms and endomorphisms, inner product spaces, and quadratic forms. It then moves on to multilinear algebra, discussing symmetric and exterior powers, before turning to the Jordan canonical form and related topics. Other more advanced topics may include Hilbert spaces, modules, algebras, and matrix Lie groups. Prerequisite: Mathematics 242; corequisite: Mathematics 332.
Coding Theory Mathematics 340 The digital transmission of information is considered extremely reliable, although it suffers the same sorts of corruption and data loss that plague analog transmission. Digital reliability comes from sophisticated techniques that encode data so that errors can be easily detected and corrected. These error-correcting codes require surprisingly beautiful mathematics. This class introduces the basics of error-correcting codes, as well as the mathematics of data compression and encryption. Prerequisites: Mathematics 242 and either Mathematics 261 or Computer Science 145.
Differential Geometry Mathematics 352 This course uses methods from multivariable calculus to study the geometry of curves and surfaces in three dimensions. Topics include curvature and torsion of curves, geometry of surfaces, geodesics, spherical and hyperbolic geometry, minimal surfaces, Gaussian curvature, and the Gauss-Bonnet theorem. Prerequisites: Mathematics 212, 242, and 261, or permission of the instructor.
Real Analysis Mathematics 361 The fundamental ideas of analysis in one-dimensional Euclidean space are studied. Topics covered include the completeness of real numbers, sequences, Cauchy sequences, continuity, uniform continuity, the derivative, and the Riemann integral. As time permits, other topics may be considered, such as infinite series of functions or metric spaces. Prerequisite: Mathematics 261 or permission of the instructor.
Complex Analysis Mathematics 362 This course covers the basic theory of functions of one complex variable. Topics include the geometry of complex numbers, holomorphic and harmonic functions, Cauchy's theorem and its consequences, Taylor and Laurent series, singularities, residues, elliptic functions, and other topics as time permits. Prerequisite: Mathematics 361 or permission of the instructor.
Computational Algebraic Geometry Mathematics 384 This introduction to computational algebraic geometry and commutative algebra explores the idea of solving systems of polynomial equations by viewing the solutions to these systems as both algebraic and geometric objects. Students learn how these objects can be manipulated using the Groebner basis algorithm. The course includes a mixture of theory and computation as well as connections to other areas of mathematics and to computer science. Prerequisite: Mathematics 332. Mathematical Logic Mathematics 405 Topics include first-order logic, completeness and compactness theorems, model theory, nonstandard analysis, decidability and undecidability, incompleteness, and Turing machines. Prerequisite: Mathematics 332.
Advanced Topics in Abstract Algebra Mathematics 432 A continuation of Mathematics 332. The primary goal is to develop the Galois theory of fields. Students explore the theory of field extensions, including algebraic extensions, automorphisms of fields, splitting fields, and separable extensions. As time permits, students may develop some topics in advanced group theory.Prerequisites: Mathematics 332 or permission of the instructor.
Modern Geometry Mathematics 453 This course looks at Euclidean, non-Euclidean (hyperbolic and elliptic), and projective geometries, making use of tools from linear algebra and abstract algebra. Prerequisites: Mathematics 242 and Mathematics 332 (which can be taken simultaneously with this course), or permission of instructor.
Knot Theory Mathematics 454 Knot theory is an active branch of contemporary mathematics that, as in number theory, involves many problems that are easy to state but difficult to solve; unlike number theory, knot theory involves a lot of visual reasoning. This course is an introduction to the theory of knots and links. Topics include methods of knot tabulation, knot diagrams, Reidemeister moves, invariants of knots, and knot polynomials. Prerequisite: Mathematics 351 or 361, or permission of instructor. |
lucid introduction to some of the mathematical ideas which are useful to biologists. Professor Maynard Smith introduces the reader to the ways in which biological problems can be expressed mathematically, and shows how the mathematical equations which arise in biological work can be solved. Each chapter has a number of examples which present further points of biological and mathematical interest. interest. Professor Maynard Smith's book is written for all biologists, from undergraduate level upwards, who need mathematical tools. Only an elementary knowledge of mathematics is assumed. Since there are already a number of books dealing with statistics for biologists, this book is particularly concerned with non-statistical topics. |
Description
Mathematical Reasoning for Elementary Teachers presents the mathematical knowledge needed for teaching, with an emphasis on why future teachers are learning the content as well as when and how they will use it in the classroom.
The Sixth Edition has been streamlined throughout to make it easier to focus on the important concepts. The authors continue to make the course relevant for future teachers by adding new features such as questions connected to School Book Pages; enhancing hallmark features such as Responding to Students exercises; and making the text a better study tool through the redesigned Chapter Summaries.
