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Important Books For IIT JEE
This book is preferred by most of the students preparing for IIT-JEE and other international Olympiads.Students refer it for 10+2 level exams like:
· IIT-JEE
· AIEEE
· Medical
· Olympiad and other exams
Expert Review:
Lines of Appreciations (Why should I buy this book?)
Chapters like Theory of Equations, Permutation & Combination, Sequences & Series and Complex number have been covered really well.
Room for improvements (Why should I keep away from this book?)
Students need to be very careful while selecting problems as this book comprises plenty of questions which are more Olympiad based.
IIT-JEE aspirants must go through this book to know tricks & important result.
User Reviews:
*
MIND TESTING PROBLEMS
Posted On:Oct 06, 2009 09:25 AM
Review By
RAHUL
THIS IS THE BEST FOR IIT JEE ALGEBRA AS EVERY IIT ASPIRANT SHOULD STUDY FROM THIS BOOK
*
rajesh
Posted On:Aug 12, 2009 10:06 AM
Review By
rajesh thakral fazilka
this is the book which coverd whole iit algebra syllabus after covering this book no need to cover any objective book
*
ALGEBRA IS GIVEN A NEXT LEVEL
Posted On:Jun 15, 2009 02:11 PM
Review By
NEELESH
I refered this book but i found the questions were good up to some level,but at this period where a student just cant depend on iit he has to pay attention to aieee and other state entrances too for which this book is way too much....
*
SHM
Posted On:May 26, 2009 01:00 AM
Review By
Arpit Kumar Mishra
i can't solve the problems . Please give me some advice.
*
PROBLEMS FOR THE NOVICE AS WELL AS THE EXPERT!
Posted On:May 09, 2009 02:06 PM
Review By
PRASHANT.C
Problems in this superb book are carefully graded so that even a beginner can become an expert in algebra.Arihant algebra contains a treasure trove of problems which every IIT aspirant would relish.{Complex number,Theory of equations etc. are really marvellous in this book}.
*
PROBLEMS FOR THE BEGINNER AS WELL AS THE GRANDMASTER!!
Posted On:May 08, 2009 02:42 AM
Review By
Prashant.C
Arihant Algebra has a collection of carefully graded problems and 3 level exercises .the book is in such a good shape that the students feel at ease while going through the problems .As far as concept clearing is concerned this is by far the best book.Really this book is jackpot for every IIT aspirant!
*
ULTIMATE THEORY&PROBLEMS
Posted On:Apr 02, 2009 03:27 AM
Review By
HAROON
FRIENDS, THIS IS THE BOOK WHICH EVERY IIT ASPIRANT MUST HAVE.THE WAY THE PROBLEMS BEING ASKED ARE AWSOME.AS FAR AS ALGEBRA IS CONCERNED,THIS IS THE BEST BOOK. |
Maths ... YUK! Love it or hate it, you can't do Biology without it! Maths, calculations or data handling of some description form about 15% of the marks for the modular exams! This rises to 50% for the ISA or EMPA component. Without a clear vsion of this facet of biology, you will inevitibly struggle to achieve a high grade. To make matters worse, each board publishes a set of minimum mathematics skills requirements that they expect you to carry over from GCSE.
Have you forgotten stuff like significant figures, powers, rearranging equations? Maybe your reading garphs and calulating increses and decreases in GCSE fell a bit short of the marks?
No worries!
CT Publications has produced the perfect solution! A book that not only takes you through the entry mathematical requirements, but takes you trhough a step-by-step process in dealing with ALL types of calculations you will meet in AS biology for AQA, OCR, Edexcel and WJEC.
There's loads of exam practice questions too! With mark schemes to make sure you get your preparation bang on! |
More About
This Textbook
Overview
Exact solutions of differential equations continue to play an important role in the understanding of many phenomena and processes throughout the natural sciences in that they can verify the correctness of or estimate errors in solutions reached by numerical, asymptotic, and approximate analytical methods. The new edition of this bestselling handbook now contains the exact solutions to more than 6200 ordinary differential equations. The authors have made significant enhancements to this edition, including:
An improved format that allows for an expanded table of contents that makes locating equations of interest more quickly and easily
Expansion of the supplement on special functions
This handbook's focus on equations encountered in applications and on equations that appear simple but prove particularly difficult to integrate make it an indispensable addition to the arsenals of mathematicians, scientists, and engineers alike.
The new edition of this bestselling handbook contains the solutions for an additional 700 ordinary differential equations (ODEs) and now provides more than 6200 solutions. It also includes a new introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ODEs, along with basic definitions and discussion of using modern computer algebra systems to solve ODEs. Subsections are now organized into paragraphs, and the rearrangement of equations into these paragraphs allows for an expanded table of contents that helps readers find equations more quickly. More than ever, the handbook is indispensable to a wide range of mathematicians, scientists, engineers, and |
This bilingual problem-solving mathematics software allows you to work through 84102 trigonometric problems with guided solutions, and encourages to learn through in-depth understanding of each solution step and repetition rather than through rote memorization. The software offers tasks on simplification and evaluation of trig expressions, proofs of trig identities and solutions of trig equations. All the basic trigonometric and inverse trigonometric functions are included. Each solution step is provided with its objective, related definition, rule and underlying math formula or theorem. A translation option offers a way to learn math lexicon in a foreign language. Test preparation options facilitate development of printable math tests and homeworks, and automate preparation of test variants around each constructed test. A number of variant tests are ready for students to review and reinforce their skills. The software supports bilingual interface and a number of interface styles. Free fully functional trial version of this program is availableThis is an advanced expression and conversion calculator. Vast array of built-in functions, constants and confersion operations that can be extended with your own user-defined functions. Now with graphs.
MaTris is a nice program for practicing the basic operations of arithmetic. The calculation method is preselectable. It includes simple counting exercises, addition with symbols, addition/subtraction, multiplication and division.
GraphiCal is a programmable graphics calculator which lets you visualize expressions and formulas as graphs in a chart. Creates animated video clips from a sequence of graphs. Built-in functions (>50) include integration, root finding .. |
Lecture: Parallel Preconditioning Techniques for Linear Systems
Description:
The term preconditioning comprises as set of
techniques to modify a given system of linear equations such
that its iterative solution is easier than the solution of
the original system. Traditional algorithms for
preconditioning are often inherently sequential. When
designing parallel preconditioning algorithms, it is
crucial to make sure that increasing the level of
parallelism does not lead to a slower convergence behavior.
Audience:
This interdisciplinary course is offered to students from
computer science, mathematics, natural sciences, and engineering
disciplines. |
Math Club
The Math Club is organized to encourage
interest in mathematics, support students in mathematics classes, and
provide an informal setting for students to share ideas and participate in
mathematical activities. This is accomplished through regular meetings. At
these meetings, invited speakers (UM students, UM faculty, and guests from
other institutions) present colloquia, films are shown, problems are
presented, and students socialize over refreshments, asking questions and
discussing their thoughts and concerns. |
Welcome: Algebra - Linear Equations Description: Developing students basic skills of mathematics while giving them a chance to see the relevance of Linear Equations and how they can apply this concept to solve real world problems. Grade Level:
9-12 Curriculum:
Math Keywords: Constant, Equation, Linear, Variable. Author(s): Tsietsi Lee |
link below is the entry point to a Pomona College undergraduate course that uses mathematical processes, ranging from difference and differential equations to probability, to address topics in biological systems.
Introduces the fundamentals of machine tool and computer tool use. Students work with a variety of machine tools including the bandsaw, milling machine, and lathe. Instruction given on the use of the Athena network and Athena-based software packages including MATLABĺ¨, MAPLEĺ¨, XESSĺ¨, and CAD. Emphasis on problem solving, not programming or algorithmic development. Assignments are project-oriented relating to mechanical engineering topics. It is recommended that students take this subject in the first IAP after declaring the major in Mechanical Engineering. From the course home page: This course was co-created by Prof. Douglas Hart and Dr. Kevin Otto.
Numerical Computing with MATLAB is a textbook for an introductory course in numerical methods, MATLAB, and technical computing. It emphasizes the informed use of mathematical software. Topics include matrix computation, interpolation and zero finding, differential equations, random numbers, and Fourier analysis.
Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed. This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems are presented. Probability theory and its use in physical modeling is covered, as is the statistical analysis of data and parameter estimation. The finite difference and finite element techniques are presented for converting the partial differential equations obtained from transport phenomena to DAE systems. The use of these techniques will be demonstrated throughout the course in the MATLABĺ¨ computing environment.
Most books that use MATLAB are aimed at readers who know how to program. This book is for people who have never programmed before. As a result, the order of presentation is unusual. The book starts with scalar values and works up to vectors and matrices very gradually. This approach is good for beginning programmers, because it is hard to understand composite objects until you understand basic programming semantics. |
Learning Upgrade
Online Courses Featuring Songs, Video & Games
800-998-8864
Teaching Content
Curriculum of Pre-Algebra Upgrade
The map below shows the 60 lessons that students must complete in order to finish the Pre-Algebra Upgrade course. Students begin with pre-algebra basics and move on to fractions, decimals, percents, exponents, linear functions, inequalities, graphing, geometry, statistics, and probability. Below the map is a table listing the content of each level. |
Let's Go Learn's Diagnostic Online Math Assessment: Pre-Algebra (DOMA: Pre-A) serves as the foundation for LGL Pre-Algebra Edge. DOMA: Pre-A diagnostically assesses students across 14 different areas of math knowledge that teachers consider essential for success at the Algebra I level, adapting to students as they respond to each question in the online program. Immediately after the assessment, students who qualify for instruction are automatically transitioned into powerful online pre-algebra lessons, addressing only the skills that each student requires.
Featuring a scoring system designed to encourage intrinsic motivation in students, LGL Pre-Algebra Edge rewards students frequently with positive feedback as they move ahead. Parents can monitor their student's progress, and repeat assessments to clearly show advances in learning. |
Course Description:
This is an introductory college mathematics course in finite difference equations
and linear algebra. Topics include sequences, differences, linear
and nonlinear difference equations, systems of difference
equations, numerical solutions of linear and nonlinear equations,
and analytical techniques for solving linear systems using linear algebra.
Applications from many fields are studied and the role of
mathematical modeling is a central focus. Formal computer labs
are a part of the course each week, with spreadsheets being the
primary software employed. This course satisfies a general liberal
arts requirement for all students and the mathematics requirement
for business majors. Prerequisite: three years of high school mathematics
through Algebra II.
Grading: Homework and In Class Work: 20%
Labs: 15%
Exam 1: 15%
Exam 2: 15%
Exam 3: 15%
Final Exam: 20%
There will be four exams in this class, a midterm covering Chapter 1 on Wednesday, September 17,
a midterm covering Chapter 2 on Monday, October 27, a midterm on Friday, Nobember 21, and a final
at the end of the term. In order to pass this class, all students
must take all four exams.
I will use a no-curve grading policy to assign final grades:
above 90% = A, 80% - 89% = B, 70% - 79% = C, 60% - 69% = D, below 60% = F.
Homework:
There will be homework due at the beginning of almost every class.
I will not accept any late homework unless you make some arragement with
me before the class period when the homework is due. I will drop your
two lowest homework scores, so you can miss two homeworks without any penalty.
In Class:
I will assign a section of the text for you to read before each class.
Rather than lecturing, I prefer to ask you questions about what we've read, and guide
a class discussion about the material, so if you haven't done the reading it is very
obvious! There will also be many short assignments that you will do in small groups
during class. Often these will require a calculator so always bring one with you to class.
Labs:
Thre are lots of things that you can do with pencil and paper, or with the help of a calculator. But
using computers can make your work much more powerful. So we will meet in the computer lab (Fortin 115)
almost every Friday, so that you can use Excel, a spreadsheet program, to do lab project that would
take way too much time to do just with pencil and paper. You may do the lab individually or in
groups of two. One week after we do the lab, you must turn in a lab report answering all the questions
in the lab, and briefly explaining what you did. This lab report must be typewritten and
professional in style. |
Environmental mathematics seeks to marry the most pressing challenge of our time with the most powerful technology of our time - mathematics. This book does this at an elementary level and demonstrates a wide variety of significant environmental applications that can be explored without resorting to calculus. Environmental mathematics in the classroom includes several chapters accessible enough to be a text in a general education course, or to enrich an elementary algebra course. Ground-level ozone, pollution and water use, preservation of whales, mathematical economics, the movement of clouds over a mountain range, at least one population model and a smorgasbord of 'newspaper mathematics' can be studied at this level and would form a stimulating course. It would prepare future teachers not only to learn basic mathematics, but to understand how they can integrate it into other topics that will intrigue students [via] |
Welcome to Algebra 1! Every student in the state is required to take this course in order to graduate from high school. We will cover all basic algebra topics: data analysis, solving equations, graphing lines, simplifying expressions, and exponents. These topics will be applied to real-world situations. I look forward to working with each one of you! |
Discrete Mathematics
The widespread use of computers and the rapid growth in computer science have led to a new emphasis on discrete mathematics, a discipline which deals with calculations involving a finite number of steps. This book provides a well-structured introduction to discrete mathematics, taking a self-contained approach that requires no ancillary knowledge of mathematics, avoids unnecessary abstraction, and incorporates a wide rage of topics, including graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra.
Amply illustrated with examples and exercises.
show more show less
Numbers And Counting
Integers
Functions and counting
Principles of counting
Subsets and designs
Partition, classification, and distribution
Modular arithmetic
Graphs And Algorithms
Algorithms and their efficiency
Graphs
Trees, sorting, and searching
Bipartite graphs and matching problems
Digraphs, networks, and flows
Recursive techniques
Algebraic Methods
Groups
Groups of permutations
Rings, fields, and polynomials
Finite fields and some applications
Error-correcting codes
Generating functions
Partitions of a positive integer
Symmetry and counting
Table of Contents provided by Publisher. All Rights Reserved.
List price:
$32.50
Edition:
1985
Publisher:
Oxford University Press, Incorporated
Binding:
Trade Cloth
Pages:
400
Size:
6.38" wide x 9.50" long x 1.31" tall
Weight:
2.07 |
Mathematics
The mathematics department is located on the first floor of the new building. Each room is equipped with an interactive whiteboard. Currently there are 12 teachers in the department, a dynamic team with a passion for mathematics.
We teach the Ordinary and Higher level syllabus to both Junior and Leaving Certificate standard and offer Foundation level where appropriate. The IB course offers Higher level, Standard level and Maths Studies. The classes are set according to the student's ability and we cater for students of all abilities.
In First year all students compete in the Junior mathematics competition. This competition helps to discover those students with a very high standard of mathematical ability. Based on Junior Certificate results, some students are invited to compete in The Irish mathematical Olympiad competition. In Sixth year a team represents the college in a national Leaving Certificate mathematics competition.
The Project Maths course started in September 2010 with changes to papers as follows: |
USING TI-83 GRAPHING CALCULATOR IN PRECALCULUS
1.0 General Information 2.0 Calculator Basics 2.1. Turning the Calculator ON/OFF 2.2. The Keyboard 2.3. Predefined Functions and Constants 2.4. The Home Screen 2.5. Adjusting the Contrast on the Screen 2.6. Selecting Items from a List or a Menu 2.7. The CATALOG Feature 2.8. Inserting and Deleting Characters 2.9. Editing and Re-executing Lines of Code 2.10. Interpreting Error Messages 2.11. Transferring Programs Between TI-83s 2.12. Executing a Program 3.0 Using the CBL System 3.1. Creating a Graph Using a Motion Detector 3.2. Matching a Graph Using a Motion Detector
4.0 Analyzing Data Collected by the CBL System 4.1. Examining the Table of Data 4.2. Viewing the Graphs 4.3. Tracing the Graphs 4.4. Zooming In 5.0 Arithmetic Operations and Expressions 5.1. Order of Operations 5.2. Entering and Evaluating an Expression 5.3. Subtraction and Negation 5.4. Implied Multiplication 5.5. Exponentiation 6.0 The MODE Key 6.1. Float/0123456789 6.2. Radian/Degree 6.3. Connected/Dot 6.4. Full/HorizontaVGraph-Table Screens 7.0 Using Variables 7.1. Real Variable Names 7.2. Assigning a Value to a Variable 7.3. Clearing a Variable 8.0 The TEST Menu 8.1. Relational Operations 8.2. Boolean Operators 9.0 The MATH Menu 9.1. Representing a Value as a Fraction 9.2. Approximating the Minimum or Maximum Value of a Function 9.3. The Absolute Value Function 9.4. The Round Function
9.5. The Greatest Integer Function 9.6. Finding the Smallest or Largest Item in a List 10.0 Representing a Function Symbolically 10.1. Storing a Function in the Y= Editor 10.2. Specifying the of Domain a Function 10.3. Selecting a Function Using the VARS Key 10.4. Evaluating a Function Stored in the Y= Editor 10.5. Creating New Functions from Old 10.6. Selecting and De-selecting Functions in the Y = Editor 11. Representing a Piecewise-Defined Function
12.0 Representing a Function Graphically 12.1. Choosing the Display Styles 12.2. Adjusting the Viewing Window 12.3. Viewing the Graph
13.0 The FORMAT Menu 13.1. GridOff/GridOn 13.2. LabeIOff/LabeIOn 14.0 The TRACE Feature 14.1. Tracing a Curve 14.2. Moving Among Curves 14.3. Evaluating a Function Using the TRACE Feature 15.0 The ZOOM Feature 15.1. ZBox 15.2. Zoom In and Zoom Out 15.3. ZStandard and ZDecimal 15.4. ZTrig 15.5. ZoomStat 15.6. ZoomFit 15.7. ZPrevious 16.0 Representing a Function as a Table 16.1. Displaying Values of a Function in a Table 16.2. Evaluating a Function Using a Table 16.3. Viewing a Table and a Graph Together 16.4. Clearing a Table 17.0 Representing a Discrete Functioniz Brondos The Adventures of Super Class Man, Yet Another Superhero DoME programmer: Help, I'm going crazy trying to keep track of our inventory! Back in the old days, it was easy because all we had to keep track of were books and CDs. Now we have v
Liz Brondos 10/28/03 Discussion Between an Angry Maintenance Programmer and his Nave Assistant Maintenance Programmer: I've been looking at this code you wrote for the application we're both working on, and, frankly. Nave Assistant: Yes? Maintenance
CSCI 250 Spring 08GOLDWEBER 3/28/08Homework 7Due Date: Wednesday, April 4, 2008. There is a possible 38 points for this homework assignment. Problem 1. (20 pts.) Draw a transition diagram for a Turing machine accepting each of the following lang
CSCI 250 Spring 08GOLDWEBER 3/10/08Study Guide #2Chapter 3 of the text in addition to all Web pages associated with the course. Push-Down Automata: Overall definition, general idea of, and how they operate: final state vs empty stack. The eq
CSCI 250 Spring 05GOLDWEBER 2/21/05Homework 4Due Date: Monday February 28, 2005. There is a possible 71 points for this homework assignment. Problem 1. (16 pts.) In each case, say what language is generated by the context-free grammar with the i
The Power Set of a Countably Infinite Set is UncountableTheorem 1 If S is a countably infinite set, 2S (the power set) is uncountably infinite. Proof: We show 2S is uncountably infinite by showing that 2N is uncountably infinite. (Given the natural
CSCI 250 Spring 06GOLDWEBER 3/13/06Homework 7Due Date: Monday, March 20, 2006. There is a possible 46 points for this homework assignment. Problem 1. (20 pts.) In each case, show using the pumping lemma that the given language is not a CFL. a) L
CSCI 250 Spring 06GOLDWEBER 3/27/06Homework 8Due Date: Friday March 31, 2006. There is a possible 38 points for this homework assignment. Problem 1. (20 pts.) Draw a transition diagram for a Turing machine accepting each of the following languag
CSCI 250 Spring 05GOLDWEBER 3/9/05Homework 6Due Date: Monday March 14, 2005. There is a possible 46 points for this homework assignment. Problem 1. (20 pts.) In each case, show using the pumping lemma that the given language is not a CFL. a) L =
CSCI 250 Spring 05GOLDWEBER 1/12/05Homework 1Due Date: Friday January 21, 2005. There is a total of 44 points for this homework assignment. Problem 1. (3 pts.) Let L be a language. It is clear from the definitions that L+ L . Under what circums
CSCI 300 Programming Languages, Fall 2005 Gary Lewandowski Exam Review Notions These questions are taken without modification from previous exams I have given. You may not be familiar with some of the languages mentioned, but you can expect the type
Presentation HW #1: Prolog1) The nature of Prolog sometimes allows for predicates to be useful in ways other than what was originally intended - by changing the order of the arguments or by replacing an explicit argument with a variable and vice ver
PROgramming in LOGicPart IIBy Forrest Pepper 12/7/07Anatomy of a Program We discussed the three main constructs of a Prolog program Facts contain a property or state a relationship between two or more objects. These are considered always true
1. What are the primary differences between certification of a company's management practices and its management systems? What is your opinion about which system would be more likely to advance the objective of sustainable forest management? Why? 2.
