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Examines currents in the development of mathematics and throughout ancient Egypt, Babylon, China, and the Middle East. It studies math's influence on society through the major events of Europe, contemporary developments, and some projections into the future, including the women and men who played key roles in evolution of mathematics.
Course Learning Outcomes:
Discuss some of the major milestones in the development of mathematics and how public thought was influenced by them: from early mysticism to the sixteenth century desire to classify and categorize that introduced Arabic numerals to England and forever altered commerce, navigation and surveying; From the belief in the power of rational, logical thought expressed by Newton or Boole to the loss of certainty expressed in Godel's Theorem. From a sense of the individual soul to the attitude of becoming a statistics and to the possibility that the human brain state can be modeled with a fairly sophisticated computer.
Do some mathematics of various time periods.
Discuss current directions in mathematics education.
Specified Program Learning Outcomes:
BACHELOR OF ARTS IN MATHEMATICS EDUCATION
Employ a variety of reasoning skills and effective strategies for solving problems both within the discipline of mathematics and in applied settings that include non-routine situations
Employ algebra and number theory ideas and tools as a base of a fundamental language of mathematics research and communication
Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs that are appropriate for the research and study in mathematics
Use language and mathematical symbols to communicate mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines
MAJOR IN MATHEMATICS
Employ a variety of reasoning skills and effective strategies for
solving problems both within the discipline of mathematics and in
applied settings that include non-routine situations
Model real world problems with a variety of algebraic and
transcendental functions
Use advanced statistics and probability concepts and methods
Use current technology tools, such as computers, calculators,
graphing utilities, video, and interactive programs that are
appropriate for the research and study in mathematics
Use language and mathematical symbols to communicate
mathematical ideas in the connections and interplay among
various mathematical topics and their applications that cover
range of phenomena across appropriate disciplines
MAJOR IN MATHEMATICS WITH A PRELIMINARY SINGLE SUBJECT TEACHING CREDENTIAL (CALIFORNIA)
Employ a variety of reasoning skills and effective strategies for
solving problems both within the discipline of mathematics and in
applied settings that include non-routine situations
Use current technology tools, such as computers, calculators, graphing utilities, video, and interactive programs that are appropriate for the research and study in mathematics
Use language and mathematical symbols to communicate
mathematical ideas in the connections and interplay among various mathematical topics and their applications that cover range of phenomena across appropriate disciplines
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Algebra
Topology is a large subject with many branches broadly categorized as algebraic topology, point-set topology, and geometric topology. Point-set topology is the main language for a broad variety of mathematical disciplines. Algebraic topology serves as a powerful tool for studying the problems inAdvanced Linear Algebra focuses on vector spaces and the maps between them that preserve their structure (linear transformations). It starts with familiar concepts and then slowly builds to deeper results. Along with including many exercises and examples, each section reviews what students need to …
Linear algebra forms the basis for much of modern mathematics—theoretical, applied, and computational. Finite-Dimensional Linear Algebra provides a solid foundation for the study of advanced mathematics and discusses applications of linear algebra to such diverse areas as combinatorics, …
Useful Concepts and Results at the Heart of Linear AlgebraA one- or two-semester course for a wide variety of students at the sophomore/junior undergraduate level
A Modern Introduction to Linear Algebra provides a rigorous yet accessible matrix-oriented introduction to the essential concepts of …
By integrating the use of GAP and Mathematica®, Abstract Algebra: An Interactive Approach presents a hands-on approach to learning about groups, rings, and fields. Each chapter includes both GAP and Mathematica commands, corresponding Mathematica notebooks, traditional exercises, and several …
Shows How to Read & Write Mathematical ProofsIdeal Foundation for More Advanced Mathematics Courses
Introduction to Mathematical Proofs: A Transition facilitates a smooth transition from courses designed to develop computational skills and problem solving abilities to courses that emphasize …
A collection of research articles and survey papers, Limits of Graphs in Group Theory and Computer Science highlights modern state of the art, current methods and open problems. The main research topics include the geometric, combinatorial and computational aspects of group theory. The book focuses …
Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior …
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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
Pearson Mathematics 8 Bridging Workbook is a write-in resource which is designed to bridge the gap between primary and secondary mathematics - the only series in the marketplace with a bridging workbook. For students that require extra support, this resource will help nurture their learning and enable a pathway into the Pearson Mathematics 8 Student Book.