To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit
Table of Contents
1. Thinking Critically
1.1 An Introduction to Problem Solving
1.2 Pólya's Problem-Solving Principles
1.3 More Problem-Solving Strategies
1.4 Algebra as a Problem-Solving Strategy
1.5 Additional Problem-Solving Strategies
1.6 Reasoning Mathematically
2. Sets and Whole Numbers
2.1 Sets and Operations on Sets
2.2 Sets, Counting, and the Whole Numbers
2.3 Addition and Subtraction of Whole Numbers
2.4 Multiplication and Division of Whole Numbers
3. Numeration and Computation
3.1 Numeration Systems Past and Present
3.2 Nondecimal Positional Systems
3.3 Algorithms for Adding and Subtracting Whole Numbers
3.4 Algorithms for Multiplication and Division of Whole Numbers
3.5 Mental Arithmetic and Estimation
4. Number Theory
4.1 Divisibility of Natural Numbers
4.2 Tests for Divisibility
4.3 Greatest Common Divisors and Least Common Multiples
5. Integers
5.1 Representations of Integers
5.2 Addition and Subtraction of Integers
5.3 Multiplication and Division of Integers
6. Fractions and Rational Numbers
6.1 The Basic Concepts of Fractions and Rational Numbers
6.2 Addition and Subtraction of Fractions
6.3 Multiplication and Division of Fractions
6.4 The Rational Number System
7. Decimals, Real Numbers, and Proportional Reasoning
7.1 Decimals and Real Numbers
7.2 Computations with Decimals
7.3 Proportional Reasoning
7.4 Percent
8. Algebraic Reasoning and Connections with Geometry
8.1 Algebraic Expressions, Functions, and Equations
8.2 Graphing Points, Lines, and Elementary Functions
8.3 Connections Between Algebra and Geometry
9. Geometric Figures
9.1 Figures in the Plane
9.2 Curves and Polygons in the Plane
9.3 Figures in Space
9.4 Networks
10. Measurement: Length, Area, and Volume
10.1 The Measurement Process
10.2 Area and Perimeter
10.3 The Pythagorean Theorem
10.4 Surface Area and Volume
11. Transformations, Symmetries, and Tilings
11.1 Rigid Motions and Similarity Transformations
11.2 Patterns and Symmetries
11.3 Tilings and Escher-like Designs
12. Congruence, Constructions, and Similarity
12.1 Congruent Triangles
12.2 Constructing Geometric Figures
12.3 Similar Triangles
13. Statistics: The Interpretation of Data
13.1 Organizing and Representing Data
13.2 Measuring the Center and Variation of Data
13.3 Statistical Inference
14. Probability
14.1 Experimental Probability
14.2 Principles of Counting
14.3 Permutations and Combinations
14.4 Theoretical Probability
Appendices
A. Manipulatives in the Mathematics Classroom
B. Getting the Most out of Your Calculator
C. A Brief Guide to the Geometer's Sketchpad
D. |
The Cartoon Guide to Calculus
"In Gonick's work, clever design and illustration make complicated ideas or insights strikingly clear." —New York Times Book Review
Larry Gonick, master cartoonist, former Harvard instructor, and creator of the New York Times bestselling, Harvey Award-winning Cartoon Guide series now does for calculus what he previously did for science and history: making a complex subject comprehensible, fascinating, and fun through witty text and light-hearted graphics. Gonick's The Cartoon Guide to Calculus is a refreshingly humorous, remarkably thorough guide to general calculus that, like his earlier Cartoon Guide to Physics and Cartoon History of the Modern World, will prove a boon to students, educators, and eager learners everywhere.
Book Description
A complete—and completely enjoyable—new illustrated guide to calculus
Master cartoonist Larry Gonick has already given readers the history of the world in cartoon form. Now, Gonick, a Harvard-trained mathematician, offers a comprehensive and up-to-date illustrated course in first-year calculus that demystifies the world of functions, limits, derivatives, and integrals. Using clear and helpful graphics—and delightful humor to lighten what is frequently a tough subject—he teaches all of the essentials, with numerous examples and problem sets. For the curious and confused alike, The Cartoon Guide to Calculus is the perfect combination of entertainment and education—a valuable supplement for any student, teacher, parent, or professional.
"How do you humanize calculus and bring its equations and concepts to life? Larry Gonick's clever and delightful answer is to have characters talking, commenting, and joking-all while rigorously teaching equations and concepts and indicating calculus's utility. It's a remarkable accomplishment-and a lot of fun."
Larry Gonick's sparkling and inventive drawings make a vivid picture out of every one of the hundreds of formulas that underlie Calculus. Even the jokers in the back row will ace the course with this book.
—
David Mumford, Professor emeritus of Applied Mathematics at Brown University and recipient of the National Medal of Science
I always thought that there are no magic tricks that use calculus. Larry Gonick proves me wrong. His book is correct, clear and interesting. It is filled with magical insights into this most beautiful subject.
—
Persi Diaconis, Professor of Mathematics, Stanford
It has no mean derivative results about the only derivatives that matter…. A spunky tool-toting heroine called Delta Wye seems the perfect role model for our next generation.
—
Susan Holmes, Professor of Statistics, Stanford
A creative take on an old, and for many, tough subject…Gonick's cartoons and intelligent humor make it a fun read.
—
Amy Langville, Recipient of the Distinguished Researcher Award at College of Charleston and South Carolina Faculty of the YearThe Cartoon History of the Modern World Part 1,... |
fun and easy way® to understand the basic concepts and problems of pre-algebra
Whether you're a student preparing to take algebra or a parent who needs a handy reference to help kids study, this easy-to-understand guide has the tools you need to get in gear. From exponents, square roots, and absolute value to fractions, decimals, and percents, you'll build the skills needed to tackle more advanced topics, such as order of operations, variables, and algebraic equations. |
ID: 333 | Video: Medium | Audio: None | Animation: None
Learn Algebra calculations in an easy, step-by-step process
This free online course in algebra from ALISON will guide you through among other things expressions, systems of equations, functions, real numbers, inequalities, exponents, polynomials, radical and rational expressions. The course is divided into 12 chapters and each chapter is divided into several lessons. Under each lesson you will find theory, examples and video lessons. This course is ideal for learners who want to study topics in algebra in detail.