Quadratic Functions Revisited When we first studied quadratic functions, we saw that their graphs are always parabolas and their formulas can be expressed in standard form as y = f (x) = ax 2 + bx + c , and (sometimes) in factored form as y = f (x) =
Power Functions Two quantities are in direct proportion if one is a constant multiple of the other; alternatively, one can say that the one quantity varies directly with the other. So for instance, the volume V of a sphere is in direct proportion to
Logarithms It is not too hard to see that the inverse function of any linear function (with nonzero slope) is another linear function. Things are not as straightforward for exponential functions: the inverse of an exponential function cannot be anoth
Functions The idea of a mathematical function was only developed about 150 years ago. It has become the central concept in applied mathematics, used widely in mathematical modeling as a way to represent quantifiable phenomena. A function is a rule (o
Linear regression Data collected from measurements of real phenomena are often well-described by linear functions. However, such data is generally subject to errors or other "noise" that corrupts the measurements, so a graph of the points in the data
Arithmetic of Functions Functions with the same domain set and outputs that are measured in the same units can be added or subtracted to build new functions. [Example: p. 379, #26(a), 7] Functions with the same domain can also be combined by multiply
MATH 120 Elementary Functionse and continuous compoundingWe have seen how compound interest works; as an investment method, it is far preferable to simple interest. Simple interest investments grow linearly, since the interest payment is a certai
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Answer Key1. How did the slave trade start in the first place? a. The Portuguese were the first Europeans to go to Africa for slaves, and they went there in the first place for Gold. b. They were captured during war or kidnapped during raiding parti
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Math 391: Homework 8 (due M November 26)This is the last GRADED homework. Note it is not due until MONDAY of dead week. There will be some more reading next week and some review questions to come too. Part I: reading. Read section 4.1 again (especia
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This document describes MathML and its
use within DAISY books. It is meant to be a short starter with further
references. The target audience is primarily teachers and students, as well as
publishers and developers of DAISY reading products and services.
Some of the content here is derived
from References 1 and 5 below. I hope that this document provides information
helpful to the audience!
1.Introduction to the issues
Readers with print disabilities have used
audio books for a long time. First introduced on cassette tapes for leisure
reading, audio books have also been used for educational purposes. With the adoption
of the DAISY Standard, digital talking books have become the de facto standard and content production
on CDs has been gradually replacing the cassette tape medium. DAISY books may
contain audio and/or text, as well as images.
One main problem of conventional audio
books and paper braille books affecting educational content is that mathematics
and other formulae were treated as either text or images. Hence, there wasn't
enough structure information to enable accessible technology to present the
formulae appropriately via audio or braille. Since the formal approval of the
MathML-in-DAISY Specification in February 2007 as the first extension to the
DAISY Standard, it is now possible to produce and use books that present
mathematical content in a synchronized and structured and therefore accessible
way.
2.What is the DAISY/NISO Standard?
DAISY is an acronym which stands for Digital Accessible Information SYstem. The term is used to refer to a
standard for producing accessible and navigable multimedia documents. In
current practice, these documents are digital talking books, digital text
books, or a combination of synchronized audio and text books.
DAISY is a globally recognized
technical standard to facilitate the creation of accessible content. It was
originally developed to benefit people who are unable to read print due to a visual
impairment, but it also has broad applications for improved access to printed material
and other media in the mainstream. The DAISY Standard has been evolving over
the last several years and has been officially recognized by an American standards-making
body in 2005. Whereas books produced in the DAISY 2.02 standard are the most common
ones by far, the use of math is only possible in the new DAISY/NISO Standard
that was introduced in 2005. This new standard is officially called
"ANSI/NISO Z39.86-2005" but commonly known as "DAISY 3".
The DAISY Consortium has been selected
by the National Information Standards Organization (NISO) as the official
maintenance agency for the DAISY/NISO Standard, officially, the ANSI/NISO
Z39.86, Specifications for the Digital Talking Book. A more thorough
description of the DAISY/NISO Standard is given in Reference 6, below.
3.What is the MathML Standard?
MathML is a W3C recommendation. The
W3C is the world-wide organization that creates the standards for the Web. The
MathML specification is, as a consequence, a normative document, which allows
MathML to be highly compatible. Also, it was created by the Math Working Group
composed of people from several countries and diverse scientific fields, so
MathML takes into account the needs from many different professions, countries,
and uses.
MathML is a so called "XML" (eXtensible Markup Language)
language. This means that new features can be added as needs arise – see, for instance, the Arabic mathematical notation
– or, can become deprecated if experience shows
they are useless. Finally, MathML can be used in combination with other Web
languages. As a bonus, MathML can easily be created with existing formula
editors and be exported to or imported from computer algebra systems like Maple
and Mathematica. It can be processed by search engines such as Google,
therefore providing multiple benefits to the user. Please note that the use of
so called "presentation MathML" is provided for DAISY/NISO, in contrast to
"content MathML".
An example of the formula "-
a/b" expressed in presentation MathML is:
<math
xmlns='
<mrow>
<mo>-</mo>
<mfrac>
<mi>a</mi>
<mi>b</mi>
</mfrac>
</mrow>
</math>
As you can see, no one would want to read
or write MathML directly. The use of additional tools is therefore necessary.
One of the biggest advantages of XML
is that it has to be well-formed, so that if you open a tag you have to close
it later on. This way, malformed MathML may be spotted immediately during the
validation process; inconsistencies are therefore avoided.
4.How do DAISY and MathML act together?
The MathML extension is the first
extension of the DAISY specification. The approach taken makes use of the
existing extension mechanism specified by Z39.86-2005.
There are many problems associated
with the use of images by authors and readers with and without visual
disabilities when working with digital documents containing math. These include:
§the
inability to magnify the image or change its colors
§fixed
speech (based on alt text) that cannot be tailored to an individual's needs
§no
local navigation and exploration of the mathematical structure
§no
synchronized highlighting of the text with the image and audio
§inability
to be translated to a braille math code
MathML offers a solution to these
problems. Because it is an XML application and has been designed to work with
XHTML, using MathML in Z39.86-2005 was the direction that the MathML Modular Extension
Working Group pursued.
MathML is not directly read.
Especially for a blind person using a braille display, the DAISY reader has to
convert MathML into a notation suitable for that person. Currently, there are
literally dozens of different math notations used worldwide. The use of LAMBDA,
LaTeX and Nemeth is planned by different organizations working on DAISY readers.
Using MathML within DAISY documents allows for a unified and well-defined
storage, while the presentation of the math content to the user is dependent on
the player used. For some possibilities on examples how math content may be
presented to the user see chapter 98NVaaaa@36C3@.
5.What if my reader doesn't support MathML (fallback issues)
The MathML-in-DAISY Specification
groups players into 3 categories:
§Players
that do not comply with this specification. These players know nothing about
MathML. They do not extract the altimg and/or alttext from a <math> tag
nor do they apply a stylesheet to transform the math to an image group. These
players are referred to as MathML-unaware players.
§Players
that conform to this specification but can not natively render the MathML. They
fall back to using either the XSL transform or grab the alttext or altimg
attributes from the <math> tag. These players are referred to as Basic
MathML players.
§Players
that natively support MathML. These players are referred to as Advanced MathML
players.
This modular extension is meant to
encourage advanced MathML players to provide a rich experience when reading
mathematics. However, the modular extension also recognizes that mathematics
may not be a focus for all vendors and provides a fallback mechanism. For the
common case of an audio only player, a predefined audio rendering is provided.
There are no local navigation points within that rendering, which is something
an advanced MathML player might provide. An advanced MathML player could allow
a user to explore the structure of the expression tactilely using a refreshable
braille display and/or with audio without having to listen to the expression in
its entirety. A future version of the DAISY MathML specification may add finer
SMIL granularity within the math audio stream. For players that do not support
MathML, an alternate image is provided as part of the MathML. Basic MathML
players must either recognize MathML enough to locate the image reference
provided on the MathML element, or they must support XSLT and apply a supplied
transform indicated in the metadata of the DTB Package file.
6.Where do we stand now?
The MathML-in-DAISY extension was
formally approved and is therefore ready for use. Production tools are currently
in development for the production of DAISY math books. One particular DAISY
software reader has been demonstrated as capable of displaying math content at
an international conference in March 2008. As new products and services are developed
by DAISY Member organizations, they are announced on the DAISY Consortium Web
site, and MathML capabilities are specifically tracked.
The best way to overcome the chicken and
egg problem is to produce DAISY books using the math extension. With the
fallback capabilities, their use would be possible today with existing players,
while new developments would add more possibilities and features.
7.Summary for students (users)
If you want to use digital books to
learn math, physics or chemistry, DAISY books with MathML are just for you. In
a little while, the first books should be available. Until then, keep yourself
informed, ask your library about digital math books and get yourself a new advanced
MathML DAISY reader.
8.Summary for teachers (producers)
Ask your software vendor about DAISY
production tools with math capabilities. If you don't know exactly what DAISY
books are, then have a look at the DAISY Consortium home page ( and watch out
especially for these new production tools.
9.Summary for libraries and publishers
Make yourself comfortable with DAISY
books and MathML. Explore the references and start producing and testing DAISY
books without math just to get a feeling for the issues at hand. Get yourself some
new production tools with math capabilities as soon as they are available.
Perhaps you can attend some conferences or meetings?
9qqajugGbabaaaaaaaaapeGaa8NVaaaa@36C4@. Math for the
blind - Presentation details for the curious
By separating the storage from the
presentation, the user as well as the publisher experience major benefits. In
regular digital texts, everybody generating or converting literature for the
blind has to choose the way to store math content by using a certain notation
(LaTeX, Nemeth, AMS, Marburg,
LAMBDA, or other). As the blind user would read the text exactly as it was
written, he would have to know this same notation as all of the books from this
producer usually contained math in this notation (and this notation alone). To
read these documents, everybody would have to learn this notation. Students from
other universities trying to access the different digital libraries had to
learn the different appropriate math notations as well, if only to read a
single book per notation. Student exchange and combined digital repositories
for the blind were substantially limited by this factor.
With DAISY books and MathML, the publisher
now only has to be concerned about proper MathML within the document. The
reader may then choose a DAISY player, either a hardware player, a software
player on a computer, or a mobile phone/PDA, which supports the math notation
of choice. Reading DAISY books from organizations unable to support specific
math notations is now possible because of the uniform storage of math content
as MathML. |
Mr
show more show less
Forward
Preface
Acknowledgments
The Calculator
Using the Calculator
Review of Basic Math Fundamentals
Numbers, Symbols of Operations, and the Mill
Addition, Subtraction, Multiplication, and Division
Fractions, Decimals, Ratios, and Percents
Math Essentials and Cost Controls in Food Preparation
Weights and Measures
Using the Metric System of Measure
Portion Control
Converting Recipes, Yields, and Baking Formulas
Food, Recipe, and Labor Costing
Math Essentials in Food Service Record Keeping
Determining Cost Percentages and Pricing the Menu
Inventory Procedures and Controlling Costs
Purchasing and Receiving
Daily Production Reports and Determining Liquor Costs
Essentials of Managerial Math
Front of the House and Managerial Mathematical Operations
Personal Taxes, Payroll, and Financial Statements
Appendix A
Glossary
Index
List price:
$124.95
Edition:
6th 2012
Publisher:
Delmar Cengage Learning
Binding:
Trade Cloth
Pages:
384
Size:
8.50" wide x 10.75" long x 0.75 Math Principles for Food Service Occupations - 9781435488823 at TextbooksRus.com. |
SpeedStudy 8th Grade Math PC Mac New Sealed
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Features 25 standards-based lessons with skill-building animations
Reinforce learning with 300+ interactive quiz questions
Includes searchable database of over 500 key terms
Boost grades and test scores! Using step-by-step animations, real-time quizzes and a fun 3-D interface, Quickstudy gives students the tools they need to master key math concepts with over 25 lessons. Take the stress out of 7th Grade middle school math |
Students will benefit most from reading and interpreting highly regarded scientific journalism, introductory texts, and essays about scientific topics. Mathematics is the exploration of how quantities relate to each other. Students usually find trouble in mathematics when they lose sight of its ultimate simplicity. |
Students will receive a textbook and answerkey for class. Parents will be provided. with answerkeys to monitor students at home work. (** SEE MATH NOTES AT THE TOP ...
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Courses: Non-FL Students
Course Name:
Algebra II
Course Code:
1200330
Honors Course Code:
1200340
AP Course Code:
Description:
This course allows students to learn while having fun. Interactive examples help guide students' journey through customized feedback and praise. Mathematical concepts are applied to everyday occurrences such as earthquakes, stadium seating, and purchasing movie tickets. Students investigate the effects of an equation on its graph through the use of technology. Students have opportunities to work with their peers on specific lessons.
Algebra II is an advanced course using hands-on activities, applications, group interactions, and the latest technology |
Emphasizes proof (combinatorial and non-combinatorial) throughout in the text and exercises, and homework problems have been designed to reinforce the book's main concepts
Contains many examples that are not present in most discrete mathematics books, including the deferred acceptance algorithm, the Boyer-Moore algorithm for pattern matching, Sierpinski curves, Persian rugs, adaptive quadrature, the Josephus problem, the five color theorem, and relational databases
Includes Quick Check problems at critical points in the reading, and it is intended for these problems to be solved before moving on to the next section in the chapter. Also, many worked examples can be found throughout, which are used to motivate the presented theorems and illustrate the conclusion of a theorem.
Features many important examples from the field of computer science, including the Halting problem, Shannon's mathematical model of information, XML, and Normal Forms in relational databases |
Specification
Aims
Brief Description of the unit
The notion of an 'integrable' differential equation can be thought of as a generalization of a
differential equation which has an explicit solution. Such equations possess special properties
such as an infinite number of conservation laws. Informally they are the opposite of equations
which have a 'chaotic' behaviour. Integrable differential equations are important in both pure
mathematics and in applications. They are a rich source of interesting algebraic and geometric
structures. The course describes various ways of making the idea of 'integrability' precise.
We introduce the main mathematical structures used in integrability theory and study various
examples of integrable equations. This course builds on the study of differential equations and
matrix theory in the first year.
The level 4 version of this course unit will be made up out of the level 3 version together with some additional reading material. |
6th Grade Honors English
Students will be challenged to develop literacy skills by exploration and application of English Language Arts concepts and practices. Reading, online discussion and activities, as well as practice, will form the structure within which students will learn literacy skills. Challenge and expectation will be enhanced consistent with abilities of students who have academic talents.
7th Grade Honors English
This course is designed to challenge students with academic talents to explore and acquire advanced seventh grade literacy skills. Recognizing that some students are ready for analytic and critical thinking, lessons are designed to grow these important thinking skills, while developing advanced literacy skills and a love of literature. Course elements include advanced novel study, investigation of the short story, grammar skill development, and writing in multiple genres.
8th Grade Honors English
Students will be challenged to master the standards of eighth grade English Language Arts when they study advanced grammar and diagramming, writing in multiple genres and writing as a social activity. Students will prepare and present a research project, and evaluate and critique media formats as they will be challenged to apply discernment in all aspects of literacy.
Pre-Algebra
Pre-Algebra helps students acquire problem-solving skills and facilitates a connection to more rigorous courses coming in later years. It centers on three themes: arithmetic, pre-algebra and pre-geometry. Students will discover the world around them in a variety of enrichment activities, group projects and explorations. The use of graphing calculators, online manipulatives and other computing experiences take learning mathematics beyond the physical classroom into a world far greater than textbook, pencil and paper.
Access to a graphing calculator or familiarity with graphing calculator websites is required for this course.
Algebra
This accelerated Algebra course builds on algebraic concepts introduced in previous courses while preparing students for any standard geometry course. Students will use online manipulatives and graphing calculators to explore equations, expressions and functions in a variety of methods including using graphs, symbols and tables. Students will study linear equations and expressions through their studies of geometry and statistics and will use probability to reinforce concepts of fractions and algebraic functions.
Access to a graphing calculator or familiarity with graphing calculator websites is required for this course.
Geometry
Geometry Online is a high school level math course, taught with middle school-aged students in mind. Students are introduced to geometry through the study of points, lines, angles and shapes. The students explore the world around them by studying reflections and symmetry and measurements like area and volume. Students use their talents for logic while being introduced to the concept of formal proofs, both indirect and coordinate. They will study order while also integrating discrete mathematics and algebra. This course employs the use of online math manipulatives, geometry-based computer drawing programs, graphing calculators, real data collection and group projects to make learning fun, relevant, and exploratory.
Spanish I
High school students who struggle with language acquisition should consider taking Spanish I online. Students who take this course will develop basic Spanish listening, speaking, reading and writing skills. Online instruction will use focus on development of vocabulary, as well as using newly developed vocabulary in discourse. Multimedia instruction will enhance the learning experience for those who benefit from alternate instructional methods. As teacher certified to teach Spanish and endorsed to teach students who have learning disabilities will teach the course.
Ready to get started? |
Algebra for College Students
This book provides a comprehensive coverage of intermediate algebra to help students prepare for precalculus as well as other advanced math. The ...Show synopsisThis book provides a comprehensive coverage of intermediate algebra to help students prepare for precalculus as well as other advanced math. The material will also be useful in developing problem solving, critical thinking, and practical application skills. Real World Data and Visualization is integrated. Paying attention to how mathematics influences fine art and vice versa, the book features works from old masters as well as contemporary artists.Hide synopsis
Description:BRAND NEW INSTRUCTOR'S 5TH EDITION WITH SEALED CD SAME AS THE...BRAND NEW INSTRUCTOR'S 5TH EDITION WITH SEALED CD SAME AS THE STUDENT'S EDITION PLUS MAY INCLUDE ANSWERS AND/OR TEACHERS NOTES. We ship DAILY with Free Tracking/Delivery Confirmation.
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Graphing calculator?
Graphing calculator?
I need to get a graphing calculator but I am not sure which one suits me best. I need it for graphing and possibly some more advanced functions. I checked out the prices and the TI-89 is somewhat expensive. It seems a little "hyped" than the other older models. Does the TI-85 have everything the 89 has, just on older hardware?
