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Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
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their education.EC 385 Spring 2005Computer Assignment #1For this assignment, you are to read the accompanying article on the growth of the U.S. economy and to download some data on real gross domestic product (GDP) and calculate rates of economic growth using Ex
Chapter 7 LEGO Designby Fred G. Martin and Randy SargentLEGO Technics are fun to play with and allow the construction of great things, but they are not always easy to use. In fact, it is often quite challenging to build a LEGO device that does not
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Chapter 1 An Overview of Financial ManagementLearning ObjectivesAfter reading this chapter, students should be able to: Identify the three main forms of business organization and describe the advantages and disadvantagesof each one. Identify
James Madison University Mathematics ColloquiumThe Algebra of Molecular EvolutionDr. John Rhodes Bates CollegeTuesday, February 3 2:40 pm(Refreshments served at 2:30)Room 30, Burruss HallAbstract Traces of the evolutionary history of living
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James Madison University Statistics ColloquiumExact Unconditional Methods for the Difference of Proportions Jimmy A. Doi North Carolina State UniversityMonday, February 3 3:30 pm Room 33, Burruss HallAbstract Exact tests based upon the differencChapter 4: Properties of the Least Squares EstimatorIn this chapter, we will Review the formulas for b1 and b2 Derive their means, variances and probability density functions To do so, we will use the assumptions we made in Chapter 3. Do a Monte
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Outline Theoretical Foundations - continued Vector clocks - review Casual ordering of messages04/27/09COP56111Announcements This is no TA for this class I will do the grading and everything else by myself Homework #1 is due this ThursdAssignment 7: Standards and Curriculum Mapping and AlignmentNational Standard [Select ONE Standard]Aligned State Standard from MD VSC or other state curriculum (provide all topics and indicators for the standard)Aligned Local Standard or
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Exercise #3 Name _ I want you to plot the distribution of asteroids in the main and the distribution of taxonomic types. Go to the Syllabus on the website. Go to October 4. Download the Class Exercise #3 Asteroid Data 1) Plot the distribution of aste
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Designed as a supplement to a beginning algebra course, where calculators are an integral component, this text aims to encourage students to use the power of the graphing calculator to enhance their ...
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Other Materials
Description
Calculus A introduces limits, differentiation, and applications of differentiation. The student will find and evaluate finite and infinite limits graphically, numerically, and analytically. The student will find derivatives using a variety of methods including the chain rule and implicit differentiation. Then the student will use the first derivative test and the second derivative test to analyze and sketch functions. Finally, the student will find derivatives using a variety of methods including substitution.
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Vector Functions
Recall that functions are much like computers or machines that take in one or several input numbers and put out a single number. And recall that vectors are mathematical entities composed of two pieces, magnitude and direction, like the...
Please purchase the full module to see the rest of this course
Purchase the Points, Vectors, and Functions Pass and get full access to this Calculus chapter. No limits found here.
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Math 41 Autumn 2012
Math 41 is a 5-unit course in introductory calculus with an accelerated pace -- the class covers limits, derivatives, applications of differentiation, and the basics of integration (up to substitution and integration by parts). It is one of three different single-variable calculus courses taught at Stanford in the autumn quarter, so you should be deciding during the first week whether it's the right calculus class for you.
If you have recently finished a
calculus class covering all of the subjects listed above and you feel confident about them, you should consider instead taking Math 41's continuation, Math 42, this fall -- even if you don't have AP credit. If you're undecided about which of Math 41/42 (or any two courses in sequence) to take, keep in mind that it will be easier to drop back than to jump ahead during the second or third week of the quarter.
On the other hand, if it's been a year or more since your last math class or you are taking math just to satisfy a DB-MATH, you should consider instead entering the Math 19-20-21 sequence -- even if you did well in calculus in high school. The sequence Math 19-20-21 covers the same material as Math 41-42, but at the more traditional year-long pace (ending with Math 21 in the spring quarter). By contrast, Math 41 moves very quickly, and leaves you very little time to get back into shape if your math skills are rusty. It is intended to quickly develop the necessary background for students who will need calculus for their further studies, and may be more intense than what students satisfying a disciplinary breadth requirement are looking for.
On Registrar deadlines: Please pay careful attention to all Registrar deadlines, especially the add/drop deadline at the end of the third week of classes. University Advising and Research has recently reaffirmed that it will not allow changes in course registrations from Math 42 to 41 after the drop deadline. However, UAR has a special provision in place to accept petitions for switches from Math 41 to 19 submitted in complete form before Friday, October 26th at 5pm. The instructions for how to properly complete the petition is contained at the bottom of this page. You can also contact your instructor for more information.
The textbook is Single Variable Calculus: Concepts and Contexts, 4th
edition, by James Stewart.
We will cover most of the material from Chapter 1 through the first half of Chapter 5.
Most homework exercises and reading
assignments are taken from the book, so you should have access to a copy throughout the quarter.
(It is not recommended that you try to use a copy of an older edition: although the text is very similar, some examples, some of the homework problems, and most of the problem numbers will be different.)
Each week you will attend three lectures and two discussion sections. The
lectures are on Monday, Wednesday and Friday, either at 9am, 10am, 11am, or 1:15pm.
The discussion sections are on Tuesday and Thursday. See the Section Assignments page to view the choices for times and locations and instructions
on the sign-up process. You will sign up for a discussion section via CourseWork,
and your available options will depend on your lecture instructor.
The lectures will be used primarily to introduce concepts and develop theory, and serve as a complement to the course textbook. You can get the most out of lecture by having first read the relevant sections in the textbook (as set in the calendar of topics on the course schedule page). In the discussion sections, you meet with your Teaching Assistant in a smaller group. Much of the time in section will be used for example problems based on topics developed in lecture and the textbook; you can get the most out of section by working on the posted daily discussion problems in advance (i.e., immediately after lectures).
Attendance at all lectures and sections is required. If you miss a lecture or a section, it is your responsibility to catch up on the topics that you missed. You should keep in mind that in this course, the material builds on itself; if you miss some of the material, subsequent lectures will be more difficult (or even unintelligible) for you.
There will be weekly homework assignments.
For more information and policies, see the Homework page.
Calculators
Calculators will not be used in a systematic way in Math 41. Calculators will
not be allowed on any of the exams, nor should there be any need for one.
Occasionally, homework problems may call for the use of a scientific or
graphing calculator.
The midterm exams will be held in the evenings on October 18 and
November 8.
The exact times and locations and other information will be posted on the
Exam Information page.
If you have a schedule conflict with one
of the midterm exams due to another course meeting, you must
at least one week before the exam to arrange to take it at an alternate
(early) sitting. (The same deadline holds for OAE accomodation requests; see below for details.)
The final exam will be held on Monday, December 10, from 7-10pm.
You must take the final exam at this time, which is set by the University.
All of the exams are closed book, closed notes, with no electronic aids.
For each exam, if appropriate, you may be provided with a formula
sheet, which will be available on the exam materials
page prior to the exam, along with other study materials.
Points available on exams: The total points available on the exams will be in approximate proportion 2:2:3. That is, the first and second midterm exams will have approximately equal numbers of total points available, and the number of points available on the final exam will be approximately 1.5 times those available on a single midterm exam.
There are no predetermined numerical cutoffs for letter grades, and the cutoffs may turn out to be rather different from what you are accustomed to from high school. In general, the grade distribution for the class is usually (roughly) as follows: around 30% of the class receive A's, around 40% receive B's, and most of the rest receive C's.
CourseWork
CourseWork
is a web-based program that will be used in Math 41 to allow
students to check grades online. It is a secure program, so your grades
will be available through CourseWork only to you.
Every student must sign into CourseWork and choose a discussion section. CourseWork will be
our primary gradekeeping tool; if you do not sign up, you could lose credit
for work that you have done.
This is completely independent of signing up for the course on Axess -- neither
program has any knowledge of the other.
Before you sign into CourseWork, make sure you read the
Section Assignments page, which contains instructions on the sign-up process for
discussion sections.
Again, remember that Axess and CourseWork are different programs, and you
will
sign up for different course components on each -- on CourseWork, you sign up for a
discussion section
based on the table on the Section Assignments
page,
but on Axess you sign up
for a lecture.
Despite its other capabilities, in this class CourseWork will be used only
for grades and possibly email announcements.
Some very good advice for college calculus students. Read this carefully and do as it suggests.
Note: Pay particular attention to #3 under "Weekly" and #6 and
#7 under "Before the exam". Students who think they're following these
tips often overlook those parts, and they're the most important
ones!
Your first resource for help outside of class meetings should be the course instructors and teaching assistants. You are encouraged to attend any of their office-hour sessions, not just those for your lecture or section leader, and no appointment is necessary at the times posted. In office hours we welcome any kind of question; we are here to help you and ready to explain the same thing as many times as necessary. You can also email us, but keep in mind that questions in office hours are answered more quickly and more clearly.
"Students who may need an academic accommodation based on the impact of a disability must initiate the request with the Office of Accessible Education (OAE). Professional staff will evaluate the request with required documentation, recommend reasonable accommodations, and prepare an Accommodation Letter for faculty dated in the current quarter in which the request is being made. Students should contact the OAE as soon as possible since timely notice is needed to coordinate accommodations. The OAE is located at 563 Salvatierra Walk (phone: 723-1066)."
"A switch from either MATH 41 or MATH 41A to MATH 19 has been
approved. Students will receive full credit for MATH 19 (3 units) upon
earning a passing grade for the course. Note: Because of the discrepancy
in units between either MATH 41 (5 units) or MATH 41A (6 units), and MATH
19 (3 units), students should be advised to consider the possible impact
this change may have on their university enrollment requirements. For
this reason, students switching from either MATH 41/41A must meet with a
UAR Advisor.
Select 'Section change' and enter the information for both courses in
the Change Requested section.
Obtain signature from the instructor of the new course. []
Sign the form.
Meet with an Advisor from the office of Undergraduate Advising and
Research to discuss the situation and obtain the Advisor's signature.
Submit the form to VPUE in the office of Undergraduate Advising and
Research (UAR) by 5:00pm, October 26, 2012.
Students will not need to write a statement regarding why they wish to
submit the petition. But they will need to obtain the instructor's
signature, as well as the signature of a UAR Advisor. The request will be
routinely approved and rather than a withdrawal with the notation of 'W,'
MATH 41 or MATH 41A will be dropped from the student's record and MATH 19
will be added. Students should be directed to speak with their new MATH
instructor regarding the grading policy for the MATH Switch."
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Publisher's description
Mathomatic is an easy to learn computer algebra system.
Mathomatic is a colorful the standard rules of algebra for symbolic addition, subtraction, multiplication, division, modulus, and all forms of exponentiation. The numeric arithmetic is double precision floating point with about 14 decimal digits accuracy. Many results will be exact.
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This course is designed for students who need to sharpen their skills or serve as a resource that teachers can employ to help struggling students stay up to speed. In this course, Professor Terry Caliste, an instructor with infectious energy and enthusiasm, helps students learn to understand and compare the properties of exponents including the rules for exponents, zero and negative exponents and scientific notation.
Benefits • Helps students sharpen their skills and stay up to speed.
• Instructor's unique presentation successfully motivates students.
• Understand the properties and the rules for exponents.
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Here is a genuine introduction to the differential geometry of plane curves for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. This well-illustrated text contains several hundred worked examples and exercises, making it suitable for adoption as a course text. Key concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The author introduces the core material of classical kinematics, developing the geometry of trajectories via the ideas of roulettes and centrodes, and culminating in the inflexion circle and cubic of stationary curvature.
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The math theory is developed in slow, simple stages and is directly applied to the solution of real problems. This method is backed up with "CHECKUPS" which act as a motivator, and "BRUSHUPS" which review the mathematical concepts immediately necessary for the continuance of the electrical development and applications.
Chapter 1 Introduction to Electricity
Chapter 2 Simple Electric Circuits
Chapter 3 Formulas
Chapter 4 Series Circuits
Chapter 5 Parallel Circuits
Chapter 6 Combination Circuits
Chapter 7 Electric Power
Chapter 8 Algebra for Complex Electric Circuits
Chapter 9 Kirchoff's Laws
Chapter 10 Applications for Series and Parallel Circuits
Chapter 11 Efficiency
Chapter 12 Resistance of Wire
Chapter 13 Size of Wiring
Chapter 14 Trigonometry for Alternating-Current Electricity
Chapter 15 Introduction to AC Electricity
Chapter 16 Inductance and Transformers
Chapter 17 Capacitance
Chapter 18 Series AC Circuits
Chapter 19 Parallel AC Circuits
Chapter 20 Alternating-Current Power
Chapter 21 Three-Phase Systems
Chapter 22 Three-Phase Transformer Connections
Chapter 23 Mathematics for Logic Controls
Chapter 24 Signal Distribution
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Based on lectures given at a summer school on computer algebra, the book provides a didactic description of the facilities available in three computor algebra systems - MAPLE, REDUCE and SHEEP - for performing calculations in the algebra-intensive field of general relativity. With MAPLE and REDUCE, two widespread great-purpose systems, the reader is shown how to use currently available packages to perform calculations with respect to tetrads, co-ordinate systems, and Poincare` gauge theory. The section on SHEEP and Stensor, being the first published book on these systems, explains how to use these systems to tackle a wide range of calculations with respect to tackle a wide range of
calculations in general relativity, including the manipulation of indicial formulae. For the researcher in general relativity, the book therefore promises a wide overview of the facilities available in computer algebra to lessen the burden of the lengthy, error-prone calculations involved in their research
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Course Descriptions
Mathematics Courses
Pre-Algebra
This course will familiarize students with manipulating numbers and equations and help them understand the general principles at work. Students will understand and use factoring of numerators and denominators and properties of exponents. Students will know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. They will know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students will convert between units of measurement. They will know and use different representations of fractional numbers (fractions, decimals, and percents). Students will use ratio and proportion to solve problems, compute percents of increase and decrease, and compute simple and compound interest. They will graph linear functions and understand the idea of slope and its relation to ratio.
Algebra I
Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations. Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers. They determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion. Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements. Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
Geometry
In this course students develop their ability to construct formal, logical arguments and proofs in geometric settings and problems. They identify and give examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. They know and use the triangle inequality theorem and measures of sides and interior and exterior angles of triangles and polygons to classify figures and solve problems. Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.
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It is easy to look at the documentation for Maple, Mathematica, or commercial Macsyma and find features that could be suitable student projects. These projects have the following positive features.
1. The design has been debugged at least once.
2. The calculation is feasible.
3. The answers from Maxima can be compared to the other system.
\
Other thoughts
There are a number of kinds of arithmetic mentioned previously here that fit under a common generic framework, that I've written in common lisp, and posted. Including automatic differentiation of programs, interval arithmetic, quad-double arithmetic (very fast 64 decimal digit floats), bigfloat Gaussian quadrature...
Handwriting input, mouse selection of displayed subexpressions...
for people who want to do user interfaces.
RJF
-------------- next part --------------
Hi Fabrizio
For math students,
I think there are many interesting areas that we had not
developped well in maxima.
Maybe Yong Tableaux is one of sufficient easy and interesting theme.
there is partition function in Set and schur (kostka,too) in Symmetries.
So by using them,your students may implemnt Young diagram,semi standard
Young tableau (SSYT),skew schur functions ,their generic functions.
see math.mit/edu/~plamen/tables/samsi06-2.pdf
many applications will be derived from these implementation,because
we can use it with other maxima's packages.
For example,Vicious random walkers have deep relations to
this.
thanks
Gosei Furuya
2007/1/17, Fabrizio Caruso <caruso at dm.unipi.it>:
>> Hi
>> The first two students I have followed are
> math students and did the following:
>> (1) implementation of 3sat-polycracker in Maxima
> - done, is it of any interest to anyone?
>> (2) optimizing (gf) finite field library for Maxima
> - almost done, it is going to be way faster
>> The next students (if they appear but it is
> very likely that they do) are computer science students.
> These might also implement something mathematical
> as long as it is understandable.
> I might also have more math students in the future
> who want to work on a software project, as well.
>> On Tue, 16 Jan 2007, Stavros Macrakis wrote:
>> > That would be great! There are many areas where they could contribute
> > without deep mathematics.
> >
> > What are their strengths and areas they want to develop? Lisp? GUIs?
> > Graphics? Scripting? Systems programming? ...
>> I don't know, yet.
> I'll let you know when they show up.
> It should also be something I must be able
> to follow...
> I use to code in Scheme lots of time ago
> but I am not a Lisp-expert.
> If you have a Lisp related suggestion I might
> need some help.
>>> My personal wishes:
>> Personally I would like to see a better
> and interactive gnuplot support in Maxima:
> the user should be able to draw on the same
> gnuplot more than once.
>> As far as the lisp is concerned I would like
> to have Maxima be compiled with a Lisp version
> that does not have an unreasonably low limit
> on the number of arguments for functions
> (CLISP is no affected but the other lisps
> fail with as few arguments as about 200).
> Could this be fixed by setting an appropriate
> parameter before compilation?
>> Regards
>> Fabrizio
>> _______________________________________________
> Maxima mailing list
>Maxima at math.utexas.edu> next part --------------
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-------------- next part --------------
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
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My Advice to a New Math 175 Student:
Math 175 is a very involved and intense course. In order to do well
and succeed, you must be willing to set aside time every night to work on
problems. With quizes every Thursday, it is crucial that you keep up
with materials and prepare. These quizes, whether you do poorly or well,
are good examples of what is to come on the exams. Even if you do poorly
on the quiz, be sure to master the problems prior to the upcoming exam. Don't
fall behind on the work because it adds up very quickly and it is hard to
recover from a poor exam score. The work is difficult, but there are
many resources to assist you in achieving your goal.
Dr. Hoar has created several sources to ensure students are capable of getting
help. There is a tutor lab, web activities, Tuesday Night Review Sessions,
as well as help from Dr. Hoar himself. Granted as college students we don't
always have the time, but I would strongly recommend that you attempt to use
these sources. Personally I found the web activities to be valuable, as
they offerred a different perspective from Dr. Hoar's and sometimes made things
clear. Be sure to get into a routine with your MTH 175 homework as well
as attending review sessions or the lab. These resources are there to help,
don't be intimidated to ask for help.
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In the very first semester of the university starting April 2012, I was a co-facilitator for the course Advanced Math I - Single Variable Calculus (course number 10.001) with Dr. Zuruzi Abu Samah and Dr. Zaichun Chen.
Unlike any other math classes, we use progressive Active Learning classes based on cohort class setting equiped with TEAL (Technology-Enhanced Active Learning) facilities with easily-reconfigurable movable tables/chairs for all students, 6 ceiling-mounted HD projectors and interactive whiteboards on all sides of the classrooms. Classes are based on practical activities within small groups of students for enhanced engagement and peer-to-peer learning, as opposed to conventional lecturing style. This is part of SUTD's innovative learning pedagogy.
course description
At the end of the term, students will be able to: Compute derivatives using the rules of calculus. Apply those calculations to find maxima and minima and accurate approximations in problems coming from engineering. Produce exact integrals by algebra and find approximate integrals numerically. Use integral calculus to solve for the important quantities in engineering design of continuous systems. Solve basic differential equations of growth and oscillation.
The subject will cover the following topics: Calculus for functions of one variable. Derivatives of the key functions of mathematics; e^x and solution of dy/dx=y; product rule, quotient rule, chain rule; inverse functions and logarithms; maximum-minimum problems; linear approximation and Newton's method; complex numbers and series; integration and Fundamental Theorem of Calculus; applications including area and probability and y' '= - y and basic differential equations.
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MAA Review
[Reviewed by Fernando Q. Gouvêa, on 05/20/2010]
Lie groups play such a central role in mathematics and its applications that all mathematics students should be aware of them. From computer graphics to quantum theory, from differential equations to number theory, Lie groups and algebras are everywhere. Nevertheless, most mathematics undergraduates have never heard of them.
Of course, the reason for this is that even the definition of a Lie group (i.e., a differentiable manifold which is also a group and whose group operations are smooth functions) seems to require more background knowledge than most undergraduates have. In a famous article on "Very Basic Lie Theory" (American Mathematical Monthly, 1983), Roger Howe argued that the absence of the theory of Lie groups from most undergraduate programs was both scandalous and unnecessary. Since then, several books attempting to respond to Howe's challenge have appeared. Harriet Pollatsek's Lie Groups is her entry in this list.
Howe's article, and many of the books that it inspired, still laid a heavy emphasis on the underlying topology and analysis, with the result that only advanced undergraduates (in fact, probably only rather strong advanced undergraduates) could really understand the material. Pollatsek is not satisfied with that approach. At Smith College, she has been teaching Lie Groups to sophomores, using a problem-driven approach that only assumes knowledge of linear algebra and multivariable calculus. From that course was born this book.