This course will help you to understand expressions, equations and functions. You will be able to explore real numbers and solve linear equations, along with gaining a good knowledge of formulating linear equations and inequalities. You will know exponents and exponential functions. This course will help you to understand factoring, polynomials and how to formulate quadratic equations and radical expressions. |
MATH 145: Quantitative Reasoning
The purpose of this course is to develop critical thinking and quantitative reasoning skills. Topics of study will include logic and set theory, problem-solving techniques, number "sense", an introduction to probability and statistics, graphs, and modular arithmetic. Applications of mathematics in other fields will be studied, including art (symmetry, perspective, patterns, golden mean and ratio), politics (voting methods, polling practices), and business (networks, scheduling, finance). Special emphasis will be placed on collaborative learning.... more »
Credits:3
Overall Rating:0 Stars
N/A
Thanks, enjoy the course! Come back and let us know how you like it by writing a review. |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
THE DIHEDRAL GROUPS DnSome authors use D2n to denote the n-th dihedral group. An excellent referencefor dihedral groups is the textbook Algebra by Michael Artin, Chapter 5.Let n 3. Let Dn be the set of all symmetries of a regular n-gon. More precisely,
1 About ScienceConceptual Physics Instructor Manual, 11th EditionScientific MeasurementsHOW ERATOSTHENES MEAURED THE SIZE OF EARTH SIZE OF THE MOON DISTANCE TO THE MOON DISTANCE TO THE SUN SIZE OF THE SUNMathematics-The Language of Science Scientific |
Elementary Algebra
Synopsis
Most students have a blend of emotions while dealing with Algebra. Talking about x and y, unknowns and equations, is exciting, and equally confusing. This is not just our premise, but this is based on feedback / direct inputs we have received from the student, teacher and parent community. We started a project to address this conceptual gap.We started stringing together a set of concepts followed by a problem set using the preceding texts. This effort left us with a skeletal structure of concepts in Algebra which progresses from basics to through to advanced topics. This formed the basis of our work on "Elementary Algebra". We sincerely hope that the student is able to get a good grasp of the subject and the techniques after working with the contents |
Can anyone recommend me a good algebra book?
Can anyone recommend me a good algebra book?
I am not sure where to post this so sorry if I posted in the wrong forum.
But my question is I took algebra 1 and 2 at high school but I forgot most it and my level of understanding in math is probably at the arithmetic level. Can anyone recommend me a good book for learning Algebra one for self study because I want to teach myself.
Can anyone recommend me a good algebra book?
The Schaum's books are good for review, but IMO not as good for learning from scratch, because they are extremely terse (which is what you want when reviewing).
I'd recommend a basic algebra text if you think you have truly forgotten everything, or a precalculus text if you just feel shaky. The only precalc texts I'm personally familiar with are those by Stewart and Swokowski, and both are good. But you might go to Amazon and search for algebra and/or precalc texts, and just read the reviews. Every book seems to have a few people who don't like it for some reason, but try to find reviews from people who sound like they have the same concerns as you do, and see which books they rate highly.
Be sure you are looking at BASIC algebra books; some advanced algebra books don't show it in their title. Look through the table of contents, and if you see topics like rings or fields, it's not what you want.
And don't spend much money on texts. You can find plenty of free, public domain materials on the net, or if you prefer a book you can hold, an old used edition will work just as well as a brand new one. |
Linear Algebra Done Right
second edition
Sheldon Axler
This text, published by Springer, is intended for a second course in linear algebra. The novel approach used throughout the book takes great care to motivate concepts and simplify proofs.
For example, the book presents, without having defined determinants, a clean proof that
every linear operator on a finite-dimensional complex vector space (or on an odd-dimensional
real vector space) has an eigenvalue.
Although this text is intended for a second course in linear algebra, there are
no prerequisites other than appropriate mathematical
maturity. Thus the book starts by discussing vector spaces, linear
independence, span, basis, and dimension. Students are introduced to
inner-product spaces in the
first half of the book and shortly thereafter to the finite-dimensional spectral
theorem.
A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
Excerpts from Reviews
Altogether, the text is a didactic masterpiece. Zentralblatt für Mathematik
Axler demotes determinants (usually quite a central technique in the finite dimensional setting, though marginal in infinite dimensions) to a minor role. To so consistently do without determinants constitutes a tour de force in the service of simplicity and clarity; these are also well served by the general precision of Axler's prose... The most original linear algebra book to appear in years, it certainly belongs in every undergraduate library. Choice
The determinant-free proofs are elegant and intuitive. American Mathematical Monthly
Clarity through examples is emphasized... the text is ideal for class exercises... I congratulate the author and the publisher for a well-produced textbook on linear algebra. Mathematical Reviews |
Book DescriptionThe one published in 1959 deserves to be one of the finest books written about vectors .The way it deals with the subject prepare the reader smoothly in mastering the basics of vector analysis, its for the engineer, physicist and mathematician.