I've owned a TI-83, a TI-84+, and I currently own a TI-89 Titanium, and I must say that the TI-89 T blows the other ones away.
There is much more memory integrated in the calculator, it is much faster. It is also much easier to use the more advanced functions (IMO), and it looks a lot nicer. I would really suggest a TI-89T, you won't be disappointed.
I'm going with Fragment. I own a TI-89 Titanium and it's a very good calculator, has plenty of features (symbolic differentiation and integration, simple ODEs, 2D curve sketching, 3D graphing, simultaneous linear equation solver...), and the learning curve isn't steep at all.
A word of warning, though - don't get addicted to it. If you're still in high school of your first year of college, try to work out stuff by hand. If you keep using your calculator to do simple calculations, you're gonna go rusty fast.
What kind of class do you need this calculator for? For other stuff, I use the European equivalent of this calculator, and it does plenty of stuff (but it doesn't have graphing capabilities), like numerical integration and differentiation, quadratic and cubic equations, up to 3 simultaneous equations, complex numbers, statistical functions, ... |
Measure and Integration for Use
9780198536086
ISBN:
0198536089
Pub Date: 1985 Publisher: Oxford University Press, Incorporated
Summary: Although of unquestioned power and practical utility, the Lebesgue Theory of measure and integration tends to be avoided by mathematicians, due to the difficulty of obtaining detailed proofs of a few crucial theorems. In this concise and easy-to-read introduction, the author demonstrates that the day-to-day skills gleaned from Legesgue Theory far outweigh the effort needed to master it. This compact account develops ...the theory as it applies to abstract spaces, describes its importance to differential and integral calculus, and shows how the theory can be applied to geometry, harmonic analysis, and probability. Postgraduates in mathematics and science who need integration and measure theory as a working tool, as well as statisticians and other scientists, will find this practical work invaluable.[read more] |
Ages: 10+ Grade Levels: 5-12 Availability:Sold out and no longer available from Timberdoodle Co. Product Code:345-500
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Technology and the Future of Mathematical Problem Solving
04.11.13 @ 09:00 AM - 10:00 AM
Location: Kellas 104
The advent of sophisticated computer programs into the classroom has made many problems found in the traditional mathematics curriculum somewhat obsolete for they can be easily solved by software. The presentation (aimed at the general audience) will discuss ways of developing problems that are both technology-enabled and technology-immune in the sense that whereas technology may be used in support of problem solving, its direct application is not sufficient for achieving the end result. |
I am happy to see that others besides myself have tried to use GAP as
a pedagogical aid in teaching abstract algebra. I am currently teaching
an undergraduate course, using Gallian's book, which I find to be an
excellent text. My students are primarily computer programming majors,
who take abstract algebra because they have to. Thus, one would think
that my class is an ideal laboratory for introducing GAP to students.
However, I can only report limited success. Perhaps some of you in the
forum can give me some suggestions.
I am reluctant to make assignments involving GAP, because I am fairly
new to it myself. I would not know how to evaluate the results. Hence,
the projects I suggest in class are "extra credit". I find the students'
intellectual curiousity is insufficient to cause them to play with GAP
on their own. A manual should include a section telling us mathematicians
how to evaluate computer homework.
I think the GAP manual is pretty intimidating to undergraduates. My students
are struggling with concepts like "isomorphism" and "coset". Even at this
level, they could benefit from some of GAP's capabilities, if they just
ignore all the stuff about character tables, representation theory, etc.
There is a much more user-friendly and simple program called "An Introduction
to Groups / A Computer Illustrated Text" (comes with a disc) by D. Asche,
available from IOP Publihsing for about $40. It does calculations in S_4,
mainly. Even with this, you have to wait until Chapter 5 (in Gallian's text)
before the students can use it. In my class, this is more than halfway through
the first semester. I might consider doing Chapter 5 sooner just so I can
use this software. Still, it seems that programmers ought to be more
interested in GAP. There is a saying, "You can lead a student to a computer,
but you can't make him think." Can we? At the undergraduate level? And with
non-math majors? After I tackle this, I will work on making them like it! |
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I was preparing some presentation slides on basics of matrices and its application. Even though, many of the participants are familiar with basic matrix operation, I planned to explain them by starting from Matrix addition, Matrix subtraction, Matrix Multiplication and Matrix Inverse in comparison with real number operation.
My theme is learning a new concept = Comparison with known old concept + where the new concept differs from know old one + Why they differs.
In this process, I thought of comparing Real number operation with Matrix operation.
Though matrices are used in various algorithms for representing document and finding out it page rank,im looking for the example which is simpler and easy to understand.
In general, im looking for various resources on matrices and its application in real world which can be shown in creative way. Any book similar to Mathematical Nature walk for matrices, will be more useful.
2 Answers
You can't talk about matrices without talking about linearity. It would practically be a sin to not mention their role as linear transforms on vector spaces, especially since that's probably the best motivation for the initially unintuitive form of matrix multiplication. A practical application from this angle would be video game graphics and geometry: understanding matrices puts every transformation (shifts, rotations, scaling, etc.) in a very nice conceptual framework that can be easily applied to otherwise difficult things, such as scaling an object mesh by calculating the new positions of all vertices in it. The fact that this is so intensely visual (it is geometry after all) is a very nice bonus that students are rarely granted in algebra, and shouldn't be passed up.
Another major application is the role of adjacency matrices in graph theory. If your students have never seen graph theory before then the use of these might not seem as immediate (after all, you'd have to explain the uses of graph theory itself), they are incredibly useful, and I would say that they're worth a mention at least. I believe Strang has a lecture as part of his Linear Algebra course where he uses these to solve circuitry problems, though I forget where the video is.
In terms of linking operations from old to new concepts: You probably won't have much trouble with addition/subtraction: for those operations a matrix can be treated as a grid of values. In my experience most students have no trouble with this, and only run into trouble with matrix multiplication. But if you introduce matrices as linear transformations, and matrix multiplication as matrix composition, then you can talk about the identity matrix, matrix multiplication, determinants, inverses, rank, and nullspaces in an extremely intuitive and easy to visualize manner. You can talk about what makes matrices matrices and not mere grids of numbers. I'd say this is your best bet for explaining "why they differ", since the why is all about linearity, which is motivated very well through geometric ideas. |
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Real Analysis Math 3360 - Fall 07 November 13, 2007Name: Section: Instructor:Exam 2The following exam is worth 100 points. You will be allowed 1 hour and 15 minutes to complete the exam. In order to receive full credit in each question you mustCSCI 539 AlgorithmsHomework 1 Due: September 27, 20011. Describe an algorithm that uses a stack to determine whether a string is in the language L, where (a) L (b) Lw w2. A deque is a data structure consisting of a list of items, o
CSCI 539 AlgorithmsHomework 2 Due: October 11, 20011. For each of the following program fragments, give an analysis of the running time. You may use summations to evaluate the running times of nested loops. (a) sum = 0 for i = 1 to n for j = 1 to i
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Finite wings We have a new set of terms associated with wings: The diagram show some planform definitions.Root chord, cr Tip chord, ctSpan, bSweep, c/4 Other definitions derived from these parameters are: Mean chord, c = (cr + ct)/2AE 301
THE UNIVERSITY OF WESTERN ONTARIO DEPARTMENT OF HISTORY HISTORY 9709 L.M.Hernndez-Senz SSC 4402 ext.84978 [email protected] EPIDEMICS: A SOCIAL HISTORY The aims of this course are first, to introduce students to some of the main issues and scholarly litera
1. 2. 3. 4. 5. 6. 7.List the cortical lobes. Differentiate between the central and peripheral nervous systems. Why was the pineal body important to Descartes? Define common descent. What is encephalization? What is the radiator hypothesis? How woul
Section: Chapter 2: Multiple Choice1.If a tree falls in the forest, does it make a sound if no one is present? _ A. _ B. _ C. _ D. Of course; sound is a physical phenomenon. Yes, because if you tape it on a recorder and play it later you will hea
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Sixth-Grade Supplemental Activities --Analysis, Compare, and Contrast Page at a Time's core materials are designed to be used with either fifth- or sixth-grade students. The sixth-grade activities in this section supplement the core activities. Their purpose is to challenge sixth graders to think in a critical and comparative manner that may be too difficult for fifth graders. Visit to see more about this collection. Author(s): No creator set
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6.253 Convex Analysis and Optimization (MIT) 6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject. Author(s): Bertsekas, Dimitri852 Manufacturing Systems Analysis (MIT) This course deals with the following topics: Models of manufacturing systems, including transfer lines and flexible manufacturing systems; Calculation of performance measures, including throughput, in-process inventory, and meeting production commitments; Real-time control of scheduling; Effects of machine failure, set-ups, and other disruptions on system performance. Author(s): Gershwin, Stanley RNA Interference: A New Tool for Genetic Analysis and TherapeuticsTo understand and treat any disease with a genetic basis or predisposition, scientists and clinicians need effective ways of manipulating the levels of genes and gene products. Conventional methods for the genetic mo Author(s): Kissler, Stephane,Ventura491J Economic Development, Policy Analysis, and Industrialization (MIT) This class analyzes the theoretical and historical reasons why governments in latecomer countries have intervened with a wide array of policies to foster industrial development at various turning points: the initiation of industrial activity; the diversification of the industrial base; the restructuring of major industrial institutions; and the entry into high-technology sectors.21 Techniques for Structural Analysis and Design (MIT) This course introduces analysis techniques for complex structures and the role of material properties in structural design, failure, and longevity. Students will learn about the energy principles in structural analysis and their applications to statically-indeterminate structures and solid continua. Additionally, the course will examine matrix and finite-element methods of structured analysis including bars, beams, and two-dimensional plane stress elements. Structural materials and their propert Author(s): Radovitzky, Raú082 Ship Structural Analysis & Design (13.122) (MIT) This course is intended for first year graduate students and advanced undergraduates with an interest in design of ships or offshore structures. It requires a sufficient background in structural mechanics. Computer applications are utilized, with emphasis on the theory underlying the analysis. Hydrostatic loading, shear load and bending moment, and resulting primary hull primary stresses will be developed. Topics will include; ship structural design concepts, effect of superstructures and dissim Author(s): Burke, David
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Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative C and882 System Design and Analysis based on AD and Complexity Theories (MIT) This course studies what makes a good design and how one develops a good design. Students consider how the design of engineered systems (such as hardware, software, materials, and manufacturing systems) differ from the "design" of natural systems such as biological systems; discuss complexity and how one makes use of complexity theory to improve design; and discover how one uses axiomatic design theory (AD theory) in design of many different kinds of engineered systems. Questions are analyzed us Author(s): Suh, Nam,Lee, Taesik101 Analysis II (MIT) This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds. Author(s): Guillemin, Victor |
* Immediate and easy access to high-quality interactive content by integrating it seamlessly with the Student Book. * Multi-lingual glossary gives audio translations for common maths terms in five languages. * Allows you to personalise content by interacting directly with the text and saving your own annotations, enabling you to reapply your thinking the next time your deliver the lesson. * Facilitates classroom management by allowing the whole class to view items in the textbook together. * Prepares your students for exam success through integrated grade improvement tools. * Make Assessment for Learning an achievable reality by tracking the progress of your whole class and then planning the most effective intervention and remediation strategies |
Career Opportunities
Mathematics and Statistics
Mathematics is being used more and more to solve problems in business, engineering, government and science. The problems sometimes require a computer to produce numerical solutions, but to understand how things work, it is still necessary to know the underlying mathematical relationships. When exploring possible careers, there are several factors to consider. Jobs Rated Almanac evaluated 244 careers according to the following criteria: Income, Outlook, Physical Demands, Security, Stress, and Work Environment.
The five most desirable professions - not surprisingly - shared one, essential feature... they all involve mathematics: Actuary, Computer Programmer, Computer Analyst, Mathematician, and Statistician. It was also noted that the top three jobs with the Best Working Environment were Statistician, Mathematician, and Computer Systems Analyst. Each one of these careers involves mathematics. But what you can do with mathematics is not limited to these sample careers, and this listing is not meant to narrow your choices. Rather, it is meant to alert you to a few of your potential avenues for success. It is up to you to decide what you want to do and let mathematics help to get you there. Career Considerations Teaching: As a mathematics teacher, you will work with students to shape the future. Mathematics is a part of our lives, woven into everyday situations such as scientific discoveries, business transactions, recreational events, and household activities. Mathematics is more than numbers; it's the ability to think logically, reason, communicate, and solve problems. If You are Considering a Career in Mathematics Education Talk with your teachers. Ask them about the career opportunities, educational requirements, value and rewards of this profession. Find opportunities to work with children and young people in your community. Participate in math clubs and contests. Assist in tutoring programs. Take the challenge - shape the future! Career in Statistics (from the American Statistical Association) Actuarial Career Information Statistical Internships (from the American Statistical Association) |
Book Description: "Deals with pricing and hedging financial derivatives.… Computational methods are introduced and the text contains the Excel VBA routines corresponding to the formulas and procedures described in the book. This is valuable since computer simulation can help readers understand the theory….The book…succeeds in presenting intuitively advanced derivative modelling… it provides a useful bridge between introductory books and the more advanced literature." --MATHEMATICAL REVIEWS |
Math software
Math software: download Math software
Math Mechanixs 1.5.0.3
Math Mechanixs is a general purpose math program with a Math Editor for solving mathematical problems and taking notes, extensive Function Library and Function Solver, 2D & 3D Graphing, and a Calculus Utility with integration and differentiation.
DPlot 2.0.7.6
Graphing software for scientists, engineers, and students. It features multiple scaling types, including linear, logarithmic, and probability scales, as well as several special purpose XY graphs and contour plots of 3D data.
EQUALS Basic Math Jigsaw Puzzle Games 1.02
Learn basic math with deep understanding easier and faster by simply practicing using tables (ex. New Multiplication Table with Pictures) that continually expose students to the big picture of how and why math works |
John Wiley and Sons Ltd, December 2009
CalNew to this edition: - Expanded Skills and Practice: The 5th edition includes a number new of skill-building and practice exercises, as well as additional problems. - Updated Data and Models: References to dates, prices, and other time-bound quantities have been updated for contemporary applied examples, problems, and projects. For example, Section 11.7 now introduces the current debate on Peak Oil production, underscoring the importance of mathematics in understanding the world's economic and social problems. - New Projects: There are new projects in Chapter 1:Which way is the Wind Blowing?; Chapter 5: The Car and the Truck; Chapter 9: Prednisone; and Chapter 10: The Shape of Planets. - More Problems: 10% more "problem"-type questions now included in the test banks and instructor's manuals. - Chapter 4 Reorganization: This chapter has been reorganized to smooth the approach to optimization. - New ConcepTests: Promote active learning in the classroom. These can be used with or without clickers, and have been shown to dramatically improve student learning. - Expanded Appendices: A new Appendix D introducing vectors in the plane has been added. This can be covered at any time, but may be particularly useful in the conjunction with Section 4.8 on parametric equations.
Features: - Foundations: The 5th edition of the text provides students with a clear understanding of the ideas of calculus as a solid foundation for subsequent courses in mathematics and other disciplines. - Rule of Four: Encourages students with a variety of learning styles to expand their knowledge by presenting ideas and concepts graphically, numerically, symbolically, and verbally. - Balanced Approach: The authors understand the important balance between concepts and skills. As instructors themselves, they know that the balance that an instructor chooses depends on the students they have: sometimes a focus on conceptual understanding is best; sometimes more drill is appropriate. The flexibility of the Fifth Edition allows instructors to tailor the course to their students. - Problems: Creative problems, of great variety, probe student understanding. - Emphasis on modeling - Student Understanding: Exposition written in a way that students can actually read and more easily understand. - Flexible approach to technology
Deborah Hughes Hallett is Adjunct Professor of Public Policy and Professor of Mathematics at the University of Arizona. She graduated from Cambridge University in England and has taught at Middle East Technical University in Ankara, Turkey. Her work is on strategies to improve the teaching of mathematics, and she is interested in promoting international cooperation between mathematicians. She has served on committees for the National Academy of Sciences and organized three international conferences on the teaching of mathematics. She is a fellow of the American Advancement of Science and the author or coauthor of seven books, which have been translated into several languages. Her work has been recognized by prizes from Harvard, Arizona, the Association for Women in Mathematics, and the Mathematical Association of America. |
Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, Sadun treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems. This is the Decoupling Principle.
Traditionally, difference equations, Markov chains, coupled oscillators, Fourier series, the wave equation, the Schrödinger equation, and Fourier transforms are treated separately, often in different courses. Here, they are treated as particular instances of the decoupling principle, and their solutions are remarkably similar. By understanding this general principle and the many applications given in the book, students will be able to recognize it and to apply it in many other settings.
Sadun includes some topics relating to infinite-dimensional spaces. He does not present a general theory, but enough so as to apply the decoupling principle to the wave equation, leading to Fourier series and the Fourier transform.
The second edition contains a series of Explorations. Most are numerical labs in which the reader is asked to use standard computer software to look deeper into the subject. Some explorations are theoretical, for instance, relating linear algebra to quantum mechanics. There is also an appendix reviewing basic matrix operations and another with solutions to a third of the exercises.
Readership
Undergraduate students interested in linear algebra; applications of linear algebra. |
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MSLC Online Resources
The MSLC, in addition to the tutor rooms, offers many resources to help you in your courses. In this section, you will find general math resources that are useful to students across courses. For example, there are guides to helping you using a graphing calculator. You will also find links to external websites that we have found to be particularly helpful to math students. You will also find study tips and tricks and information where you can go throughout OSU to get help with any problems you are having with you math class.
Be sure to also visit the course pages for course specific materials and information. |
Educational level
Academic level (A-D)
Subject area
Grade scale
Learning outcomes
Basic laws of nature are typically expressed in the form of partial differential equations (PDE), such as Navier's equations of elasticity, Maxwell's equations of electromagnetics, Navier-Stokes equations of fluid flow, and Schrödinger's equations of quantum mechanics. The Finite element method (FEM) has emerged as a universal tool for the computational solution of PDEs with a multitude of applications in engineering and science. Adaptivity is an important computational technology where the FEM algorithm is automatically tailored to compute a user specified output of interest to a chosen accuracy, to a minimal computational cost.
This FEM course aims to provide the student both with theoretical and practical skills, including the ability to formulate and implement adaptive FEM algorithms for an important family of PDEs.
The theoretical part of this course deals mainly with scalar linear PDE, for which the student should be able to:
derive the weak formulation.
formulate a corresponding FEM approximation.
estimate the stability of a given linear PDE and it's FEM approximation.
derive a priori and a posteriori error estimates in the energy norm, the L2-norm, and linear functionals of the solution.
state and use the Lax-Milgram theorem for a given variational problem.
In the practical part of the course the student should be able to:
modify an existing FEM program to solve a new scalar linear PDE.
implement an adaptive mesh refinement algorithm, based on an a posteriori error estimate derived in the theoretical part. |
Linus McGinty
Mastery of the following: signed numbers, equations, graphing, word problems, factoring, inequalities and rational expressions. Also, increased reasoning skills and increased competency with calculators and computers. Juniors will be reviewing for the PSAT and SAT tests. |
How are textbooks used in teaching and learning mathematics?Discuss How are textbooks used in teaching and learning mathematics?