Lie Groups is fundamentally a problem book: each chapter presents a sequence of problems that students should solve. In each chapter, the main sections are followed by a summary section called "Putting the pieces together." Finally, a section called "A broader view" tries to give a wider context to the material in that chapter. Everything important is done through problems. Thus, this is a book to be used, not a book to be read.
I must admit that I find teaching this material to sophomore mathematics majors to be a little bit too much of a reach. Instead, I used the book in a seminar course that followed our standard one-semester introduction to abstract algebra. In the class were six seniors, three juniors, and (yes!) a sophomore; all had taken algebra, either in the previous semester or a year before. Most, but not all, had taken other advanced courses as well, including Real Analysis. My students were assigned problems to solve and present in class, and we developed the theory in that way. Every once in a while, I would step in and give a broader view.
Did it work? Yes, it mostly did, though in the process I discovered that some aspects have to be tweaked a little bit. Because Pollatsek doesn't want to assume any algebra background, there are lots of "check that SL(2,R) is a group" problems — more than I or my students wanted. Because she doesn't want to assume much knowledge of topology, she does not have the chance to make much of connectedness, compactness, covering spaces, and (most significant in this context) simple connectedness. This seems like an opportunity lost.
Some choices I just don't understand. Why, for example, is there a section on differential equations? It seems totally unrelated to the rest of the book. Why make such a meal of continuity versus differentiability in the definition of one-parameter subgroups? In this setting, one might as well just state that all one-parameter subgroups are differentiable and be done with it. Why not do more with the fact that SU(2) is a three-sphere? (My students were fascinated.) Why work only with the one-dimensional Lorenz group? Why not have more pictures? After all, it's easy to draw pictures of the one-dimensional Lie groups.
In many of the problems, there is more handholding than I wanted my students to have; at some points, this included "hints" that led towards unnecessarily messy ways of doing things. Pollatsek clearly thinks that students at this level prefer computation to theory. She is probably right, but I would rather not indulge that preference.
Some issues had to do with the fact that my students knew some things that her students didn't (what a group is, what a normal subgroup is) but did not have a sure grasp of some things that her students clearly do have well under control (the example that stands out in my mind is the Jacobian matrix of a differentiable map). The bibliography is also a little strange, too selective for my taste. This proved significant towards the end, when my students were working on term papers and all of them wanted the same books… which were not in our library.
There is no representation theory at all. The adjoint representation is described, but not put into any sort of context. With no representation theory, one cannot do much more than say "the physicists use this a lot," without showing how or why. That seems like a pity.
Pollatsek's book faces stiff competition. Perhaps the closest competitor is John Stillwell's Naïve Lie Theory, a beautiful book aimed at upper-level undergraduates that is very much in the same spirit. Kristopher Tapp's Matrix Groups for Undergraduates is also in a similar spirit. The main difference, of course, is that Stillwell and Tapp have written textbooks, while Pollatsek gives us a problem book. Using it requires buy-in: you need to want to teach in this way, and you will need to convince your students that the work is worth doing. If that applies to you, give this book a try.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College. He'll be doing the Lie groups thing again soon.
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To introduce students to selected topics of combinatorics and
elementary analytic number theory.
Intended
Learning Outcomes:
On successful completion of the course students will be:
Able to use generating functions to solve a variety of combinatorial problems
Proficient in the calculation and application of continued fractions.
Pre-requisites:
None
Dependent Courses:
None
Course Description:
The combinatorial half of this course is concerned with
enumeration, that is, given a family of problems P(n), n a natural number, find a(n), the number of
solutions of P(n) for each such n. The basic device is the generating function, a
function F(t) that can be found directly from a description of the problem and for which
there exists an expansion in the form F(t) = sum {a(n)gn(t); n a
natural number}. Generating
functions are also used to prove a family of counting formulae to prove combinatorial
identities and obtain asymptotic formulae for a(n).
In Number Theory we look at the
question of identifying irrational numbers and approximating them by rationals. We
introduce continued fractions which we study in detail. These lead also to solutions of
certain equations (Pell's equations) in integers. When identifying irrational numbers we
find criteria which guarantee that a number is transcendental.
Teaching Mode:
2 Lectures per week
1 Tutorial per week
Private Study:
5 hours per week
Recommended Texts:
H S Wilf, Generatingfunctionology, Academic Press. 2nd ed.,
1994.
A Baker, A Concise Introduction to the Theory of Numbers,
CUP, 1984.
Niven, Zuckerman and Montgomery, An Introduction to the
Theory of Numbers, (5th edition), 1991, Wiley.
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I was an intern last year. I didn't always have the time to look at the files of other teachers at 10pm at night. LessonPlanet saved me so many times I've lost count. I would look all over other websites for quality lesson plans and, no surprise, I always ended up here.
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In this calculus instructional activity, learners solve problems using differentiation and the chain rules. They take the derivatives of equations using specific equations. There are 21 problems with an answer key.
In this calculus worksheet, students identify functions based on different Theorems as it relates to calculus and the Fundamental Theorem. There are 13 questions dealing with differentiation and trigonometric graphs.
For this electrical worksheet, students draw a schematic design circuit board to grasp the understanding amplification in linear circuitry before answering a series of 35 open-ended questions pertaining to a variety of linear circuitry. This worksheet is printable and there are on-line answers to the questions. An understanding of calculus is needed to complete these questions.
Are your calculus pupils aware that they are standing on the shoulders of giants? This lesson provides a big picture view of the connection between differential and integral calculus and throws in a bit of history, as well. Note: The calculus controversy paper is not included but one can find a number of good resources on the Internet regarding the development of calculus and the role of Newton and Leibnez.
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Textbook prices have continued to rise leading faculty and governing bodies to seek ways of decreasing the financial burden placed on our students. While the internetThis book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.
The coverage is standard: linear systems and Gauss' method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues. Prerequisites: A semester of calculus. Students with three semesters of calculus can skip a few sections. Applications: Each chapter has three or four discussions of additional topics and applications. These are suitable for independent study or for small group work. What makes it different? The approach is developmental. Although the presentation is focused on covering the requisite material by proving things, it does not start with an assumption that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise the level of mathematical maturity of the class.
This text is intended for a one- or two-semester undergraduate course in abstract algebra and covers the traditional theoretical aspects of groups, rings, and fields. Many applications are included, including coding theory and cryptography. The nature of the exercises ranges over several categories; computational, conceptual, and theoretical problems are included.
Hardcover
418 pages
· ISBN-10: 0982406231
· ISBN-13: 978-0982406236
Ordinary and Partial Differential Equations by John W. Cain and Angela M. Reynolds
List Price: 19.95
Differential equations arise in a variety of contexts, some purely theoretical and some of practical interest. As you read this textbook, you will find that the qualitative and quantitative study of differential equations incorporates an elegant blend of linear algebra and advanced calculus. This book is intended for an advanced undergraduate course in differential equations. The reader should have already completed courses in linear algebra, multivariable calculus, and introductory differential equations.
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Type of assessment:
Aid:
Evaluation:
Previous Course:
Qualified Prerequisites:
General course objectives:
This course will lay the mathematical foundations for analyzing the dynamical systems that appear in engineering and science. The mathematical techniques will be brought to bear on problems from physics and chemistry.
Learning objectives:
A student who has met the objectives of the course will be able to:
Determine when there are existence and uniqueness of solutions to a system of ordinary differential equations.
Prove and disprove stability of a solution using Hartman-Grobman theorem and Lyapunov exponents.
Operate with dynamically defined, invariant manifolds.
Apply Poincaré-Bendixon theorem to show the existence of limit cycles.
Apply Index theory in the plane as well as compactification to rule out certain dynamical descriptions.
Classify local bifurcations in general and find the possible local bifurcations in a specific system.
Simulate a dynamical system
Combine the aforementioned points to give a global description of certain dynamical systems.
Content:
Existence and uniqueness of solutions to systems of ordinary differential equations. Attracting, repelling and neutral manifolds. Stability analysis including the Hartman-Grobman theorem and Lyapunov exponents. Theory of planar systems including Poincaré-Bendixon theorem and index theory. Local bifurcation theory
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Course number 424
Mathematica
Mathematica is a computer algebra system that is particularly suited for
carrying out mathematics in all its facets. Mathematica is based on a consistent language. Mathematica is not just a programme for symbolic
computations, the Mathematica package itself contains all important numerical and graphic possibilities. Add-ons for working with
OpenGL, for a seamless integration of Java applications, for connection with Matlab et cetera are standard tools.
Since version 3, technical scientific text-processing facilities have been added to Mathematica. Books can be
produced from Mathematica without interference of other packages.
In the present releases the speed of numerical calculations is even maximal, so it is comparable to standard
implementations.
Mathematica offers the user an integrated environment for perpetrating mathematics, from executing draft
calculations and experimenting to the production of publications and making presentations.
For our university, WEB-Mathematica is available free of charge. With WEB-Mathematica making interactive
(mathematic) web pages becomes a piece of cake. The W3C-standard for technical scientific texts in the Web,
MathML, has been set notably by Mathematica.
The following subjects will be treated:
symbolic calculations
numerical calculations
graphic facilities
the internal structure of Mathematica
programming
working with text documents (notebooks)
Documentation
Electronic documentation will be given at the beginning of the course
Language
The documentation used in this course is available in both Dutch and English
The language of communication can be either Dutch or English, to be
decided by mutual arrangement with the students.
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Complex Numbers in n Dimensions
Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functions. of the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions. In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible. The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, th
This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, ...
The untold story of the renegade burger chain that evokes a passionate following unlike any other. In fast-food corporate America, In-N-Out Burger stands apart. Begun in a tiny shack in the shadow of ...
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Here is a copy
of the Department of Mathematics syllabus
that applies to all MAT and STA classes.
Monday, August
20
For Wednesday, August 22:Solve
the cryptogram that you received and create two cryptograms (around 120
characters).One cryptogram should show
word length and punctuation; the other should not – it should be blocked
in 5-letter blocks.
Wednesday,
August 22
For Friday, August 24:Solve the
cryptogram that you received that included word length and punctuation.Be prepared to discuss your solution and how
you constructed the key for the ciphertext that you created.
Next week we will discuss how you
did with the ciphertext that did not have word length and punctuation.
Friday, August
24
Create a Caesar cipher to exchange on
Monday.Do not give word length or punctuation;
block in five-letter blocks.
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Heya guys! Is someone here know about prentice hall chapter 4 project worksheet 1? I have this set of problems about it that I just can't understand. Our class was asked to answer it and understand how we came up with the solution. Our Math professor will select random students to solve the problem as well as explain it to class so I require thorough explanation about prentice hall chapter 4 project worksheet 1. I tried answering some of the questions but I think I got it completely wrong. Please assist me because it's urgent and the due date is quite close already and I haven't yet figured out how to answer this.
I know how annoying it can be if you are not getting anywhere with prentice hall chapter 4 project worksheet 1. It's a bit hard to give you advice without a better idea of your problems. But if you can't afford a tutor, then why not just use some piece of software and see if it helps. There are an endless number of programs out there, but one you should consider would be Algebrator. It is pretty easy to use plus it is quite affordable.
I fully agree with that. It truly is a great software. Algebrator helped me and my classmates again and again till you actually understand it, unlike in a classroom where the teacher has to move on due to time constraints. Go ahead and try it.
A great piece of math software is Algebrator. Even I faced similar difficulties while solving graphing, radicals and perfect square trinomial. Just by typing in the problem workbookand clicking on Solve – and step by step solution to my algebra homework would be ready. I have used it through several algebra classes - Remedial Algebra, College Algebra and Remedial Algebra. I highly recommend the program.
For more information you can try this link: There is one thing that I would like to highlight about this deal; they actually offer an unrestricted money back assurance as well! Although don't worry you'll never need to ask for your money back. It's an investment you won't regret.
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Calculator - A desktop utility
Introduction
This is a simple calculator used for ordinary and scientific calculations
.It is just like the windows simple calculator along with source code.
There
is a one function beyond each button. You
can use Calculator to perform any of the standard operations for which you
would normally use a handheld calculator. Calculator performs basic arithmetic,
such as addition and subtraction, as well as functions found on a
special tasks, such as 1/x, x^
and sqrt.
To add the displayed number to the number already in memory, click M+.
To see the new number, click MR.
To add the displayed number to the number already in memory, click M-.
To recall a stored number, click MR.
Note
When you store a number, an M appears in the box above the memory
options. If you store another number, it replaces the one currently in memory.
You can use Calculator to perform any of the standard operations for which you
would normally use a handheld calculator. Calculator performs basic arithmetic,
such as addition and subtraction, as well as functions found on a scientific
calculator, such as logarithms and factorials.
History
v1.1 (16/February/2006)
First release
License
This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.
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Dist
Instructors
Textbooks
Course Websites
This course integrates discrete mathematics with algorithms and data structures, using computer science applications to motivate the mathematics. It covers logic and proof techniques, induction, set theory, counting, asymptotics, discrete probability, graphs, and trees. MATH 19 is identical to COSC 30 and may substitute for it in any requirement.
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Category: Math Methods
How did Methods students find the VCE Math Methods exams (1 and 2) for 2010? What was hard? What was easy? How do you think you went? Let us know your thoughts and comments below (please keep them clean!)…cheers
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this short book, the authors discuss three types of problems from combinatorial geometry: Borsuk's partition problem, covering convex bodies by smaller homothetic bodies, and the illumination problem. They show how closely related these problems are to each other. The presentation is elementary, with no more than high-school mathematics and an interest in geometry required to follow the arguments. Most of the discussion is restricted to two- and three-dimensional Euclidean space, though sometimes more general results and problems are given. Thus even the mathematically unsophisticated reader can grasp some of the results of a branch of twentieth-century mathematics that has applications in such disciplines as mathematical programming, operations research and theoretical computer science. At the end of the book the authors have collected together a set of unsolved and partially solved problems that a sixth-form student should be able to understand and even attempt to solve. less
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Working with vectors
The following fast-loading webpages describe some
properties and physical applications of vectors.
Each section builds on the previous ones to make a logical
sequence and
I have used hot links within sections so that it is easy to refer back
if you want to.
September 2003
The second edition of my book Maths: a student's
survival guide is published this month.
I've registered  
as its homepage in case I
change my ISP. There is a link from there to this page.
For this new edition, I've included some changes and additions to the text
arising from reader feedback and suggestions.
I've also added a new chapter on vectors which will be based
on these pages. Putting them in book form has made it possible to
expand them and add lots of examples and problems.
If you want any more information please
email me by taking out the xyz from
xyzjenolive@netcomuk.co.uk but please don't send attachments as I don't
open them. The xyz is against robot viruses.
Here is a list of all the vector topics which I've included so far on
this site.
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ICT Course 2 Notes.
The Project Maths Development Team is pleased to inform you that the course notes pertaining to the workshops on using ICT to teach Strands 3, 4 and 5 are now available.
The PMDT has collaborated with the NCTE to provide this course which will show you how you can use readily available software in your classroom to teach geometry, trigonometry and calculus for both Junior and Leaving Certificate.
Note: you must have Geogebra installed on your machine to use this software. Visit for more information on how to download.
14 November 2011
A Relations Approach to Algebra.
The activities contained in this document focus on the important role that functions play in algebra and characterise the opinion that algebraic thinking is the capacity to represent quantitative situations so that relations among variables become apparent.
Created by the Project Maths Development Team.
17 October 2011
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Machine Tool Math 1
Credits: 2Catalog #31804381
Open only for Machine Tool and Industrial Maintenance students. This course includes the study of machine tool problems involving calculations with fractions, decimals, and percentage. Includes work with the metric system, measurement conversion, geometry, trigonometry of right triangles, and use of a scientific calculator. Formulas with application to the trade are also studied. Prerequisites: Basic Algebra, 77-854-793 or appropriate placement score.
Course Offerings
last updated: 07
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Mathematical Modeling For The Scientific Method - 10 edition
Summary: Part of the International Series in MathematicsMathematical Modeling For The Scientific Methodis ideal for sophomore or junior-level students that need to be grounded in math modeling for their studies in biology, engineering and/or medicine. it reviews what the scientific method is and how it is important and connected to mathematical modeling. it unites topics in statistics, linear algebra, and calculus and how they are interrelated and utilized
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News
Languages
Overview
Blind people have always considered the study of Mathematics as a difficult problem to solve, that strongly hindered the chance to approach scientific studies for generations of visually impaired people. The use of computer is very large among blind students, who appreciate more and more its advantages (speed, efficiency, access to a large quantity of papers, almost unlimited), yet in the field of Mathematics, the benefits are still limited, due to its complex symbols and its bi-dimensional writing. The LAMBDA-project team designed a system based on the functional integration of a linear mathematical code and an editor for the visualization, the writing and the manipulation of the text.
The code (Lambda Mathematical Code) directly derives from MathML and it was designed to be used with Braille peripherals and the vocal synthesis. It is automatically convertible, in real time and without mistakes, into an equivalent MathML version and, through it, into the most popular mathematical formats (LaTeX, MathType, Mathematica...), both input and output.
The editor allows to write and to manipulate mathematical expressions in a linear way and provides a series of compensatory functions. In fact, the user is supplied with some aids to reduce the difficulties in understanding and managing the text, due to the visual handicap and to the need to use a linear code to manage the formulas. LAMBDA was meant for secondary-school to university students; some basic skills in computer science are necessary
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NOTES
1.
The study of functions, as we define it here, overlaps substantially with the topic of "algebra" traditionally taught in the United States in ninth grade, though national and many state standards now recommend that aspects of algebra be addressed in earlier grades (as is done in most other countries). Although functions are a critical piece of algebra, other aspects of algebra, such as equation solving, are not addressed in this chapter.
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You are here: Home » Laptop Software » 20 Pack Of High Achiever Educational Computer Software Fun and Entertaining for Middle and High School Students Grades 6 7 8 9 10 11 and 12th Grade Math Mathematics Algebra Geometry Trigonometry Study Skills US History Government English Spelling Science
For Middle and High School Students ~ Windows 95/98/Me/XP/Vista compatible
Many children including those with Asperger's Syndrome and other Autism Spectrum Disorders learn very well with the assistance of computer software
Kids can learn with these programs at home where they are free from school classroom distractions.
Build Your Own Custom Lessons, Ability to Print Each Lesson
Please contact me for full description, no room here to list all that's included! First-Degree Equations ? Linear Equations with one variable ? Linear Equations with Two ? Variables ?
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Mathematics for Game Developers with CDROM
(Paper Textbook)
Mathematics for Game Developers with CDROM Book Description
The author introduces the major branches of mathematics that are essential for game development and demonstrates the applications of these concepts to game programming.Mathematics for Game Developers is just that?a math book designed specifically for the game developer, not the mathematician. As a game developer, you know that math is a fundamental part of your programming arsenal. In order to program a game that goes beyond the basics, you must first master concepts such as matrices and vectors. In this book, you will find some unique solutions for dealing with real problems you?ll face when programming many types of 3D games. Not only will you learn how to solve these problems, you?ll also learn why the solution works, enabling you to apply that solution to other problems. You?ll also learn how to leverage software to help solve algebraic equations. Through numerous examples, this book clarifies how mathematical ideas fit together and how they apply to game programming.
Popular Searches
The book Mathematics for Game Developers with CDROM by Christopher Tremblay
(author) is published or distributed by Course Technology [159200038X, 9781592000388].
Mathematics for Game Developers with CDROM has Paper Textbook binding and this format has 625 number of pages of content for use.
This book by Christopher
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Math
NOTE: For all Mathematics courses, students need a calculator. Beyond Grade 9, it should be a scientific calculator and for grade 12 a graphing calculator is required.
Common Math 10 (FMP 10) 4 credits
(Foundations of Mathematics & Pre-Calculus 10)
Prerequisite: C+ (67%) or better in Math 9
Units of Study
- Real Numbers
- Exponents and Radicals
- Measurement
- Polynomials
- Coordinate Geometry
- Relations and Functions
- Systems of Equations
- Trigonometry
There is a required Provincial Exam at the end of the course worth 20% of the final mark.
Common Math 10 Honours (FMP 10) 4 credits
(Foundations of Mathematics & Pre-calculus 10)
Prerequisite: an "A" in MA 9 or a "C+" in MA 9H
Common Math 10 Honours takes the concepts of Common Math 10 and expands them and focuses more on the application of the material covered. The curriculum is the same as Common Math 10 but the emphasis is on enrichment by adding material that complements the topics. Students taking Common Math 10H will be prepared for any of the new grade 11 math courses. Common Math 10H students write the same final exam as the regular Common Math 10 students but receive a 5% bump on their class mark each term.
There is a required Provincial Exam at the end of the course worth 20% of the final mark.