By the way the full name of the book is "Vector Analysis and an Introduction to Tensor Analysis"
This is great as a preparatory or supporting text. I worked through virtually all of the 'supplementary' problems and found the chapters on curvilinear coordinates and tensor analysis very useful preparation for the study of General Relativity texts. Major parts of Landau and Lipschitz 'Classical Theory of Fields' and many other texts were readily accessible after doing the sums from Spiegel. Eminently suitable for independent study.
I love this book. I've owned three copies of it over the years and I can honestly say that I would not have achieved the final class of degree in Physics that I did without it.
The learning curve is very gentle - really nothing is assumed about the reader's background beyond basic integral and differential calculus. The concepts of vectors are introduced one by one, and the book builds logically towards its final stages (introductory tensor analysis) via, inter alia, dot and cross products, partial differential operators on vector spaces (grad, div, curl, Laplacian etc.), line and surface integrals (along with vital allied therorems such as Stokes' and Green's theorems), and general theory of curvilinear coordinate systems (in which the differential operators are refined and generalised).
This book is absolutely ideal for an undergraduate course in Physics, Electronic Engineering or Vector Analysis. |
work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties but geometrical meaning has been emphasised throughout. Volume 2 gives an account of the principal methods used in developing a theory of algebraic varieties in spaces of n dimensions. Applications of these methods are also given to some of the more important varieties which occur in projective geometry. The ground field is without characteristic. Since geometry over any field without characteristic conforms to the general pattern of geometry over the field of complex numbers, a sound algebraic basis for classical geometry is provided. The other two volumes of Hodge and Pedoe's classic work are also available. Together, these books give an insight into algebraic geometry that is unique and unsurpassed. less |
My Advice to a New Math 175 Student:
The biggest thing I could emphasis to a new student is do the homework
and do not miss lecture. The reviews at the end of the chapters are
key
to helping you pull things together. They are not assigned but
they are key to understanding the major points of each chapter. The
review sessions if made available are great tools too. Consider them
part of your class. It is always good to hear other way of approaching
a problem. If possible try to study in groups. Talk to the people
next
to you and meet the night before tests and quizzes to work through
problems together. |
Upper school > course description math
Mathematics in grades 9-12 is a sequential, college preparatory program. It emphasizes the development of math concepts, as well as computational, problem solving, and critical thinking skills. Comprehensive and appropriately challenging, this curriculum is designed to provide students with the math background necessary for their future endeavors.
Grade Level: 8-9 - Algebra ICP - This course is offered to students who have completed pre-algebra. Topics covered include variable expressions, linear and quadratic equations and inequalities, systems of linear equations, factoring polynomials, and simplifying radial and rational expressions. The interpretation and solution of verbal problems follows each topic. Students are introduced to graphing calculator technology.
Grade Level 8-9 - Algebra I Honors - This course is offered to students who have completed pre-algebra and display strong mathematical skills. Topics covered include variable expressions, linear and quadratic equations and inequalities, systems of linear and non-linear equations, factoring polynomials, and simplifying radical and rational expressions. The interpretation and solution of verbal problems is incorporated within each skill area. Inquiry-based learning and graphing calculator technology are both utilized in this course. Students are encouraged to develop precise and accurate habits of mathematical expression.
Grade Level 9-10 - Geometry Honors - This course follows Algebra I. Postulates, theorems, definitions, and algebraic properties are combined with deductive reasoning and logical thinking to develop proofs. Emphasized are the concepts of congruency and similarity, the properties of particular polygons, the right triangle, and the circle.
Grade Level: 10-11 - Algebra II CP - This course is offered to students who have successfully completed Algebra I and Geometry. Coursework builds directly upon the topics and concepts introduced in Algebra I. Students explore a variety of solution strategies for solving systems of equations, as well as linear, quadratic, rational, radical, and exponential equations. Students are required to interpret and solve application problems in each of these contexts. A working knowledge of the graphing calculator will be developed.
Grade Level: 10-11 - Algebra II Honors - This course covers similar topics to Algebra II CP. In addition, students at the Honors level are expected to delve more deeply into each concept. Application problems have increased focus at the Honors level. More emphasis is placed on independent problem solving and mathematical justification of each step in students work.
Grade Level: 11-12 - Pre- Calculus CP - This course is offered to students who have completed Algebra I and II and Geometry and may follow Advanced Algebra. The concepts and skills developed in Algebra II are reviewed and expanded. Topics covered include conic sections, logarithmic and exponential functions, the trigonometric functions, and sequences series and probability.
Grade Level: 11-12 - Pre- Calculus Honors - This course lays the foundation for calculus and is designed for the student who has a solid background in Algebra II and Geometry. The course is a more advanced study of algebra integrated with coordinate geometry and emphasizes linear and quadratic functions and their graphs, the conic sections, logarithmic and exponential functions, the trigonometric functions, the concept of vectors, the study of limits, sequences, series, and probability. The approach stresses the understanding and application of concepts.
Grade Level: 11-12 - AP Statistics - This course is offered on-line for an additional fee. AP Statistics data analysis is dependent on the use of technology. Students should have access to computers that include software capable of doing data analysis and students will be required to interpret output generated by statistical software programs. Students are not expected to learn how to use various statistical programs.