Fri, 24 May 2013 02:12:28 --800JComments |
Self Help Calculus Guide: Calculus for Cats
The Bottom Line
Calculus often spells out fear for the math student. Fear often stems from not having the confidence in yourself to succeed or to understand the concept. Amdahl and Loats open the doors to understanding the main concepts in Calculus. Instead of trying to memorize procedures, you'll come away with a much better understanding of functions, tangents, limits, rules which are the Big Ideas behind Calculus. Their guide is a support resource, it does not replace your text and it geared toward the student about to take Calculus or the student who has started taking the subject but the confusion reigns!
Pros
A Strong Focus on the 'Big Idea's in Calculus
Simple Easy to Follow Instructions
If You Want to 'Make Sense' of the Main Concepts in Calculus - This is the Book!
Written for the Beginner Calculus Student or those who 'Just Don't Get It'.
An Easy Read, Easy to Follow Guide to Augment Your First Course Text in Caculus
Cons
No Practice Problems with Solutions
Not A Step by Step 'How To' Resource
For the Beginner Calculus Student
Description
Considering taking Calculus? Have some trepidation? This guide will certainly help you through that first year.
The 'Big Ideas' (main concepts) are flushed out so that the reader can really make sense of what's going on in the math.
An easy to follow guide that all users will be able to make sense of. A great reference to fall back upon when needed.
A great introduction to Calculus. Even if you're not certain that you'll be taking Calculus.
This book is written for those that struggle and need some confidence boosting by understanding the math behind the concepts.
As a teacher, I thorougly enjoyed the additional explanations given - we know that students don't all learn the same way.
Very authentic, analogies are plentiful to help readers make sense of the very nature of 'change in relationship' - Calculus.
Key calculus concepts are addressed in a very understandable nature - I doubt this resource will confuse you.
Takes the stage fright out of the pencil performance. Great explanations of concepts and that calculus jargon.
Guide Review - Self Help Calculus Guide: Calculus for Cats
Some time ago, I read Algebra Unplugged (another resource written by Amdahl and Loats)and was initially a skeptic regarding the approach used until I tried it with my own students. Students are notorius for struggling with positive and negative integers while working with the 4 operations. They tend to memorize the rules (a negative times a negative = a positive, a positive divided by a negative = a negative etc.)and rarely understand why they work and why we use the procedures that we do. So I tried the 'weight club' approach discussed early in the book. Needless to say, I had immediate success with my students. I read the rest of the book and was very pleased with the methods, descriptions and instructions given to succeed in Algebra.
Well, Amdahl and Loats have done it again, this time with Calculus. They successfully take a subject that conjures up fear for many students and make it 'doable'. This book is not your typical, read about the concept, see the example and then work through 10 similar problems and check your solutions. No, quite contrary! This book helps you to make sense of the big ideas in Calculus. It is an introductory book and an extremely useful one. |
9780534495015
ISBN:
053449501x
Pub Date: 2005 Publisher: Brooks/Cole
Summary: An increasing number of computer scientists from diverse areas are using discrete mathematical structures to explain concepts and problems. Based on their teaching experiences, the authors offer an accessible text that emphasizes the fundamentals of discrete mathematics and its advanced topics. This text shows how to express precise ideas in clear mathematical language. Students discover the importance of discrete ma...thematics in describing computer science structures and problem solving. They also learn how mastering discrete mathematics will help them develop important reasoning skills that will continue to be useful throughout their careers.[read more g053449501X Purchased as new and in great condition. We cannot guarantee the availability of CD/DVD or other resource materials such as access code etc if the book is so descr [more]
053449501X |
Introduction: This page is a brief outline for Intermediate Algebra with Mr. Hoven.
Attendance: In nearly three decades of teaching, good attendance is one of the most important things that a student can have to help him/her be successful. If a class is missed, it is important to get caught up as soon as possible….math builds one day upon the previous.
Daily Work: In class work and homework are essential for success. Homework counts as 25% of the class grade. Work is due at the start of the next class period. Late work is given half credit, if turned in by the end of the current chapter.
Tests and Quizzes: Tests and quizzes account for 75% of the class grade. Retests are not given.
Office Hours and Extra Help: Mr. Hoven encourages all students to come in for extra help when needed. Office hours are available every morning before school that there is not a meeting (every Wednesday has a meeting). Students are kept informed as soon as possible when Mr. Hoven learns of a scheduled meeting. After school hours Monday through Thursday until 3:30 p.m. are available when there are no meetings.
Contact: Mr. Hoven checks voice mail and email each school day (unless out of the building for meeting or illness). Voice and email are not checked evenings or weekends. Every attempt will be made to respond within 24 hours. Voice mail is 768 – 5438 and email is [email protected]
Behavior: Appropriate behavior is expected from all students. If a student is not able to improve behavior, or if improper behavior is significant, parents/ guardians/ administration will possibly become involved.
Calculators: It is very helpful if your student has a scientific calculator. A graphing calculator is not necessary, but will be helpful (I lend out some graphing calculators during class time so all students can keep up with the graphing, when necessary). If purchasing a graphing calculator, the TI 83 and 84 series is the preferred calculator.
Books: Books are new and should be cared well cared for. The entire textbook is online and available for all students/ parents/ guardians… my.hrw.com with username and password both being : WHSINTALG.
Monday, April 1 - review for big quiz tuesday and .....see bottom of this page for quiz review copy
Tuesday, April 2 - big quiz...after quiz homework p. 740 #1-22
Wednesday, April 3 - p 747 #2-12
Thursday, April 4 - a day of learning...and no HW. absent should either read all of section 10-7 or watch the Dr. Berger videos from the my.hrw.com website...either way is acceptable.
Friday, April 5 - On the Packet (three hole punched...given to students last week...the first page says "Lesson 14" on it....Read example #1 on page 90...only pay attention to Mean, Median, Mode, and Range on all these problems. HW from page 92-93 is #1-4,8,9,24,25 Those in class will be doing a coin and card experimental probability.
Monday, April 8 - Finally grade p.747. Learn about combinations and permutations. p. 764 #1-12. Absent students must also, read their packets on lesson 19 and 20, and if they haven't already, do p.93 (in packet) #23 and 24. Also, below the Friday lesson plan...do the combination and permutation practice worksheet......UPDATE: YIKES, the lecture took too long...we did not get to the homework today.
Tuesday, April 9 - All day practice problems from the chapter worksheet....UPDATE....today we will do the combination and permutation practice worksheet listed below Friday April 12. Also, you will get the first page of the "pretend" test. Also, learn how to do Combinations and Permutations the long way, and the short way. HW page 764 #1-11.
Tuesday (period 4 and 6) Wednesday (period 3): Learn about compound interest...and the formula A = P (1 + r/n)^(nt)...no homework due to testing.
Thursday, April 18- Period 2 learn the A = formula along with the following:
All classes, graphs of exponentials. Homework for period 2 is p. 800 #5,8,10 and page 808 #2,3,5,16. For period 3,4,6 the homework is p.800 #3,4,5,9,18 and page 808 #2,3,4,5,14,15,16
Friday, April 19 - learn how to see if it's an exponential graph from a table. Homework is practice worksheets 11-2,11-3
Showing work, or what you did, can help you earn potential partial credit.
Forumlas: C = ( F – 32)
Probability of Independent Events: P (A and B) = P(A) * P(B)
Probability of Dependent Events: P (A and B) = P(A) * P(B after A)
1.The following are degrees in Fahrenheit. 55, 66, 66, 67, 84. Convert them to Celsius to the nearest tenth of a degree. Write them down. Calculate and/or state the mean, median, and range of these degrees.
2.How many committees (all members being equal) can be formed with 8 people choosing 4 people.
3.7 people out of 10 are going to line up. How many ways might this happen?
4.Calculate 5. Calculate
5.In faction form, what is the probability of rolling a number cube twice, and four showing up both times?
6.In fraction form, from a standard deck of cards without replacement (52 total cards, 4 of them are eights) what is the probability that you choose an eight, then your next pick you get another eight.
7.There is a class of 17 girls and 13 boys. Each day the teacher randomly gives one lucky student a Safety Sucker. Assuming no absences, in percent form, what is the probability that a girls is the lucky student two days in a row? |
Basic Geometry (5 periods, 5 credits)
Prerequisite: Algebra I
This course is designed for those students who are non-college bound and need additional support in mathematics. Basic concepts from geometry will be covered including properties from geometric figures and concepts of congruence and similarity. Students will work with parallel lines, triangles, polygons and circles. Perimeter, volume and area will be computed for plans and solid figures. Students will also review basic algebraic concepts.
Algebra II, College Prep (5 periods, 5 credits)
Prerequisites: Algebra I, Geometry and Teacher Recommendation
Algebra II is the third year of sequential mathematics for college bound students. This course stresses the relationship between concepts and skills and emphasizes analytical thinking skills and problem solving strategies that are essential to the mastery of advanced high school and college mathematics. |
This is a course in precalculus and statistics, designed to prepare students to enter college at the calculus level. It includes rational, trigonometric, and inverse trigonometric functions; basic trigonometric identities and the laws of sines and cosines; sequences and series; vectors; the central limit theorem and confidence intervals. (Prerequisite: Successful completion of Mathematics 3 or Accelerated Mathematics 2.)Make sure you can work all these problems.. Study, Study, Study!! See you in the am if you need help! Have this ready to turn in tomorrow before the tardy bell rings! Put in the tray!!! Have a highlighter, and your colored pencils ready as well!! Get some rest!!!
Rational Inequality Answers for Examples
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M4 Review for Unit 2 Test Part 2 Answer Key pages 1,2
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M4 Raional Inequality Notes/Examples Answer Key
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M4 Review for Unit 2 Test Part 2 Answer Key "the rest"
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Math 4 Data Analysis Unit Review for Test Answer Key
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M4 Intro to Trig Quiz Review Answers Page 1
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M4 Intro to Trig Quiz Review Answers Page 2
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The Math Without BordersHome Study Companion series provides a complete high school math experience for homeschoolers by supplementing the best existing high school math textbooks with solid teaching by an experienced teacher.
The challenge facing homeschool students and adults studying mathematics at home is that mathematics textbooks are not designed to be used alone. A lot goes on in a good math class besides reading the text and doing problem sets. Textbooks are designed to be taught by an experienced teacher. A good teacher should be able to:
give an overview of the subject to "put the text in context."
model the thinking skills and strategies that go into analysis and problem solving.
illustrate, demonstrate, and clarify (as well as prove) the underlying concepts.
point out links between different parts of the subject and applications beyond what is in the text.
Rather than start from scratch with yet another textbook, I decided to start with the best existing textbooks (selected based on 35 years of teaching experience) and provide the kinds of additional support for home study students that a good teacher would provide in a classroom.
DVD ROM solution manual, with commentary, extensions, and nearly 300 dynamic demonstrations using ®The Geometer's Sketchpad designed to accompany the exceptional text, Geometry: A Guided Inquiry, by G.D. Chakerian, Calvin D. Crabill, and Sherman K. Stein. Now also includes a complete video solution guide to the Review section of each chapter.
Companion to Algebra and Trigonometry: Functions and Applications, by Paul A. Foerster
Whiteboard video lessons on DVD ROM covering the "classroom presentation" portion of a full high school Algebra 2 course based on Algebra and Trigonometry: Functions and Applications by Paul Foerster. Also includes a video solution guide for a large selection of problems for each lesson.
Companion to Precalculus with Trigonometry: Concepts and Applications, by Paul A. Foerster (The Precalculus DVD will be available in June. Order now for shipment as soon as it becomes available.)
Whiteboard video lessons on DVD ROM covering the "classroom presentation" portion of a full high school Precalculus course based on Precalculus with Trigonometry: Concepts and Applications by Paul Foerster. Also includes a video solution guide for a large selection of problems for each lesson. |
Real-Life Math
eBook version
Published by Gale
This set helps students better-understand commonly studied math concepts by illustrating their use in everyday life. Everyday tasks -- such as buying insurance, constructing a budget, reading graphs, adjusting cooking recipes or planning for retirement -- are designed to support the modern mathematics curriculum and contain examples related to the global economy.
While Gale strives to replicate print content, some content may not be available due to rights restrictions.Call your Sales Rep for details.
Review:
"Once in a while there comes a truly exceptional book and, in my opinion, this is one of them. I am a mathematician who taught both high school and college before becoming a librarian and I can see what a wonderful approach this book has to the much maligned subject of Mathematics. I have never seen the relevance of Mathematics explained this well. Reading it has been a great pleasure.
I now know how I-pods work! And how much wood a woodchuck can chuck!"
--Nancy F. Carter, University Libraries, University of Colorado, Boulder |
MEL3E Grade 11 Mathematics for Work & Everyday Life
MEL3E Grade 11 Math Course Description
This MEL3E grade 11 math course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking |
It's a pilot project, so it remains to be seen if this approach makes a difference in improving the pass rates for students in lower-level math courses like College Algebra, which have been at around 60 |
Maths & Statistics AS Level is the first half of the complete Maths & Statistics A Level syllabus.
The Maths & Statistics AS Level course covers 2 of the 3 units from the Pure Mathematics AS Level syllabus but replaces one of the Pure Mathematics units with Statistics Paper 1.
A good grounding in Mathematics is not only intellectually rewarding, but also often provides the passport to a wide variety of jobs, as well as further work in scientific research.
The A-level Mathematics specifications changed in 2004 and for this reason did not change in September 2008. These specifications remain six module qualifications and are now unlikely to change until 2014 at the earliest.
The full A Level qualification consists of an AS and A2 syllabus and would be split into six Mathematics AS level syllabus 5361, for examination in 2009 and later years. To complete the full A Level candidates would also need to study the AQA Mathematics A2 level syllabus 6361 for examinations in June 2009 and later years centres |
Humble PrecalStudent are taught how to set of and solve elementary word problems. Algebra 2 basically introduces the notion of a function, and it extends this notion to a variety of different types of functions. We see polynomial, exponential, logarithmic functons and more. |
154 The Nature of Mathematics, 3 credit hours (GE)
Basic concepts from set theory, logic, geometry, statistics; the fundamental ideas of calculus, and a survey of the development and application of modern mathematics. This course is designed to satisfy the general education requirement in mathematics while providing an overview of the discipline. Prerequisite: MATH 131 or equivalent.
160 Basic Mathematics for Elementary Teachers I, 3 credit hours
An overview of induction and deduction, sets, numbers, and numeration. Topics include patterns and sequences, counting techniques, sets, relations and functions, logic (implication and validity), numeration (base and place syntax and algorithms), number systems (axioms, rational operations, and modular arithmetic), and measurement. Where appropriate, these topics are applied to problem-solving strategies. This course is intended for Elementary Education majors and is aligned with the Alabama Course of Study—MATHEMATICS, but is open to any student meeting the prerequisite. (Note: Students who have completed MATH 164 with a "C" or better will not get credit for MATH 160.) Prerequisite: A grade of C or better in MATH 144 and MATH 147.
162 Basic Mathematics for Elementary Teachers II, 3 credit hours
A continuation of MATH 160. Topics include the real number system (irrational numbers), geometry (geometric shapes, angles, constructions, and measures of length, area, and volume), the metric system, symmetries, descriptive statistics (frequency distributions, measures of central tendency and variation, and normal distributions), and elementary inferential statistics. This course is intended for Elementary Education majors and is aligned with the Alabama Course of Study–MATHEMATICS, but is open to any student meeting the prerequisite. Prerequisite: A grade of C or better in MATH 160.
164 Basic Mathematics, 3 credit hours
Topics (selected in concert with Alabama Course of Study-MATHEMATICS) include an introduction to logic, basic number theory, arithmetic algorithms, elementary geometry and measurement, congruence and similarity, and skills and strategies for problem solving. Prerequisite: A grade of C or better in both MATH 144 and 147.
170 Calculus I, 4 credit hours (GE)
The study of the limit of a function; the derivative of algebraic, trigonometric, exponential, and logarithmic functions; the definite integral and its basic applications to area problems. Applications of the derivative are covered in detail, including approximations of error using differentials, maximum and minimum problems, and curve sketching using calculus. Prerequisite: MATH 149 or 150 or equivalent.
171 Calculus II, 4 credit hours
The study of vectors in the plane and in space, lines and planes in space, applications of integration (such as volume, arc length, work, and average value), techniques of integration, infinite series, polar coordinates, and parametric equations. Prerequisite: MATH 170 or equivalent.
185 Survey of Mathematics, 1 credit hour
This course provides an overview of the nature of mathematics in both a historical and modern context, and its relationship to other disciplines. Students will learn about what mathematicians do and why, and will hear a variety of speakers discuss career opportunities in mathematics and related disciplines. The course is graded pass/fail, and is open to all majors. Prerequisite: MATH 144 or higher.
205 Introduction to the History of Mathematics, 3 credit hours
Introduction to the history of mathematics, from early numeration systems through the beginnings of calculus. Prerequisite: MATH 170.
222 Algorithm Development, 3 credit hours
Introduction to programming and algorithm development. Includes basic I/O and file operations, data types, loops and decisions, functions and procedures, and the use of these topics in developing algorithms applicable to various mathematical problems. Prerequisites: MATH 144 and CIS 161 or consent of instructor.
287 Introduction to Graph Theory, 3 credit hours
An introduction to the basic concepts of graph theory, including the properties and applications of various types of graphs. Although some material will be presented in the standard theorem-proof format, most of the classwork will be computational in nature. Prerequisite: MATH 170 or consent of instructor.
295 Special Topics, 3 credit hours
Topic will be announced prior to registration. Prerequisite: A grade of C or better in MATH 170.
299320 College Geometry, 3 credit hours
Concepts and methods of geometry for advanced study and for teaching geometry at the secondary-school level. Includes Euclidean, solid, and spherical geometry. Prerequisite: MATH 170 or consent of instructor.
385 Mathematics Colloquium, 1 credit hour
Topics will be announced prior to registration. This course provides students with the opportunity to explore areas of mathematics not normally found in the undergraduate curriculum, in an informal, lecture/discussion format. The course is graded pass/fail, and may not be used as an upper-level mathematics elective. Prerequisite: MATH 310.
387 Graph Theory, 3 credit hours
Advanced topics in graph theory, including graphs and diagraphs, vertex and edge colorings, planar graphs, and Ramsey numbers. Although some of the class will be computational, much of it will be presented in theorem-proof format. Prerequisite: MATH 310 or consent of instructor.
395 Special Topics, 3 credit hours
Topics will be announced prior to registration.
399484 Directed Reading in Mathematics, 1 credit hour
In this course students will explore areas of interest in mathematics and propose a topic for the senior seminar project. The course is graded pass/fail. Prerequisite: MATH 310 or permission of department chair.
485 Senior Seminar, 1 credit hour
This course provides students with the opportunity to synthesize previous work through the preparation and presentation of a research paper. Prerequisite: MATH 484.
495 Special Topics, 3 credit hours
Topic will be announced prior to registration.
498 Mathematics Colloquium, 1 credit hour
Opportunity to engage in mathematics at the professional level, through weekly talks given by UM mathematicians and invited speakers. Graded pass/fail. Corequisite: MATH 310 and junior standing.