Apprenticeship Math 10 (AWM 10) 4 credits
(Apprenticeship & Workplace Math 10)
Prerequisite: any Math 9
Units of Study
- SI and Imperial Measurement
- Surface Area and Volume
- Pythagorean Theorem
- Trigonometry
- Angles
- Unit Pricing and Currency
- Personal Finance
- Puzzles and Games
There is a required Provincial Exam at the end of the course worth 20% of the final mark.
Although Math 12 is not required for University or College entrance, it is essential for students wishing to pursue further education in science or technology. This course requires a thorough understanding of Math 11. There is very little review of the prerequisite concepts. A student should have at least a "B" in Math 11 to be successful in Math 12. The topics covered in Math 12 include:
Polynomial functions Trigonometric Identities
Circular functions Geometric proofs
Logarithms Conics
Trigonometry Theory Combinatorics
Trigonometric Proofs Transformations
Sequences and Series Problem Solving
There is an optional Provincial Exam at the end of this course worth 40% of the final mark.
Calculus 12 (CALC 12)4 credits
Prerequisite: Math 11 ("B" or better) or Math 12 ("C+" or better). ). Usually Math 12 is taken in the first semester with Calculus 12 in second semester.
Calculus 12 would be of interest to students planning further education in such areas as Science, Engineering, Technology and Business. Traditionally, first year university Calculus courses have been extremely challenging, especially to students with little Calculus background. This course will provide students with a basic understanding of limits, derivatives, and integrals. Applications and problem solving will be emphasized throughout the course. This course will also provide students with an understanding of the historical development of Calculus and of the people who contributed to this development. Strong Math skills, good work habits and an ability to deal with abstract concepts are essential.
**Note: This is not AP Calculus 12 and is offered in second semester only.
AP Calculus 12 (ACAL 12)4 credits
Prerequisite: Math 11 ("B" or better) or Math 12 ("C+" or better.
Advanced Placement Calculus gives the students the opportunity to pursue college-level studies while still in secondary school and to receive advanced placement credit on entering college. It is based on the belief that college-level courses can be successfully taught to motivate and to provide enrichment for mathematically able secondary school students. The course is intended for students who have thorough knowledge of college preparatory mathematics, including algebra, geometry, trigonometry and analytic geometry. Calculus 12 consists of a full academic year of work in elementary and transcendental functions, differential and integral calculus with its methods and applications.
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However, they're not diving into axing algebraic manipulation from the curriculum yet; rather Computer Based Math (abbreviated CBM) is planning to "rewrite key years of school probability and statistics from scratch". This is a reasonable first step given statistics is often taught computer based or at least calculator based these days (my colleague who teaches AP Statistics next door does so) and it does feel very silly to work through a passel of "figure out the standard deviation" problems by hand.
However, I'm going to play devil's advocate again with a thought experiment. Since algebraic manipulation is not being removed at this time, these questions aren't going to be applicable to Estonia yet, but presuming Computer Based Math continues working with them it should come up soon.
Suppose you are in a curriculum where you are used to algebraic manipulations being done by a CAS system. You are learning about statistics and come across these formulas:
What is necessary to use the formulas conceptually? What understandings might someone lack by not having experienced the algebra directly? Is it possible to understand the progressive nature and relations with these formulas just by looking at them? Is it necessary (to be well-educated in statistics) to do so? If it is necessary, what specific errors could somebody potentially make in a statistics calculation? Could this be mitigated by the text? Could this be mitigated by steps taking during the CAS portion of the education that while not leading to lengthy practice in "manipulate the algebra" problems will still allow understanding of the text above?
Like this:
3 Responses
Reblogged this on evangelizing the [digital] natives and commented:
I go back and forth on the importance of calculation in my instruction. It only bugs me when kids don't even know their basic multiplication.
I'm a proponent of the movement to make everything computer based. I could write a thesis on why, but let's just say my personal experience as a statistics instructor made me realize that 99% of students just want to be able to get the answer, not understand why. The TI-83 is a Godsend to these students…its wonderful to see the light in their eyes when they realize they don't actually have to calculate anything! Now, if they were to be statisticians (I have yet to come across a prospective statistician in my community college classes), then the answer is yes — they should know the reasoning and the conceptualization behind the "answer."
I came across your blog via David Wees, and as a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show for preteens about math that we're putting together. "The Number Hunter" is a cross between Bill Nye The Science Guy and The Crocodile Hunter — bringing math to children in an innovative, adventurous way. I'd really appreciate your help in getting the word out about the project.
Our
I also use Triola's 11th. I ask my students to do one standard deviation calculation without technology (the sample SD of three numbers) so that hopefully they see the process, but then afterwards they get to use technology. By the way, I think Triola has the best sense of humor among math textbook authors I have ever seen – I can't find the page reference right now, but he does an experiment that he says is "more fun than humans should be allowed to have."
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Description fundamental
Table of Contents
1. Linear Equations in Linear Algebra
Introductory Example: Linear Models in Economics and Engineering
1.1 Systems of Linear Equations
1.2 Row Reduction and Echelon Forms
1.3 Vector Equations
1.4 The Matrix Equation Ax = b
1.5 Solution Sets of Linear Systems
1.6 Applications of Linear Systems
1.7 Linear Independence
1.8 Introduction to Linear Transformations
1.9 The Matrix of a Linear Transformation
1.10 Linear Models in Business, Science, and Engineering
Supplementary Exercises
2. Matrix Algebra
Introductory Example: Computer Models in Aircraft Design
2.1 Matrix Operations
2.2 The Inverse of a Matrix
2.3 Characterizations of Invertible Matrices
2.4 Partitioned Matrices
2.5 Matrix Factorizations
2.6 The Leontief Input—Output Model
2.7 Applications to Computer Graphics
2.8 Subspaces of Rn
2.9 Dimension and Rank
Supplementary Exercises
3. Determinants
Introductory Example: Random Paths and Distortion
3.1 Introduction to Determinants
3.2 Properties of Determinants
3.3 Cramer's Rule, Volume, and Linear Transformations
Supplementary Exercises
4. Vector Spaces
Introductory Example: Space Flight and Control Systems
4.1 Vector Spaces and Subspaces
4.2 Null Spaces, Column Spaces, and Linear Transformations
4.3 Linearly Independent Sets; Bases
4.4 Coordinate Systems
4.5 The Dimension of a Vector Space
4.6 Rank
4.7 Change of Basis
4.8 Applications to Difference Equations
4.9 Applications to Markov Chains
Supplementary Exercises
5. Eigenvalues and Eigenvectors
Introductory Example: Dynamical Systems and Spotted Owls
5.1 Eigenvectors and Eigenvalues
5.2 The Characteristic Equation
5.3 Diagonalization
5.4 Eigenvectors and Linear Transformations
5.5 Complex Eigenvalues
5.6 Discrete Dynamical Systems
5.7 Applications to Differential Equations
5.8 Iterative Estimates for Eigenvalues
Supplementary Exercises
6. Orthogonality and Least Squares
Introductory Example: Readjusting the North American Datum
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram—Schmidt Process
6.5 Least-Squares Problems
6.6 Applications to Linear Models
6.7 Inner Product Spaces
6.8 Applications of Inner Product Spaces
Supplementary Exercises
7. Symmetric Matrices and Quadratic Forms
Introductory Example: Multichannel Image Processing
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
Supplementary Exercises
8. The Geometry of Vector Spaces
Introductory Example: The Platonic Solids
8.1 Affine Combinations
8.2 Affine Independence
8.3 Convex Combinations
8.4 Hyperplanes
8.5 Polytopes
8.6 Curves and Surfaces
9. Optimization (Online Only)
Introductory Example: The Berlin Airlift
9.1 Matrix Games
9.2 Linear Programming–Geometric Method
9.3 Linear Programming–Simplex Method
9.4 Duality
10. Finite-State Markov Chains (Online Only)
Introductory Example: Google and Markov Chains
10.1 Introduction and Examples
10.2 The Steady-State Vector and Google's PageRank
10.3 Finite-State Markov Chains
10.4 Classification of States and Periodicity
10.5 The Fundamental Matrix
10.6 Markov Chains and Baseball Statistics
Appendices
A. Uniqueness of the Reduced Echelon Form
B. Complex Numbers
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A complete Algebra curriculum by the end of eighth grade! This exciting program, developed in cooperation with Education Development Center, Inc., makes mathematics accessible to more of your middle-school students. They will spend less t
Glencoe Algebra 1
Editorial review
Oklahoma edition
Lie algebras, (International series of monographs in pure and applied mathematics, v. 104)
This pack contains test papers for mathematics (tiers 3-5, 4-6, 5-7, 6-8) as well as mark scheme booklets for each tier and extension paper designed for Key Stage 3. Notes for invigilators are also included.
This text contains the actual questions set in the 1998 Maths test for 10-and 11 year-olds (Key Stage 2), with answers, and the official information on how the test differs in 1999. It also explains the mark scheme from which teachers mar
Maths Revision: a Guide to the National Curriculum
Editorial review
This is a revision guide for the National Curriculum Key Stage 1 Maths. It aims to provide a thorough account of the syllabus, and offers guidance on compiling the best answers. It is written in a simple style, allowing children to read a
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Mathematics
In the Mathematics Department at Doha College we are keen to inspire a deep appreciation of the many aspects of the subject. As much as possible we link them to everyday life. It is important that our students develop a logical process to their problem solving skills and we encourage them to structure solutions in the most ordered fashion.
We have high expectations of our students and have outstanding success in external examinations, this is achieved through a process of encouragement and expectation, coupled with the nurturing of students' enjoyment and appreciation of the work covered. The high numbers of students who continue their studies of the subject to A Level bears testimony to the success of this approach.
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The intent of each activity in this brief book is to allow students to use the TI-83 Plus and TI-84 Plus families of graphing calculators to explore and make conjectures related to key geometry concep... More: lessons, discussions, ratings, reviews,...
A rotation around a point is one of three types of rigid transformations. It is a transformation that turns a figure a certain number of degrees about a certain point. This activity explores the prope... More: lessons, discussions, ratings, reviews,...
A teaching unit on fractals for students and teachers in grades 4 to 8, that adults are free to enjoy, designed to introduce students to fractals and the underlying mathematics. It focuses on fractals... More: lessons, discussions, ratings, reviews,...
This activity is an enhancement to an age old activity of students drawing a "dot-to-dot" picture using coordinates on a coordinate plane. In this case, however, students will design a picture of theiGeometria is free (GPL) cross-platform software based on a two-role (teacher, student) model. The teacher creates a problem, provides it with an answer and saves the problem in a file. The student ope... More: lessons, discussions, ratings, reviews,...
Use the discovery approach to mathematics while your students explore six different simulated geometry environments. Built-in lessons provide individualized support allowing students to progress while... More: lessons, discussions, ratings, reviews,...
A quick way to find solutions to complicated mazes. The author writes: "While doing a maze activity with a group of elementary school homeschoolers, I started exploring mazes as systems of walls rathe... More: lessons, discussions, ratings, reviews,...
KSEG is a Free (GPL) interactive geometry program for exploring Euclidean geometry. It runs on Unix-based platforms (according to users, it also compiles and runs on Mac OS X and should run on anythin
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Presented in an easy-to-follow, step-by-step tutorial format, Puppet 3.0 Beginner?s Guide will lead you through the basics of setting up your Puppet server with plenty of screenshots and real-world solutions.This book is written for system administrators and developers, and anyone else who needs to manage computer systems. You will need to be able... more...,... more...
In a detailed and comprehensive introduction to the theory of plane algebraic curves, the authors examine this classical area of mathematics that both figured prominently in ancient Greek studies and remains a source of inspiration and a topic of research to this day. Arising from notes for a course given at the University of Bonn in Germany,... more...
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Microsoft Math 3.0 Software Review and Ratings
Editors' Rating:
Our Verdict:
For math and science students who need a little extra help, the easy-to-use Microsoft Math 3.0 could be just the thing. Read More…
What We Liked…
Inexpensive
Offers step-by-step equation solving
What We Didn't…
Tutorials cover program functionality, but aren't math lessons
Microsoft Math 3.0 Software Review
By Matthew Murray, reviewed May 31, 2007
Share This Review:
Interested as we are in technology, there are reasons we didn't go into computer science. Chief among them: The high-level math required at just about every stage of the game. So we're thrilled to find a program as comprehensive and inexpensive as Microsoft Math 3.0, which might help the next generation solve quadratic equations and figure out chemical reactions more easily than we could.
Available as a small download from Microsoft's Web site for only $19.95, Microsoft Math offers lots of tools for simplifying and clarifying math and science questions. You get a graphing calculator optimized for both standard and linear algebra, trigonometry, statistics, and calculus; a library of formulas and equations that also encompasses key entries from the worlds of chemistry and physics; a triangle solver; and a unit-conversion utility for easily converting units of measure for length, volume, temperature, and more. If by chance you run the software on a Tablet PC, Math's handwriting recognition can help you enter expressions that way.
Perhaps the best feature is the step-by-step equation solver, which breaks down complicated calculations into their component pieces, along with gently explanatory text to help you understand each step of the solving process. (You can also turn off the step-by-step solutions so you have to make the journey to the answer yourself.) You can even solve systems of up to six equations.
The program provides five built-in video tutorials: an overview of the program; introductions to graphing, equation solving, and step-by-step solutions; and a how-to on assigning variables and evaluating expressions. While these are helpful for detailing the ins and outs of how the software works, they're useless as crash courses on any of these potentially bewildering topics. The software assumes you know what you're getting yourself into, which could baffle parents who (like us) forgot the law of cosines the instant first-semester trig ended.
Even so, for struggling students of all ages, Microsoft Math 3.0 can make the process a lot less frustrating—and maybe even a little bit fun.
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From the first day your students begin to learn the vocabulary of algebra until the day they take final exams and standardized tests, these programs strengthen student understanding and provide the tools students need to succeed.
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The essential skills needed for learning mathematics at Robert College are based on an understanding of operations and a sound knowledge of basic facts. These basic facts were taught in an elementary school mathematics program which included concepts from Arithmetic, Algebra and Geometry.
The Robert College mathematics department encourages students to: Ø concentrate on the problem-solving process rather than on the calculations associated with the problem. Ø perform those tedious computations that arise when working with real datain a problem-solving situation with a graphing calculator. Ø gain access to mathematics beyond the students' level of computational skill. Ø discover and reinforce mathematical concepts including estimation, computation,approximation, and properties. Ø experiment with mathematical ideas and discover patterns. Ø go from concrete experience to abstract mathematical ideas.
Conceptual understanding of Lise mathematics is developed in three different modes:
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"New Math"
The impetus for the "new math" was the successful launch of Sputnik, the Soviet Earth-orbiting satellite, in 1957. In the United States, there was concern that we were so far behind the Soviet Union, our cold war foe, that our national security was in danger. In response, a spate of federal funds became available to improve the mathematics, science, and foreign language competence of our school children. University mathematicians saw the necessity of having some students understand the structural underpinnings of mathematics as the basis for their future work in mathematics. These mathematicians intended to "jump-start" young people who demonstrated a talent for mathematics and better prepare them for the rigors of university mathematics programs. Their strategy was to introduce topics into the school mathematics curriculum that aided the development of mathematical reasoning and proof.
Two components of the "new math" that appeared in elementary and secondary textbooks at the time were set theory (including set notation) and the structural properties of mathematics (commutative, associative, closure, etc.). Sometimes structural properties were developed through the study of number systems other than our Hindu-Arabic base-lO system. These topics often were presented abstractly in textbooks, not connected to any practical applications. For example, in typical eighth-grade texts of that era, integer addition was introduced by giving a set of principles, such as the commutative, associative, and distributive principles, that could be extended from the whole number system to prove relationships on the set of integers, and later to verify operations on rational numbers. Algebra texts continued this approach with particular emphasis on additive and multiplicative inverses and their applications to equation solving. Justification by deductive reasoning was the intent.
Society's Concerns with "New Math"
Many elementary teachers, already insecure in their own mathematical knowledge, failed to fully understand or appreciate the mathematical implications of "new math's" structural approach. Indeed, many had difficulty connecting their familiar calculation skills with the abstract underpinnings promoted in materials grounded in the new approach. Exacerbating their lack of content knowledge was the fact that insufficient professional development was provided to support the change.
Likewise, support materials for teachers and students did not account for parents' needs and reactions. Worksheets on abstract reasoning were sent home, instead of worksheets on calculations. The result was considerable parental confusion and consternation. In short, most parents had no understanding of what their children were learning and its relationship to their conception of arithmetic. Parents complained, for example, that students could identify the associative property underlying multiplication and addition but were not able to get correct answers on standard arithmetic exercises. Most elementary programs based on the "new math" were soon discontinued.
The overall response in the mathematics community, however, was not to do away with "new math" altogether. Most current textbooks continue to include lessons emphasizing fundamental concepts important to student understanding and appreciation of mathematics. For example, various sorting activities still appear in elementary textbooks, with or without set notation. Sets are used in algebra (solution sets, for example) and in probability (sample space). Learning multiplication facts is made simpler by knowing that the operation is commutative, whether the term is introduced or not. In fact, students working with matrices, a topic now occurring in some ninth-grade materials, are astonished to realize that some mathematical systems are not commutative under multiplication.
Continuing Influence of "New Math"
At the high school level, one of the most popular series of algebra textbooks, commonly known as Dolciani in reference to one of the major authors, was published in 1970 with the title Modern Algebra: Structure and Method, Books 1 and 2. The two major authors of these books, as well as the editorial adviser, were involved with the School Mathematics Study Group (SMSG), an outgrowth of the reform movement of the 1960s. Sets and mathematical structure play a major role throughout this algebra curriculum. Many iterations later, long after the death of Mary Dolciani, those textbooks remain among the most widely used in the United States. The "new math" did not go away. Rather, it was adapted to enhance and extend the skills-based algebra textbooks that were commonly used in the 1950s.
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Student's Solutions Manual for Beginning Algebra
Summary
KEY MESSAGE: The Lial series has helped thousands of readers succeed in developmental mathematics through its approachable writing style, relevant real-world examples, extensive exercise sets, and complete supplements package. The Real Number System; Linear Equations and Inequalities in One Variable; Linear Equations and Inequalities in Two Variables: Functions; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring and Applications; Rational Expressions and Applications; Roots and Radicals; Quadratic Equations For all readers interested in Beginning Algebra.
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Discover Mathematics Through Investigation In Symmetry, Shape, and Space, geometry is the framework for an introduction to mathematics. The visual nature of geometry allows students to use their intuition and imagination while developing the ability to think critically. The beauty of the material lies in students discovering mathematics as mathematicians do through investigation. Many of the exercises require students to express their ideas clearly in writing, while others require drawings or physical models, making the mathematics a more hands-on experience. The book is written so that each chapter is essentially independent of the others to allow for flexibility. The text activities and exercises can serve as enrichment projects at elementary and secondary levels. Mathematics professionals and educators will enjoy its informal approach and will find the explorations of nontraditional geometric topics such as billiards, theoretical origami, tilings, mazes, and soap bubbles intriguing. A companion Sketchpad Student Lab Manual can be packaged with The Geometer Sketchpad or KaleidoMania at a special price.
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"Not only is it an excellent introduction for someone who needs to come up-to-speed on the math behind games and graphics, it's a well-organized reference for anyone in the field. Short version: If you program graphics, let alone games, you need this book. Shelve it near your desk, next to your Foley and your Knuth. Highly Recommended." -Rick Wayne from a review in Software Development Magazine"This excellent volume is unique in that it covers not only the basic techniques of computer graphics and game development, but also provides a thorough and rigorous--yet very readable--treatment of the underlying mathematics. Fledgling graphics and games developers will find it a valuable introduction; experienced developers will find it an invaluable reference. Everything is here, from the detailed numeric issues of IEEE floating point notation, to the correct way to use quaternions and spherical linear interpolation to represent orientation, to the mathematics of collision detection and rigid-body dynamics." -David Luebke, University of Virginia, co-author of Level of Detail for 3D Graphics"When it comes to software development for games or virtual reality, you cannot escape the mathematics. The best performance comes not from superfast processors and terabytes of memory, but from well-chosen algorithms. With this in mind, the techniques most useful for developing production-quality computer graphics for Hollywood blockbusters are not the best choice for interactive applications. When rendering times are measured in milliseconds rather than hours, you need an entirely different perspective. Essential Mathematics for Games and Interactive Applications provides this perspective. While the mathematics are rigorous and perhaps challenging at times, Van Verth and Bishop provide the context for understanding the algorithms and data structures needed to bring games and VR applications to life. This may not be the only book you will ever need for games and VR software development, but it will certainly provide an excellent framework for developing robust and fast applications." -Ian Ashdown, President, ByHeart Consultants Limited"With Essential Mathematics for Games and Interactive Applications, Van Verth and Bishop have provided invaluable assistance for professional game developers looking to shore up weaknesses in their mathematical training. Even if you never intend to write a renderer or tune a physics engine, this book provides the mathematical and conceptual grounding needed to understand many of the key concepts in rendering, simulation, and animation." -Dave Weinstein, Red Storm Entertainment "Geometry, trigonometry, linear algebra, and calculus are all essential tools for 3D graphics. Mathematics courses in these subjects cover too much ground, while at the same time glossing over the bread-and-butter essentials for 3D graphics programmers. In Essential Mathematics for Games and Interactive Applications, Van Verth and Bishop bring just the right level of mathematics out of the trenches of professional game development. This book provides an accessible and solid mathematical foundation for interactive graphics programmers. If you are working in the area of 3D games, this book is a 'must have.'" -Jonathan Cohen, Department of Computer Science, Johns Hopkins University, co-author of Level of Detail for 3D Graphics
I have read many math books for video games and there are two aspects of this book I really like. The first is the book is encyclopedic and terms of the amount of information that it covers. The second reason that I like this book is that it clearly explains where the equations come from not just what the equations are.