Features & benefits
Write-in resource
The only bridging workbook in the marketplace for a maths series
Supports students through the transition between primary and secondary mathematics
Helps to support students who require more support
Pearson Mathematics Bridging Workbook is available for both Years 7 and 8
Target audience
Suitable for Year 8
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Peer Review
Ratings
Overall Rating:
This site provides graphs and in-depth historical background on dozens of famous mathematical curves such as the cycloid, conic sections, Lame curves, Lissajous curves, the tractrix, the Witch of Agnesi, and many others. It traces the development of each curve from its discovery to its further applications and includes the graph along with Cartesian and parametric or polar equations. Most of the curves have accompanying interactive Java applets to illustrate related curves such as inverse and evolute. The site contains many cross-references to math history topics and other sources. This is one of a number of sites that are part of the award-winning MacTutor History of Mathematics Archives; please see the review of the MacTutor site for more details.
Learning Goals:
Resource material for student papers on general math/history/mathematicians. Classroom enrichment for instructors.
Target Student Population:
General arts students with little mathematical knowledge or advanced users wanting to investigate the history aspect of the curves.
Prerequisite Knowledge or Skills:
None, but some background knowledge of calculus is useful for a deeper understanding.
Type of Material:
Reference material
Technical Requirements:
Most of the materials simply require a browser; to view the interactive Java applets for famous curves, the browser must be Java-enabled. Java applets work fine on Windows operating systems and on Mac systems using Internet Explorer; however, they do not seem to work using Macintosh operating systems and Netscape Navigator.
Evaluation and Observation
Content Quality
Rating:
Strengths:
Useful for both experienced and casual student users. Nicely written and easy to read. The interactive Java applets offer interesting insight into related curves. This site includes many links for those who want to follow up on more of the math details.
Concerns:
Please see the review for the MacTutor History of Mathematics Archives, the parent site for the Famous Curves web page. The MacTutor site is a rich and growing source of materials pertaining to the history of mathematics including biographies of mathematicians, mathematics in various cultures, time lines, famous curves (with Java interactivity), overview of math history, in-depth coverage of a large number of history topics, and more. Individual pages contain many crosslinks and material is well-written and useful for both casual and experienced users. There is also a searchable quotation index as well as a selection of recent articles on the history of mathematics education and Indian mathematics. Faculty as well as students will find much here to enrich their mathematical understanding and enjoyment.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
Many crosslinks as well as references to other famous curves, mathematicians, math history topics, and more.
Concerns:
None.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Easily readable. Many links, both internal and external, to related topics and mathematicians.
Concerns:
Interactive JAVA on famous curves didn't run on a number of Mac operating systems with Netscape as a browser. Otherwise seemed stable and fast - especially the search engine.
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Mathematics
Introduction
The course is suitable for students who achieved a grade D in GCSE Mathematics at school. It is another opportunity to gain this most important of qualifications. It is a modular course taught at Foundation level. It includes the study of number, algebra, shape & space and handling data.
Further Details
This is an essential qualification that is highly regarded by employers and Universities and is a prerequisite for many careers and courses.
Progression Options
Successful students may be able to access AS Levels which require GCSE Grade C+.
Additional Info
Qualification:GCSE Level 2
Entry Requirements:College entry requirements.
Duration:1 year
Assesment:The GCSE course is taught and assessed in 3
modules. Written modular exams are taken in
November, March and June. Two modules are
assessed with a calculator paper with the third being
assessed with a non-calculator paper.
Functional Mathematics is taught as part of the
GCSE course and gives an opportunity to obtain
another Level 2 qualification. There is one written
calculator paper to assess the course.
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in Our World
"Mathematics in Our World" is designed for mathematics survey courses for non-science majors. The text covers a variety of topics designed to foster ...Show synopsis"Mathematics in Our World" is designed for mathematics survey courses for non-science majors. The text covers a variety of topics designed to foster interest in and show the applicability of mathematics. The book is written by our successful statistics author, Allan Bluman. His easy-going writing style and step-by-step approach make this text very readable and accessible to lower-level students. The text contains many pedagogical features designed to both aid the student and instill a sense that mathematics is not just adding and subtracting0073311821-5-1-3 Orders ship the same or next business day. Expedited shipping within U.S. will arrive in 3-5 days. Hassle free 14 day return policy. Contact Customer Service for questions. ISBN: 9780073311821.