499 |
MAA Bookstore - Mathematical Association of America
A searchable list of books, with descriptions, in the following categories: Algebra; Analysis; Applied Mathematics; Calculus; Career Information; Computing and Computers; Elementary Models; Games, Puzzles, and Popular Exposition; Geometry and Topology;
...more>>
Making of America Books - University of Michigan
This digital library of primary sources in American social history includes dozens of schoolbooks on arithmetic and other mathematical subjects that date to the antebellum period through reconstruction. Search or browse scanned graphics or transcribed
...more>>
MathAction Online Services - Bill Page
Axiom is a general purpose Computer Algebra system. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler. You can enter mathematics using LaTeX, Axiom commands, or Reduce commands, and
...more>>
Math Crosswords - Cheryl Harrigan; SCORE Mathematics
Students create crossword puzzles that use the definitions of math terms as clues. The terms are the answers that go into the puzzle. Aligned to the California State Standards. From the Schools of California Online Resources for Educators SCORE Mathematics
...more>>
Math - Don Potter
Links and resources include the 1878 publication First Lessons in Arithmetic, a family heirloom that this teacher at Odessa Christian School (Texas) has scanned chapter by chapter, complete with woodblock illustrations and "slate exercises." From the
...more>>
Matheatre - Sadie Bowman and Marc Gutman
Blog of the performers starring in "Calculus: The Musical!" This comic "review" blend of sketch comedy, musical theatre, and lecture about the concepts and history of calculus emerged as a teaching tool from the classroom of Gutman, who "... found that
...more>>
Mathematical Copyright - Wilfrid Hodges
What do you want from your publisher? This page links to a PDF document on aspects of copyright in mathematical publication, featuring an extensive checklist on what an author and a publisher might expect from each other, and how the law can help or hinder.ical Words: Origins and Sources - John Aldrich
"Notes that describe in general terms the origins of the modern vocabulary of mathematics and the sources of information" on which Jeff Miller based his Earliest Uses of Some of the Words of Mathematics. See, in particular, "When and whence for some English and The Human Condition - Victor M. Selby
An enrichment supplement for high school math teachers that integrates math/science with
cultural evolution. This book describes and includes student produced essays connecting the
algebra 1, geometry, and algebra 2 curriculums with the history ofThe Math Life - Conquest, Drake, Rockmore
A 52-minute movie that shows the general public that the inside of the head of a mathematician is not such a scary place. There are interviews with Freeman Dyson, David Mumford, Ingrid Daubechies, Persi Diaconis, Michael Freedman, Fan Chung Graham, KateML and Math on the Web - Wolfram Research
An October 20-21, 2000 conference to present current research and applications
involving MathML, an XML application for describing mathematical notation
and capturing both its structure and its content. The primary goal of
MathML is to enable mathematicsThe Math Wizard - Susan Kennison
A book on teaching and learning math from the top down instead of the bottom up. Kennison contends that this approach is crucial to spreading numeracy, and catching those students who otherwise fall through the cracks into thinking they can't do math.
...more>>
Math - Wonderopolis®
Each Wonder of the Day® includes several paragraphs' overview (Did you know?), modeling suggestions (Try it out!), a vocabulary list (Wonder Words), and other information to stimulate children's curiosity. Share your wonderments, questions, and answers
...more>>
Maxwell's Demon - Edmund Harriss
Harriss, a mathematician and artist of substitution tilings, tilings with a scaling symmetry like the Penrose Tiling, writes that "the major themes of this blog revolve around mathematics communication and mathematics art." His posts, which date back
...more>>
MSRI Journal - Ivars Peterson (MathTrek)
The new journalist-in-residence program at the Mathematical Sciences Research Institute (MSRI) in Berkeley, California represents one effort to improve communication of mathematics. Peterson will spend the summer of 1999 there.
...more>>
The Nature of Mathematics - Ouida B. Kinzey; Kodak
A description of how students created a mathematical slide show based on research projects. Colorado State Standard addressed: students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning
...more>>
NumberQuotes - Steve Duncan
Enter some digits, and get data containing that number to help put that figure in perspective -- or to just associate it with a fun factoid. Learn what cities have your number as a population, or about its purchasing power in dollars. Many five-digit
...more>>
Numericana.com - Gérard P. Michon
The online companion of Numericana, this site contains excerpts from Michon's book, including the entire glossary of scientific terms. Browse an index with pithy summaries, browse by popularity, or search nearly two hundred of his "final answers" of readers'
...more>> |
This collection is included inLens:Community College Open Textbook Collaborative By: CC Open Textbook Collaborative Algebra: VectorsFor our purposes, a vector is a collection of real numbers in a one-
dimensional array.1 We usually think of the array as being arranged in a
column and write
x=x1x2x3|xnx=x1x2x3|xn .
Notice that we indicate a vector with boldface and the constituent elements
with subscripts. A real number by itself is called a scalar, in distinction from
a vector or a matrix. We say that xx is an n-vector, meaning that xx has nn
elements. To indicate that x1x1 is a real number, we write
x1∈R,x1∈R,
(1)
meaning that x1x1 is contained in RR, the set of real numbers. To indicate that
xx is a vector of nn real numbers, we write
x∈Rn,x∈Rn,
(2)
meaning that xx is contained in RnRn, the set of real n-tuples. Geometrically,
RnRnis n-dimensional space, and the notation x∈Rnx∈Rn means that xx is a
point in that space, specified by the nn coordinates x1,x2,...,xnx1,x2,...,xn. Figure 1
shows a vector in R3R3, drawn as an arrow from the origin to the point xx.
Our geometric intuition begins to fail above three dimensions, but the linear
algebra is completely general.
Figure 1: A Vector in R3
We sometimes find it useful to sketch vectors with more than three
dimensions in the same way as the three-dimensional vector of Figure 1. We
then consider each axis to represent more than one dimension, a hyperplane, in
our n-dimensional space. We cannot show all the details of what is happening
in n-space on a three-dimensional figure, but we can often show important
features and gain geometrical insight.
Vector Addition. Vectors with the same number of elements can be
added and subtracted in a very natural way:
Example 1
The difference between the vector x=111x=111 and the
vector y=001y=001 is the vector z=x-y=110z=x-y=110. These vectors are illustrated in Figure 2. You can see that this result is consistent with the definition of
vector subtraction in Equation 3. You can also picture the subtraction in
Figure 2 by mentally reversing the direction of vector yy to get -y-y and then
adding it to xx by sliding it to the position where its tail coincides with the
head of vector xx. (The head is the end with the arrow.) When you slide a
vector to a new position for adding to another vector, you must not change
its length or direction.
Figure 2: Subtraction of Vectors
Exercise 1
Compute and plot x+yx+y and x-yx-y for each of the following
cases:
x=132,y=123x=132,y=123 ;
x=-13-2,y=123x=-13-2,y=123 ;
x=1-32,y=132x=1-32,y=132.
Scalar Product. Several different kinds of vector multiplication are
defined.2 We begin with the scalar product. Scalar multiplication is defined
for scalar aa and vector xx as
ax=ax1ax2ax3|axn.ax=ax1ax2ax3|axn.
(4)
If |a|<1|a|<1, then the vector axax is "shorter" than the vector x; if |a|>1|a|>1, then the
vector axax is '"longer" than x. This is illustrated for a 2-vector in Figure 3.
Figure 3: The Scalar Product axax
Exercise 2
Compute and plot the scalar product axax when x=11/2l/4x=11/2l/4 for
each of the following scalars:
a=1;a=1;
a=-1;a=-1;
a=-1/4;a=-1/4;
a=2.a=2.
Exercise 3
Given vectors x,y,z∈Rnx,y,z∈Rn and the scalar a∈Ra∈R, prove the
following identities:
Footnotes
In a formal development of linear algebra, the abstract concept of a
vector space plays a fundamental role. We will leave such concepts to a
complete course in linear algebra and introduce only the functional techniques
necessary to solve the problems at hand.
The division of two vectors is undefined, although three different "divisions" are defined |
Prerequisite: Placement through the assessment process or MATH 075 or MATH 075SP or equivalent
Note: In this computer-assisted self-paced class, students study from the textbook, online, during weekly face-to-face meetings and take a combination of online and in-class exams. The online labs require computer access and may be completed either on or off campus. The face-to-face meetings will be held in the DVC Math Lab (for lab schedule go to for Pleasant Hill or for SRC). Students are encouraged to complete MATH 110SP in one semester, or take up to 2 semesters. MATH 110SP is equivalent to MATH 110; students who have completed MATH 110 will not receive credit for MATH 110SP.
This course is a computer-assisted self-paced equivalent to MATH 110. The topics include linear equations and inequalities, development and use of formulas, algebraic expressions, systems of equations, operations on polynomials, factoring, graphs, and an introduction to quadratic equations. |
Discovering Algebra: An Investigative Approach
*This is a good text for discovering Algebra 1 principles through investigation and discovery. The text is not overly wordy and makes sense in context with the examples and illustrations within each section.
*One significant improvement over most discovery learning texts and programs is the attention |
Damon Prealgebra hel...A branch of mathematics that substitutes letters for numbers. An algebraic equation represents a scale, what is done on one side of the scale with a number is also done to the other side of the scale. The numbers are the constants. |
Real Analysis
Aims
The aim of the module is to introduce the students to the fundamental ideas of Real Analysis: limits of sequences, infinite series, limits of real functions, continuity, differentiability and the Riemann integral. The module should encourage students to think clearly and critically and to begin to be able to prove simple statements on their own.
Learning objectives
At the end of the module students should:
Understand the Axiom of Completeness.
Understand the concept of a limit.
Be able to determine whether some simple sequences and series diverge or converge.
Understand the differences between convergence and absolute convergence.
Be able to prove statements on their own using "epsilon" arguments.
Understand, and be able to test, the continuity of functions of one real variable.
Understand the derivative as a limit.
Understand some of the properties and consequences of continuity and differentiability.
Elective information
Please check prerequisites carefully before asking to take this module as an elective. In choosing this module as an elective it will be assumed that you are familiar with all the material taught in the first year courses Calculus and Core Algebra, or are willing to learn the material if necessary.
Prerequisites
Familiarity with algebraic manipulation of equalities and inequalities, the notation of set theory, proof techniques including induction and contradiction. |
Online course materials are available through the MATH34042 page in Blackboard
Specification
Aims
To introduce nonlinear
discrete time dynamical systems and study some of their properties, in
particular the kinds of dynamics they can exhibit.
Brief Description of the unit
This course introduces
discrete time dynamical systems (iterated mappings) and analyses them
using the sort of qualitative approaches developed for continuous time
systems in MATH10202 or MATH10232. Mappings of the interval [0, 1] to
itself are studied in detail; these are simple examples of discrete time
systems but they can show remarkably complex dynamical behaviour,
including chaotic dynamics. The existence of fixed points and
periodic points is explored, and the way these change as the system
changes (bifurcation theory) is investigated. The basic ideas of
symbolic dynamics as a way of analysing dynamical systems is introduced,
and the method is used to show some simple maps have chaotic
behaviour.
Learning Outcomes
On successful completion of this course unit students will
have acquired a basic understanding of
discrete time dynamical systems on the interval;
be able to find the fixed and periodic
points of simple dynamical systems on the interval, and determine their stability;
have some familiarity with some of the
simpler bifurcations that fixed and periodic points can undergo;
have some familiarity with the notion of
self-similar fractals, and how they arise as attractors. |
Griffin, GA Precalculus taught about 20 or so students that ranged in age from about 15 to 23 years old. I taught from a text book offered by IYF for teaching English and it is through that text book and work books that I based our curriculum last year. The ministry of IYF gave me great creative license in order to develop the course the way that I saw fit and appropriate.
...Solving Equations and Inequalities
Solutions and Solution Sets We introduce some of the basic notation and ideas involved in solving in this section. Linear Equations In this section we will solve linear equations, including equations with rational expressions. Applications of Linear Equations We will take a quick look at applications of linear equations in this section. |
Effectively preparing college bound students for college-level mathematics: University math faculty perceptions
by Harms, Kristine, Ed.D., UNIVERSITY OF SOUTH DAKOTA, 2010, 94 pages; 3427696
Abstract:
Visit with any university math faculty member throughout the United States, and you will soon hear how the freshman students are not prepared to be successful in introductory college algebra classes. The opinions are varied regarding why the students are unsuccessful; however, the concern and frustration is universal. According to American College Testing (ACT), nationally, only 42% of the high school students who took the ACT in 2009 scored a benchmark score of 22 or higher on the ACT math test, an indicator of preparedness for college algebra success (ACT, 2009). A score of 22 in mathematics indicates a 50% chance of obtaining a B or higher or about a 75% chance of obtaining a C or higher in college algebra (ACT, 2009).
This study used a qualitative methods approach and was conducted through a phenomenological method of open-ended interviews in order to explore the perceptions of university mathematics faculty, who were important to this study because they provided contexts for further describing the phenomenon of effective practice for preparation of perspective college students for college algebra. This research involved interviewing faculty members from one college and two universities, whose interviews were recorded, transcribed, and analyzed for themes and trends that seem to contribute to the determinant behaviors and effective practices for preparing students for college algebra.
A thorough analysis of the interview transcripts identified five emerging themes among the data: the need for higher expectations from high school teachers, too much reliance on calculators, improvements to curriculum, lack of study skills, and expected math skills.
The results of the study indicated that university faculty members feel that the high school teachers are too soft on their students and do not require the mastery of skills necessary to be successful in college algebra. Most freshman students lack the basic study skills and basic math skills to be successful in college algebra. To facilitate the improvement of preparation, students should be required to take math all four years in |
1.To help each student attain confidence and recognize their potential worth and ability to solve problems.
2.To enable the student to attain an appreciation for the role of mathematics as a tool in problem solving.
3.To encourage the student to search and discover reasons for the principles found in algebra.
4.To help the student to think in terms of abstracts.
5.To develop skills, understandings, and competencies in the area of elementary algebra.
6.To prepare the student for college-level mathematics.
II. Real Number System
1. Basic Definition
2. Structure of the Real Number System
3. Properties of Real Numbers
4. Operations on the Real Numbers
5. Ratios and Percent
6. Use of Calculators in Calculation
VIII. Linear Equations and Inequalities
1. The Number Line and the Coordinate System
2. Graphing in Two Dimensions
3. Distance Between Points and Midpoint
4. Slope of a Line
5. Parallel and Perpendicular Lines
6. The Equations of a Line
7. Linear Inequalities and Their Solution Sets
8. Variation |
The course will focus on the mathematical aspects of public-key
cryptography, the modern science of creating secret ciphers (codes), which
is largely based on number theory. Additional topics will be taken from
cryptanalysis (the science of breaking secret ciphers) and from
contributions that mathematics can make to data security and privacy.
4-dimensional geometry
Math 53 - Visualizing the Fourth Dimension(Fall).
This course investigates the idea of higher dimensions and some of the
ways of understanding them. The classic novel, Flatland, will serve
as the starting point, and through discussions, writing, projects and
interactive computer graphics, we will extrapolate ideas from two and
three dimensions to their analogues in four dimensions and higher.
Ancient Greek mathematicians invented the notion of abstraction (in
mathematics and other fields), absolute precision, and proof. The
approach to mathematics that we take today can be traced back to these
Greek mathematicians. After examining some pre-Greek mathematical
traditions, we study Greek mathematics, beginning with Thales and
Pythagoras. Topics include the intellectual crisis caused by the discovery
that not all magnitudes are commensurable; Plato and his academy; Euclid
and his Elements; the three special construction problems (trisecting an
angle, squaring a circle, doubling a cube); and the greatest of the Greek
mathematicians, Archimedes.
history of mathematics
Math 56 - History of Mathematics(Spring).
Traces the development of mathematical ideas and methods in literate
cultures from ancient Egypt and Mesopotamia, to Hellenistic Greece and
medieval China, India and the Islamic world, up through the dawn of
calculus at the start of the Scientific Revolution in early modern Europe.
philosophy, literature, linguistics, the humanities, psychology
Math 57 - Game Theory and its Applications in the Humanities and
Social Sciences(not offered 2012-13).
Completely self-contained introduction to the mathematical theory of
conflict, including parlor games, auctions, games from the Bible and games
commenting on the existence of superior beings, game-theoretic analyses in
literature, philosophical questions and paradoxes arising from game theory,
and game theoretic models of international conflict.
economics, management or
a course that will help prepare you for calculus
Differential and integral calculus with applications in the social
sciences. Not open to students who have passed a college calculus course;
students who wish to continue the calculus should enroll in Math 112.
Prerequisite: Math 58.
political science
Math 60 - Topics in Mathematical Political Science(Winter). (Same as Political Science 123)
A mathematical treatment (not involving calculus or statistics) of
political power, social choice, and international conflict. No previous
study of political science is necessary, but PS 111 or 112 would be
relevant.
public policy
Math 61 - Math in the Public Interest(not offered 2012-13).
Explores key mathematical topics including statistics, probability,
exponential and logarithmic functions, and visual/graphical representation
of numbers, in the context of contemporary public policy issues such as the
2008 financial crisis, gaming institutions, population demographics, and
climate change.
public policy
Math 64 - Statistical Thinking(Fall).
Seeks to provide the conceptual foundation and analytical skills required
to understand a complex, data-rich and uncertain (stochastic) world from a
stochastic versus deterministic perpective, and to navigate through the
daily bombardment of data from all sides. |
Mathematicians
Onet SOC Code 15-2021.00
Career Description:
Conduct research in fundamental mathematics or in application of mathematical techniques to science, management, and other fields. Solve or direct solutions to problems in various fields by mathematical methods.
Related Clusters:
Programs of Study
Career Summary:
Job Zone Five: Extensive Preparation Needed
Experience-- Training- Employees may need some on-the-job training, but most of these occupations assume that the person will already have the required skills, knowledge, work-related experience, and/or training.
Examples-Physics - Knowledge and prediction of physical principles, laws, their interrelationships, and applications to understanding fluid, material, and atmospheric dynamics, and mechanical, electrical, atomic and sub- atomic structures and processes.
Abilities
Mathematical Reasoning - The ability to choose the right mathematical methods or formulas to solve a problem.
Oral Comprehension - The ability to listen to and understand information and ideas presented through spoken words and sentences.
Written Comprehension - The ability to read and understand information and ideas presented in writing.
Originality - The ability to come up with unusual or clever ideas about a given topic or situation, or to develop creative ways to solve a problem.
Number Facility - The ability to add, subtract, multiply, or divide quickly and correctly.
Fluency of Ideas - The ability to come up with a number of ideas about a topic (the number of ideas is important, not their quality, correctness, or creativity).
Deductive Reasoning - The ability to apply general rules to specific problems to produce answers that make sense.
Oral Expression - The ability to communicate information and ideas in speaking so others will understand.
Inductive Reasoning - The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated eventsSpeed of Closure - The ability to quickly make sense of, combine, and organize information into meaningful patterns.
Category Flexibility - The ability to generate or use different sets of rules for combining or grouping things in different ways.
Near Vision - The ability to see details at close range (within a few feet of the observer).
Flexibility of Closure - The ability to identify or detect a known pattern (a figure, object, word, or sound) that is hidden in other distracting material.
Problem Sensitivity - The ability to tell when something is wrong or is likely to go wrong. It does not involve solving the problem, only recognizing there is a problem.
Making Decisions and Solving Problems - Analyzing information and evaluating results to choose the best solution and solve problems.
Interacting With Computers - Using computers and computer systems (including hardware and software) to program, write software, set up functions, enter data, or process information.
Interpreting the Meaning of Information for Others - Translating or explaining what information means and how it can be used.
Provide Consultation and Advice to Others - Providing guidance and expert advice to management or other groups on technical, systems-, or process-related topics.
Communicating with Supervisors, Peers, or Subordinates - Providing information to supervisors, co-workers, and subordinates by telephone, in written form, e-mail, or in person - Estimating sizes, distances, and quantities; or determining time, costs, resources, or materials needed to perform a work activity.
Interests
Investigative - Investigative occupations frequently involve working with ideas, and require an extensive amount of thinking. These occupations can involve searching for facts and figuring out problems mentallyAutonomy - Workers on this job plan their work with little supervision.