R. Falck |
24/07/2005
Fabulous teaching!
See my other review. I bought this book and the other. I got stuck in that other book. I am learning linear algebra for the first time. This book is doing it! Although it gets quite abstract at times, and seems to be presenting the subject as if it is not related to 3D programming (like solving equations for an n-dimensional space), and it explains something and then says it is not used in 3D programming, it explains the concepts extremely well, and although it may take a while for a new concept to sink in for me, I do not find myself having to go elsewhere for help.
One note though, I tried to email one of the authors to find out about errata for the book and never got a response. I did eventually find it though. Don't expect the authors to be available. They do not have a message board.
Dave Astle |
28/04/2005
One of the best game math books
If only every topic in game and graphics programming were covered as well as math. Over the past several years, a number of exceptionally good books covering math for game and graphics programming have been released, and I've had the opportunity to review most of them. Although, not surprisingly, there is some overlap between them all, each covers unique material and presents information in an original way so that collectively, the books provide an impressive body of work.
Essential Mathematics stands out as one of the best books in the pack, especially in regards to its coverage of the math behind low-level rendering techniques.
The book is broken into 4 parts. The first part, Core Mathematics, covers vectors and matrices, transformations, and number representation. This part will be useful to anyone doing 3D graphics.
Part II, Rendering, covers topics such as lighting and shading, texturing, projection, and rasterization. This part was of particular interest to me because I've been working on a commercial renderer, but it should also be useful to those who want a better understanding of what graphics engines do under the hood.
Part III, Animation, covers curves (very in depth) and representation of orientations (Euler vs. axis-angle vs. quaternions). Finally, Part IV, Simulation, covers intersection testing and rigid body dynamics. There are also a couple of appendices to help you brush up on trig and calculus, if needed.
The book includes many C++ code samples and demos, including a handy math library and a simple rendering/game engine using OpenGL and GLUT. The authors are to be commended for their writing style as well. It's very easy for a book of this nature to get bogged down in an extremely heavy academic tone, but this book manages to avoid that, making for a remarkably easy read.
I'm glad I don't have to choose just one game math book, but if I did, this would probably be the one I'd pick.
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The Java programming language and the math extensions in
Commons Lang provide implementations for only the most basic
mathematical algorithms. Routine development tasks such as
computing basic statistics or solving a system of linear equations
require components not available in Java or Commons Lang.
Most basic mathematical or statistical algorithms are available in
open source implementations, but to assemble a simple set of
capabilities one has to use multiple libraries, many of which have
more restrictive licensing terms than the ASF. In addition, many
of the best open source implementations (e.g. the R statistical
package) are either not available in Java or require large support
libraries and/or external dependencies to work.
Commons Math is a library of lightweight, self-contained
mathematics and statistics components addressing the most common
problems not available in the Java programming language or Commons
Lang.
Guiding principles:
Real-world application use cases will determine development
priority.
This package will emphasize small, easily integrated components
rather than large libraries with complex dependencies and
configurations.
All algorithms will be fully documented and follow generally
accepted best practices.
In situations where multiple standard algorithms exist, a
Strategy pattern will be used to support multiple
implementations.
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Top homeschooling websitesPurplemath contains practical algebra lessons demonstrating useful techniques and pointing out common errors. Lessons are written with the struggling student in mind, and stress the practicalites over the technicalities. Links and other resources also ava
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What
materials are
provided for an
AP Computer Science class?
The A+ Computer Science
material packages include materials that can be used to teach a
stand-alone AP CS A course or an AP CS A course that follows a pre-AP
CS / introductory Computer Science course.
Syllabi are provided that detail using the materials to teach a
stand-alone AP CS A course as well as docs detailing how to use the
materails to teach a
pre-AP class followed by an AP CS class.
Slides, java examples, labs, worksheets, tests, and quizzes
are
provided. Solutions to all materials are provided as well. Tests are
provided in numerous formats, including MS Word, Examview, and Moodle.
Hundreds
of labs are included which provide students
with numerous
opportunities to get their hands dirty solving problems and writing
code. Each topic has many
different assignments of varying difficulty levels which alllows
students
of all learning styles to experience success and show mastery.
The vast amount of lab assignments allows
greatly flexibility and more
opportunities for differentiation.
The AP Computer
Science GridWorld
case study is covered extensively. The GridWorld case study
has been integrated throughout all materials.
GridWorld works well as a component of an introductory Computer Science
class as well.
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Mathematica: An Introduction
Introduces the basic features needed to become an adept user of Mathematica, including programming, working with data, creating visualizations, deploying interactive computable documents, and using the Wolfram Predictive Interface. Small class sizes allow for interaction with the instructor, and in-person courses have extra time for Q&A. This course is also available in French.
Level: Beginner
The course is for anyone who would like to become a proficient Mathematica user. This course is helpful for people with little Mathematica experience as well as for experienced users who would like to broaden their basic understanding of the system.
Programming, Working with Data, and Solving Equations Programming, including functional, rule-based, and procedural techniques; working with files and data; solving symbolic and numeric equations and inequalities; functions for calculus; parallelization
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2011 summer boot camp mini Review sessions
The Title V STEM Learning Communities Program and Mathematics Department will offer a series of Summer Boot Camp Mini Review Sessions (College Algebra Readiness, College Algebra and Pre-calculus) to help students succeed in their mathematics courses.
These sessions are FREE to all UTB/TSC students, you are entitled to take these reviews if you fall into one of the following categories:
For College Algebra:
If you are going to take college algebra during the summer session II or fall semesters.
If you did not pass the College Algebra course/test and need a free review course before retaking it.
If you passed the third level of developmental math and would like to test out of College Algebra or improve your chances to be successful in the course.
If you need to bridge your high school math courses with college algebra or pre-calculus.
If you need to test out of college algebra and get into pre-calculus or statistics.
For Pre-Calculus:
If you are pursuing a degree program that mandates you to take Pre-Calculus and Calculus.
If you did not pass the Pre-Calculus course/test and need a free review course before retaking it.
If you need to bridge your high school math courses with Pre-Calculus and Calculus.
If you need to test out of Pre-Calculus and get into Calculus or other higher level Calculus-required courses.
For College Algebra Readiness:
If you are going to take college algebra during fall semester.
If you did not pass the COMPASS test and have to take developmental math courses in the Fall semester. This course gives you a second chance, if you finish the two week course work and pass the post-test, you can register for college algebra without taking developmental math.
If you need to bridge your high school math courses with developmental math in college or college algebra.
If you need to review developmental math and gain a better ground before you get into college algebra or pre-cal.
The two-week College Algebra Mini Review Course will be held during June 4-18. The lecture will be in the morning from 9:00-12:00 and the lab will be in the afternoon from 1:00 to 3:00pm. Students who take this mini-course will have the opportunity to test out of college algebra and/or improve their grade and chances to do better in the regular course in the fall.
The two-week Pre-Calculus Mini Review Course will be held during June 25 -July 9. The lecture will be in the morning from 9:00-12:00 and the lab will be in the afternoon from 1:00 to 3:00pm. Students who take this mini-course will have the opportunity to test out of pre-calculus and/or improve their grade and chances to do better in the regular course in the fall.
The two-week College Algebra Readiness Camp will be held during July 15 -July 30. The lecture will be in the morning from 9:00-12:00 and the lab will be in the afternoon from 1:00 to 3:00pm. Students who take this readiness camp course will have the opportunity to test out of developmental math and get chances to do better in the regular math course in the fall.
These mini courses are FREE of Charge and will be open to all students. The capacity will be limited to 50 students each. Space is limited, register online now or call (956) 882-7004 or (956) 882-5792 to register by phone.
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To access this page as it is meant to fuinction please use a Javascript enabled browser.
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Abstract Algebra : A Geometric Approach - 96 edition
Summary: This book explores the essential theories and techniques of modern algebra, including its problem-solving skills, basic proof techniques, many unusual applications, and the interplay between algebra and geometry. It takes a concrete, example-oriented approach to the subject matter.
Features
Provides sample foundational material - both at the beginning of the text and in the appendices - w...show morehile not avoiding calculus.
Features a "rings" first approach to make abstract concepts more accessible. Over 225 substantial examples and 750 exercises (many having multiple parts) are provided.
Geometry is slowly integrated through the text to make the abstract concrete and permit more structures to play with.
Culminates in Chapter 8 with the true integration of geometry and algebra.
Encourages the use of geometric models to discover the relations between group theory and geometry.
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Synopsis
ating the importance of math in all areas of real life.
procedural skills necessary for effective collaboration while working on
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Math Olympiad Training Program
Avid Academy for Gifted Youth provides math problem solving curriculum to gifted students in grades K - 11. We prepare our students to take on the following rigorous curriculum sequences:
grade
math class
6
Honors Pre-Algebra
7
Honors Algebra I
8
Honors Geometry
9
Honors Algebra II/College Algebra
10
Trigonometry/AP Calculus AB
11
AP Calculus BC
12
AP Statistics or Multivariable Calculus
Highly gifted students who exhaust the above math courses will be placed into courses at local universities. We also provide road-maps for students with exceptional talent to achieve national recognition through selective training programs and summer camps. Educational planning and college guidance services are available to meet individual needs. Please email us at info@avidacademy.com for consultation.
Avid Academy Math Talent Development Model: The Four E's
We have developed a proven curriculum to develop a student's mathematical talent in four stages.
Excite: for students in grade K - 2, our classes focus on building excitement toward mathematics through hands-on manipulative activities, interactive math games, mental math training, and exploration of math in daily life. Developing an early interest in math and motivating students to advance their math skills are critical at this stage.
Explore: for students in grade 3 - 5, our classes focus on exploring problem solving strategies with mental math training, logic reasoning, and study skills training. A unique feature of our program is the integration problem solving, elementary school math competition with school-level academics to place students on an advanced academic track such as GATE, APAAS (APAAS-Alternative Program for Academically Advanced Students), and other forms of learning accelerations.
Expand: for students in grade 6 - 8, our classes focus on expanding mathematical skills through subject-based classes in pre-algebra, algebra, and geometry enhanced with problem solving topics in number theory, counting and probabilities. Students are encouraged to participate in middle school math competitions to test their math skills and use their math skills as a foundation to develop other interests in science, technology, research, and community services.
Excel: for students in grade 9 - 12, our classes focus on providing frameworks for students to excel in national competitions such as Math Olympiad, Physics Olympiad, Chemistry Olympiad, Biology Olympiad, Science Fairs, and many other areas where students can demonstrate their talent and build a unique profile for college applications.
Excite - Grades K - 2
M20K - Math Olympiad Level K
M201 - Math Olympiad Level 1
M202 - Math Olympiad Level 2
Explore - Grades 3 - 5
If a student has intense curiosity about numbers, learns math concepts quickly, and demonstrates the ability to think abstractly at a young age, it is likely that he or she is talented in math. The student may be bored with the math class at school, show signs of underachieving, and consequently suffer untapped potentials. We believe a solution is to guide the student to explore the art of problem solving, which makes math fun, interesting and challenging.
Expand - Grades 6 - 8
With a solid problem solving foundation, a talented student will be in an advantageous position to expand learning beyond school math instruction, and well prepared to take on the most rigorous math and science curriculum when entering high school. EXPAND Programs continue development of problem solving, critical thinking, communication, teamwork, time-management, test-taking and study skills.
We mentor gifted students through math competitions to build their self-confidence in applying their problem solving skills in interactive environments. We believe these experiences motivate them to develop passion, challenge the boundaries, and build success in life.
We create our curriculum to enable our students to complete Geometry in their 8th grade, if not earlier. We offer two problem solving tracks.
Math Olympiad Track
Excel - Grades 9 - 12
We help gifted students excel in the most challenging high school math and science classes and complete their math and science graduation requirements before 11th grade so that they can take college-level classes in their junior and senior years in high school. Avid Academy students will have time to build more attractive profiles for applying to highly selective colleges.
Our curriculum is designed to integrate problem solving training, academic competitions, and preparation for PSAT, SAT and AP exams to achieve stellar grades, excellent test scores, thoughtful academic research, and attractive competition results to maximize admission chances to elite colleges. We mentor our students in brainstorming science fair research projects, searching for scholarships and summer opportunities with universities and businesses, applying strengths or passions in leadership and community service activities, and exploring careers. By the time our students start their college application process, they have all the key components to present their unique portfolio—GPA, test scores, awards/scholarships, research projects, intern/work experience, leadership, community services, essay topics, career plan, and interview skills.
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Winder ACT MathI particularly enjoy studying set theory (including logic) and point-set topology. As an undergrad, discrete math was a course required by my curriculum. I have also taken courses on point-set topology, abstract algebra, and probability theory, as part of my graduate studiesDuring
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Exam1_StudyGuide
Course: MATH 260, Fall 2009 School: illinoisstate.edu Rating:
Word Count: 317
Document Preview problems could appear on the exam; therefore it is highly recommended that you make every effort to complete those problems. Exam 1 Topics: 1. Sets: showing two sets are equal, showing one set is a subset of another, set notation, setbuilder notation, finding the power set of a given set, the sets N, Z, Q, R. 2. Set operations: union, intersection, set difference, complement, symmetric difference, cartesian product. Given various sets, applying these operations. 3. De Morgan's Laws and Set Properties proving various set properties are true or finding a counter-example to show a statement is false. 4. Binary relations, reflexive, symmetric, transitive: showing that given a relation is reflexive, symmetric, or transitive or finding a counter-example to show that the relation does not satisfy any one of these properties. 5. Equivalence relations: determining whether a given relation is an equivalence relation, finding the equivalence classes. 6. The relationship between equivalence relations and partitions. 7. Definition of a function. 8. Surjections, injections, and bijections: showing that a function is one-to-one or onto. 9. Composition of functions: what is it, how is it defined. 10. The Division Algorithm, finding the "q" and the "r". 11. Definition of divides and properties of div. Jordon Math 260 Fall 2008Reading Assignment GuidelinesFor almost every class meeting this term, you will be given a reading assignment together with two or three questions to which you must respond. Below is a description of the requirements you will
Math 260, Fall 2008 H. JordonExtra Homework ProblemsInstructions: Answer each of the following questions on a separate piece or pieces of paper. Each question is worth 5 points. You may work with each other to solve the problems but the final write-up m
Systems Analysis and Design in a Changing World, Fourth Edition22Learning ObjectivesxExplain the purpose and various phases of the systems development life cycle (SDLC) Explain when to use an adaptive approach to the SDLC in place of a more predictiv
Math 105 Prelim #2 October 28, 2004This exam has a formula sheet, 7 problems and 7 numbered pages. You have 90 minutes to complete this exam. Please read all instructions carefully, and check your answers. Show all work neatly and in order, and clearly i
Math 105, Fall 2004 Solutions to Prelim 21.(a) Henri has to take 3 bottles from 5+7=12, and the order in which they are taken doesn't matter. Therefore, there are 12 3 possible choices. (b) Henri has to choose 1 bottle from the 5 bottles of red and 2 bo
Prelim 1 SolutionsProblem 1 (Total 10 points) Give the least square line that has the best fit to the following data points: (0, 2), (1, -2), (2, -2) and (3, 2). Hint: Recall that the slope and y-intercept of the best fit line are given by the formulasn
IT430 Lab 2 - Network Protocols and Scanning Name _, _ Directions: Work in groups of 2 to complete this lab. Goals: - Learn how to use VMWare - Understand the importance of using secure network protocols - Understand why hackers can transport a great quan
Scenario 1: Mobile Tactical Network for Special Operations Customer: J6, US Special Operations Command Support Staff: 1 Army officer and 20 brand-new enlisted troops with a mix of all services. You are tasked with designing a network for Special Operation
IT430 Lab 4 Gaining Network Access Names _, _ Directions: Work in groups of 2 to complete the following tasks and provide answers Goals: - Understand how hackers might use a listener program to gain access to a network - Understand how programs bypass ant
IT430 Network and Firewall Lab Name _, _ This lab is to be completed in teams of 2, no more than 3. Goals: Understand basic networking components Connect a simple network Understand Cisco Commands Understand the difference between a host firewall and a ne
IT430 Lab 8 Penetration Testing Demo Name(s) _, _ Goals: - Analyze vulnerabilities and determine possible attack vectors for many of the exploits learned in class Part I Metasploit Open the each image and go to the initial snapshot for each Open Green-XP
IT430 Lab 5 Linux and Unix Security Names _, _ Directions: Work in groups of 2 to complete the following tasks and provide answers Goals: - Understand the basic steps in improving the security on a Linux system Stopping unnecessary services/closing ports
Systems Analysis and Design in a Changing World, Fourth Edition1414Learning ObjectivesxDiscuss examples of system interfaces found in information systemsxDefine system inputs and outputs based on the requirements of the application programxDesign
Chapter 7Reporting and Interpreting Cost of Goods Sold and InventoryANSWERS TO QUESTIONS1. Inventory often is one of the largest amounts listed under assets on the balance sheet which means that it represents a significant amount of the resources avail
Lecture 25 Appendix B: Some sample problems from Boas Here are some solutions to the sample problems concerning solutions of 2 nd order differential equations, sometimes with time dependence as in Chapter 13.13.4: 2 Solutions: Here we consider the 1-D wa
Final Exam: Economics 101 June 12, 2002READ THE INSTRUCTIONS: You have three hours. Do all 5 questions; each has equal weight. Please be sure to number each problem by number and part, especially if you choose to do them out of order. You will get creditMidterm Exam: Economics 101You have one hour and fifteen minutes. Do all 3 questions; each have equal weight. Good luck.February 10, 1997 David K. Levine1. Short AnswersFor each of the normal form games below, find all of the Nash equilibria. Which arChapter 6 Circular Motion and GravitationCircular MotionConsider an object moving at constant speed in a circle. The direction of motion is changing, so the velocity is changing. Therefore, the object is accelerating. The direction of the acceleration i
A. 1. SamuelAbstract: Two machine-learning procedures have been investigatedin some detail using the game ofcheckers. Enough work has been done to verify the fact that a computer can be programmed so that it will1learn to play a better game of checke
COVER FEATUREThe Architecture of Virtual MachinesA virtual machine can support individual processes or a complete system depending on the abstraction level where virtualization occurs. Some VMs support flexible hardware usage and software isolation, whi
A Case for End System MulticastYang-hua Chu, Sanjay G. Rao, and Hui Zhangfyhchu,sanjay,hzhangg@cs.cmu.eduCarnegie Mellon UniversityABSTRACTThe conventional wisdom has been that IP is the natural protocol layer for implementing multicast related funct
Network Working Group R. DanielRequest for Comments: 2168 Los Alamos National LaboratoryCategory: Experimental M. Mealling Network Solutions, Inc. June 1997 Resolution of Uniform Resource Identifiers using the Domain Name SystemStatus of this Memo
Congestion Avoidance and ControlVan JacobsonLawrence Berkeley LaboratoryMichael J. KarelsUniversity of California at BerkeleyNovember, 1988IntroductionComputer networks have experienced an explosive growth over the past few years and with that growNotes on Using gdb, the GNU Debugger Benjamin ZornUsing a symbolic debugger will make writing and debugging the programs you will write in this course much easier. The best debugger to use with the version of C+ we are using in this class is gdb, the GNU
The Chubby lock service for loosely-coupled distributed systemsMike Burrows, Google Inc.AbstractWe describe our experiences with the Chubby lock service, which is intended to provide coarse-grained locking as well as reliable (though low-volume) storag
I. refinement A. definition- REFINEMENT GIVES A STRONGER SPECIFICATIONA specification S1 is refined by S2 (S1 <= S2)if and only if every correct implementation of S2is a correct implementation of S1.A refinement is "plug compatible"; this includes
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Abstract
A not-insignificant number of undergraduate engineers have problems with mathematics. School mathematics often has to be reinforced during undergraduate studies, where a lack of
understanding at the lower level often impedes learning at the higher level. Here, visualisations can help - either by contextualising the mathematics, or by using graphical
visualisations. In this latter case, "A picture is worth a thousand words" is most appropriate. However, even students who have problems rearranging equations are almost invariably able to "read", understand and draw graphs - basically visualisations of mathematical equations, be
they as simple as the straight-line equation or as complicated as the solution of a second-order
partial differential equation. Consequently, displaying graphs (i.e. visualising) can help deepen insight into mathematical processes. This, in turn, can raise a student's mathematical proficiency, predilection, awareness and eventual achievement. This paper deals with, amongst others, the following questions. Does using MathinSite improve mathematical achievement and if so, how? How does using MathinSite score over other computer-based learning techniques?