Reviews of Mathematics in Our World
This book was in terrific condition and came sooner than expected for my husband's college course. Even better, the book is the teacher's edition and had some great helps for those of you who are rusty on math procedures for different real-world applications.
If you need tyo brush up your math
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A First Course in Linear Algebra, Waldron Edition
This is a bound, softcover version of the textbook, with the majority of the Version 2.00 content. $5 of the purchase price will support this experiment in making quality textbooks available at reasonable prices.
A First Course in Linear Algebra is an introduction to the basic concepts of linear algebra, along with an introduction to the techniques of formal mathematics. It begins with systems of equations and matrix algebra before moving into the theory of abstract vector spaces, linear transformations and matrix representations.
It has numerous worked examples and exercises, along with precise statements of definitions and complete proofs of every theorem, making it ideal for independent study.
Distributed under the open-content GNU Free Documentation License (GFDL), evaluation copies, an online version and updates are available at the book's website,
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Contents
While everyone is welcome in the course, the primary purpose of the course
is to prepare students for teaching geometry in middle and high school.
Thus on the one hand, the course aims to instill a broad understanding and appreciation
for geometry and on the other hand it aims to help students to acquire the competence
in geometry they need to be mathematics professionals.
In addition, it is important that students experience a variety of ways of learning geometry so
that they can make informed choices for methods of instruction when they become teachers. Thus
the course provides experiences in working in groups, problem solving, mathematical writing,
making and experimenting with physical models and manipulatives.
Elementary and Plane Euclidean Geometry.
This will include a quick review of high school geometry and then quickly move to
important ideas such as the idea of a locus and how loci are used to solve problems.
Intermediate Geometry of Triangles.
The approach will be synthetic (no coordinates) at the beginning, but will later
include coordinates and algebraic tools.
Vector and Coordinate Geometry.
The approach will be synthetic (no coordinates) at the beginning, but will later
include coordinates and algebraic tools.
Beginning Polyhedra.
The Platonic solids and derived polyhedra will be studied using physical models.
Plane Transformations and Symmetry.
An important tool for thinking about geometry is the concept of a transformation.
We will begin with the nature of transformations,
their classification, how they combine, and how they can be used for geometric
problem solving. Then the theory of transformations will be applied to study
symmetry in the plane and plane tessellations.
The course is organized fairly conventionally in some respects, with regular homework
assignments, a midterm, some quizzes, and a final exam.
In addition, because of the preservice teaching role of the course, there will be a number
of assigned activities that involve presentation and evaluation of mathematics.
One unusual feature of the grading is that we will attempt to measure and
count a very high level of mastery of the more elementary topics (i.e., "high
school geometry") as well as a more conventional approach to more advanced
topics.
There is some homework in Math 444 which is based on what has been learned in
the required computer lab, Math 487.
This is a computer lab required of all 444 students. The
two-hour labs will generally consist an exploratory geometry
investigation with software such as The Geometer's Sketchpad.
There may be a small amount of additional work outside the lab
to finish the 487 assignment for the week.
However, the 487 work may segue into a homework activity in Math
444. It is probably most useful to think of 444 and 487 as two
parts of a single course. It is misleading to think of every
computer-based assignment as part of 487 just because it uses
computers.
The prerequisites are listed in the catalog, but the most frequently asked questions
or concerns are these.
I haven't had geometry for 5, 10, 10 years. Will this be a problem?
How much linear algebra or calculus do I need to know?
Not much specific knowledge from high school geometry is
required, but a lot more "mathematical maturity" is expected
than from a high school geometry student. For example, students
in 444 are expected to have a good understanding of functions,
of algebra, of coordinates and some experience with mathematical
reasoning.
From linear algebra, a student should understand linear
equations in 2 and 3 variables and to have some knowledge of
vectors and matrices.
In addition, some facility is expected with visualizing shapes
in two and three dimensions, as done in Math 126 multivariable
calculus.
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Specification
Aims
To introduce students
to a sophisticated mathematical subject where elements of different
branches of mathematics are brought together for the purpose of solving an
important classical problem.