Grade Level: 12 - Advanced Algebra - This course is offered to students who have completed Algebra I, Geometry, and Algebra II, and who wish to maintain proficiency in algebra skills in preparation for college mathematics. Topics include exponents, factoring, equation solving, rational expressions, radicals, quadratic equations, graphs of functions, conic sections, and trigonometric concepts.
Grade Level: 12 - Calculus - This course introduces limits, differentiation, and integration of functions. Students will find and evaluate finite and infinite limits graphically, numerically and analytically. They will find deriviatives using a variety of methods including the Chain Rule and Implicit Differentiation. They will use the First Derivative Test and the Second Derivative Test to analyze and sketch functions.
Grade Level: 12 - Advanced Placement Calculus (AB) - AP Calculus (AB) is a college-level mathematics course intended to be challenging and demanding. A strong performance in Pre-Calculus is a prerequisite. Topics include: functions, graphs, limits, derivatives and integrals. College credit may be awarded to those students who are successful on the national AP exam given in May. |
10 Units 2000 Level Course
Available in 2012
Differential equations arise in all branches of science and engineering. In Chemical Engineering students encounter problems involving heat transfer, diffusion and vibration which involve functions of 2 variables and their derivatives. The resulting equations are partial differential equations. Usually the solutions must satisfy physical restrictions - the resulting equations are called boundary value problems. Students will apply their knowledge of calculus and ordinary differential equations, as well as learning new techniques. Theoretical methods such as Fourier series are covered in lectures and applied methods such as the finite difference method are studied using specialised computer software.
Math2470 cannot count for credit with MATH2800.
Objectives
1. Provide the necessary mathematical knowledge and skills in solving boundary-value problems related to the diffusion of heat, mass and momentum. |
This be asked several questions and will be given feedback regarding their answers. Detailed solutions are provided, but users should try to answer the questions on their own before consulting the detailed solutions. The end of the tutorial contains some "thought" questions |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
SELECT exp_id AS exp_id, exp_short_desc AS exp_short_desc, exp_long_desc AS exp_long_desc, author_id AS author_id, sense_id AS sense_id, loc_id AS loc_id, rank_id AS rank_id, date AS date, time AS time, 'ilee4320' FROM ilee4320.experience WHERE 1SE
Review for Final Exam Math 230, Fall 2006 The final exam is scheduled on 12/18/2006 12:20 PM - 2:10PM, 121 Sparks (Section 7 and 8) This is a comprehensive exam, you should consult your previous midterm review sheets for highlights of Sections 13.1-1
Math 230, Fall 2006Review sheet for Exam 1Our rst midterm exam will be given on October 5, 2006. It will cover the material from Chapters 13-14.Some important skillsSection 13.1: Three-dimensional Coordinate Systems Find the distance from a po
Math230 Take home quiz No. 6, Oct.20, Name:, StudentID:(1) ( 2 points) Find the first partial derivative$ of the function:(2) ( 3 p oints) Find the equation of the tangent plane to the given surface a t the specified point.
Outline Object-oriented programming Objects and classes, examplesObject-Oriented Programming (OOP) A programming technique based on objects. Advantages:Good at modeling real-world objects you find in everyday life. Speedy development, high
To-do ReviewMembers in class definition Object creation ArrayClasses Name the class members you know about variables (i.e. fields)instance variables, class variables (with keyword static) A special kind of method A constructor is calle |
This is a free, online book that was originally published as a university lecture series in 1992. Chapters include the following: 1. Mathematical model 2. First integrals of boundary motion 3. Algebraic solutions 4. Contraction of a gas bubble 5. Evolution of a multiply connected domain 6. Evolution with topological transformations 7. Contraction problem on surfaces. |
Calculus: Understanding Its Concept and Methods is a complete electronic textbook featuring live calculations and animated, interactive graphics. It uses the included Scientific Notebook® program to display text, mathematics, and graphics on your screen and to provide an interactive environment including examples with user-defined functions, animations, and algorithmically generated self-tests. This environment encourages a focus on mathematical problem solving, experimentation, verification, and communication of results.
This electronic book covers the content normally taught in a three-semester calculus sequence. The material is presented in a way that encourages mathematical problem solving, experimentation, exploration, and communication. It includes explanations, examples, explorations, problem sets, self tests, and resource information. Many of the files contain animations that you can manipulate and control. Other files are interactive: you can define your own function, or change some parameters, and observe the results. This allows you to achieve important insights from specific examples.
Calculus: Understanding Its Concept and Methods is thoroughly indexed and hyperlinked to provide easy access to relevant information. It is appropriate for independent study, as a supplement to any standard calculus text, or for distance learning.
Calculus is the mathematics of change and approximation. With the computer algebra system in Scientific Notebook®, you can interactively explore examples and carry out experiments. The skills you develop will help you to solve problems you encounter in the future because you are always dealing with natural mathematical notation and general problem-solving methods. |
umerical Mathematics and Computing
Authors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give ...Show synopsisAuthors Ward Cheney and David Kincaid show students of science and engineering the potential computers have for solving numerical problems and give them ample opportunities to hone their skills in programming and problem solving. The text also helps students learn about errors that inevitably accompany scientific computations and arms them with methods for detecting, predicting, and controlling these errors. A more theoretical text with a different menu of topics is the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, THIRD EDITIONEx-Library book-will contain library markings. Very good...Ex-Library book-will contain library markings. Very good condition book with only light signs of previous use. Sail the Seas of Value |
Maple
Maple 16 for Academics
Maple™ is an essential tool for researchers,
teachers, and students in any mathematical or technical discipline.