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Environmental Engineer's Mathematics Handbook approaches advanced math matics used in environmental engineering that emphasizes the relationship between the principles in natural processes and those employed in engineered processes. The text covers principles, practices and math involved in the design and operation of environmental engineering works. It also presents engineering modeling tools and environmental algorithm examples. Major subjects covered in this book include modeling, algorithms, and air and water pollution assessment and control calculations, offering concepts, definitions, descriptions, and derivations in an intuitive manner. It is both a textbook and reference tool for practitioners involved in the protection of air, water, and land resources.
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Mathematical Ideas Expanded tenth edition of Mathematical Ideas is the best ever! We have continued with the features and pedagogy that have made this book so successful over the years and at the same time, we've spent a considerable amount of time to incorporate fresh data, new photos, and new content (by way of a new chapter on trigonometry). We have tried to reflect the needs of our usersboth long-time readers and those new to the Math Ideas way of teaching liberal arts math. We hope you'll be pleased with the results. Like its predecessors, this edition has been d... MOREesigned with a variety of students in mind. It is well-suited for several courses, including the aforementioned liberal arts audience, survey courses in mathematics, and mathematics for prospective and in-service elementary and middle school teachers. Ample topics are included for a two-term course, yet the variety of topics and flexibility of sequence make the text suitable for shorter courses as well. Our main objectives continue to be to provide comprehensive coverage of topics, appropriate organization, clear exposition, an abundance of examples, and well-planned exercise sets with numerous applications. One of the biggest issues college math instructors face is capturing and keeping student interest. Over the years, John Hornsby has refined a creative solution--bringing the best of Hollywood into his mathematics classroom. Mathematical Ideas applies
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Mathematics & Computer Science
Mathematics Courses
MTH 101: Topics in Mathematics
Topics selected from various areas of mathematics such as discrete mathematics, logic, number systems, geometry, probability, and graph theory. The course is designed to give the student an appreciation of mathematics as an integral part of our culture as well as applications to various other disciplines.
Meets general academic requirement G.
MTH 104: Statistical Methods
Provides an introduction to statistical methods, including descriptive statistics, sampling, estimation, hypotheses testing, correlation and regression, and chi-square procedures. Students may not receive credit for both MTH 104 Statistical Methods and MTH 119 Statistical Analysis. Department permission required for students who have been placed in MTH 119 Statistical Analysis.
Meets general academic requirement G
MTH 114: Fundamentals of Mathematics
A study of fundamental mathematical principles underlying the concepts of number and shape. Topics include number systems, number theory, measurement systems, geometry, and functions with emphasis on applications and problem solving. Four meetings per week.
Differentiation of algebraic and transcendental functions, application of the derivative to related rates, max-min problems, and graphing. Introduction to integration, the Fundamental Theorem of Calculus. Four meetings per week.
Prerequisite: 3.5 years of high school mathematics
Meets general academic requirement G
MTH 122: Calculus II
A continuation of MTH 121 Calculus I. Applications of the integral, integration techniques, infinite sequences and series and improper integrals. Four meetings per week.
Geometry of the plane and space, including vectors and surfaces. Multivariable calculus, including partial derivatives, Taylor's Theorem in two variables, line and surface integrals, and Green's Theorem. Four meetings per week.
An introduction to abstract mathematical thought with emphasis on understanding and applying definitions, writing arguments to prove valid statements, and providing counterexamples to disprove invalid ones. Topics may include logic, introductory set theory, and elementary number theory, but the focus is on the process of reasoning rather than any particular subject or subdiscipline. It is strongly recommended that mathematics majors complete this course by the end of the sophomore year.
A study of the theory, methods of solution, and applications of differential equations and systems of differential equations. Topics will include the Laplace Transform, some numerical methods, and applications from the physical sciences and geometry.
Examines selected masterpieces of classical mathematics, including Euclid's Elements, Archimedes' determination of the surface area of a sphere, Heron's formula for triangular area, and Ptolemy's table of chords. Emphasis will be placed on the brilliance of the mathematics and the reverberations of these ideas down to the present age.
Does not satisfy a major/minor requirement.
Prerequisite: one course in calculus
MTH 252: Landmarks of Modern Mathematics (0.5 course unit)
Examines selected mathematical masterpieces from the Renaissance to the dawn of the twentieth century. Theorems to be considered include those of Cardano, Newton, the Bernoullis, Euler, Gauss, and Cantor. Besides the mathematics, the course focuses on the context in which the theorems were discovered and the lives of the discoverers. Offered in alternate years.
Does not satisfy a major/minor requirement.
Prerequisite: one course in calculus
MTH 314: Applied Mathematics & Modeling
Models describing physical and economic conditions will be constructed, analyzed, and tested. The computer will be used in model verification. Offered in alternate years.
The numerical solutions of equations, numerical integration and differentiation, systems of equations, curve fitting, and numerical solutions of ordinary and partial differential equations. Offered in alternate years.
Rigorous treatment of the real number system, sequence and function limits, continuity, differentiability, intermediate and mean value theorems, uniform continuity, the Riemann integral, and the Fundamental Theorem of Calculus. Offered in alternate years.
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Product is a digital download of the complete solution manual for this textbook in PDF format. No solution manaul or textbook will be shipped to you. Digital downloads will generally be immediately available to download after sucessfull payment.
From the Publisher
This book is for sophomore-level or junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.
This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualization play in understanding linear algebra.
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Automotive Mathematics 1st Edition
0131148737
9780131148734
Automotive Mathematics: Offering examples and applications tailored specifically to the automotive trades, Automotive Mathematics, 1st Edition, gives students a sound background in the mathematical skills necessary to be skilled and competent technicians. Early chapters of the text focus on fundamental mathematics skills such as ratios, percents, measurement systems and geometry; later chapters apply basic skills to topics such as engine balancing, camshaft event timing, modifying compression ratio, planetary gear ratios and hydraulics. Designed with versatility in mind, the text offers diverse problem sets (organized by level of difficulty), flexible organization, and in-depth examples that make math meaningful and relevant to the automotive technology student. «Show less
Automotive Mathematics: Offering examples and applications tailored specifically to the automotive trades, Automotive Mathematics, 1st Edition, gives students a sound background in the mathematical skills necessary to be skilled and competent technicians. Early chapters... Show more»
Rent Automotive Mathematics 1st Edition today, or search our site for other Rouvel
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Description of Courses
MAT MATHEMATICS (School of Mathematical and Natural Sciences)
105. Nature of Mathematics - 3-0-3 An exploration of mathematical ideas with an emphasis on conceptual understanding and effective thinking. Topics may include, but are not limited to, elementary number theory, infinity, mathematical aesthetics, chaos and chance.
201. Calculus I - 4-0-4 An introduction to calculus including the following topics: functions; limits; continuity; derivatives and their applications; introduction to integrals; fundamental theorem of calculus; applications of the definite integral, trigonometric, logarithmic and exponential functions; and beginning integration techniques. PR: Grade of C or better in MAT 120 or CI.
220. Mathematics for Teachers P-8 - 3-0-3 Development of numeration systems, number sense and number relationships, concepts of whole-number and rational-number operations, number theory, estimation, statistics and probability. Modeling of effective mathematical pedagogy for children, emphasizing the development of patterns and relationships and the view of mathematics as solving problems, communicating, reasoning and making connections. PR: majors in early childhood or middle-grades education and sophomore standing or CI.
304. Differential Equations - 3-0-3 Elementary study of methods, nature and existence of solutions to first order, linear, higher order and systems of ordinary differential equations, including LaPlace transformations, solutions in power series and oscillation theory. Applications considered. PR: MAT 202 or CI.
312WI. Modern Geometry - 3-0-3 Euclidean geometry from an advanced standpoint requiring problem solving and rigor. Introduction to non-Euclidean geometries. Development of geometries from both an axiomatic mathematical system standpoint and an investigative viewpoint, with the use of appropriate manipulatives and technology. Includes a project on an enrichment topic. PR: MAT 305WI or CI.
324. Geometry for the Middle Grades - 3-0-3 A postulational development of Euclidean geometry using a variety of approaches: Informal, Formal, Measurement, Coordinate and Transformation. This course does not apply to a major or minor in mathematics or mathematics education. PR: MAT 220.
340. Technology-Enhanced Instruction in Mathematics 5-12 - 3-0-3 Mathematical investigations appropriate to the middle grades and secondary school using various technology tools. Focus on developing effective technology-enhanced mathematics instruction in keeping with current reform standards. PR: MAT 145 or MAT 201 or CI and Junior/Senior standing.
401. Mathematics Minor Seminar - 1-0-1 A seminar for juniors and seniors who are minoring in mathematics. Topics of discussion will include: a selection of seminal theorems and their historical and/or practical significance; a survey of significant open problems that are guiding current mathematical research; and the use of Calculus and combinatorial mathematics to study a variety of phenomena through mathematical modeling. PR: MAT 201, MAT 219, JR or SR standing, 13 hours of MAT courses.
420. Advanced Topics in Mathematics - 3-0-3 An advanced mathematical topic to be chosen by the instructor. Students may repeat this course provided the topic is different during each term. PR: MAT 305WI and CI.
490. Mathematics Seminar - 1-0-1 Mathematics literature and research reports by faculty, students and visiting speakers. Each student is required to investigate a topic in mathematics and perform an oral presentation. For junior and senior mathematics and math education majors only. May be repeated once for credit. PR: MAT 305WI, JR or SR standing and CI.
496. Academic Internship - 3 to 9 hours Problem-oriented experiences on specific academic projects relating to the individual student's program of study, planned in consultation with the student's advisor. PR: See general provisions for academic internships in this catalog.
498. Directed Study - 1 to 3 hours Supervised independent study in mathematics when the area of study is specialized or not otherwise available. No student may apply more than three hours of credit for MAT 498 toward the requirements for the major. Last-semester JS or SS and approval of school dean.
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Mathematics - Annenberg Media
The video, software, and print guides in the math collection show concrete examples of good teaching and active learning in all sorts of settings: public school classes, multi-age classes in rural areas, bilingual classes, magnet and charter schools,Netlib Conference Database Search Form
The Netlib Conferences Database contains information about upcoming conferences, lectures, and other meetings relevant to the fields of mathematics and computer science. Unless otherwise specified in the "Starting Date" field below, your search will beNoga Alon
Noga Alon researches combinatorics, graph theory, their applications to theoretical computer science, combinatorial geometry and number theory, and the relationship of combinatorial algorithms and circuit complexity. Some of his papers, along with a
...more>>
Numerical Integration Tutorial - Joseph L. Zachary
A tutorial that explores rectangular and trapezoidal methods for numerical integration. Includes a Java applet that opens in a separate window, for use alongside the tutorial. From a Computer Science course at the University of Utah, and the book IntroductionOrder - Kluwer Online
A journal on the theory of ordered sets and its applications. Order occurs throughout mathematics and especially in algebra, combinatorics, geometry, model theory, set theory and topology.
...more>>
Project Euler - Colin Hughes
Browse hundreds of challenging problems that require mathematical insights as well as computer and programming skills to solve. Popular puzzles include "Add all the natural numbers below one thousand that are multiples of 3 or 5," "By considering the
...more>>
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Bezier Splines This applet introduces the user to the usage and mathematics of spline curves and includes a tutorial, exercises, and an interactive play space.
Coordinate Transformations The Coordinate System Transformations applet teaches several concepts. The first is how a transformation applied to a coordinate system affects the axes of that coordinate system. Second, this applet shows how looking at only a very small portion of any curve produces a straight line (linear approximation) of that curve. Finally, this applet shows how a transformation of the coordinate system affects any objects within that coordinate system.
Dot Product The Dot Product applet shows how the scalar dot product value of two vectors depends on both the vectors' lengths and the angle between them. It also demonstrates the dot product's property of rotational invariance. Editable equations are displayed, as are concept explanations and help text. The dot product is an essential building block in linear algebra and for doing almost any type of transformation or rendering in computer graphics.
Normal Scaling 2D The 2D Surface Normals applet shows students how surface normals are affected by non-proportional (non-uniform) scaling. Without this knowledge, the shading of non-uniformly scaled objects is often calculated incorrectly.
Reflection 2D The 2D Reflection applet is an interactive illustration letting users reposition a light source and automatically recalculate the reflection vector. The standard equation is used with N, L and R for, respectively, the surface normal, normalized direction to a light source, and normalized reflection of L off of a surface. All equations are automatically updated with a user's changes to the illustration. A series of tips/concept explanations are available.This applet helps enhance complete understanding of essential task.
Transformation Game This applet introduces the user to the usage and mathematics of two-dimensional transformations using a fun, interactive play space.
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Thompsons Precalculus use Mathematica mostly in heavily formulated physics problems such as molecular spins and fractional calculus where equations are concise but complex. It is always advisable for a student to be conversant in both languages. Perl was an indispensable shell language for many codes written within the unix/linux environment.
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About McGraw -Hill's Top 50 Math Skills for GED Success
Written for the millions of students each year who struggle with the math portion of the GED, "McGraw-Hill's Top 50 Math Skills for GED Success "helps learners focus on the 50 key skills crucial for acing the test.
From making an appropriate estimate and solving for volume, to interpreting a bar graph and identifying points on a linear equation, this distinctive workbook from the leader in GED study guides features step-by-step instructions; example questions and an explanatory answer key; short concise lessons presented on double-page spreads; an appealing, fully correlated pretest and computational review of basic skills; application, concept, and procedure problems; and more.
About McGraw -Hill's Top 50 Math Skills for GED
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From time to time, not all images from hardcopy texts will be found in eBooks, due to copyright restrictions. We apologise for any inconvenience.
Description
Appropriate for courses in Introductory Linear Algebra for science, computer science, engineering, and social science students.
Norman/Wolczuk's An Introduction to Linear Algebra for Science and Engineering has been widely respected for its unique approach, which helps students understand and apply theory and concepts by combining theory with computations and slowly bringing students to the difficult abstract concepts. This approach includes an early treatment of vector spaces and complex topics in a simpler, geometric context. An Introduction to Linear Algebra for Science and Engineering promotes advanced thinking and understanding by encouraging students to make connections between previously learned and new concepts and demonstrates the importance of each topic through applications.
The highly anticipated second edition of this book will retain the student-friendly writing of the first edition while enhancing pedagogical features by including new mid-section exercises, new and expanded examples and end-of-chapter problems, and improved motivation behind each theorem. The second edition features a fresh two-colour design and a companion website for students that will include additional applications, resources, practice quizzes, and the first edition's "Essay on Linearity and Superposition in Physics."
NEW! MyMathLab is now available for this text. The course features assignable homework exercises plus the complete eBook, in addition to tutorial and assessment tools that make it easy to manage your course online.
New to this edition
Early introduction of basic theory and important concepts. The second edition introduces all the concepts of subspaces, linear independence, spanning, and bases in Chapter 1 and revisits them in Chapter 2 and 3 before using them in abstract vector spaces. By introducing the theory slowly, students don't have to cope with it all at once when they get to the general concept of a vector space in Chapter 4. They are familiar with the concepts so the abstraction is a natural extension.
Expanded Geometric approach. Building on the first edition's strong emphasis on geometry, the second edition introduces more advanced concepts such as Spanning and Linear Independence through geometry early in order to aid in visualizing the concepts. This allows for a better understanding of the concepts before they are turned into abstract concepts.
New mid-section exercises. These short, computational questions allow students to use and check their understanding of a concept before moving on. Solutions are provided in the back of the book.
New interior design. The second edition has a new two-colour interior design that enhances readability. Definitions, algorithms, theorems, and examples are called out in the margins for easy reference.
Proven, class tested approach. Norman/Wolczuk's approach has been class tested at the University of Waterloo for eight semesters. Students who study with the text experience higher retention of the material after the course ends, allowing for more challenging work to be covered in following courses.
Flexible Order of Topics.
Chapter 5: Determinants and Chapter 6: Eigenvectors and Diagonalization are self contained chapters that can be moved earlier, before Chapter 4: Vector Spaces.
Standardized notation. The second edition includes standardized notation for vectors in R^n (arrow-hat) and column vectors.
Additional Examples. Additional worked out examples have been added. Students benefit from have a good number of well selected examples to learn from.
End of Section Problems. End of Section problems have been reorganized and additional exercises have been added.
New Chapter 9: Complex Vector Spaces. Discussion of complex numbers and complex vector spaces has been collected into a single chapter.
Companion Website. The CW will have practice quizzes, additional applications, and the "Essay on Linearity and Superposition in Physics" from the first edition. The self-quizzing in Multiple Choice and True/False format will help students gauge their conceptual understanding of key concepts
Features & benefits
Student-friendly language. This text is written in a conversational, effortless tone, creating a truly student-friendly text.
Balances theory and computations.An Introduction to Linear Algebra for Science and Engineering introduces students to the theory and computational aspects of linear algebra simultaneously. This ensures that students realize that linear algebra is not just computations. It allows important concepts to be developed and extended slowly and it encourages the use of computational problems to understand the theory rather than the memorization of algorithms.
Strong emphasis on geometry. Students are usually familiar with the geometrical interpretation of vectors from high school math and physics. Concepts that are introduced early are done so using geometry to explain and motivate.
Applications support theory. This text distributes applications of linear algebra throughout text where relevant (rather than gathering them in a separate section.) Applications are included where the relevant theory is developed keeping the focus on the theory. Applications include:
Minimum distance from a point to a plane (Section 1.4)
Area and Volume (Section 1.5, Section 5.4)
Electrical Circuits (Section 2.4, Section 9.2)
Planar Trusses (Section 2.4)
Linear Programming (Section 2.4)
Magic Squares (Chapter 4 Review)
Markov Processes (Section 6.3)
Differential Equations (Section 6.4)
Curve of Best Fit (Section 7.3)
Overdetermined Systems (Section 7.3)
Graphing Quadratic Forms (Section 8.3)
Small Deformations (Section 8.4)
The Inertia Tensor (Section 8.4)
The problem set at the end of each section includes four types of questions
A: practice problems intended to provide a variety and number of standard computational problems, with some theoretical problems, necessary for students to master the techniques of the course. Answers to A-type problems are provided at the back of the text.
B: homework problems similar to A problems but without answers in the back of the text.
C: problems that require the use of a suitable computer program and help student familiarise themselves with using computer software to solve linear algebra problems. These problems remind students that linear algebra uses real numbers as well as integers and simple fractions. C-type problems are platform-neutral; they can be used with any linear algebra software.
D: problems that require students to work with general cases, write simple arguments or invent examples, all of which are important aspects of mastering mathematics ideas that all students should attempt.
End-of-chapter Chapter Review. Contains Suggestions for Review, Chapter Quiz, Further Exercises, and aids students in reviewing material presented in each chapter.
A Test Bank with a large selection of questions for every chapter of the text.
Customizable Beamer presentations for each chapter.
Image Library.
Author biography
Daniel Norman, born 1938. B.A. (University of Toronto), M.A.(Queen's University at Kingston), Ph.D. (University of London, King's College). His Ph.D. thesis was in General Relativity. Appointed to the Department of Mathematics at Queen's in 1965, he remained interested in applied mathematics. He taught undergraduate courses at all levels, mostly calculus, linear algebra and differential equations, to engineering students. After teaching introductory linear algebra for several years, he was frustrated with texts then available for those students so he began writing Introduction to Linear Algebra for engineering students in 1989. Versions of it were used in the large first year engineering class from 1991 until its publication as a book in 1995 and it continued to be used until he retired from the Department of Mathematics and Statistics at Queen's, as an Associate Professor, in 2001.
Dan Wolczuk has been lecturing at the University of Waterloo since 2004. Since he teaches nine courses a year, mostly first and second year linear algebra and calculus courses, he has spent considerable effort researching how to teach these courses more effectively. Dan is very passionate about teaching and spends much of his spare time teaching mathematics to gifted elementary and high school students.
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Mathematics 4 builds off of the concepts of Mathematics 3 but extends further by studying rates of change, logarithmic functions, polynomial and rational functions, and various forms of problem solving. This course includes an introduction to number theory and calculus. A graphing calculator is required for this course.