Brief Description of the unit
Galois theory is one of the most spectacular mathematical theories. It
establishes a beautiful connection between the theory of polynomial
equations and group theory. In fact, many fundamental notions of group
theory originate in the work of Galois. For example, why are some groups
called 'soluble'? Because they correspond to the equations which can be
solved! (Solving here means there is a formula involving algebraic
operations and extracting roots of various degrees that expresses the roots
of the polynomial in terms of the coefficients.) Galois theory explains why
we can solve quadratic, cubic and quartic equations, but no formulae
exist for equations of degree greater than 4. In modern language, Galois theory deals with
'field extensions', and the central topic is the 'Galois correspondence'
between extensions and groups. Galois theory is a role model for
mathematical theories dealing with 'solubility' of a wide range of problems.
Learning Outcomes
On successful completion of this course unit students will
have deepened their knowledge about fields;
have acquired sound understanding of the Galois correspondence between intermediate fields and subgroups of the
Galois group;
be able to compute the Galois correspondence in a number of simple examples;
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VerticalNews Mathematics
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Glencoe/McGraw-Hill
Glencoe's Math Intervention Program 'Math Triumphs' Helps Struggling High School Students
February 24th, 2009
To support struggling students enrolled in Algebra 1, Geometry, or Algebra 2 courses, Glencoe/McGraw-Hill has developed a new Response to Intervention (RtI) Tier 3 math series, Math Triumphs.
Designed to support students needing the most intensive intervention, Math Triumphs: Foundations for Algebra 1, Math Triumphs: Foundations for Geometry, and Math Triumphs: Foundation for Algebra 2 help build mastery of the foundational skills and concepts from prior grades that are prerequisites to the current grade level.
The research-based series has a similar format to Macmillan/McGraw-Hill's Math Triumphs Grades K-5 and Glencoe's Math Triumphs Grades 6-8...
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{"itemData":[{"priceBreaksMAP":null,"buyingPrice":12.98,"ASIN":"0679747885","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":10.36,"ASIN":"0743217764","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":12.77,"ASIN":"0465019374","isPreorder":0}],"shippingId":"0679747885::MwpF7zNtmACrYZSXNTw7WEw6msovKj5tsVoHSUWTPxjTJFy9FZjxLBqyT54XA%2BDaGnNwSRPldHcfuVG8Dm1Szoe5l1jSQ3ArNcNRkUXiRQw%3D,0743217764::TdOMzsH6eC3TdUwCFIZbUuhE41YyW%2FAk2o6S3%2BYWsoXGZINamUnkl8lFgCDPDmgGwaic3BRTWnh81c%2BhYPRK%2Fj0iOaZrsmpuHemiTeA%2FiD4%3D,0465019374::zwhxywdPoamKRx9naDUOfCBDuH4Tq5IFKwom9GVC5oyKSk4D6q9MjpuX0IcBN7tVofHBVwb38JPwdiVanwMn6V1DOuJfXgnJFPKkq1Et7D9jEBCRx3TBerlinski (Black Mischief: The Mechanics of Modern Science, LJ 2/15/86) presents an unconventional work on the foundations of calculus. It is in part an informal history of the subject, the author inrerweaves the historical fragments with expository sections that explain the concepts from a modern viewpoint. He gives special attention (very appropriately) to the concept of limits and to several of the fundamental theorems that underpin calculus. He also shows how differential calculus deals with rates of change and how integral calculus works to determine areas under curves. Writing in a breezingly informal style, the author includes a plethora of humorous asides as well as a number of clearly fictitious anecdotes. At times his prose gets a bit too ripe, but the overall effect is to make the book quite readable. The work should be especially useful for providing perspective to college and advanced high school students currently learning calculus. Recommended for all public and college libraries.?Jack W. Weigel, Univ. of Michigan Lib., Ann Arbor Copyright 1995 Reed Business Information, Inc.
--This text refers to an out of print or unavailable edition of this title.
Even those who flailed through calculus class sense the power and perfection of that branch of mathematics, and Berlinski rekindles the interest of lapsed students in this pleasing excursion through graphs and equations. Berlinski's goal is to explain the mystery of motion and the area and volume of irregular shapes, issues that gave rise to Leibnitz and Newton's invention of calculus. He makes his points one concept at a time, but not so dryly as asking and answering, "What is a function?" No, with dashes of biography or images of his walking around old Prague (to illustrate continuity), Berlinski tangibly grounds the abstract notions, so that attentive readers can ease into and grasp the several full-blown proofs he sets forth, as of the mean-value theorem. Though the math-shy won't necessarily jump to the blackboard to begin differentiating and integrating polynomial equations, Berlinski's animated presentation should tempt them to sit forward and appreciate the elegance of calculus--and perhaps banish recollections of its exam-time terrors. Gilbert Taylor--This text refers to an out of print or unavailable edition of this title.