Ability Utilization - Workers on this job make use of their individual abilitiesIndependence - Workers on this job do their work alone.
Working Conditions - Workers on this job have good working conditions.
Responsibility - Workers on this job make decisions on their own.
Achievement - Workers on this job get a feeling of accomplishment.
Security - Workers on this job have steady employment.
Creativity - Workers on this job try out their own ideas.
Moral Values - Workers on this job are never pressured to do things that go against their sense of right and wrong.
Working Conditions-Mean Extent - Occupations that satisfy this work value offer job security and good working conditions. Corresponding needs are Activity, Compensation, Independence, Security, Variety and Working Conditions.
Activity - Workers on this job are busy all the time.
Social Status - Workers on this job are looked up to by others in their company and their community.
Company Policies and Practices - Workers on this job are treated fairly by the company.
Recognition - Workers on this job receive recognition for the work they do.
Compensation - Workers on this job are paid well in comparison with other workers.
Recognition-Mean Extent - Occupations that satisfy this work value offer advancement, potential for leadership, and are often considered prestigious. Corresponding needs are Advancement, Authority, Recognition and Social Status.
Tennessee Board of Regents is an AA/EEO employer and does not discriminate on the basis of race, color, national origin, sex, disability, or age in its programs and activities. Full Non-Discrimation Policy. |
Mathematics
Pupils who decide to study sixth form mathematics should be prepared for a very exciting, nerve-wracking, fretful, fun-filled, occasionally frustrating, but ultimately rewarding couple of years. At least, that is what we aim for in the King's Mathematics Department.
AS and A2 mathematics and further mathematics are not easy courses, in spite of what some newspapers, and talking heads seem to indicate. Thus, for a student to be successful they will require, most obviously and importantly, an interest and enjoyment in the subject. This, allied with superior algebraic skills, should allow the student to emerge triumphant at the end of their course.
Sixth form mathematics is taught by experienced teachers in a generally relaxed setting, where students will be expected to contribute to their own learning, both in the classroom and via independent study. |
"…useful both in the academia and industry…suited for students taking specialist courses…[and] a valuable reference for practicing engineers." (IEEE Circuits & Devices Magazine, November/December 2006)
"This book is warmly recommended to anyone having to design or understand how computer arithmetic operates at almost every conceivable level of detail." (Computing Reviews.com, June 8, 2006) |
Book Description: Anyone trying to learn algebra and trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous examples are also included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry.
Buyback (Sell directly to one of these merchants and get cash immediately)
Currently there are no buyers interested in purchasing this book. While the book has no cash or trade value, you may consider donating it |
Lecture 20: Introduction to Ratios (new HD version)
Embed
Lecture Details :
What a ratio is. Simple ratio problems.
Course Description :
This is the original Algebra course on the Khan Academy and is where Sal continues to add videos that are not done for some other organization. It starts from very basic algebra and works its way through algebra II. |
Maths Helper Plus 2.12 description
Turns your PC into an incredible math machine! Have fun with live interactive graphing tools for linear functions, parabolas, ellipses, circles and more! Use any of 5 parameters simultaneously in graph and function definintions to model real life problems and create working demonstrations! Many interactive tools for tracing around functions, finding integrals, roots, turning points and more. Calculate statistics with full working steps shown! Import text data files and tabulate or make statistical plots and calculations. Solve and plot triangle solutions with full working! Includes conics, (x,y) point plotting and regression, vectors, matrics, complex numbers and MUCH MORE! You can even import pictures then overlay the graphs for mathematical analysis. Graphs can be up to 1m square! This amazing program has hundreds of pages of beautiful HTML help included, along with many ready to use applications and example files!
Pipeline Plus * Two challenging adventures, eight large levels in total! * A huge number of pipe elements link together, and you will often be moving around through these pipes. * Create your own mind Free Download
Science Teacher Helper was designed with a single purpose in mind - to save you time when editing math, chemistry and physics in documents. You can easily add 765 functions, graphs and charts of physical, chemical and math into MS WORD document. Free Download
Science Teachers Helper was designed with a single purpose in mind - to save you time when editing math, chemistry and physics in documents. You can easily add 1200 functions, graphs and charts of phy Free Download |
Whom to Contact
Mathematics
Major and Minor
At Knox, mathematics is marked by a commitment to analytic rigor, an emphasis on clear understanding, the ability to communicate effectively with others, and an excitement about the unlimited possibilities within this field of knowledge.
Today, the pleasure and the excitement of studying mathematics are intensified by the capacities of modern computers, which have helped bring new developments within the reach of the serious undergraduate. Knox has been at the forefront in capturing the power of computers, both for class assignments and in research.
The Program A distinctive feature of the mathematics major at Knox is the importance given to effective communication. In all courses students are expected to write clearly. In the course "Mathematical Structures" and in Senior Seminar, classes literally write their own textbooks. Students also are regularly asked to give professional-quality presentations.
Mathematics students begin with a solid foundation in calculus, linear algebra and mathematical structures before proceeding to a variety of advanced courses and independent work. Some majors undertake a College Honors project, which involves a year of research on a mathematical topic, a paper and an oral defense. Recent Honors projects have dealt with topics such as fundamental solutions for partial differential equations and options pricing.
As a "capstone" experience, mathematics majors are required to participate in the independent study of a topic of current interest and produce a talk on the topic.
Resources A unique resource in the Mathematics Department is the Mathematica Lab, which contains a powerful server that gives optimal performance for large numbers of simultaneous users of the "Mathematica" package. The Stellyes Lab provides Macintosh and IBM computers in the Umbeck Science and Mathematics Center. Additional facilities include several science-related computer labs, a data analysis lab in George Davis Hall, and a 24/7 general computer lab in Seymour Union.
The mathematics department is housed in the Umbeck Science and Mathematics Center. Its Kresge Science and Mathematics Library holds relevant reference works and journals. Knox has superb computing facilities for student use. Knox's high speed fiber optic and wireless networks give students access anywhere on campus, including their own rooms, free DS-3 access to the Internet and to advanced software, including Mathematica |
Mathematics
Departmental Staff
_
Head of Department: Mr M McKey
Mr E Hollywood
Miss U McLaughlin
Mrs B McArdle
Miss A Kearney
Mrs L Hollywood
Mrs M Laverty
Mrs E Cahill
Mr M Canavan
_
With six general-purpose classrooms, two fully-equipped ICT rooms and nine dedicated full-time staff, the Mathematics department is well-equipped to offer courses in Key Stage 3, GCSE Mathematics, Vocational, AS and A Level Mathematics
_
Curriculum
KS3 (Year 8,9 & 10)
_
The present year 10 students will be the last to follow the Key Stage 3 programme, in its current format.
The out-going system consists of two written papers and a mental Maths paper. The papers a student sits determines their level:
Paper 1 = Level 3
Paper 1 & 2 = level 3,4,5
Paper 2 & 3 = Level 4,5,6
Paper 3 & 4 = Level 5,6,7
Paper 4&5 = Level 6,7,8
From September 2012 the existing system of sitting two linear papers will be replaced by a series of controlled assessment, taken in the first two terms of year 10.
Below is a Guide to Assessment, if you want further information you can click on the link below which will take you to the CCEA website: Click Here
_
GCSE (Years 11 & 12)
_
At GCSE students sit examinations under the auspices of the AQA examinations board. For the current year 11 and year 12 students, this involves 3 units. Each unit may be taken at, either, Foundation or Higher level.
The weightings for each unit are as follows:
Unit 1: Number & Statistics (Calc)
Marks: 54
Percentage: 26.7%
UMS: 80
Unit 2: Number & Algebra (Non-Calc)
Marks: 66
Percentage: 33.3%
UMS: 100
Unir 3: Geometry & Algebra (Calc)
Marks: 80
Percentage: 40%
UMS: 120
How are papers constructed?
Unit 1: Number & Statistics (Calc)
Number – 14 Marks
Statistics – 40 Marks = Total 54
1 Hour Exam
Unit 2 (Foundation): Number & Algebra (Non-Calc)
Number – 44 Marks
Algebra – 22 Marks = Total 66
1 Hour 15 mins
Unit 2 (Higher): Number & Algebra (Non-Calc)
Number – 25 Marks
Algebra – 41 Marks = Total 66
1 Hour 15 mins
Unit 3 (Foundation): Number, Algebra & Geometry
Number – 15 Marks
Algebra – 15 Marks
Geometry – 50 Marks = Total 80
1 Hour 30 mins
Notes:
40% must be done on completion, therefore Unit 3 must be done at the end, however Unit 3 is not a Terminal paper and therefore the tier of entry of Unit 3 will not determine final grade.
From September 2012, GCSE Maths will return to linear examinations, with pupils studying for two years and then, taking two written papers at the end of their year 12.
For further information, including syllabus and past papers/marking schemes visit the AQA website at:
A Level (Year 13 & 14)
_
A level Mathematics involves 6 units. The first 3 units may be taken as an AS level.
In year 13 students will study modules:
Core 1, Core 2 and Mechanics 1/Statistics 1
In year 14 students will study modules:
Core 3, Core 4 and Statistics 1/Mechanics 1
For further information, including syllabus and past papers/marking schemes visit the EDEXCEL website at: |
Fundamentals of Precalculus is designed to review the fundamental topics that are necessary for success in calculus. Containing only five chapters, this text contains the rigor essential for building a strong foundation of mathematical skills and concepts, and at the same time supports student
Normal 0 false false false Dugopolski's Precalculus: Functions and Graphs, Fourth Edition gives students the essential strategies they need to make the transition to calculus. The author's emphasis on problem solving and critical thinking is enhanced by the addition of 900 exercises i... |
Richard Beals, "Analysis: An Introduction"
Cambridge University Press (September 13, 2004) | ISBN: 0521600472 | 272 pages | PDF | 1,8 Mb
Review
"Analysis: An Introduction is most appropriate for a undergraduate who has already grappled with the main ideas from real analysis, and who is looking for a succinct, well-written treatise that connects these concepts to some of their most powerful applications. Beals' book has the potential to serve this audience very well indeed."
MAA Reviews, Christopher Hammond, Connecticut College
Book Description
This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics. Read More » |
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues.
In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems.
Included are
• an overview of computational methods together with their properties and advantages
• topics from statistical regression analysis that help readers to understand and evaluate the computed solutions
• many examples that illustrate the techniques and algorithms
Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering.
This book aims to illustrate with practical examples the applications of linear optimization techniques. It is written in simple and easy to understand language and has put together a useful and comprehensive set of worked examples based on real life problems.
Mel Gibson teaching Euclidean geometry, Meg Ryan and Tim Robbins acting out Zeno's paradox, Michael Jackson proving in three different ways that 7 x 13 = 28. These are just a few of the intriguing mathematical snippets that occur in hundreds of movies. Burkard Polster and Marty Ross have pored through the cinematic calculus and here offer a thorough and entertaining survey of the quirky, fun, and beautiful mathematics to be found on the big screen.
Math Goes to the Movies is based on the authors' own collection of more than 700 mathematical movies and their many years using movie clips to inject moments of fun into their courses. With more than 200 illustrations, many of them screenshots from the movies themselves, this book provides an inviting way to explore math, featuring such movies as
• Good Will Hunting
• A Beautiful Mind
• Stand and Deliver
• Pi
• Die Hard
• The Mirror Has Two Faces
The authors use these iconic movies to introduce and explain important and famous mathematical ideas: higher dimensions, the golden ratio, infinity, and much more. Not all math in movies makes sense, however, and Polster and Ross talk about Hollywood's most absurd blunders and outrageous mathematical scenes. They round out this engaging journey into the realm of mathematics by conducting interviews with mathematical consultants to movies.
This fascinating behind-the-scenes look at movie math shows how fun and illuminating equations can be.
This magisterial annotated bibliography of the earliest mathematical works to be printed in the New World challenges long-held assumptions about the earliest examples of American mathematical endeavor. Bruce Stanley Burdick brings together mathematical writings from Mexico, Lima, and the English colonies of Massachusetts, Pennsylvania, and New York. The book provides important information such as author, printer, place of publication, and location of original copies of each of the works discussed.
Burdick's exhaustive research has unearthed numerous examples of books not previously cataloged as mathematical. While it was thought that no mathematical writings in English were printed in the Americas before 1703, Burdick gives scholars one of their first chances to discover Jacob Taylor's 1697 Tenebrae, a treatise on solving triangles and other figures using basic trigonometry. He also goes beyond the English language to discuss works in Spanish and Latin, such as Alonso de la Vera Cruz's 1554 logic text, the Recognitio Summularum; a book on astrology by Enrico Martínez; books on the nature of comets by Carlos de Sigüenza y Góngora and Eusebio Francisco Kino; and a 1676 almanac by Feliciana Ruiz, the first woman to produce a mathematical work in the Americas.
Those fascinated by mathematics, its history, and its culture will note with interest that many of these works, including all of the earliest ones, are from Mexico, not from what is now the United States. As such, the book will challenge us to rethink the history of mathematics on the American continents.
In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices.
The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.
What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world's population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness?
In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders.
These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry |
These
programs allow students to use TI-83 Plus calculators to investigate
the mathematics they are learning.
Please
be sure to download the appropriate file for your platform. After
downloading, consult your TI-83 Plus user's manual for instructions
on how to transfer the file to your calculator using a TI GraphLink
cable and software. If you need additional assistance, please access
the Texas
Instruments Calculator site.
PC
users can directly download the file to the desktop. Macintosh
users should download the associated *.sea file to the desktop
and double-click to Unstuff it.
Chapter 1 (page 10) Description: plots points in a relation Special Instructions: The program will prompt you to enter
the x- and y- values you wish to graph. It will then ask if you wish
to graph more points or to quit. PC - MAC
Chapter
3 (page 133) Description: determines whether a function is even, odd,
or neither Special Instructions: Enter the function you are testing
as Y1 in the Y= menu before running the program. The program will
prompt you to enter an x-coordinate that lies on the graph of the
function and then will calculate whether the function is odd, even,
or neither. PC - MAC
Chapter
4 (page 226) Description: computes the value of a function Special Instructions: Enter the function you are testing
as Y1 in the Y= menu before running the program. The program automatically
repeats itself until you quit. PC - MAC
Chapter
5 (page 331) Description: determines the area of a triangle, given the
lengths of all sides of the triangle Special Instructions: The program will prompt you to enter
the measure of each side of the triangle. PC - MAC
Chapter
5 (page 333) Description: determines the lengths of the sides and the
angle measures of a triangle, given the coordinates of the vertices
of the triangle Special Instructions: Make sure the calculator is set in
DEGREE mode. The program will prompt you to enter each vertex. Enter
each coordinate separately followed by pressing ENTER. PC - MAC
Chapter
7 (page 470) Description: computes the distance from a point to a line
Special Instructions: Make sure the equation of the line
is written in standard form before beginning the program. Enter
the information from each prompt in the program.
Chapter
8 (page 512) Description: determines the components of the cross product
of two vectors Special Instructions: The program will ask you to identify
the two vectors as (A, B, C) and (X, Y, Z). Enter each coordinate
separately followed by ENTER. The result will appear as three values
in order of their appearance in the ordered triple. PC - MAC
Chapter
9 (page 582) Description: performs complex iteration Special Instructions: Make sure the calculator is in complex
(a + bi) mode before beginning the program. When entering the number,
enter it in a + bi form. PC - MAC
Chapter
9 (page 604) Description: draws Julia sets
Special Instructions: Make sure the calculator is in complex
(a + bi) mode. Set the calculator window for [0, 100] scl:1 by
[0, 100] scl:1. CX and CY correspond to a and b, respectively, in
a + bi. Select values from -1.5 to 1 for CX and CY to make the program
run more efficiently. This program takes 35-60 minutes to run. PC - MAC
Chapter
10 (page 620) Description: determines the distance and midpoint between
two points Special Instructions: The two points are entered as (X1,
Y1) and (X2, Y2). Each coordinate is entered separately followed
by ENTER. The coordinates of the midpoint are displayed on two separate
lines. PC - MAC
Chapter
10 (page 628) Description: determines the radius and the coordinates of
the center of a circle from an equation written in general form
Special Instructions: Write the equation of the circle in
standard form before beginning the program. Enter the values of
D, E, and F when prompted. PC - MAC
Chapter
12 (page 780) Description: calculates the value of the nth term of a continued
fraction sequence Special Instructions: Each term of this sequence equals the
sum of A and the reciprocal of the previous term. When prompted,
enter any value for A, the initial term of the sequence. PC - MAC
Chapter
14 (page 961) Description: uses rectangles to approximate the area under
a curve Special Instructions: The program approximates the area between
the graphs of two functions by dividing the region into rectangles.
Store the two functions as Y1 and Y2 in the Y= list before beginning
the program. It is a good idea to look at the graphs of the two
functions to help you determine the lower and upper bounds from
which the rectangles are to be made. PC - MAC |
ALGEBRA II
INTRODUCTION
California Mathematics Framework
Algebra II expands on the mathematical content of Algebra I and Geometry. There is no single
unifying theme. Instead, it introduces many new concepts and techniques that will be basic to
more advanced courses in mathematics and the sciences as well as useful in the work place. In
general terms, the emphasis is on abstract thinking skills, the function
concept, and the algebraic solution of problems in various content areas.
The study of absolute value and inequalities is now extended to include simultaneous linear
systems; it paves the way for linear programming---the maximization or minimization of linear
functions over regions defined by linear inequalities. The relevant standards are:
1.0. Students solve equations and inequalities involving absolute value.
2.0. Students solve systems of simultaneous linear equations and inequalities (in two or
three variables) by substitution, with graphs, or with matrices.
The concept of Gaussian elimination should be introduced for 2x2 matrices and simple 3x3
ones. The emphasis is on concreteness rather than on generality. Concrete applications of both
simultaneous linear equations and linear programming to problems in daily life should be brought
out, but there is no need to emphasize linear programming at this stage. For the purpose of
graphing regions in connection with linear programming, while it would be inadvisable to
advocate the use of graphing calculators all the time, such calculators are helpful once students
are past the initial stage of learning.
At this point of students' mathematical development, knowledge of complex number is
indispensable:
5.0. Students demonstrate knowledge of how real and complex numbers are related
both arithmetically and graphically. In particular, they can plot complex numbers as
points in the plane.
6.0. Students add, subtract, multiply, and divide complex numbers.
It is important to stress the geometric aspect of complex numbers from the beginning, for
example, the addition of two complex numbers in terms of a parallelogram. Also point out the
key difference: the complex numbers cannot be linearly ordered the same way real numbers are
(the real line).
The next general technique is the formal algebra of polynomials and rational expressions.
3.0. Students are adept at operations on polynomials, including long division.
4.0. Students factor polynomials representing the difference of squares, perfect square
trinomials, and the sum and difference of two cubes.
1
7.0. Students add, subtract, multiply, divide, reduce, and evaluate rational expressions
with monomial and polynomial denominators and simplify complicated rational
expressions including those with negative exponents in the denominator.
The importance of formal algebra is sometimes misunderstood. The argument against it is that it
has insufficient real world relevance and it leads easily to an over-emphasis on mechanical drills.
There seems also to be an argument for placing the exponential function ahead of polynomials in
school mathematics because of the former's appearance in many real world situations
(compound interest, for example). However, there is a need to affirm the primacy of
polynomials in mathematics and the importance of formal algebra. The potential for abuse in
Standard 3.0 is all too obvious, but such abuse would be realized only if the important ideas
implicit in it are not brought out. These ideas all center on the abstraction and hence the
generality of the formal algebraic operations on polynomials. Thus the division algorithm (long
division) leads to the understanding of the roots and factorization of polynomials. The factor
theorem (x-a) divides a polynomial p(x) if and only if p(a)=0) should be proved and students
should know the proof. The rational root theorem could be proved too, but only if there is
enough to explain it carefully; otherwise many students would be misled into thinking that all the
roots of a polynomial with integer coefficients are determined by the divisibility properties of the
first and last coefficients.