It lets you explore, visualize, and solve even the most complex mathematical
problems, reducing errors and providing greater insight into the math.
Teachers can bring complex problems to life, students can focus on
concepts rather than the mechanics of solutions, and researchers can
develop more-sophisticated algorithms or models.
Key Features Browse the key features that make Maple the essential tool for researchers,
teachers and students in any technical discipline |
M1314lesson 1 Math 1314 Lesson 1 Limits What is calculus?1The body of mathematics that we call calculus resulted from the investigation of two basic questions by mathematicians in the 18th century. 1. How can we find the line tangent to a curve
M1314Lesson 9 Math 1314 Lesson 9 Marginal Functions in Economics Marginal Cost1Suppose a business owner is operating a plant that manufactures a certain product at a known level. Sometimes the business owner will want to know how much it costs
M1314lesson 2 Math 1314 Lesson 2 One-Sided Limits and Continuity One-Sided Limits1Sometimes we are only interested in the behavior of a function when we look from one side and not from the other. Example 1: Consider the function f ( x) =x x .
M1314Lesson 10 Math 1314 Lesson 10 Applications of the First Derivative Determining the Intervals on Which a Function is Increasing or Decreasing From the Graph of f1Definition: A function is increasing on an interval (a, b) if, for any two num
M1314Lesson 18 Math 1314 Lesson 18 Area and the Definite Integral1We are now ready to tackle the second basic question of calculus the area question. We can easily compute the area under the graph of a function so long as the shape of the regiM1314lesson 11 Math 1314 Lesson 11 Applications of the Second Derivative Concavity1Earlier in the course, we saw that the second derivative is the rate of change of the first derivative. The second derivative can tell us if the rate of change o
M1314Lesson 19 Math 1314 Lesson 19 The Fundamental Theorem of Calculus1In the last lesson, we approximated the area under a curve by drawing rectangles, computing the area of each rectangle and then adding up their areas. We saw that the actual
M1314Lesson 4 Math 1314 Lesson 4 Basic Rules of Differentiation1We can use the limit definition of the derivative to find the derivative of every function, but it isn't always convenient. Fortunately, there are some rules for finding derivative
M1314Lesson 12 Math 1314 Lesson 12 Curve Sketching1One of our objectives in this part of the course is to be able to graph functions. In this lesson, we'll add to some tools we already have to be able to sketch an accurate graph of each functio
M1314Lesson 13 Math 1314 Lesson 13 Absolute Extrema1In earlier sections, you learned how to find relative (local) extrema. These points were the high points and low points relative to the other points around them. In this section, you will lear
M1314lesson 21 Math 1314 Lesson 21 Area Between Two Curves1Two advertising agencies are competing for a major client. The rate of change of the client's revenues using Agency A's ad campaign is approximated by f(x) below. The rate of change of
M 1314Lesson 14 Math 1314 Lesson 14 Optimization1Now youll work some problems where the objective is to optimize a function. That means you want to make it as large as possible or as small as possible depending on the problem. The first task is
M1314lesson 22 Math 1314 Lesson 22 Functions of Several Variables1So far, we have looked at functions of a single variable. In this section, we will consider functions of more than one variable. You are already familiar with some examples of th
M1314Lesson 7 Math 1314 Lesson 7 Higher Order Derivatives1Sometimes we need to find the derivative of the derivative. Since the derivative is a function, this is something we can readily do. The derivative of the derivative is called the second
M1314lesson 15 Math 1314 Lesson 15 Exponential Functions as Mathematical Models1In this lesson, we will look at a few applications involving exponential functions. Well first consider some word problems having to do with money. Next, well consi
M1314lesson 23 Math 1314 Lesson 23 Partial Derivatives1When we are asked to find the derivative of a function of a single variable, f (x), we know exactly what to do. However, when we have a function of two variables, there is some ambiguity. W
M 1314lesson 8 Math 1314 Lesson 8 Some Applications of the Derivative Equations of Tangent Lines1The first applications of the derivative involve finding the slope of the tangent line and writing equations of tangent lines. Example 1: Find the
Homework Module 4 3303 Name: email address: phone number:Who helped me:Who I helped:This is a 55 point assignment. Homework rules: Front side only. Keep the questions and your answers in order. If you send it pdf, send it in a single scanned
Math 1300 1. Homework is due before class begins. a. True b. FalsePopper 012. I must bubble in _ on popper scantrons or I will get a zero for that grade. a. Section number b. Assignment number c. Grading ID d. Form A e. All of the above 3. All te |
(To see all Half.com copies: Click Back to Main Product Page in Half.com product page.)
Numerical Analysis, designed to be used in a one-year course in engineering, science and mathematics, helps the readers gain a deeper understanding of numerical analysis by highlighting the five major ideas of the discipline: Convergence, Complexity, Conditioning, Compression, and Orthogonality and connecting back to them throughout the text. Each chapter contains a Reality Check, an extended foray into a relevant application area that can be used as a springboard for individual or team projects. MATLAB is used throughout to demonstrate and implement numerical methods |
Im taking quite a bit of math this year and would like to know what is learned from these courses
.pre calculus is it just alg 2and trig?