I hoped for an insightful view into calculus. Indeed, there are many deep and interesting aspects of calculus which are generally obscured in a typical calculus textbook (or in a calculus class). This is not such a book.
Most disappointing was the constant distraction of mathematical errors, small and large, throughout the book. For example, there are typos, errors in notation, and misleading or confusing notation. For these problems, I understood the author's intention at these points (being a calculus teacher myself), but to a reader less familiar with calculus, these problems will hinder understanding. When a reader can't understand the mathematical details, much of the meaning is lost.
A few errors were utterly irreparable, such as the proof of the Intermediate Value Theorem. In that case, a correct proof would diverge greatly from that of the author. This specific error is unfortunate because it is for this theorem that the author develops the real numbers (which takes chapters), and upon this theorem that all later theorems are based.
Finally, I found the author's style annoying, especially the fictional accounts of specific actions taken by historical mathematicians (crossing a river, contemplating calculus while sitting in an overstuffed chair, etc.). The author must enjoy hearing himself wax poetic on any subject which enters his head, but I don't.
The book's back cover likens this book to Douglas Hofstadter's classic _Godel, Escher, Bach_, but the comparison is laughable. Hofstadter's book has a direct and clear style of writing, whereas _A Tour of the Calculus_ is unfocused and its numerous errors makes it is mathematically a sham.
By reading some of these reviews, one thing is obvious: anyone who first lists their qualifications as a mathematician or calculus teacher is basically going to nay-say the heck out of the book. And in a way, I'd say this is semi-appropriate: the book is definitely not a math book; I think the grievances arise basically because it's sold as one. Sure, the word "tour" is in the title, but that does little to suggest that this book would be more appropriately marketed as....well....a memoir? Maybe?
Don't get me wrong though: the book isn't absolutely terrible. Some commenters have derided the author for using words that are too big, widely unknown, etc. But that's one of the things I enjoyed about the book: a few years back when I read it I underlined every word I didn't know or was fuzzy about and used this book as a way to build my vocabulary. I wouldn't describe myself as a cheery optimist, but I definitely turned the heightened language of the book to my advantage...instead of just whining about it on Amazon.
As for learning calculus: if you are a new student to calculus, this book won't really help. I bought this book years ago as a supplement to my calculus course and quickly found I was just wasting my time reading it. If you are a non-mathematician and just want a little glimpse into calculus, then this might be a good book. I would laugh at anyone who said they learned calculus from the book though.
In other news (finally, my qualifications...bla, bla, bla): since I've bought the book, I've taken all the calc and differential equations courses, abstract and linear algebra courses, analysis courses, graduated with a degree in physics and have completed one year of graduate school physics. With this in mind: Upon re-reading sections of the book recently, I would say that this is a pretty fun SUMMER READ for super nerds who already know it all, but just want to leisurely read about some elementary calculus by an author who writes in a conversational tone.
I seem to be rather in the minority when I say that I actually liked Berlinski's verbose style; frankly, I don't really see what was so difficult to understand about it. On the other hand, I approached this book from the position of wanting something fun to read, and that's what I got, with the welcome addition of what I thought was lovely writing - if I had been searching for something that would give me an in-depth look at calculus, I would have looked elsewhere. Basically, I thought the book was really well-written and exciting (I had just begun calculus when I read it, so I found it really interesting to look at all the stuff we hadn't yet done.), and I highly reccomend it for a piece of fun reading and a decent overview.
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Usually dispatched within 9 to 11 days. Dispatched from and sold by Amazon. Gift-wrap available.
Trade In this Item for up to £1.56
Trade in Computer Graphics: Mathematical First Steps for an Amazon.co.uk gift card of up to £1.56, which you can then spend on millions of items across the site. Trade-in values may vary (terms apply). Learn more
Book DescriptionI am currently doing a Masters in Games Programming and this is the reccommended text, it assumes no prior knowledge and leads you through the stages with lots of examples and help along the way, definately worth a look!
If, like me, the topic of computer graphics has been frightening because of mathematics then this is the book for you.
I found that this book explained the topic very clearly. One only needs to know the basic school geometry, such as those to do with right-angled triangles, to be able to read this book.