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MAA Review
[Reviewed by Mark Hunacek, on 02/17/2013]
The MAA Guide series — a subset of the Dolciani Mathematical Expositions — is rapidly becoming one of my favorite series of books. I like expository books that provide a quick and interesting entrée into an area of mathematics, or a useful source of examples, and that is precisely what these are. They are also, thanks to careful selection of authors, generally very well-written, informative and particularly useful as a resource for a varied audience. This book, the most recent one in the series (number 8, following books on complex variables, advanced real analysis, real variables, topology, elementary number theory, advanced linear algebra and plane algebraic curves) continues this tradition.
Each volume in this series is addressed to readers who, although mathematically sophisticated, are not experts in the subject matter of the book. The canonical example, I would think, would be graduate students seeking an efficient way of helping prepare for qualifying exams. However, faculty members who haven't had occasion to work extensively in a given area and who want a quick overview of the basic ideas and how they hang together would also find these books valuable. The emphasis in most of the Guides that I have read (this one most definitely included) is providing a survey of the subject in a reasonably short amount of pages, providing a book that is accessible and informative but likely does not contain the kind of technical detail that, although obviously necessary for complete mastery of the material, may serve as an impediment to a person who just wants to know "what's what" in an area.
So, for example, this book, like many in the Guide series (one possible exception is Weintraub's Advanced Linear Algebra) is not really intended as a text. There are no exercises, and most proofs are omitted; some that are fairly easy are provided, though never in the rigid theorem/proof format of most textbooks. Instead of proofs, Gouvêa provides discussions of the results and, quite often, a helpful sort of intuition as to why something should be true. (The author uses the phrase "shadows of proofs" in this connection.) To compensate for the lack of proofs, there is an excellent bibliography, to which the author makes frequent specific references throughout the text.
There are also lots of nice examples. A professional algebraist may be able to immediately give an example of a projective module that is not free, or a ring that does not have the invariance of basis number property, but people who don't work with algebra all the time may not have such examples on the tip of their tongues. The reader will find such examples here (along with, in connection with the latter, a succinct explanation of why such an example must be noncommutative). The reader will also find some examples that involve completely different branches of mathematics; there is, for example, a nice little one-page discussion of how modular forms arise from group actions, and the author also makes occasional remarks about topics such as topology and elliptic curves. The discussions here are not deep or technical, just brief overviews that give the reader some idea of what the terms mean; perfect for a student or non-specialist faculty member who may wind up hearing the phrase in a talk somewhere. In conformity with the intended readership, examples are not necessarily set off with big margins and the word EXAMPLE in large letters, but are often incorporated directly into the text.
The book is divided into six chapters, the first three of which are largely prefatory to the last three, which in turn comprise the meat of the book. Chapter 1 provides a succinct, interesting historical look at algebra, in which the author briefly tracks the development of algebra from its classical origins through its modern period (i.e., the axiomatic approach of Artin and Noether) up to its "ultramodern" period of category theory. Chapter 2 continues the study of categories; not being a huge fan of what Serge Lang once famously referred to as "abstract nonsense", I feared, when I saw this early chapter on the subject, that the entire book would be filled with commutative diagrams and exact sequences, but was pleased to discover, as I read on, that Gouvêa does not overdo this; these things generally don't appear unless their appearance really does enhance the discussion. Chapter 3 is a bestiary of algebraic terms, some of which are re-defined later and discussed in more detail.
The remaining three chapters discuss, in order, the three algebraic structures mentioned in the title of the text: groups, rings and fields (including skew fields). Chapter 4 on groups starts with the definition and then proceeds to discuss all of the general topics that one would expect to encounter in a first year graduate course, and perhaps a somewhat more: the chapter talks about Sylow theory, nilpotence and solvability, the word problem, group representation theory (in characteristic 0) and more. The discussion, even of elementary concepts, is done at a mathematically mature, but nonetheless accessible, level (for example, cosets of a subgroup H of a group G are defined as orbits under a certain group action), which I think is entirely appropriate, given the intended readership, and which also has the advantage of letting the reader see how these ideas really fit into the "big picture" (for example, the fact that distinct cosets partition the group is now seen to be just a special case of the more general result about orbits).
The next chapter is on rings and modules, and here, too, we are treated to an excellent survey of that area of mathematics: basic definitions, followed by discussions of topics such as localization, Weddeburn-Artin theory, the Jacobson radical, factorization theory, Dedekind domains (with a look at algebraic numbers), and various kinds of modules (free, projective, injective, etc.). As in the earlier chapter on group theory, the discussion here is at a mature level, with the author frequently stating things at a somewhat greater level of generality than might usually be encountered. (Examples: a quite general statement of Nakayama's lemma is given, and the usual results about modules over PIDs are deduced as a special case of the more general situation of modules over Dedekind domains.) Notwithstanding this, however, Gouvêa also keeps the needs of students firmly in mind; for example, there is a section titled "Traps", in which he points out, with simple specific examples, some of the ways in which modules can differ from vector spaces. (He tells of a friend who once described modules as "vector spaces with traps".)
The final chapter is on field theory. Galois theory is covered, of course (in a considerably general way, including infinite Galois groups and their topologies) but the chapter also contains material on such topics as algebras over a field, function fields, central simple algebras and the Brauer group.
Because the author is writing for people who already have some mathematical sophistication, including some prior exposure to abstract algebra, he does not feel obliged to follow a strictly linear order of presentation. So, for example, the chapter on groups, which precedes the chapters on rings and fields, nonetheless contains references to things like finite fields, semisimple rings and algebraic numbers; as another example, Nakayama's Lemma in ring theory is stated in a form involving tensor products, which are not formally discussed until a few sections later. This provides a certain freedom that an author of a strictly introductory text does not have, and helps, I think, enhance one's overall understanding of the subject by providing a broader point of view than might otherwise be possible. Likewise, even within a chapter, the level of difficulty is not necessarily monotonically increasing, and sometimes fairly sophisticated topics (e.g., profinite groups) are discussed before much more elementary ones (e.g., permutation groups). So, if you find a certain section to be fairly heavy going, just keep reading, and chances are, within a page or two, you will find things more comfortable.
The writing style throughout the book is of uniformly high quality. The author is one of those rare people who has the ability to write like people talk, with a nice, conversational tone that sometimes elicits a smile as well as a nod of understanding. Here, for example, is how he ends his discussion of groups of small order: "The next interesting case is order 16, which is, alas, a bit too interesting. There are five different abelian groups (easy to describe) and there are nine different nonabelian ones (most of them not easy to describe). So we will stop here." And see also page 160 for a cute little comment that will appeal to fans (of a certain age) that remember Tom Lehrer.
It should be apparent from the preceding discussion that I liked this book — a lot. Nevertheless, it seems inevitable that any reviewer will find some nits to pick, just because no two people will ever write the same book. The ones I have, though, are neither numerous nor particularly significant, and basically just reflect my personal preferences. I would have liked, for example, to have seen an example of non-isomorphic groups with the same character table (Everybody's Favorite Example is D4 and the quaternion group), as well as a specific example of a rational polynomial of degree 5 that is not solvable (the author states that the "generic" polynomial of degree at least five is not solvable and also states that an irreducible polynomial of prime degree with two real roots and at least one non-real root is not solvable by radicals, but does not give an actual fifth-degree polynomial meeting these conditions). I think the phrase "special linear group" should have been introduced when the group SL(n,K) was first defined on page 33, rather than fifty pages later, and also think that discussing unique factorization without at least mentioning Fermat's Last Theorem can only be described as a lost opportunity.
Additionally, one of my favorite cute applications of transcendence bases has always been the proof that the field of complex numbers has infinitely many automorphisms (a fact that I think is insufficiently well known); the author develops all the machinery necessary to establish this, but doesn't say so explicitly. Finally, in connection with the definition of algebraically closed fields, the author states the Fundamental Theorem of Algebra (that the field of complex numbers is algebraically closed) and says that all proofs "depend on the topology of the complex field". This statement, though true, may lead students to believe that all proofs are very analytic or topological in nature; in fact, there is at least one proof that uses Sylow and Galois theory and only two simple facts from analysis, namely (a) that any real polynomial of odd degree has at least one real root, and (b) that any quadratic polynomial with complex coefficients has a complex root.
But these are quibbles. Overall, this is a valuable book — a pleasure to read, and packed with interesting results. It should be very helpful to graduate students and non-specialists wanting a succinct summary of the subject, and even professional algebraists may find something new and interesting here. It is a splendid addition to an excellent series.
One final comment: in the interest of full disclosure, I should mention that, as faithful readers of this column probably already know, the author of this book is also the editor of this column. This raises, I suppose, at least the question of a conflict of interest. This same issue arose when another of the author's books, p-adic Numbers, was favorably reviewed in this column by Darren Glass more than two years ago, and since I don't think that I can improve on the way Professor Glass addressed it, I will simply quote him verbatim: "[T]he reader can rest assured that this reviewer would have said equally flattering things about the book even if it wasn't written by his editor. Besides, I couldn't think of anything that an editor could use to bribe his volunteer reviewers with (More prominent placing on the site? First crack at the new Keith Devlin?) so I didn't even bother asking."
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Basic Topology
9780387908397
ISBN:
0387908390
Pub Date: 1983 Publisher: Springer Verlag
Summary: In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of ...various difficulties will help students gain a rounded understanding of the subject
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56 minute basic algebra lesson is for the beginning algebra student or for anyone who has not recently studied algebra. It includes the language and symbols of algebra, (plus or minus ±, equal to =, not equal to ≠, approximately equal to, less than <, less than or equal to ≤, greater than >, greater than or equal to ≥) and introduces the polynomial. In this lesson you will be introduced to the variable "x", learn what a term, factor, exponent and degree of a term mean and be able to:
- understand what a polynomial, binomial, trinomial, are
- evaluate a polynomial with integers (numbers)
- simplify polynomials by collecting like terms
- simplify polynomials with brackets
- simplify polynomials using the distributive property
- do application problems such as by how much does 2x^2 -3x + 5 exceed 3 x^2 - 5x + 6
This lesson contains explanations of the concepts and 27
Recent Reviews
All the terms and concepts of Algebra are here. Was an excellent refresher for me and would probably have made my earlier math classes go by much smoother. No frills and no fluff but it gets the job done.
All the terms and concepts of Algebra are here. Was an excellent refresher for me and would probably have made my earlier math classes go by much smoother. No frills and no fluff but it gets the job done.
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Revision history of "Math for Computer Graphics and Computer Vision"
From Math Images13, 29 June 2009Gene (Talk | contribs)(945 bytes)(New page: The Drexel group may also want to focus on the math used in computer graphics and computer vision. Here are some examples. :* Vectors and matrices :* Transformations :* Quaternions :* Hie...)
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Key Maths Gcse: Foundation: Ocr Question Book
Synopsis
Test questions are provided for each chapter together with detailed mark schemes to make assessment easy. Two versions of each question are provided. One allows pupils to write their answers in the spaces provided, and the other requires pupils to have separate writing paper. Questions can be grouped according to needs. Master grids are provided to cut and paste tests together in a consistent format to use the resource in any order. Chapter tests can be grouped to form a 'module test' after chapters. End-of-chapter examinations can also be produced in this way. A free non-calculator supplement organised by unit/chapter is also included in this resource.
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Book Description: Whether you're new to algebra or just looking for a refresher, Algebra Success in 20 Minutes a Day offers a 20-step lesson plan that provides quick and thorough instruction in practical, critical skills. Stripped of unnecessary math jargon but bursting with algebra essentials, this extensive guide covers all vital algebra skills, including combining like terms, solving quadratic equations, polynomials, and beyond. This proven study aid is completely revised with updated lessons and exercises that give students and workers alike the algebra skills they need to succeed. Algebra Success in 20 Minutes a Day also includes: Hundreds of practice exercises, including word problems Application of algebra skills to real-world (and real-work) problems A diagnostic pretest to help pinpoint strengths and weaknesses Targeted lessons with crucial, step-by-step practice in solving algebra problems A helpful posttest to measure progress after the lessons Glossary, additional resources, and tips for preparing for important standardized or certification tests
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Integral Calculus
It is not an exaggeration that the fort of Mathematics is Calculus and the most important part of it is Integral Calculus. It is quite a lot scoring and should be taken very seriously in the preparation of IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations. The Calculus is said to be complete only if you have mastered the topic of Integral Calculus.
Since the prerequisite to the preparation of Integral Calculus is the study of Differential Calculus, we can judge a student in Calculus by seeing his comfort level and proficiency in Integral Calculus. The importance of Integral Calculus is not just restricted to Mathematics but it is of profound importance in the major part of Physics and Physical Chemistry. The major portions of study of Integral Calculus include Indefinite Integral and Definite Integral and they are rightly termed as tools which are further used in its applications under the topics of Area. The topic of Area is the one which used the most in Physics and should be taken very seriously. The next topic of Differential Equations is also quite important. Since the syllabus do not demand differential equations of higher order so it is easy for the students to have proficiency in the subject.
It is true that most of the students fear from Integral calculus, but all the high rank holders in IIT JEE are always very comfortable in the topic. It is advised to do a practice in Integral Calculus at an early stage as it is one of the new topics which students study while preparing for IIT JEE, AIEEE, DCE, EAMCET and other engineering entrance examinations.
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@ Pete,Victor and Greg: First,I agree with your interpretation of the paragraph Greg's referring to.
Secondly,despite loving Pugh's book-I call it "Rudin Done Right"-I was also very disappointed at the very terse preface.You'd think someone with Pugh's teaching experience would have a LOT to say on the subject having taught so many years to some of the best students in the world.
Third-I seriously doubt one of the world's experts in differential equations thinks real analysis is devoid of real world applications.But that being said-what compels people teaching this course to strip it down to Bourbakian purity? Tradition? Or something darker and deeper?
I'm waiting for a balanced text at this level that unifies physical applications with a comprehensive introduction to real analysis. If it never arrives,I may have to write it myself.
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e-books in this category
High School Algebra
by J.T. Crawford - The Macmillan Company , 1916 This text covers the work prescribed for entrance to the Universities and Normal Schools. The book is written from the standpoint of the pupil, and in such a form that he will be able to understand it with a minimum of assistance from the teacher. (206 views)
Advanced Algebra
by Arthur Schultze - The Macmillan Company , 1906 The book is designed to meet the requirements for admission to our best universities and colleges. The author has aimed to make this treatment simple and practical, without, however, sacrificing scientific accuracy and thoroughness. (413 views)
Fundamentals of High School Mathematics
by Harold O. Rugg, John R. Clark - Yonkers-on-Hudson, N.Y. , 1918 The text is organized to provide the pupil with the maximum opportunity to do genuine thinking, real problem-solving, rather than to emphasize the drill or manipulative aspects which now commonly require most of the pupil's time. (418 views)
Numbers and Symbols: From Counting to Abstract Algebras
by Roy McWeeny - Learning Development Institute , 2007 This book is written in simple English. Its subject 'Number and symbols' is basic to the whole of science. The aim the book is to open the door into Mathematics, ready for going on into Physics, Chemistry, and the other Sciences. (705 views)
Problems Solved! An Algebra Study Guide
by John Redden - College of the Sequoias , 2006 This study guide is designed to supplement your current textbook. It is a solutions oriented approach to Algebra. This guide shows what steps to include when working Algebra problems. Take time to try the problems without looking at the solutions. (1103 views)
Primary Mathematics
- Wikibooks , 2012 This book focuses on primary school mathematics for students, whether children or adults. It is assumed that no calculators are used, to encourage mental arithmetic. This course uses as much lay language as possible to also be helpful to parents. (3114 views)
A Review of Algebra
by Romeyn Henry Rivenburg - American Book Company , 1914 The object of this book is to provide a thorough and effective review that is necessary in order to prepare college candidates for the entrance examinations and for effective work in the freshman year in college. This is the 1914 edition. (1756 views)
Elementary Algebra
by John Redden - Flat World Knowledge , 2011 This book takes the best of the traditional, practice-driven algebra texts and combines it with modern amenities to influence learning, like online/inline video solutions, as well as other media driven features that only an online text can deliver. (5161 views)
A Problem-Solving Approach to College Algebra
by Marcel B. Finan - Arkansas Tech University , 2002 This book is a non traditional textbook in college algebra. Its primary objective is to encourage students to learn from asking questions rather than reading a detailed explanations of the material discussed in a typical textbook. (4574 views)
A First Book in Algebra
by Wallace C. Boyden - Project Gutenberg , 2004 It is expected that this work will result in a knowledge of general truths about numbers, and an increased power of clear thinking. The book is prepared for classes in the upper grades of grammar schools, or any classes of beginners. (8993 views)
A Practical Arithmetic
by Frank Lincoln Stevens - C. Scribner's sons , 1910 The primary object of arithmetic is to enable the student to acquire skill in computation. In addition to the attainment of this essential end, great benefit is derived from the exercise of the reasoning powers and their consequent development. (6415 views)
Fundamentals of Mathematics
by Denny Burzynski, Wade Ellis - Saunders College Publishing , 1989 The text covers the topics studied in a modern prealgebra course, as well as topics of estimation, elementary analytic geometry, and introductory algebra. Useful for students who need to review fundamental mathematical concepts and techniques. (17792 views)
Elementary Algebra
by Denny Burzynski, Wade Ellis - Saunders College Publishing , 1989 This text covers the traditional topics studied in a modern elementary algebra course for students who have no exposure to elementary algebra, have had an unpleasant experience with elementary algebra, or need to review algebraic concepts. (16265 views)
Inner Algebra
by Aaron Maxwell - Lulu.com , 2005 Learn to do algebra mentally and intuitively: mathematicians use their minds in ways that make math easy for them. This book teaches you how to do the same, focusing on algebra. As you read and do the exercises, math becomes easier and more natural. (8345 views)
College Algebra
by Paul Dawkins - Lamar University , 2011 These notes are accessible to anyone wanting to learn Algebra or needing a refresher for algebra. While there is some review of exponents, factoring and graphing it is assumed that not a lot of review is needed to remind you how these topics work. (7926 views)
Essential Mathematics
by Franco Vivaldi , 2006 Essential Mathematics is written for students who reach university without elementary algebra and arithmetic skills. The book consists of exercises on fractions, roots, monomials and polynomials, linear and quadratic equations. (10429 views)
Reasonable Basic Algebra
by Alain Schremmer , 2008 Reasonable Basic Algebra (RBA) is a course of study developed to allow a significantly higher percentage of students to complete Differential Calculus in three semesters. It may serve in a similar manner students with different goals. (8029 views)
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Elementary Algebra
9780495108399
ISBN:
0495108391
Edition: 8 Pub Date: 2007 Publisher: Thomson Learning
Summary: Algebra is accessible and engaging with this popular text from Charles "Pat" McKeague! ELEMENTARY ALGEBRA is infused with McKeague's passion for teaching mathematics. With years of classroom experience, he knows how to write in a way that you will understand and appreciate. McKeague's attention to detail and exceptionally clear writing style help you to move through each new concept with ease. Real-world applications... in every chapter of this user-friendly book highlight the relevance of what you are learning. And studying is easier than ever with the book's multimedia learning resources, including ThomsonNOW for ELEMENTARY ALGEBRA, a personalized online learning companion495108399-3-0-3 Orders ship the same or next business day... [more]
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Time and Venue
Course Description
Overview:
This course is an introduction to numerical methods for differential equations. Differential equations are common mathematical models of many realistic applications from physics, biology, finance and engineering. In order to quantitatively study these problems, one needs to find the solutions of the differential equations under consideration. However, analytical solutions to these differential equations are typically very difficult to compute. It is therefore important to design some methods to obtain approximate solutions in an efficient way. The focus of this course is to present some basic numerical methods for solving differential equations. We will consider both ordinary and partial differential equations.
Requirement:
In addition to the derivation of the methods, we will also prove stability and convergence theorems. A solid background in analysis and differential equations (ODE and PDE) is thus a very important prerequisite for this course. Moreover, there are some computational assignments, and some knowledge in MATLAB or C is needed.
Outline:
1. One step methods for ODE
2. Runge-Kutta methods for ODE
3. Multi-step methods for ODE
4. Systems of ODEs
5. Stiff problems
6. Boundary value problems
7. Finite difference methods for parabolic PDEs
8. Finite element methods for elliptic PDEs
Textbooks
Numerical Mathematics and Computing, by Cheney and Kincaid. (7th Edition)
Quizzes and Exams
Solutions
Assessment Scheme
Assignment
10%
Mid-term (March 13)
35%
Final Exam
55
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Institute of Mathematics
The St. Mark's Institute of Mathematics is an established center of mathematical excellence.