Physics 1honors would pre calc help me to get a better understanding?
College algebra- is it like pre calc (taking it at the community college)
AP Statistics- I have no idea what math is in it, is it hard
Also do you think these classes will look good for UCF? Thanks in advance also going to be a junior
I had no idea what category to put this in, sorry in advance
Precalc is typically a review of trig and algebra 2.
College Algebra is typically a remedial class equivalent to algebra 2.
AP Statistics is concerned with analysis of data and various types of ways of analyzing data (for example, a way to calculate whether there is a correlation between two variables and how strong that correlation is). It also covers basic probability. It also covers statistical inference testing. For example, given a set of data (let's say, heights of randomly selected people), you will run a statistical test (and this involves looking at a normal distribution) , and determine with a 95% level of confidence that the actual average height of humans falls within the range of X to Y.
The math in AP Stat is very simple (plug into calculator). It's all about memorizing rules and equations and different situations. |
Our users:
I think this program is one of the most useful learning tools I have purchased (and believe me, I purchased a lot!), It's easy for us as parents- to work with, it saves a lot of our children's precious time. Keith Erich Johnston, KS
Ive been a high-school math teacher for over sixteen years and luckily, Ive had computers aiding me in the classroom since the Apple II. But nothing has ever gotten the results or helped my students understand as many advanced equations and concepts as Algebrator has! Thats why nowadays, I make sure every student system in the school (even the notebooks) are running it! If nothing else, it makes our jobs a lot easier! Ashley Grayden, MA
I like algebra but was not able to finish the homework on time. Things have changed now for me. Zoraya Christiansen
Algebrator is easy to use and easy to understand and has made algebra the same for me. I am thankful that I got it. Billy Hafren, TX
I started with this kind of programs as I am in an online class and there are times when "I have no clue". I am finding your program easier to follow. THANK YOU! Jeff Brooks, ID17:
free math problem answers algebra solutions equations
how to solve for standard form of linear equations
factoring binomial calculator
dividing polynomials by monomials calculator
algebra with pizzazz
how to do lu decomposition on ti-89
algebra tiles hardest
solving polynomials
kumon G14 cheats
pre algebra clicking calculator using inequalities
how to factor equations
factor finder
Inequalities Algebra Solver
free algebra help
free simplifying radical expressions calculator
how to multiply and divide rational numbers
LCD of expressions solvers
examples of real story
y-intercept to vertex for beginners
simplify equivalent expressions
learning algebra in sequence gcse level
examples of QT factoring
holt algebbra
find the zero function for a linear equation
partial fractions with nonlinear denominator
Examples of Quadratic Equations
algebra helper
tic tac toe study guide examples
algebrator word problems
parabola vertex calculator free online graph
holt algebra 1 book
how do you work out binomial numbers
synthetic division calculator online free
ks3 free sats papers
polynomial factoring calculator
how do i write algebraic expression =100 but not anything over 100 except 999 |
word history
one of the first representations of algebra is the Aryabhattiya, a mathematical text book of the Indian mathematician Aryabhatta from that 5. Century; used methodology was called Bijaganitam. In 13. Century took over and refined the Arabs this method and called it aluminium-jabr ("joining more broken (bone) parts"), which from the title of the computing text book Hisab aluminium-dschabr wa-l-muqabalathe Persian mathematician aluminium-Khwarizmiis taken. Four centuries after the appearance of the book appeared its latin translation Ludus algebrae et almucgrabalaeque. Out aluminium-jabr the word "algebra" shortened today developed.
algebra as subsection of mathematics: Definition and arrangement
contentsand methods of algebra have themselves in the course of history so strongly extended that it became heavy to indicate in a scarce definition what algebra actually are. Also it would be not practicably, all aspects of algebra in an encyclopedia article tootreat. We do not differentiate between therefore the following, by any means sharply from each other defined subsections:
Elementary algebra is algebra in the sense of school mathematics. It covers the arithmetic rules of the natural, whole, broken and real numbers, handling expressions, which contain variables, and waysto the solution of simple algebraic equations.
Computer algebra concerns itself with the symbolic manipulation of algebraic expressions.Accurate counting on whole, rational and algebraic numbers as well as on polynomials over these ranges of numbers forms an emphasis. On the theoretical side the search for efficient algorithms as well as the determination of the complexity of these algorithms are to be assigned to this subsection. On thatpractical side a multiplicity of computer algebra systems was developed, which make the computer-aided manipulation possible of algebraic expressions.
Real algebra examines algebraic number bodies, on which an arrangement can be defined. For it positive polynomials are continued to examine.
algebra as mathematicalStructure
as algebra (also: Algebraic structure) one designates also the Grundkonstrukt of abstract algebra: a quantity, on which one or more linkages are defined and apply into certain axioms. Groups, rings, bodies are thus examples of specialAlgebras.
To "algebra" designation also concrete algebraic structures, which are Verallgemeinerungen of the ring term, seealgebra (structure).