It would be natural to first prove the division algorithm and the factor theorem for polynomials
with real coefficients. But it would be vitally important to revisit both and point out that the same
proofs work, verbatim, for polynomials with complex coefficients. This not only provides a
good exercise on complex numbers, but also nicely illustrates the
built-in generality of formal algebra.
Two remarks about Standard 7.0 are relevant: (i) a rational expression should be treated
formally and its function-theoretic aspects (the domain of definition, for example) need not be
emphasized at this juncture, and (ii) fractional exponents of polynomials and rational expressions
should be carefully discussed here.
The first high point of the course is the study of quadratic (polynomial) functions:
8.0. Students solve and graph quadratic equations by factoring, completing the square,
or using the quadratic formula. Students apply these techniques in solving word
problems. They also solve quadratic equations in the complex number system.
9.0. Students demonstrate and explain the effect changing a coefficient has on the graph
of quadratic functions. That is, students can determine how the graph of a parabola
changes as a, b, and c vary in the equation y=a(x-b)2 + c.
10.0 Students graph quadratic functions and determine the maxima, mimima, and zeros of
the function.
What distinguishes Standard 8.0 from the same topic in Algebra I is the newly-acquired
generality of the quadratic formula: it now solves all equations ax2 + bx +c =0 with real a, b, and
2
c regardless of whether b2 - 4ac < 0 or not, and it does so even when a, b and c are complex
numbers. Again it should be stressed that the purely formal derivation of the quadratic formula
makes it valid for any object a, b and c so long as the usual arithmetic operations on numbers
can be applied to them. In particular, it makes no difference whether they are real or complex.
This provides another illustration of the built-in generality of formal algebra. Students need to
know every aspect of the proof of the quadratic formula. They should also be made aware that
(i) with the availability of complex numbers, any quadratic polynomial ax2 + bx +c =0 with real
or complex a, b and c can be factored into a product of two linear polynomials with complex
coefficients, (ii) c is the product of the roots and -b is their sum, and (iii) if a, b and c are real
and the roots are complex, then the roots are a conjugate pair.
Standard 9.0 brings the study of quadratic polynomials to a new level by regarding it as a
function. This leads to the exact location of the maximum, minimum, and zeros of this function by
use of the quadratic formula (or more precisely, by completing the square) without recourse to
calculus. The practical applications of these results are as
important as the theory here.
Another application of completing the square is given in standard 17.0 where students learn,
among other things, how to write the equation of an ellipse or hyperbola when only geometric
data are given, such as focus, major axis, minor axis, etc.
A second high point of Algebra II is the introduction of two of the basic functions in all of
mathematics: ex and log x.
11. Students prove simple laws of logarithms.
11.1. Students understand the inverse relationship between exponential and logarithms
and use this relationship to solve problems involving logarithms and exponents.
11.2. Students judge the validity of an argument according to whether the properties of
real numbers, exponents, and logarithms have been applied correctly at each step.
12.0. Students know the laws of (fractional) exponents, understand exponential functions,
and use these functions in problems involving exponential growth and decay.
15.0. Students determine whether a specific algebraic statement involving rational
expressions, radical expressions, or logarithmic or exponential functions is
sometimes true, always true, or never true.
The theory should be done carefully, and students are responsible for the proofs of the laws of
exponents for am where m is a rational number, and of the basic properties of loga x: loga (x1 x2)
= loga (x1)+ loga (x2), loga (1/x) = - loga x, and loga(xr) = r loga x, where r is a rational number
(Standard 15.0). The functional relationships loga(ax) = x and a log(t) = t where a is the base of
the log function, should be taught without a detailed discussion of inverse functions in general, as
students are probably not ready for it yet. Practical applications of this topic to growth and
decay problems are legion.
A third high point of Algebra II is the study of arithmetic and geometric series:
3
23) Students derive the summation formulas for arithmetic series and for both finite and
infinite geometric series.
The geometric series, finite and infinite, is of great importance in mathematics and the sciences,
physical as well as social. Students should be able to recognize this series under all its guises and
compute its sum with ease. In particular, they should know by heart the basic identity that
underlies the theory of geometric series:
xn – yn = (x-y)(xn-1 + xn-2 y + · · · + xyn-2 + yn-1).
This identity gives another example of the utility of formal algebra, and the identity is used in
many other places as well (the differentiation of monomials, for instance).
It should be mentioned that while it is tempting to discuss the arithmetic and geometric
n
series using the sigma notation ∑, it would be advisable to resist this temptation so as not
I =1
to overburden the students.
Students should learn the binomial theorem and how to use it:
20.0. Students know the binomial theorem and use it to expend binomial expressions that
are raised to positive integer powers.
18.0. Students use the fundamental counting principles to compute combinations and
permutations.
19.0. Students use combinations and permutations to compute probabilities.
In this context, the applications almost come automatically with the theory.
Finally, Standards 16.0 (geometry of conic sections), 24.0 (composition of functions and
inverse functions), and 25.0 can be taken up if time permits.
4 |
Calculus Problem Solver
4.00 (1 votes)
Document Description
calculus
Topics covered in Calculus
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Calculus Problem Solver calculus Topics covered in Calculus Given below are the topics covered by our online calculus help program: * Functions Limits and Continuity * Differentiation * Differential Equations * Indefinite Integrals * Definite Integrals * Application of Derivatives * Exponential and Logarithmic Series Understand all these topics with personalized attention and gain quality help online.
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2005 Hardcover New Book New and in stock. 4MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools. This second edition of MATLAB Guide completely revises and updates the best-selling first edition and is more than 30% longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB 7 and the Symbolic Math Toolbox.
What People Are Saying
Charles Van Loan
This introduction is perfect for many classroom needs. I love the choice of topics and the examples. I see now that the only thing better than Higham or Higham is Higham and Higham!(Charles Van Loan, Professor and Chair, Department of Computer Science, Cornell University.)
Floyd B. Hanson
"I use the Higham brothers' MATLAB Guide as a reference for myself and my students in all my applied mathematics and computational science courses. The clarity and usefulness of their writing are major attractions for using their books. Consequently, I look forward to the very much improved second edition, as if that were possible for a much admired book. In particular, the new chapter on case studies looks quite interesting with its useful applications. In addition, new treatments of new functions and features like nested functions, ODE as well as DDE functions will be of great interest. "
—PhD, Professor of Mathematics (Applied Math and Computational Science), University of Illinois at Chicago
James Nagy
"Matlab Guide is an excellent reference book for Matlab programming. This new version of Matlab Guide contains material on important changes introduced in Matlab 7, including single precision arithmetic and anonymous and nested functions. The new edition also contains many more examples; readers will have the advantage of learning Matlab by essentially looking over the shoulder of two experts. This is a book that all users, new and experienced, will find valuable."
—Associate Professor of Mathematics and Computer Science, Emory University
Kathryn A. Moler
What a charming book! I like to think of myself as an adequately skilled MATLAB user, but I learned a lot from it.(Kathryn A. Moler, Assistant Professor of Applied Physics, Stanford University)
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Nick Trefethen
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"MATLAB Guide, Second Edition, is my new favorite MATLAB reference because it not only teaches MATLAB, it fosters a love for all things related to scientific computation. This well-written book features top notch examples, the latest MATLAB features, and offers MATLAB insights that can't be found anywhere else!"
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Editorial Reviews
Booknews
Desmond (mathematics, U. of Strathclyde) and Nicholas (applied mathematics, U. of Manchester) introduce the popular software for matrix computations to new users. They describe MATLAB 6 (but the book can be used with earlier versions), explaining all that most users will ever need to know<-->the most popular features, the Symbolic Math Toolbox, etc.<-->but also they consider more advanced topics for existing users, among them structures and cell arrays, function handles, profiling, vectorization, sparse matrices, and Handle graphics |
Course essentials. I am one of those who believe that Calculus is among our species' deepest, richest, farthest-reaching and most beautiful intellectual achievements.
This course provides an opportunity for you to discover and appreciate some of the jewels of Calculus. It is my privilege to be in a position to assist you in making those discoveries.
Course Description: (from the catalog) Applications of the integral and techniques of integration. Trigonometric, logarithmic and exponential functions. Prerequisite: grade of C or higher in 220.
Text: James Stewart, CALCULUS, Concepts and Contexts, Brooks Cole.
Second edition.
Supplements: Weaknesses in basic algebra and trigonometry often present a major obstacle for a progress in calculus. Even though we tried to address those in Calculus I, it is quite possible (likely?) that we will run into some of those difficulties again. It will be your responsibility to bring yourself to the level necessary. Two main tools that we used in Calculus I:
• A computer software: ALEKS. It can be obtained through the Mc- Graw Hill publisher. We will talk some more about this software during the first week of class. might still be needed. However, I will not be monitoring use of those in this course
1
2 MATH 221 - CALCULUS II SYLLABUS - SPRING 2005
main Thinking
Communication Skills: Students will . . .
(a) . . . read with comprehension and the ability to analyze and evaluate.
Life Value Skills: Students will analyze, evaluate and respond to ethical issues from an informed personal value system.
The basic principles (strategies) of thinking that we will use over and over go beyond calculus, beyond mathematics. I believe that those principles have a value of lessons for life. Please check
Ten Principles1 for a short list of those principles/lessons. Cultural Skills: Students will . . .
(a) . . . understand culture as an evolving set of world views with diverse
historical roots that provides a framework for guiding, expressing, and
interpreting
Aesthetic Skills: Students will develop an aesthetic sensitivity. InFundamental Theorem of Calculus. Various techniques of integration, i.e., various applications of substitution rule and integration by parts. Integration of rational, algebraic, trigonometric, exponential and logarithmic functions. Numerical integration. Applications of calculus, including some differential equations. Infinite series, including power series, Taylor and
Maclaurin series, Binomial series.
1
MATH 221 - CALCULUS II SYLLABUS - SPRING 2005 3
In other words, we are talking about chapters 5 − 8 from the book.
Mathemat
Problem be
By now, all of you should have some familiarity with a CAS (Computer
Algebra System), such as DERIVE, for example. I encourage you to use a
CAS as a tool to check your calculations. However, we are going to raise your proficiency in using CAS to another level; see about the semester project below.
It is becoming customary these days to communicate your work via some form of electronic media. To type up your mathematics HW, assuming you want all your symbols and formulas look good . . . , is considerably more complicated than with an English paper, say. All of you are expected to take some more serious math/science courses after this one. The tool for typesetting mathematical, chemical, . . . formulas is (at least in my opinion)
LATEX. We will try to get some rudimentary "hands on" experience of dealing with LATEX as well., for this class, is at least 10 hours. Working every day on calculus problems is a must. Also, an active class
4 MATH 221 - CALCULUS II SYLLABUS - SPRING 2005 participation, working in small groups, not hesitating to ask me for help both in class and in my office can greatly enhance the success and quality of your learning.
You which
As I would prefer that you use a pen for writing in that journal. If you are going to use pencil, then please do not use erasers, and in any case, do not tear pages out. For a learning to take place, you have to try to do something. In trying, you are likely to make mistakes. The real learning will start taking place once you start understanding and correcting your mistakes.
You turn that journal in together with your exam, and then you will be graded for the portion of that journal that covers the period preceding that current exam. Up to 30% of the exam score is possible to earn this way.
The The work in class, your book, HW, and practice exams should give you a pretty clear idea what is that you are expected to learn. It is your job to, perhaps through
MATH 221 - CALCULUS II SYLLABUS - SPRING 2005 5 a group project (150 points), class participation (5%), take-home problems, and the Learner's Journal (30% of the corresponding exam).
There might be an in-class presentation (worth 50 points), if the time permits. The project will involve some use of technology (CAS and LATEX). The details will be given later. You will be required to work hard, and will have every opportunity to show what you have learned.
One of the writing assignments will be graded in two parts - the second part will require you to come to my office and explain your reasoning, answer some questions.
One, or more, of those assignments will be "group assignments".
InImportant University Policies: Please follow the links at:
Viterbo Policies2 and read the corresponding statements on attendance, plagiarism, and sexual harassment.
Americans with Disability Act: If you are a person with a disability and require any auxiliary aids, services or other accommodations for this class, please see me and Wayne Wojciechowski in Murphy Center Room 320 (796-Schedule outline
Topic Week Book - Section
Antiderivatives Jan 17 Chapter 4
Definite R, FTC Jan 24, Chapter 5
Integration techniques Jan 31 Chapter 5
More R, Exam 1 Feb 7 Chapter 5
Numerical integration Feb 14 Chapter 5
Sequences Feb 21 Chapter 8
Power Series Feb 28
Spring Break March 7
Taylor Series March 14
Series - applications, Exam 2 March 21 Easter break
Applications of R March 29 Chapter 6
April 4 Chapter 6
Differential Equations April 11 Chapter 7
April 18
Project presentations April 25
Review May 2
Important dates.
Classes begin: January 17, 2005.
Midterm break: March 5-13.
Easter Break: March 24 − 28.
Last day of class: Friday, May 6.
No class: -
• Friday, April 15;
due to my absence - attending a conference.
Semester Exams: • Exam 1: at the end of Chapter 5
• Exam 2 - Chapter 8.
Final Exam: Monday May 9, 12:50-2:50
This syllabus is tentative and may be adjusted during the semester.
I am looking forward to explore this fascinating subject with you, and for all of |
Beginning Algebra : Text / Workbook - 7th edition
Summary: Pat McKeague's passion and dedication to teaching mathematics and his ongoing participation in mathematical organizations provides the most current and reliable textbook series for both instructors and students. When writing a textbook, Pat McKeague's main goal is to write a textbook that is user-friendly. Students develop a thorough understanding of the concepts essential to their success in mathematics with his attention to detail, exceptional writing style, and or...show moreganization of mathematical concepts.
BEGINNING ALGEBRA: A TEXT/WORKBOOK, Seventh Edition offers a unique and effortless way to teach your course, whether it is a traditional lecture course or in a self-paced format. In a lecture-course format, each section can be taught in 45-to-50 minute class sessions, affording instructors a straightforward way to prepare and teach their course. In a self-paced format, Pat's proven EPAS approach (Example, Practice Problem, Answer and Solution) moves students through each new concept with ease and assists students in breaking up their problem-solving into manageable steps.
The Seventh Edition of BEGINNING ALGEBRA: A TEXT/WORKBOOK has new features that will further enhance your students' learning, including boxed features entitled Improving Your Quantitative Literacy, Getting Ready for Chapter Problems, Section Objectives and Enhanced and Expanded Review Problems. These features are designed so your students can to practice and reinforce conceptual learning. Furthermore, iLrn/MathematicsNow, a new Brooks/Cole technology product, is an assignable assessment and homework system that consists of pre-tests, Personalized Learning Plans, and post-tests to gauge concept mastery. ...show less
Paired Data and Graphing Ordered Pairs. Solutions to Linear Equations in Two Variables. Graphing Linear Equations in Two Variables. More on Graphing: Intercepts. The Slope of a Line. Finding the Equation of a Line. Linear Inequalities in Two Variables.
Multiplication with Exponents. Division with Exponents. Operations with Monomials. Addition and Subtraction of Polynomials. Multiplication with Polynomials. Binomial Squares and Other Special Products. Dividing a Polynomial by a Monomial. Dividing a Polynomial by a Polynomial.
6. FACTORING.
The Greatest Common Factor and Factoring by Grouping. Factoring Trinomials. More Trinomials to Factor. The Difference of Two Squares. Factoring: A General Review. Solving Equations by Factoring. Applications.
Definitions and Common Roots. Properties of Radicals. Simplified Form for Radicals. Addition and Subtraction of Radical Expressions. Multiplication and Division of Radicals. Equations Involving Radicals.
0495108987 Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc... All day low prices, buy from us sell to us we do it all!!
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Equation is a useful software that can let you study and solve the equations of the second degree, enter only the values of a, b, and c and this software will do the rest. Once all the values are entered, the application will display ...
Equation Illustrator V has been designed to ease the ... graphics and complicated formatted text such as math equations in electronic and printed documents. A WYSIWYG interface ... what you want where you want it. Formatted equation macros can be stored and retrieved with a ... also included, over 50 drawing tools in all. Equation Illustrator V is designed for people who know ...
The program allows you to solve algebraic equations in the automatic mode. You just enter an equation in any form without any preparatory operations. Step by step Equation Wizard reduces it to a canonical form performing ... After that it determines the order of the equation, which can be any - linear, square, cubicQuadratic equation has the form ax2 + bx + c ... two different values of x that make the equation true. It can happen that both solutions are the same number, and it is possible that the solutions will be complex or imaginary numbers. To use this software, type in values ...
FX Equation software was designed to be an equation editor that takes the chore of formatting equations away from you. It is for people who love the output from the modern equation editors but hate using them. FX Equation automatically formats, with a minimum of input from you, just about all of the equations an average mathematics teacher uses everyday. FX ...
AutoAbacus is a powerful equation solving library that finds solutions to equation sets with a snap. A set of equations can be passed in as text, while AutoAbacus ... find a solution that satisfies all constraints. The equations are not limited to be only linear, but ... include arbitrary functions. By profiling the types of equations in the system and their dependencies on each ...
MathType is a powerful interactive equation editor for Windows and Macintosh that lets you ... MathML documents. More Ways to Create Equations * Entering Math by Hand: Enter equations as easily as you would write math with ... 7. * Point-and-Click Editing with Automatic Formatting: Create equations quickly by choosing templates from MathType's palettes and ...
MathCast is an equation editor, an application that allows you to input mathematical equations. These equations can be used in written documents and webpages. The equations can be rendered graphically to the screen, to ... interface is suited for rapid development of mathematical equations. A part of this interface is called The
... user to create scientific mail messages with complex equations. This modern and beautiful scientific software makes the exchange of complex ideas simple. The scientific equation editor used in this software allows you to create complex letters, including complex scientific equations, at almost the same speed as typing standard ... Scientific Letter, will see the message text with equations included in it as graphical parts. The recipient ...
DeadLine is a free program useful for solving equations, plotting graphs and obtaining an in-depth analysis of ... numerical calculus, in a very intuitive approach. Most equations are supported, including algebraic equations, trigonometric equations, exponential equations, parametric equations. DeadLine solves equations graphically and numerically. It displays the graph of ... a list of the real roots of the equation. You can evaluate the function and the first ...
Basically an equation editor, however not focused over one single equation, but you can write your mathematical artwork over ... pages. You can easily move and copy your equations and expressions by mouse touch. Illustrate your equations using hand-drawing tools. Use symbolic calculator and function |
MATLAB for Engineers, 3e, is ideal for Freshman or Introductory courses in Engineering and Computer Science. With a hands-on approach and focus on problem solving, this introduction to the powerful MATLAB computing language is designed for students with only a basic college algebra background. Numerous examples are drawn from a range of engineering disciplines, demonstrating MATLAB's applications to a broad variety of problems. This book is included in Prentice Hall's ESource series. ESource allows professors to select the content appropriate for their freshman/first-year engineering course. Professors can adopt the published manuals as is or use ESource's website to view and select the chapters they need, in the sequence they want. The option to add their own material or copyrighted material from other publishers also exists.