The St. Mark's School Institute of Mathematics offers workshops, courses, and activities for students of all ages (both from St. Mark's School and from the wider community), for teachers and home-school educators, and for all those interested in practicing and promoting the joy of mathematical thinking and creative pursuit. The mission of the Institute is to:
Provide community outreach of mathematical excellence; and
Enhance and promote creative mathematical thinking, awareness, and enjoyment of the subject.
The Institute of Mathematics provides research experiences for young scholars, promotes innovative mathematics thinking through its quasi-weekly e-mail puzzles and through its monthly hard-copy newsletter. This letter is full of intriguing mathematical tidbits, curious mathematical challenges and accessible research problems for students (and others!) to ponder upon.
Upcoming Events for Spring 2013.
The St. Mark's Institute of Mathematics Presents
AN INTRODUCTION TO THE MATHEMATICAL MODELING OF EPIDEMICS
Instructor: Dr. Lauren Riva Director of the St. Mark's Institute of Mathematics
Course Begins: March 25th 2013
Course Length: 6 weeks long
Workload:2-4 hours/week
ABOUT THE COURSE
Infectious diseases are some of the leading causes of death around the world. Mathematical models are increasingly being use to understand the transmission of infectious diseases and to inform public health strategies for predicting and controlling epidemics. This course is designed to give students a thorough introduction to the conceptual ideas and mathematical tools used in infectious disease modeling.
Students should be very comfortable with basic algebra. Calculus isn't necessary but a conceptural understanding of derivatives would be helpful.
REquired Reading
This course is self-contained, and the lecture notes will be available on-line.
COURSE FORMAT
The class consists of lecture videos punctuated by short quizzes. There will also be homework assignments that are not part of the video lectures. Students will also have the opportunity to interact with peers through online discussion board.
COURSE COMPLETION
Students who successfully complete all class assignments will receive a certificate of completion signed by the instructor. The certificate is not transferable for course credit.
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Short description
This popular series was developed after extensive classroom research and testing by the very experienced and acclaimed Classroom Mathematics team.
Class discussions, practical activities and group work encourage learners to get actively involved in real maths. The books aim to show learners the delights of maths while at the same time building a solid knowledge of mathematical principles.
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Mathematics Enrichment Workshop Program (MEWP)
Fall 2013 SCHEDULE What is the Mathematics Enrichment Workshop Program (MEWP)? * MEWP is a specially designed program that offers optional math enrichment workshops for students of all math ability levels who are enrolled in Developmental Math Coures (Math 090, 091, and 092), College Algebra (Math 173), Trigonometry (Math 175), Precalculus (Math 185), Calculus I (Math 187), and Calculus II (Math 202). * MEWP is a high-achieving program, not a remedial program. * MEWP students participate in their required math course (e.g., Calculus I) and a corresponding workshop (e.g., Mathematics Enrichment Workshop for Calculus I). Each MEWP workshop meets for one-hour twice a week (2 hours total). As a workshop participant, you will solve homework problems assigned in your required math course within small peer groups while receiving guidance from a trained undergraduate peer leader. * Workshops are 1 credit hour and pass/fail (students are required to consistently attend and participate in the workshops to pass). * MEWP is funded by the following grant: Enhancing Career Opportunities in Biomedical and Environmental Health Sciences at an Urban Hispanic Serving Institution: An HSI STEM and Articulation Initiative, U.S. Department of Education, $4,345,618, 2011-2016.
"I have a student that has taken Calculus I twice before and failed, but this time around she is expected to have an 'A' in the class. She said that the reason for her past failures were a direct result of her exam scores. She said she would freeze up because the exam problems were much harder than the homework and usually involved some tricks to solve. She said the workshop has allowed her to be confronted with difficult problems and learn the proper methods to solving them by demonstrations and talking with the other students." (Calculus I workshop peer leader, SP12) "The experience was primary beneficial in that each participant was able to actively participate in problem solving activities which either reinforced knowledge, process and technique used to solve problems, or it provided appropriate scaffolding to bring a student to the level they needed to be. The atmosphere was supportive. There was no judgment about errors in working through problems, only concern in helping each individuals elevating to levels needed...An added benefit of the program has been the ability to gain perspective from the workshop leader about future classes in the math sequence." (Calculus I workshop participant, SP12) Why should you join a MEWP workshop? * Whether you want to pass your math class or receive an A or B, participation in the workshops can help improve your grade in your standard math course and strengthen your understanding of mathematics. * In the workshops, you will solve actual homework problems assigned in your required math course. This may help significantly cut down the amount of time that you need to spend on solving homework problems independently. * The workshops are not one-on-one tutoring. Instead, they provide a comfortable environment where you will solve problems collaboratively with peers, while receiving guidance from a trained undergraduate peer leader. * The workshops will allow you to form friendships and study groups for current and possibly future math courses. MEWP also offers non-academic activities like pizza lunches throughout the semester. * The workshops are modeled after the successful Peer Led Team Learning (PLTL) and Emerging Scholars Program (ESP) models, which are nationally recognized for helping students succeed in mathematics! Research indicates that students who participate in math workshops modeled after the PLTL and/or ESP models have a higher probability of earning an A or B in their required mathematics courses. * There is also a possibility that in later semesters you may be hired as a paid peer leader for the program! Additional important information about MEWP * Registration andtuition: Students who would like to participate in a math enrichment workshop are encouraged to register for a workshop in NEIUport. If you register for a workshop, the cost is 1 credit hour. Students who are not registered are also encouraged to participate and should contact Dr. Cordell at S-Cordell@neiu.edu. * Workshop schedule: Workshop times can be changed. Contact Dr. Cordell to discuss this issue. * Scheduling conflicts: If you have a scheduling conflict that prevents you from participating in the workshop two days a week, it may be possible for you to attend the workshop one day per week. (Note: Students are not allowed to attend a workshop at random times throughout the semester.) Contact Dr. Cordell at S-Cordell@neiu.edu to discuss this issue. If you have additional questions about MEWP please contact Dr. Cordell, the MEWP Coordinator, at S-Cordell@neiu.edu.
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Variables and Expressions
In this first Algebra lecture on Educator.com, Dr. Fraser will briefly cover the history and origin of algebra, The word 'algebra' and why it is so powerful compared to arithmetic in solving real world problems till date. You will then cover basic definitions such as variable, algebraic expression, and operations. The lecture concludes with four examples where you will convert an algebraic expression from a sentence.
This content requires Javascript to be available and enabled in your browser.
Variables and Expressions
An algebraic
expression combines numbers and variables with arithmetic
operations.
Review these
terms: product, factor, power, base, exponent
Practice
translating verbal expressions into algebraic expressions. This is
an essential skill you will need to solve word problems throughout
this course.
Evaluating an
expression means to find the value of the expression.
Variables and Expressions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
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Learning Outcomes: On completion of the unit the student should be able to:
* use vector and scalar quantities to solve problems;
* determine unknown values using complex number techniques;
* investigate mathematical modelling techniques;
* use higher order calculus techniques;
* determine probable outcomes using statistical methods.
Skills: During this unit students should gain the following skills:
Intellectual:
* continued development of the appreciation of a rigorous proof
Professional:
* development of an appropriately analytic approach
Practical:
* continue (from part 1) the process of acquisition of suitable mathematical tools and procedures which are of universal application in engineering, science and related fields of employment
Key:
* mathematical proficiency and maturity
* a broad introduction to, and understanding of, fundamental ideas and tools of modern pure and applied mathematics
* appreciation of the role and power of rigorous proof in mathematics, and a further study of constructing and following such proofs.
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8th Grade Algebra
For students: The Important Files (documents and power points) are located at the bottom of the page.
Overview of 8th Grade Algebra
GOALS: There are several major goals for students in Algebra: 1. to identify and define a function, 2. to graph and solve functions, 3. to perform operations with polynomials and factor them, 4. to apply the skills learned to real world problems, and 5. to use technology to assist us in solving and representing mathematical concepts.
INTRO TO FUNCTIONS: Students begin the year introducing the concept of functions. We define functions and relations and learn various ways to represent relations-- equations, graphs, tables, and mapping diagrams. From those representations, we identify what relations are and are not functions.
LINEAR FUNCTIONS:The first family of functions we study is linear functions. We investigate the various general equations to represent these functions such as slope-intercept form, standard form, direct variation form, and point-slope form. We learn how to graph these functions in these different forms and convert from one form to another. We practice writing equations to represent real world situations, graph data, and interpret what these graphs of these functions mean. We use both Microsoft Excel and graphing calculators to apply skills we learn in this unit. We culminate this unit with a chapter project in which students collect data from an experiment they design.
LINEAR SYSTEMS:We extend our investigation of linear functions by studying linear systems. We learn what a solution of a linear system means and study various methods of how to solve a linear system. Students write a persuasive essay of which method they feel is the best way to solve a linear system.
INEQUALITIES:Students review the basic concept of inequalities and analyze what their solutions mean graphically. They learn about a new type of inequality--an absolute value inequality. They also learn how to graph inequalities on the coordinate plane.
POLYNOMIALS:We shift from functions and graphing to defining polynomials. We first learn how to perform operations with polynomials and then we learn various methods of factoring polynomials. We will analyze various polynomials and determine which method is necessary to factor them.
QUADRATIC FUNCTIONS & EXPONENTIAL FUNCTIONS: We finally move on to new families of functions other than linear! We examine the famililes of quadratic and exponential functions and learn their equations and graphic patterns. We also learn how to solve quadratic and exponential equations using a variety of methods. All of these skills are applied to word problems involving quadratic functions.
TECHNOLOGY:Graphing calculators will be used throughout the year to enhance our study of functions. Microsoft Excel will also be used to show another method of graphing data.
END OF THE YEAR EXAM: Students will take an Algebra Acuity Test at the end of the year for the Archdiocese. Neither I nor the Archdiocese make the exam. It is made through a computer program that the Archdiocese hired. What we learn throughout the year will prepare the students for the exam. Certain high schools within the Archdiocese ask for the exam scores to determine math placement. However, public schools and other private schools do not typically ask to see these scores.We will most likely not cover every single concept on the exam but that is typical. I give more information as the exam approaches toward the end of May.
SETUP: There is a focus on vocabulary. Students must keep up with the key terms in the vocabulary section of their notebooks. There are several quizzes throughout a chapter. Quizzes involve vocabulary and word problems. There is a major test at the end of a chapter. There are some projects and/or writing assignments throughout the year.
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MTH/HMTH202 Linear Mathematics 2
Duration :1 semester
Core Course for Major
24 lectures
Aim:
This course, which assumes and builds upon a basic knowledge of matrix
theory from MTH102, is designed to give a good grounding in all linear
aspects of mathematics. The emphasis in sections A and B will be on actual
examples and only basic results are proved. A more abstract approach is
offered in the course in Algebra 1 (MTH005).
The main aim in section C (which could be studied before section B) is to
expose the link between matrix theory and linear transformations. This
material, together with that in Section D, has applications to almost all
areas of pure and applied mathematics. It is applied (within
this course) to diagonalization of matrices and solutions of differential
equations.
(B) INNER PRODUCT SPACES.
Basic definitions with many examples, the notions of norm (length)
and distance (emphasis will be on the Euclidean inner product), the
Cauchy-Schwarz inequality, the angle between two vectors, orthogonal
vectors --- the Gram-Schmidt orthogonalization process, orthonormal basis.
3
(C) LINEAR TRANSFORMATIONS.
Basic definitions and results, including images and kernels, with examples;
matrix representations of linear transformations from $\BbbR^n$
to $\BbbR^n$, geometric interpretations of linear
transformations from $\BbbR^2$ to $\BbbR^2$.
4
(D) EIGENVALUES AND EIGENVECTORS.
The eigenvalues and eigenvectors of a matrix, the characteristic
polynomial of a matrix, linear independence and orthogonality of
eigenvectors, algebraic and geometric multiplicity of eigenvalues,
eigenspaces, eigenvalues of powers of matrices, formulas for
finding inverses of matrices and powers of matrices.
3
(E) VARIOUS TYPES OF MATRICES.
Symmetric, skew symmmetric, unitary, hermitian matrices
etc., their eigenvalues and eigenvectors, some basic results
and theorems about them.
3
(F) DIAGONALISATION OF MATRICES.
Similar matrices and their eigenvalues and vectors, identification
of matrices that are diagonalizable, the Cayley-Hamilton theorem and
its applications, quadratic forms and canonical forms.
3
(G) DIFFERENTIAL EQUATIONS.
Application of diagonalization of matrices to solutions of systems of
differential equations; the emphasis is on method --- no theorems are
proved.
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Find a Tolleson Calculus TutorLinear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many ...
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Short Description: This book contains hands-on exercises and math problems which allow students to explore magnetism and magnetic fields. The activities include drawing and geometric construction, and introduce students in the use of simple algebra to quantitatively examine magnetic forces, energy and magnetic field lines and their mathematical structure.
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DYNAMIC CONTENT Some demonstrations contain
dynamic content. The user may receive an alert
concerning a potential security issue. However,
all of the demonstrations on this webpage
are completely safe. To proceed, click ENABLE
DYNAMICS.
Simulated Epidemics BY PHILLIP BONACICH CDF: SimulatedEpidemics.cdf
Explore how the density and size of a network
affects the simulated growth of an infectious disease.
CHAPTER 2 SETS
Boolean Algebra BY PHILLIP BONACICH CDF: BooleanAlgebra.cdf
Use homomorphisms to analyze social group
memberships
Set Intersection and Union BY PHILLIP BONACICH CDF:
SetIntersectionandUnion.cdf
This demonstration selects two randomly selected subsets of the alphabet
and shows their intersection, union, and set differences.
Venn Diagrams BY GEORGE BECK AND LIZ KENT Wolfram:
Link
Visualize the complete 127 nonempty unions
and intersections of three sets, A, B, and C through Venn Diagrams
CHAPTER 3 PROBABILITY
The Binomial Fit BY PHILIP S LU CDF: BinomialFit.cdf
Explore the binomial distribution by fitting a
curve to a randomly generated distribution. Adjust the n and
p values and see how close you can come!
Convergence of Proportions BY PHILLIP BONACICH CDF: Convergence.nbp
This demonstration shows that while the
proportion of coin flips approaches the
probability in the long run, the difference
between the number of heads and expected number
increases in the long run.
Finding Bridges BY PHILLIP BONACICH Wolfram:
Link
This demonstration will help you discern bridges
from local bridges. Generate random networks of different sizes and
density and challenge yourself to correctly categorizing each edge.
Random Graphs BY STEPHEN WOLFRAM Wolfram:
Link
Generate an array of random graphs and familiarize yourself with the
qualitative and quantitative similarities.
CHAPTER 7 MATRICES
Graphs from Matrices BY GEORGE BECK Wolfram:
Link
Each square matrix can correspond to a graph.
Design a zero-one matrix and see the resulting network structure based
on your matrix.
CHAPTER 8 ADDING AND MULTIPLYING MATRICES
Matrix Multiplication BY ABBY BROWN Wolfram:
Link
Learning to multiply matrices? This demonstration
helps you visualize the row and column operations that result in a
matrix product.
Finding Cliques BY PHILLIP BONACICH Wolfram:
Link
This demonstration will locate n-cliques and
k-plexes in randomly generated networks. Vary n and k
and observe how strict or lenient each group definition is.
Community Structure BY PHILLIP BONACICH CDF:
CommunityStructure.cdf
Explore how the community structure algorithm assigns group membership
in a network. Unlike other group definitions, community structure
partitions the networks, so each vertex belongs to one and only one
group.
CHAPTER 10 CENTRALITY
Network Centrality BY PHILLIP BONACICH CDF: MeasureCentrality.cdf
Generate random networks of different sizes and densities and explore
the various aspects of centrality, represented by node size.
Centrality Game BY PHILIP S LU CDF: CentralityGame.cdf
Centrality measures can be independent. Challenge yourself by designing
a network where the top vertex is the most central under one measure,
but near the bottom under another.
CHAPTER 11 SMALL WORLD NETWORKS
Small World Networks: Lattice Model BY FELIPE DIMER DE OLIVEIRA Wolfram:
Link
Generate small-world networks based on random rewirings of a circular
lattice.
CHAPTER 12 SCALE-FREE NETWORKS
Contagion in Random and Scale-Free Networks BY PHILLIP BONACICH Wolfram:
Link
This demonstration compares the spread of an epidemic in random and
scale-free networks of identical densities with and without inoculation
of the most central 10% of the nodes.
Attack in Random and Scale-Free Networks BY PHILIP S LU CDF: Attack.cdf
Explore how random and scale-free networks with the same density hold up
against random failure and calculated attack. Multiple methods are
offered to measure damage.
Zipf's Law BY GIOVANNA RODA Wolfram:
Link
Power-laws are everywhere. This demonstration highlights the prevalence
of the distribution in important political documents.
CHAPTER 13 BALANCE THEORY
Triad Census on Random Graphs BY PHILIP S LU Wolfram:
Link
This Demonstration illustrates the expected frequencies in which these
triads occur in random graphs of varying density.
CHAPTER 14 MARKOV CHAINS
Transition Matrices for Markov Chains BY PHILLIP BONACICH Wolfram:
Link
Create your own Markov matrix and explore the equilibria in the matrix
after a set number of transitions.
CHAPTER 15 DEMOGRAPHY
Population Projection Using Leslie Matrices BY PHILIP S LU CDF: PopProjection.cdf
Expose an initial population to death and birth
rates and observe how the population changes over time, eventually
approaching equilibrium. View the population as both a graph and a
Leslie Matrix.
CHAPTER 16 EVOLUTIONARY GAME THEORY
Evolutionary Prisoner's Dilemma Tournament BY PHILLIP BONACICH CDF: PDTournament.cdf
Vary an initial population of strategies and let them compete in a
100-round PD tournament. Strategies reproduce themselves based on their
payoff in the previous set of rounds. Learn how the effectiveness of a
strategy is dependent on the composition of other strategies.
Nash Equilibrium in 2x2 Mixed Extended Games BY VALERIU UNGUREANU Wolfram:
Link
Adjust payoffs in a 2x2 matrix, and observe how it affects the set of
Nash Equilibria.
CHAPTER 17 POWER AND COOPERATIVE GAMES
Exchange Networks BY PHILLIP BONACICH Wolfram:
Link
Explore a simulation of behavior and development of power differences in
negatively connected exchange networks. Observe how network position
affects payoffs in repeated rounds of bargaining over 24 points.
CHAPTER 18 COMPLEXITY AND CHAOS
Classic Logistic Map BY ROBERT M LURIE Wolfram:
Link Use the classic logistic map to explore the
properties of chaos dynamics.
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From signed numbers to story problems — calculate equations with easePractice is the key to improving your algebra skills, and that's what this work ... more »book is all about. This hands-on guide focuses on helping you solve the many types of algebra problems you'll encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, this workbook shows you how to work with fractions, exponents, factoring, linear and quadratic equations, inequalities, graphs, and more!100s of problems!Hundreds of practice exercises and helpful explanationsExplanations mirror teaching methods and classroom protocolsFocused, modular content presented in step-by-step lessonsPractice on hundreds of Algebra I problemsReview key concepts and formulasGet complete answer explanations for all problems
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Graphical Analysis
Recommended for High School and Middle School Science.
Graphical Analysis 3 is an inexpensive, easy-to-learn program for producing, analyzing, and printing graphs.
Description
Graphical Analysis has been one of our most popular products for years and now it's even better! We have recently rewritten Graphical Analysis, adding new features and updating its look and capabilities.
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Systems of equations and inequalities are examined both graphically and algebraically. This course also touches on complex numbers and DeMoivre's theorem as well as sequences, induction, counting, and probability. As a PhD student, I spent many hours reading complex books and articles and I am confident that I can help your student achieve higher reading comprehension levels.
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Mathematics
This subject is required each year through tenth grade, or longer if the uses an incremental approach to topics such as adding, subtracting, multiplying, and dividing of signed numbers (including fractions and decimals); simplification of expressions containing parentheses; work with exponents, square roots, geometric formulas; and more.
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Mathematics 1, Web-Based
Mathematics is a central subject in primary schools and in teacher education programmes. Teacher education programmes in mathematics cover several aspects of the subject. For instance, in addition to the pure knowledge of the subject, there is also a special focus on its unique characteristics and their effect on the teaching of mathematics.
Module 2: Functions, statistics, probability, history of numbers, geometry, didactics
Each study unit consists of two modules of 15 ECTS credits and may be taken individually. The study programme is designed for teachers in schools.
Career opportunities/Further studies
The study programme is suitable for teachers who teach or will teach mathematics in primary and lower secondary schools, but who lack formal education in the subject. Teachers who completed Mathematics 1 (5 old-style credits/15 ECTS) under the 1994 Curriculum can extend their education with 15 ECTS by taking module 2 under the new curriculum. The study programme is also relevant for teachers in upper secondary schools who wish to improve their formal qualifications in the subject, and for pre-school teachers who want further education in order to teach in the school system.