A set algebra, sometimes also only algebra mentioned, is a subset of Aof a power quantity of Π (X), with combination and complementation as linkages andthe axiomatic demand X ∈ A.
An σ-algebra is a set algebra, which is finally also concerning a countable infinite consequence from linkages. Σ-algebras form a basis of the masstheorie.
"algebraic" as attribute of numbers, functions, equations
An algebraic equation is only finite an equation, to their formulation many elementary arithmetic operations (addition,Subtraction, multiplication, division) are necessary, in which thus for example no typical analytic functions occur.
One receives the algebraic numbers as zeros from polynomials with rational coefficients; the quantity of the algebraic numbers forms the algebraic conclusion of the quantity of the rationalNumbers.
The algebraic element extends the term of the algebraic number on zeros of polynomials with coefficients from any given body…
S. Long: Algebra. Revised 3rd edition, Springer publishing house 2002.ISBN 038795385X extensive standard work with many resuming notes and tasks. The representation is possibly too abstract for a first entrance.
B. L. van the Waerden: Algebra I, II. Berlin, Springer publishing house 1993. ISBN 3-540-56801-8 the classical author, for its first expenditures into the 1930er years still the title modern trend algebra carried and that for the first time consistently the axiomatic beginning of E. Noether represented. In the language in the meantime somewhat becomes outdated. |
... read more
Customers who bought this book also bought:
Our Editors also recommend:
Elementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figuresPoint Set Topology by Steven A. Gaal Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 Algebraic Topology by Andrew H. Wallace This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961 edition.Algebraic Geometry by Solomon Lefschetz An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Product Description:
and axiomatic approach for easier accessibility. Includes exercises and a |
Linear Algebra For Dummies
Synopsis
Your hands-on guide to real-world applications of linear algebra
Line up the basics — discover several different approaches to organizing numbers and equations, and solve systems of equations algebraically or with matrices
Found In
eBook Information
ISBN: 9780470538166 |
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Biology 111 Lecture 1 - Introduction to Content and Science 8/29/2007What is organismal biology? ! - Study of diversity of life on EarthI. Intro to ScienceA. What is Science? ! ! ! ! ! ! - A way of asking questions and gaining answers according t
Fall 2008Econ 3130Problem Set 1: Budget SetsThis problem set must be done on graph paper. If a problem calls for two or more graphs on the same axes, use dierent colors. 1. You have a wealth of $400 to spend on two commodities. Commodity 1 costs
Fall 2008Econ 3130Problem Set 2: Preferences and UtilityThis problem set must be done on graph paper. If a problem calls for two or more graphs on the same axes, use dierent colors. 1. Adam likes both pizza and wings. More,of course, is always b
Laboratory Exercise Number 1 Getting Started with Matlab Background: This laboratory exercise is intended to begin our introduction to programming in Matlab, its Integrated Development Environment (IDE), and its ability to draw graphs based on an equ
Laboratory Exercise Number 2 Assignment Statements and Functions Hot enough for you?orIt aint the heat, its the humidityorYes, I know its 122E here in Phoenix, but its a dry heat Assignment: This laboratory and its associated homework exercise
Math 115 First Midterm ExamFebruary 7, 2006Name: Instructor: Section Number:1. Do not open this exam until you are told to begin. 2. This exam has 8 pages including this cover. There are 8 questions. 3. Do not separate the pages of the exam. If 10, 2004 anMATH 115 FIRST MIDTERM EXAMOctober 8, 2003 any
MATH 115 FIRST MIDTERM EXAMOctober 8, 2003NAME: INSTRUCTOR: SOLUTION KEY SECTION NO:1. Do not open this exam until you are told to begin. 2. This exam has 9 pages including this cover. There are 10 questions. 3. Do not separate the pages of the
MATH 115 FIRST MIDTERM EXAM SOLUTIONS1. (2 points each) Circle True or False for each of the following problems. Circle True only is the statement is always true. No explanation is necessary.1 (a) log( A ) = log(A).TRUEFalse(b) If f (x) =
Practice Final Exam Each of the following species contains two bonds EXCEPT A) O2 B) HCCH C) CO2 D) CNE) N2 Which of the following species is(are) planar? (i) CO32(ii) XeF4 (iii) H2NNH21.2.A) (i) only B) (i) and (ii) only C) (i) and (iii) only
Math 115 First Midterm ExamSolutionsName: Instructor: Section Number:1. Do not open this exam until you are told to begin. 2. This exam has 8 pages including this cover. There are 8 questions. 3. Do not separate the pages of the exam. If any pagPractice Exam 3a 1. Figure 10.21 from the text shows HCl, with one orbital centered on hydrogen and one orbital centered on chlorine. What is the orbital centered on chlorine?(A) (B) (C) (D) (E)2p 3p 3d 3s 4s2. Which of the following ground sta
Thalassemia results in the under production of globin protein, often through mutations in regulatory genes, or structural abnormalities in the globin proteins themselves. The two conditions may overlap, however, since some conditions which cause abno |
Includes seven chapters: Number Sequences, Re-arranging Formulae, Simultaneous Equations, Quadratic Equations and Trial and Error. Each chapter contains at least one virtual laboratory, which allows students to input their own examples and produces a step-by-step solution. Main theory is general, but the plug-in question books allow for subject-specific, or harder/easier questions and examples to be incorporated. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.