However what is missing is the application of mathematics to create new graphical applications. This book does not cover how to transform mathematical models into screen images or how to code. It does not cover solid models or anti-aliasing. It was not suppose to either. It is a very good introduction to mathematics. You will need to purchase, for example, "Computer Graphics: Principle and Practice" by D. Foley later on.
A rare find these days, a book that just covers the essentials and doesn't bother padding it with useless code snippets and CD offerings. I really appreciated the brevity of style and found that my interest was maintained thoughout the text. There are clear, concise graphical representations that compliment the text very well but if the reader is looking for code examples, I suggest that they look elsewhere.
1 of 1 people found the following review helpful
4.0 out of 5 starsGreat place to start25 April 2000
By A Customer - Published on Amazon.com
Format:Textbook Binding
This is a very good place to start if you are just getting into computer graphics and you need a gentle introduction. I discovered it while reading the book 'Advanced Renderman...' in the section under mathematical preliminaries. The authors recommend it as a good introduction, and I would have to second that. The only gripe I have is that there are several annoying typos (which seems to happen all too often these days).
2 of 3 people found the following review helpful
5.0 out of 5 starsA Must Have If You Are Learning Graphics Programming9 May 2001
By Stephen Rowe - Published on Amazon.com
Format:Textbook Binding
If you are like I was, your math is rusty enough that diving into Foley et al is like reading Greek. This is the best book I've found to teach the mathematical underpinnings of computer graphics. The book starts with basic trig and goes on to linear algebra and some calculus. After this book, you'll be ready to tackle most computer graphics texts. This book is hard to find but well worth it. An acceptable alternative is Mathematics for Computer Graphics Applications.
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Math/Physics Curriculum
Because a thorough understanding of mathematics and physics is vital to success in science and engineering, it is AITSE's goal to develop online and video tutorial materials on mathematics and physics. The AITSE supervising engineer consulting on this project boasts of a superior method that significantly increases student comprehension. The consulting mathematician has proven success as an college educator. Our goal will be to support both of these highly qualified individuals in developing curriculum for use by high school and college students.
Meanwhile, please click left to view a worksheet developed by AITSE president Dr. Crocker for use by students wanting to evaluate whether their math skills are adequate for success as a science major.
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These lectures give a brief introduction to the Computer Algebra
systems Reduce and Maple. The aim is to provide a
systematic survey of most important commands and concepts. In
particular, this includes a discussion of simplification schemes and
the handling of simplification and substitution rules (e.g., a Lie
Algebra is implemented in Reduce by means of simplification rules).
Another emphasis is on the different implementations of tensor calculi
and the exterior calculus by Reduce and Maple and their application in
Gravitation theory and Differential Geometry.
I held the lectures at the Universidad Autonoma
Metropolitana-Iztapalapa, Departamento de Fisica, Mexico, in November
1999.
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Zionsville, PA CalculusIdentify a slope from two points or draw a line with a slope and a point. See how word problems help you translate your math skills to your real world.
1. Identify properties and principles of equations.
2DanDiscrete Math is often coined as "finite mathematics". It does not deal with the real numbers and it's continuity. I have studied discrete math as I obtained my BS in mathematics from Ohio University
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Mathematics for Grob Basic Electronics Instructor Solutions Manual
9780078271281
ISBN:
0078271282
Edition: 9 Pub Date: 2002 Publisher: McGraw-Hill Higher Education
Summary: Provides students with the mathematical principles needed to solve numerical problems in electricity and electronics. 13 chapters cover keeping track of the decimal point when multiplying and dividing; working with fractions; manipulating reciprocals; finding powers and roots of a number; powers of 10; logarithms; metric system; solving equations; trigonometry; binary and hexadecimal numbers; and complex numbers.
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Go beyond the answers--see what it takes to get there and improve your grade! This manual provides worked-out, step-by-step solutions to the odd-numbered problems in the text. This gives you the information you need to truly understand how these problems are solved.
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In GAMM-Mitteilungen original scientific contributions to the fields of applied mathematics and mechanics are published. In regular intervals the editor will solicit surveys on topics of current interests.