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Department of Mathematical Sciences
The United States Military Academy
West Point, New York
Abstract
The Department of Mathematical Sciences at the United States Military
Academy (USMA) is fostering an environment where students and faculty
become confident and competent problem solvers. This assessment will
reevaluate and update the math core curriculum's program goals to incorporate
the laptop computer, enabling exploration, experimentation, and discovery
of mathematical and scientific concepts.
Background and Goals:
Technology has made a dramatic impact on both education and the role
of the educator. Graphing calculators and computer algebra systems
have provided the means for students to quickly and easily visualize
the mathematics that once took effort, skill, and valuable classroom
time. The Calculus Reform movement sought to improve instruction, in
part, by taking advantage of these technological resources. Mathematical
solutions could now be represented analytically, numerically, and graphically.
The shift in pedagogy went from teaching mathematics to teaching mathematical
modeling, problem solving, and critical thinking. Ideally the problem
solving experiences that students encountered in the classroom were
interdisciplinary in nature. Mathematics has truly become the process
of transforming a problem into another form in order to gain valuable
insight about the original problem.
Portable notebook computers provide an even greater technological resource
that has led us to once again reexamine our goals for education. Storage
and organization coupled with powerful graphical, analytical, and numerical
capabilities allow students to transfer their learning across time and
discipline.
The Department of Mathematical Sciences at USMA is committed to providing
a dynamic learning environment for both students and faculty to develop
self-confidence in their abilities to explore, discover, and apply mathematics
in their personal and professional lives. The core math program attempts
to expose the importance of mathematics, providing opportunities to
solve complex problems. The program is ideally suited and committed
to employing emerging technologies to enhance the problem solving process.
Since 1986, all students at USMA have been issued desktop computers
with a standard suite of software; this year the incoming class of students
(class of '06) will be issued laptop computers with a standard suite
of software. The focus of this assessment is to reevaluate the program
goals of the math core curriculum and update these goals to incorporate
the ability of the laptop computer to not only explore, experiment,
and discover mathematical and scientific concepts in the classroom,
but provide a useful medium to build and store a progressive library
of their analytical and communicative abilities.
Description
The general educational goal of the United States Military Academy
is "to enable its graduates to anticipate and to respond effectively
to the uncertainties of a changing technological, social, political,
and economic world.‰
The core math program at USMA supports this general educational goal
by stressing the need for students to think and act creatively and by
developing the skills required to understand and apply mathematical,
physical, and computer sciences to reason scientifically, solve quantitative
problems, and use technology effectively.
Cadets who successfully complete the core mathematics program should
understand the fundamental principles and underlying thought processes
of discrete and continuous mathematics, linear and nonlinear mathematics,
and deterministic and stochastic mathematics. The core program consists
of four semesters of mathematics that every student must study during
his/her first two years at USMA. The first course in the core is Discrete
Dynamical Systems and an Introduction to Calculus (4.0 credit-hours).
The second course is Calculus I and an Introduction to Differential
Equations (4.5 CH). The sophomore year's first course is Calculus II
(4.5 CH), and the final core course is Probability and Statistics (3
CH). Five learning thread objectives have been established for each
core course. They are: Mathematical Modeling, Mathematical Reasoning,
Scientific Computing, Communicating Mathematics, and the History of
Mathematics. Each core course builds upon these threads in a progressive
yet integrated fashion.
The assessment focuses on the following aspects of our core math program.
1) Innovative curriculum, instructional, and assessment strategies
brought on by the integration of the laptop computer.
2) Student attainment of departmental goals.
Innovative Curriculum and Assessment Strategies
Projects: In-class problem solving labs serve as a chance for
the students to synthesize the material covered in the course over the
previous week or two. Students use technology to explore, discover,
analyze, and understand the behavior of a mathematical model of a real
world phenomenon. Following the classroom experience, students will
be given an extension to the problem in which they are required to adapt
their model and prepare a written analysis of the extension. Students
are given approximately seven-ten days to complete the project. For
the most part, these out-of-class projects will be accomplished in groups
of two or three. An example of a project is provided in Appendix A.
Two-day Exams: Assessment of student understanding and problem-solving
skills will take place over the course of two days. Paramount in this
process is determining what concepts and/or skills we want our students
to learn in our core program. We understand that, what you test is
what you get; therefore, we have adapted our exams to assess these desired
concepts and skills.
The first day of the exam will be a traditional in-class exam in which
students do not have access to technology (calculator or laptop computer).
This exam portion focuses on basic fundamental skills and concepts associated
with the core mathematics program. Students are also expected to develop
mathematical models of real world situations. Upon completion of this
portion, students are given a take-home scenario that outlines a real
world problem. They have the opportunity to explore the scenario on
their own or in groups. Upon arrival in the classroom the next day,
the scenario is and/or adapted to allow students to apply their problem-solving
skills in a changing environment. An example of a take-home scenario
and the adapted scenario is provided in Appendix B.
Modeling and Inquiry Problems: To continue to develop competent
and confident problem solvers, students are not given traditional examinations
in the second core mathematics course. Instead, they are assessed with
Modeling and Inquiry Problems (MIPs). Each MIP is designed as an in-class
word problem scenario to engage the student for about 45 minutes in
solving an applied problem with differentiable or integral calculus
or differential equation methods. The student must effectively communicate
the situation, the solution, and then discuss any follow-on scenarios,
similar to the Day Two portion outlined above, all in a report format.
As an example, a MIP may involve using differential calculus to solve
a related rates problem.
The Situation portion of the MIP involves transforming the words into
a mathematical model that can be solved, by drawing a picture, defining
variables with units, determining what information is pertinent, what
assumptions should be made, and most importantly, what needs to be found.
Finally, the Situation ends with the student stating which method (related
rates in this case) will be used to solve the problem.
The Solution portion involves writing the step-by-step details of the
problem and determining what is needed to be found. Any asides or effects
of assumptions can be written in as work progresses, and this portion
ends with some numerical value, to include appropriate units. For example,
the rate at which the oil slick approaches the shore is two meters per
minute.
The MIP itself has a second paragraph that asks follow-on questions.
Suppose the volume of the oil slick is now doubled. How does that affect
your rate? Or what is the exact rate the moment the slick reaches the
shore? These follow-on questions prod the student to go back to the
method and rework the problem with new information.
The final portion of the MIP write-up is the Inquiry/Discussion section.
The MIP write-up must be coherent and logical in its flow. Students
must tie together the work and stress the solution back in the context
of the problem. The Inquiry section is vital in student understanding
of the problem. Students do not stop once they determine a numerical
answer. They must continue and communicate how that answer relates
to the problem, and more importantly, if the answer passes the common
sense test.
As of the time of this writing, the third core course has also incorporated
MIPs, in addition to traditional exams. The probability and statistics
course is considering the use of MIPs in future years. An example of
a MIP (focusing on a differential equations problem) is provided in
Appendix C.
Electronic Portfolio: The notebook computer provides a tremendous
resource for storage and organization of information. This resource
avails the opportunity for students to transfer learning across time
and between courses. In the novel, Harry Potter and the Goblet of Fire,
Dumbledore refers to this capability as a pensieve.
At these times, says Dumbledore, indicating the stone basin, I use
the Pensieve. One simply siphons the excess thoughts from one's mind,
pours them into a basin, and examines them at one's leisure. It becomes
easier to spot patterns and links, you understand, when they are in
this form.
The portable notebook computer provides the resource for students to
create their own pensieve. Creative exercises offer the student exposure
to mathematical concepts with the ability to explore their properties,
determining patterns and connections which facilitate the process of
constructing understanding. Thorough understanding is feasible in either
a controlled learning environment or at the student's leisure. Instructors
will provide early guidance to incoming students on organizational strategies
and file-naming protocol. Informal assessments of a student's electronic
portfolio will provide information regarding the ability to understand
relationships between mathematical concepts.
Attitude and Perceptions Survey: One tool that will be used
to assess if students are confident and competent problem solvers in
a rapidly changing world is a longitudinal attitude and perceptions
survey. Students will be given a series of sixteen common questions
upon their arrival at the Academy and as part of a department survey
at the conclusion of each of the four core math courses. A comparison
of their confidence, attitudes, and perceptions will be made against
those students who in prior years took the core math sequence without
a laptop computer. The questions used in the survey are provided in
Appendix D.
Revisions Based on Initial Experience: The assessment began
in the Fall of 2002 and will track students over a period of four semesters.
A pilot study was run in the Spring of 2002 and the following lessons
were learned.
Student use of computers on exams: In the initial implementation
of the two-day exam, students were allowed to use the computer on both
days. Many students used their computers as electronic crib sheets.
This problem may be further exacerbated when student computers in the
classroom have access to a wireless network. The day one portion of
the exam has been reengineered to assess skills and concepts that do
not require technology of any sort.
Electronic imprints of exams: Core math courses are all taught
in the first four hours of the day. The students' dorms are all networked
and word travels very quickly. It is currently against our policy to
prohibit students from talking about exams with students who have not
yet taken the exam. Enabling the use of laptops on exams creates a
situation in which an imprint of the exam is on some cadet's computer
following the first hour of classes. The day two portion of the exam,
which is designed to test the students' ability to explore mathematics
concepts using technology, will be given to all students at the same
time, during a common lab period after lunch.
Power: Computer reliability, particularly in the areas of power
is an area of concern. Students will be issued a backup battery for
their laptops. It is forecasted that an exchange facility will be available
in the academic building for cadets who experience battery problems
in the middle of a test.
Findings
Projects: Students overwhelmingly stated that the course projects
helped to integrate the material that was taught in the course. The
students' ability to incorporate the problem-solving process (i.e.,
modeling) increased with each successive project.
Two-Day Exams: The two-day exams provided a thorough assessment
of the course objectives. Course-end surveys revealed that the students
felt that these two-day examinations were fair assessments of the concepts
of the course. The technology portion (Day two) magnified the separation
between those who demonstrated proficiency in solving problems using
technology and those who didn't; there was no significant in-between
group of students.
Electronic Portfolios: Assessment of the electronic portfolios
consisted of individual meetings of all students with their individual
instructors. The results of these meetings brought out the point that
students needed assistance in determining what material should be retained
and how it should be kept. Students realized that material in this
course would be needed in follow-on courses, so file naming would be
key. Guidance was given to students to incorporate a file management
system for later use, but no universal scheme was provided; in this
manner, students could best determine their own system.
Additional Findings: Unless assessed (tested), the students
did not take the opportunity to learn how to effectively use the computer
algebra system, Mathematica. Students embraced the use of the graphing
calculator (TI-89) as the preferred problem-solving tool; they overwhelmingly
reported that the laptop computer was a hindrance to their learning.
Use of the Findings:
Projects: We will continue to use group projects to assess
knowledge; however, we will phase the submission of the projects to
provide greater feedback and opportunity for growth in problem-solving
and communication skills. Our plan is to have students submit the projects
as each portion (Introduction, Facts and Assumptions, Analysis, and
Recommendations and Conclusions) is completed.
Two-Day Exams: Content on the Day-one (non-technology) portion
needs to be more straightforward, emphasizing the concepts we want students
to internalize and understand without needing technology. For the Day-two
(technology) portion, questions should be asked to get students to outline
and explain their thought processes, identifying possible errant methods.
We need to keep in mind that problems with syntax should not lead to
severe grade penalties.
Additional Use of the Findings: We are going to introduce graded
homework sets designed to demonstrate the advantage of the computer
algebra system and the laptop as a problem-solving tool. Use of the
graphing calculator will be limited to avoid confusion and overwhelming
students with too many technology options. We plan to review course
content and remove unessential material, thus providing more lessons
for exploration and self-discovery.
Next Steps and Recommendations:
The assessment cycle will continue as we implement the changes outlined
above into the first course. The majority of students will enter the
second core course, Calculus I which will continue the use of laptops.
Six Modeling and Inquiry Problems and one project will be used to assess
the progress of our students' problem-solving capabilities.
Acknowledgements
We would like to thank the leaders of the Supporting Assessment in
Undergraduate Mathematics (SAUM) for their guidance and support. In
particular, our team leader, Bernie Madison, has been instrumental in
keeping our efforts focused.
Appendix A Sample Project
The following Problem Solving Lab is an in-class exercise that allows
the students to model and solve a system of interacting Discrete Dynamical
Systems.
Humanitarian Demining
Background
The country of Bosnia-Herzegovina has approximately 750,000 land mines
that remain in the ground after their war ended in November 1995. The
United Nations (UN) has decided to establish a Mine Action Center (MAC)
to coordinate efforts to remove the mines. You are serving as a U.S.
military liaison to the director of the UN-MAC.
The UN-MAC will initially have 1000 trained humanitarian deminers working
in country. Each of these trained personnel can remove 65 mines per
week during normal operations.
Unfortunately, there is a rebel force of about 8,000 soldiers that
opposes the UN-MAC's efforts to support the legitimate government of
Bosnia-Herzegovina. They conduct two major activities to oppose the
UN-MAC: killing the deminers and emplacing more mines. They terrorize
the deminers, killing 1 deminer for every 1,000 rebels each week. However,
due to poor training and funding, each of these soldiers can only emplace
an average of 5 additional mines per week.
Meanwhile, the accidental destruction of the mines maim and kill some
of both the deminers and the rebel forces. For every 1,000,000 mines,
1 deminer is permanently disabled or killed each week. The mines have
the exact same quantitative impact on the rebel forces.
Modeling and Analysis
Your current goal is to determine the outcome of the UN-MAC's efforts,
given the current resources and operational environment.
1. Model the strength of the demining organization,
the rebels, and the number of mines in the ground. Ensure you define
your variables and domain and state any initial conditions and assumptions.
2. Write the system of equations in matrix form A(n+1) = R * A(n).
3. If the interaction between the rebels and deminers as well as their
respective efforts to affect the minefields remain constant, what happens
during the first five years of operations?
4. Graphically display your results. Ensure you display your results
for each of the three entities you model.
5. What is the equilibrium vectors, D or Ae, for this system? Is
it realistic?
6. The General and Particular Solution for the new system of DDS's
using eigenvalue and eigenvector decomposition.
We add a little more realism to the scenario by creating interaction
between the model's components. The following extension is the project
that forces the students to adapt their model and prepare a written
analysis.
Humanitarian Demining
BETTER ESTIMATE ON CASUALTIES DUE TO MINES
We now have more accurate data on the casualties due to mines; it may
(or may not) change part of your model. Better estimates show that
for every 100,000 mines, 2 deminers are permanently disabled or killed
each week. The mines have the exact same quantitative impact on the
rebel forces.
OTHER MINEFIELD LOSSES
Other factors take their toll on the number of emplaced mines as well.
Weather and terrain cause some of the mines to self-destruct, and civilians
occasionally detonate mines. Approximately 1% of the mines are lost
to these other factors each week.
NATURAL ATTRITION OF FORCES
Due to other medical problems, infighting, and desertion, the rebel
forces lose 4% of their force from one week to the next. The deminers
have a higher attrition due to morale problems; they lose 5% of their
personnel from one week to the next.
RECRUITING EFFORTS
Both the rebel forces and the deminers recruit others to help. Each
week, the rebels are able to recruit an additional 10 soldiers. Meanwhile,
the UN-MAC is less successful. They only manage to recruit an additional
5 deminers each week.
For the project, your report should address the following at a minimum:
1. Executive Summary in memo format that summarizes your research.
2. The purpose of the report.
3. Facts bearing on the problem.
4. Assumptions made in your model, as well as the viability of these
assumptions.
5. An analysis detailing:
a. The equilibrium vector, D or Ae, for
the system and discuss its relevance.
b. The General and Particular Solution for
the new system of DDS's using eigenvalue and eigenvector decomposition.
c. A description of what is happening to
each of the entities being modeled during the first five
(5) years of operations.
6. The director of the UN-MAC also wants your recommendation on the
following:
a. If the demining effort is going to be
successful within the first five years, when will it succeed in eradicating
all mines? If the demining effort is not going to be successful, determine
the minimum number of weekly demining recruits needed to remove all
mines within five years of operations.
b. Describe at least one other strategy
the UN-MAC can employ to improve its efforts to eradicate all of the
mines. Quantify this strategy within a mathematical model and show
the improvement (graphically, numerically, analytically, etc.).
7. Discussion of the results.
a. Reflect on your assumptions and discuss
what might happen if one or more of the assumptions were not valid.
b. Integrate graphs and tables into your
report, discuss them, and be sure to label them correctly.
8. Conclusion and Recommendations.
Appendix B Example Day Two Exam
Take Home Scenario
While home on Spring Break, you explain to your parents
the fundamental concepts that you have learned in your Discrete Dynamical
Systems course. Following dinner one evening you provide them a quick
10 minute presentation on how you were able to use DDS to assist with
car buying decisions. Due to your improved ability to communicate about
mathematics, your parents immediately say, "Hey, I think you might
be able to help us". They share with you the fact that they are
negotiating the purchase of a 2003 Toyota Camry. The Wasko Federal
Credit Union has agreed to finance a vehicle loan of up to $20,000 at
a yearly interest rate of 6%.
Adapted Scenario
Recall from the read-ahead that your parents have
asked for your assistance to help them determine the financing option
for their purchase of a 2003 Toyota Camry. They have successfully negotiated
a price of $18,000 for the car. In order to boost slumping car sales,
the dealer has offered two financing options.
In Option One the dealer has offered to finance the car at a rate
of 1.9% interest for 48 months. Develop a model that predicts the
car loan balance after n months, given the loan requires 48 equal
payments of p dollars. Define all variables, state the domain, and
any initial conditions.
Determine the payment p, to the nearest cent, if your parents bought
the Camry using the 1.9% loan financed by Toyota? Explain how you
used technology to obtain this figure. Include the actual formulas
used in EXCEL or the TI-89.
In Option Two, the dealer has offered a $1500 rebate
in lieu of the 1.9% financing. The finance rate for this option is
5.2% interest over 48 months. Develop a model that predicts the car
loan balance after n months, given the loan requires 48 equal payments
of q dollars. Define all variables and state the domain, and any
initial conditions.
Should your parents take the 1.9% financing or the
$1500 rebate with a 5.2% financing rate? Explain how you used technology
to assist in your decision. Provide clear mathematical backing to
support your decision. Include the actual formulas used in EXCEL
or the TI-89.
Appendix C Example Modeling and Inquiry Problem
Scenario: Your friend borrowed a 1 kg mass and two springs from the
Physics Department. The springs have the following properties:
Spring
Spring Constant (N/m)
A
(
B
(2
She wants to build an undamped harmonic oscillator to keep time like
a watch. After displacing the mass an initial 5 cm and letting it go,
she wants it to move through the position of the system's natural length
(equilibrium) every second. Which spring will accomplish this? Justify
your answer with appropriate differential equation(s), solution(s),
and/or graph(s).
Follow-up: What's fundamentally wrong with your friend's plan to build
a spring-mass system to keep time? Explain your answer using terminology
from the course.
The format used for assessment is broken down as follows:
Part I: Modeling the Situation
1. Draw a picture.
2. Define variables with appropriate units.
3. What are you trying to find?
4. What information is given?
5. What are your assumptions? (They must be valid and necessary.)
6. Describe the technique you will use to solve the model.
Part II: Determining a solution
1. The solution follows logically from the equations.
2. The solution to the follow-up question follows logically.
3. No magical "leaps of faith".
4. The solutions are given in correct units.
Part III: Inquiries and Discussion
1. Summarize your answer to the MIP in the context of the problem.
2. Discuss your solution to the follow-on question in context.
3. Perform a common sense check.
4. Explanations are communicated clearly.
This format is given to the students.
Appendix D Questions used in Attitude and Perceptions Survey
The following questions were given to students and were rated on a
Likert-Scale from 1 (strongly disagree) to 5 (strongly agree).
1. An understanding of mathematics is useful
in my everyday life.
2. I believe that mathematics involves
exploration and experimentation.
3. I believe that mathematics involves
curiosity.
4. I can structure (model) problems mathematically.
5. I am confident in my ability to solve
problems using mathematics.
6. Mathematics helps me to think logically.
7. There are many different ways to solve
most mathematics problems.
8. I am confident in my ability to communicate
mathematics orally.
9. I am confident in my ability to communicate
mathematics in writing.
10. I am confident in my ability to transform
a word problem into a mathematical
expression.
11. I am confident in my ability to transform
a mathematical expression into my
own words.
12. I believe that mathematics is a language
which can be used to describe the world
around us.
13. Learning mathematics is in individual
responsibility.
14. Mathematics is useful in my other courses.
15. I can use numerical and tabular displays
of data to solve problems.
16. I can use graphs and their properties
to solve problems.
USMA Academic Board and Office of the Dean Staff (1998),
Educating Army Leaders for the 21st Century, West Point, New York.
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