You can earn a 5% commission by selling MATLAB for Engineers |
GCSE mathematics linked pair
The GCSE mathematics linked pair (MLP) is a mathematics qualification that is currently being piloted.
The original idea stems from one of the recommendations made by by Professor Adrian Smith in Making Mathematics Count (2004) that consideration be given to redesigning GCSE mathematics as a double award, similar to English.
The Advisory Committee on Mathematics Education (ACME) subsequently led on the development of the original proposal and the former Qualifications and Curriculum Development Agency (QCDA) set up the pilot. The Department took policy responsibility for the qualification and the pilot in 2011.
There are two mathematics GCSEs in the MLP and they must be taken together.
They are:
GCSE applications of mathematics
GCSE methods in mathematics.
The qualifications emphasise problem-solving, functionality and mathematical thinking. However each of the pair of qualifications is different:
The applications of mathematics GCSE is intended to assess skills relating to how mathematics is used to interpret, analyse and solve problems relating to a range of realistic contexts, including financial and statistical applications; place an additional emphasis on the interpretation of graphical information and the use of approximate methods.
The methods in mathematics GCSE is intended to assess powers of reasoning and logical deduction; assess fluent use of symbolisation and exact methods of solution; assess understanding of probability.
Students have been studying for the GCSE mathematics linked pair (MLP) since September 2010. This qualification is available between September 2010 and summer 2014 (with examinations available until September 2015).
In line with all other GCSEs there will be linear assessment for the two-year GCSE courses to be taught from September 2012.
Alphaplus Consultancy is evaluating the qualifications over the first two years under contract to the Department for Education and has published reports on their findings.
These qualifications meet the requirements of the national curriculum at key stage 4 and the regulators' criteria frameworks. Both elements of the GCSE Mathematics Linked pair must be taken to meet the performance measure, although a pass in either is sufficient.
You can find out more about the content of the syllabuses for the qualifications by contacting the mathematics subject teams at the awarding organisations offering the qualifications: AQA, Edexcel, OCR and WJEC. |
The aim of a travelling salesperson problem is to visit every vertex of the network and return to the starting vertex using the route that has the minimum total weight.
The problem requires students to find the best route for a courier to take to deliver parcels to a number of towns and return back to base.
Travelling salesperson…
The aim of the route inspection problem is to find a route that is as short as possible yet goes down every road once and returns to the starting point. The task informs students that there has been a heavy snowfall overnight and that the students are required to clear the roads in the town centre as quickly as possible, then return…
Many topological graphs have edges that cross. The aim is to re-draw the graph in such a way that none of the edges cross. The task informs students they are required to design a printed circuit board and since the wires are not insulated they must not cross.
Planarity: presentation - an introduction to the problem outlining the…
The aim of a minimum spanning tree is to connect every vertex of the network using the edges having the least possible total weight. The task requires students to analyse information about a town centre and suggest which roads should be pedestrianized.
Minimum spanning tree: presentation - an introduction to the problem outlining…
A matching is a set of edges on a bipartite graph in which no two edges share a common vertex. A bipartite graph consists of two sets of vertices X and Y. The edges only join vertices in X to vertices in Y. A matching in a bipartite graph is the pairing of some or all of the vertices in X with some or all of the vertices in Y. If…
Linear Programming involves creating a function that represents a real life problem. The aim is to optimise this function given certain constraints. Simple examples of linear programming will have few variables and constraints, however, real life situations will have many more variables and constraints that will need to be considered.
Problems…
The network flow problem involves finding the optimum route through a flow network; a directed graph where each arc has a capacity and each arc receives a flow. Typical examples include: evacuation plans and delivery services.
The problem involves students analysing the plan of a school canteen and deciding whether, given relevant…
Dijkstra's algorithm finds the shortest path for a given problem. Dijkstra's algorithm can be used to find the shortest route between two cities. This algorithm is so powerful that it not only finds the shortest path from a chosen source to a given destination, it also finds all of the shortest paths from the source to…
Critical path analysis is a project management technique and is used to lay out all of the activities which are needed to complete a task. Starting some activities will depend on completing others first, while independent activities can be started any time. Critical path analysis helps to predict the project completion time.
The…
The purpose of bin packing is to pack a collection of objects into containers called bins. The bins are all the same size and the objects to be packed are different sizes. The aim is to pack the objects into the bins using the fewest possible bins. In this example students are asked to save computer files onto a CD.
Bin packing: biology |
Readable rigor: The writing of this text is cogent, clear, and compelling while carefully maintaining mathematical precision.
Exercise sets have real depth and are organized into three parts: skills exercises (Problems for Practice), more challenging and thought-provoking exercises (Further Theory and Practice), and technology exercises (Calculator/Computer Sciences) |
Elementary Number Theory
9780072325690
ISBN:
0072325690
Edition: 5 Pub Date: 2001 Publisher: McGraw-Hill Higher Education
Summary: "Elementary Number Theory," Sixth Edition, is written for the one-semester undergraduate number theory course taken by math majors, secondary education majors, and computer science students. This contemporary text provides a simple account of classical number theory, set against a historical background that shows the subject's evolution from antiquity to recent research. Written in David Burton's engaging style, Elem...entary Number Theory reveals the attraction that has drawn leading mathematicians and amateurs alike to number theory over the course of history |
MST Course Descriptions
Required Courses
MATH
900: Bridges From Classroom to Mathematics (1 credit) ONLINE
An introduction
to the goals of the MST program.
Students will have the opportunity to explore mathematical problems; to
complete activities that make connections between several areas of mathematics,
including the mathematical content in the MST degree program and the secondary
school mathematics classroom; and to participate in readings/on-line
discussions on the nature of mathematics.
MATH 905: Euclidean and
Non-Euclidean Geometries from a Synthetic Perspective
An axiomatic development of geometry,
beginning with finite geometries; emphasis is given to the fundamental concepts
of Euclidean and non-Euclidean geometries from a synthetic perspective.
MATH 906: Analytic and
Transformational Geometry
Fundamental concepts of transformational,
projective geometry, and inversive geometry, including the properties of conics
and quadratic surfaces.
MATH 909: Probability and Statistics for Teachers
An introduction to the fundamental concepts of probability, including
combinatorics and probability distributions; statistical
applications, including sampling, statistical inference and
significance tests; linear regression; and the Central Limit
Theorem.
MATH 913: Graph Theory and Discrete Mathematics
Key
theoretical, and computational aspects of graph theory and related areas of
discrete mathematics. Applications of graph theory as well as current "open"
problems will be explored.
MATH 915: Algebraic Structures
An exploration of the structural similarities between and
among seemingly disparate number systems, beginning with counting numbers, and
progressing to the integers, the rational numbers, the real numbers, and the
complex numbers; and leading to a discussion of polynomials as an integer
analogue and to fields as polynomial "quotients" through the basic concepts of
splitting fields and Galois Theory.
MATH 918: Analysis – Real Numbers and Real
Functions
An
introduction to the fundamental concepts in real analysis that provide the
mathematical foundation for calculus.
Content focuses on properties of sequences and series; properties of
functions, including continuity, the derivative and the Riemann integral.
MATH
925: Problem Solving Seminar (Pass/Fail)
A study of a variety of problem solving strategies
and techniques used in the context of solving mathematical problems.
Problems will emphasize the connections between the core areas of Algebra,
Geometry, and Analysis. Other mathematical topics may also be included.
Typically, taken in conjunction with Concluding Experience Problem Set.
Elective Courses
MATH 902: Classroom Practicum
(1 credit) ONLINE
A
follow-up course to the six core mathematics content courses of the MST degree program.
During the course, students will choose a mathematical topic and/or set of
concepts learned in one of the core MST courses and develop and teach a unit
based on these concepts at the middle school or secondary school level.
MATH 910: Topics in Mathematics Education (1 credit) ONLINE
Special topics in Mathematics Education
that are not included in the regularly offered courses. Possible topics
include: development of mathematical reasoning across the grades, action
research in mathematics classrooms, algebraic thinking across the grades, formal
and informal assessment strategies, cooperative learning strategies, and
mathematical software in secondary teaching.
MATH 914:
Topology for Teachers
An introduction to the foundational
notions of general topology, including neighborhood, open set, closed set,
limit point and closure; and to the topological properties of separation,
connectedness and compactness.
Emphasis is given to the usual topology for the real line.
MATH
916: Number Theory ONLINE
An introduction to number theory,
including divisibility theory, congruences, perfect and amicable numbers,
Fermat's Little Theorem, Euler's phi-function and other number-theoretic
functions, Diophantine equations, and cryptography.
MATH
917: Proof and Problem Solving
Introduction
to abstract mathematics with an emphasis on problem solving and proof
structure, methods, and techniques. Content includes logic, set theory, and
basic number theory.
MATH 919:
The Real Number System
A
postulational approach to fundamental aspects of algebraic structure; limits, sequences,
and continuity.
MATH
920: History of Mathematics ONLINE
An examination of the historical development of number
theory, geometry, probability, algebra, and analysis that notes the significant
mathematical contributions to these topics by prominent mathematicians.
MATH 928: Topics in Mathematics (1 credit)
Special topics in Mathematics that are
not included in the regularly offered courses. Possible topics include: knot
theory, and spherical geometry.
MATH 929: Directed Reading (variable credit)
A directed reading project
on a selected topic in mathematics or mathematics education, planned in
collaboration with a faculty member. |
When Less Is More
Claudi Alsina and Roger Nelsen
Inequalities permeate mathematics, from the Elements of Euclid to operations research and financial mathematics. Yet too often, especially in secondary and collegiate mathematics, the emphasis is on things equal to one another rather than unequal. While equalities and identities are without doubt important, they donít possess the richness and variety that one finds with inequalities.
The objective of this book is to illustrate how the use of visualization can be a powerful tool for better understanding some basic mathematical inequalities. Drawing pictures is a well-known method for problem solving, and the authors will convince you that the same is true when working with inequalities. They show how to produce figures in a systematic way for the illustration of inequalities and open new avenues to creative ways of thinking and teaching. In addition, a geometric argument cannot only show two things unequal, but also help the observer see just how unequal they are.
The concentration on geometric inequalities is partially motivated by the hope that secondary and collegiate teachers might use these pictures with their students. Teachers may wish to use one of the drawings when an inequality arises in the course. Alternatively, When Less Is More might serve as a guide for devoting some time to inequalities and problem solving techniques, or even as part of a course on inequalities. |
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Review
.
(MAA Online )
Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts.
(Choice 2003)
Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik's Cube. Enthusiastic students will learn a lot of mathematics from this book.
(American Scientist 2003)
The book begins with some lecture notes of discrete mathematics and group theory. These theoretical notions are very nicely applied to some practical problems, e.g.: Rubik's cube, Rubik-like puzzle groups, crossing the rubicon, God's algorithm and graphs. The work ends with a rich bibliography and index.
More About the Author
I'm a math professor and enjoy writing about mathematics and related topics. Not all my books are listed in the Amazon author's page (and at least one that is was not written by me), so feel free to use the search feature if you don't find something.
I can't figure out who the intended audience is for this book. It's not a textbook; the subject is not developed in a systematic manner, nor are there useful problems sets. The reader exercises, referred to as 'Ponderables' in the book, can be extremely challenging and off-topic, beginning with the chess problems in the first chapter. It's also too technical to be a popularization, although it seems to be targeted as such. I was looking for friendly introduction to group theory, and the core concepts are there. However, a focus on the Rubik's cube and other similar games as primary examples of groups introduces a lot of complexity.
The book is written in an entertaining fashion with many historical references, quotes, puns and quips. I often found them to be a distraction.
The SAGE programming code provides quite a few examples but it is often not decipherable to a reader unfamiliar with this relatively obscure language based on Python; a little explanation would have gone a long way. Frequently terminology and notation are used before they are defined. Apparently this second edition cleaned up some errors, but there are still a number of typos and statements which are simply wrong. Theorems are stated imprecisely, and the proofs in the book are often hand-waving exercises rather than actual proofs. Important results are presented without justification or the proof left to the reader.
I don't intend to imply there is no value here. Parts of the book provide a relatively accessible introduction to group theory, but the reading experience can be very frustrating. |
The exact same formulachart is also found in the test booklet at the beginning of the mathematics test. The formula charts have changed over the years. The separate chart now has a metric ruler on one side and a customary ruler on the other side for students to use if
square and by using the quadratic formula. A1.6.A M1.5.A A1.6.A Use and evaluate the accuracy of summary statistics to describe ... Microsoft Word - Cross-Reference Chart High School Mathematics Standards Organized by Courses Author:
Will the Grade 7 MathematicsFormulaChart be helpful on this problem? Why or why not? 3. How can I determine the scale factor for this relationship? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5.
Will the Grade 7 MathematicsFormulaChart be helpful on this problem? Why or why not? 3. Will a picture or diagram be helpful on this problem? If so, how? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5.
the use of the formulachart? The mathematics curriculum framework does not require students in grades 3 and 4 to know formulas. However, students in grades 5-8 are expected to know any formulas indicated in the curriculum framework.
Mathematics, Grade 8 Course Author Janet Martin Your grader may be different from the author. MATH 8A features: ... A formulachart will be provided. Calculators MAY NOT BE USED on the final exam. Show all of your work so that you can receive
CMT FormulaChart 3 Organization of CMT Strands by Content Standard 4 Mastery Criteria Map 6 Point Values for Each Standard 8 ... mathematics vocabulary, by grade level, with which all students should be familiar to be successful in mathematics; and
of mathematics and the evolving nature of mathematics and mathematical knowledge. 14 TExES Preparation Manual — Mathematics 4−8 STUDY TOPICS 3 ... If the family constructs a pie chart using these figures, what is the approximate measure
Bridges in mathematics Grade 2 supplement set a2 Numbers & Operations: Solving Equations The Math Learning Center, PO Box 12929, Salem, Oregon 97309. ... H pocket chart H Work Places currently in use advance preparation Have students help you set up a
Mathematics, Grade 8 Course Author Janet Martin Your grader may be different from the author. MATH 8B features: ... A formulachart will be provided. Calculators MAY NOT BE USED on the final exam. Show all of your work so that you can receive
Mathematics Students Scott A. Sinex Barbara A. Gage ... region is a Formula bar. Cell contents are displayed here. If you activate a cell ... chart by clicking on the axes, moving labels, or using the menu choices as before.
mathematics. They are like recipes and can be used every time you need to find certain information such as perimeter, area, volume, ... Use this formula to complete the chart on the right. 0 Answers are on page 21. 10 . 4 About Math and Life
All CAPT mathematics items are written in a real world context and require students to solve a problem. In addition, all ... CAPT FormulaChart Questions on the CAPT Mathematics Assessment measure students understanding of mathematical |
Maths for science and technology
You're about to start a course in science and technology and you're...
You're about to start a course in science and technology and you're wondering whether your level of maths is going to be enough to get you through. This unit will show you how to reflect on what you know, identify which skills you might need for your course, and help you to learn those skills using worked examples and activities.
Through a number of activities, you will be taught how to reflect on the maths you need for your course, in order to identify which areas you will need to concentrate.
Through instruction, worked examples and practice activities, you will gain an understanding of the following mathematical concepts:
indices;
equations and algebra;
units, significant figures and scientific notation;
basic trigonometry;
logarithms.
You will be provided with a list of references to further reading and sources of help, which can help you improve your maths skills.
Maths for science and technology
Introduction
How do you feel about the mathematics in your course materials? It is quite possible that you do not feel as confident as you would like. If you have not done any mathematics recently, you may feel that you need to refresh your memory or there may be a specific topic that you never really fully understood.
Other students have said:
When I'm faced with a triangle, I never know which trig ratio to use.
I'm alright until I get to the point where a question asks me to use logs to solve a problem, then my mind goes blank.
This unit is one in a series of Student Toolkits; there are others to help you with such things as note taking, essay and report writing, effective use of English, revision and examinations, and working with charts, graphs and tables |
Book DescriptionProduct Description
AboutAs a word of warning, do not purchase this book expecting it to teach you math fundamentals. If you do not have a background of at least algebra and trigonometry (and preferably a bit of calculus), you owe it to yourself to pick up another book and brush up on these fundamentals. While there are a few appendices covering a handful of topics, they are less about explaining the topic and more of reference pages.
Mathematics for 3D Game Programming and Computer Graphics is an excellent reference book for anyone doing 3D work. The topics are very to the point and few pages are wasted explaining basic math principles (hence the warning about having a decent math background). The book probably won't teach anyone who doesn't know they underlying principles but will be your go-to reference for any algorithm you implement.
The book starts with the reviews of the requisite vector, matrix, transformation (including rotations by quaternions) and basic geometry for a view frustum, but quickly dives into more advanced topics. Ray tracing is covered for all areas of use, from light maps to reflections. The lighting chapter covers texturing using several map types as well as lighting models with a very enjoyable discussion of specular reflection models.
Solid chapters on culling using bounding volumes and portal systems, shadowing and curve algorithms round out the first half of the book. The second half is devoted to the mathematics of physics, with chapters on basic collision detection, linear and rotational physics. The simulation of fluids and cloth (one of the more difficult physical models to accurately compute in a game) gets it's own chapter and it's a highlight for anyone implementing character clothing animation or a realistic water volume.
Every chapter has exercises (with and appendix of answers) to reinforce the material. The C++ and GLSL shader code is available on the books companion website ( much of which forms the basis for the math classes of the authors own engine.
Anyone who needs a math reference book for 3D would do well to own this book. If you are writing your own engine, you owe it to yourself to pick up what will be the only math book you will need. While many technical books do not age well, this hardcover book will last through many late-night coding sessions both physically and with regard to the material within at a low price point. Never again will you have to scour through your old textbooks or search online for the algorithm you are trying to implement. The author has done the impossible; make a truly terrific math textbook.
This book is just what I have been looking for: something that presents and cogently explains the math that is most useful for implementing 2d and 3d computer graphics. If the Kindle edition did not have the problems it has, I would give it 5 stars. However, it gets a poor rating for two reasons. One, the diagrams are too small! Other Kindle documents allow the reader to scale images, but not this one. Two, and this is just INEXCUSABLE: The Kindle edition, but not the print edition, has errors that make the equations and proofs worthless. I can't quote examples exactly because special characters don't show up properly, but here's a description of three examples: |
Contest Problem Book I
Compiled and with solutions by C. T. Salkind
A great many students have participate annually in the Annual High School Mathematics Examinations (AHSME) sponsored by the Mathematical Association of America (MAA) and four other national organizations in the mathematical sciences. In 1960, 150,000 students participated from about 5,200 high school. In 1980, 416,000 students participated from over 6,800 high schools.
Since 1950, when the first of these examinations was given, American high school students have tested their skills and ingenuity on such problems as:
The rails on a railroad are 30 feet long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in miles per hour is approximately the number of clicks heard in how many seconds? |
Author's Description
Basic Algebra Shape-Up - Hands-on basic algebra tutorials, easily understood steps. The program is self-paced and self-monitored. Students advance as they demonstrate readiness. They may track their own improvement through progress-to-date and last session scores. Scores are kept in a record management system that allows teachers to view and print detailed reports. Designed for students in U.S. grades 6 through 9 (age 10 and up), the program can also be used by ESL and adult students interested in improving their algebra skills.
Basic Algebra Shape-Up 4.0 is licensed as Shareware for the Windows operating system / platform. Basic Algebra Shape-Up is provided as a free to try download for all software users (Shareware).
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Basic Algebra Shape-Up Merit Software. Please be aware that we do NOT provide Basic Algebra Shape-Up cracks, serial numbers, registration codes or any forms of pirated software downloads. |
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