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Synopsis
Canonical methods are a powerful mathematical tool within the field of gravitational research, both theoretical and experimental, and have contributed to a number of recent developments in physics. Providing mathematical foundations as well as physical applications, this is the first systematic explanation of canonical methods in gravity. The book discusses the mathematical and geometrical notions underlying canonical tools, highlighting their applications in all aspects of gravitational research from advanced mathematical foundations to modern applications in cosmology and black hole physics. The main canonical formulations, including the Arnowitt-Deser-Misner (ADM) formalism and Ashtekar variables, are derived and discussed. Ideal for both graduate students and researchers, this book provides a link between standard introductions to general relativity and advanced expositions of black hole physics, theoretical cosmology or quantum gravity.
Found In
eBook Information
ISBN: 9780511985
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I know, it's been a long time coming, and it's still not perfect, but I am working on making this site the wealth of information you are clearly looking for... stay tuned.
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This document provides a very well articulated example of finding the equation of a line given two points. I love this one!
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Expressions are all the bits of math you get in problems that are not actually equations on their own. A central skill for Test Day is the ability to evaluate and transform expressions into easier things.
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8th Grade Algebra I - Mrs. Loch
Welcome to my website which is designed to inform you of the procedures, events, and learning activities for the 2012-2013 school year.
My name is Mrs. Loch and I am the Math teacher for the 8th grade Red Team.
This year 8th grade students will gain knowledge in the areas of number sense, geometry, expressions and equations, functions, statistics and probability. This course introduces students to the fundamentals of algebraic concepts. Students will begin to explore patterns, relations, and functions. They will learn to represent and analyze mathematical situations using algebraic symbols and graphing in preparation for high school. The course will emphasize problem-solving strategies and incorporate applications to real world situations while aiding students in becoming 21st century learners.
This year we will be utilizing the "Flipped Classroom" concept. Students will watch instructional videos at home at their own pace. Class time will be spent communicating with peers and the teacher in discussions about the video, completing practice problems related to the topic, and doing interactive activities to illustrate the concept. For more information regarding the "Flipped Classroom," see "What is the Flipped Classroom?" in the document section to the right.
For valuable information regarding algebra class, assignments, or to see what we have coming up in class, please view the content below or the links listed in the "classroom pages" section to the right.
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Newnan GeometryFactoring polynomials will appear in pretty much every chapter in this course. Without the ability to factor polynomials you will be unable to complete this course. Rational Expressions In this section we will define rational expressions and discuss adding, subtracting, multiplying and dividing them
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Tips for Success in Math 3113-3118 Come to class prepared. This means with your homework ready to turn in, prepared to discuss or present the assigned problems, and having read the next section of the text. Note that we will collect homework before
Math 3118Name_This exam is open book and open notes. Calculators are allowed, but probably won't be very helpful. Correct answers without justification will receive no credit. When you're using choose notation, please explain what is being picked
Software Engineering ICSci 5801 Summer 2008 Take Home FinalThis is a take home test. You have all the time in the world. It is an open book test and you are free to use the textbook, any material handed out in class, and any other resources. Note,
Homework-5To: CC: From: Date: Re:CSci 5801, All Students All TAs Dr. Heimdahl 7/10/2008 ASW Implementation.The ProblemWe have a design for the ASW, the customer wants it, and we need to build it.The AssignmentImplement the ASW design you han
Software Engineering ICSci 5801 Summer 2008 Take Home MidtermThis is a take home test. You have all the time in the world. It is an open book test and you are free to use the textbook, any material handed out in class, and any other resources.No
CombiMap explanationCombiMap is a transform for mapping input features, L dimensional data space, into one dimension (mapping multi-dimensional data to a scalar value). Mathematical representation of this transform has four terms that are:CombiMap
Answer's to the Tornado QuizDark or greenish skies, wall cloud, large hail, loud roar that sounds like a freight train. 2.) 3-4 days 3.) A tornado watch means there could possibly a tornado. 4.) A tornado warning means a tornado has been spotted by
AnthemClass DiscussionECO 284 Microeconomics Dr. D. Foster Is there scarcity in Anthem? How are choices made? What? How? For whom? What is the moral contrast? What sentiment is collectivism trying to usurp? How is individualism a thre
CVEN 1317: Introduction to Civil Engineering - Homework 1 [25 pts total] On a separate sheet, answer the following based on class web notes or links (http:/ceae.colorado.edu/~silverst/cven1317/). Your assignment should be typed/printed (1 point for f
Determine the Specific Heat of a Solid in a CalorimeterAREN 2110 ITL Lab AssignmentCalorimeter is a multicomponent, adiabatic process1st Law Statement: Ui = 0 Where components are the calorimeter mass and the sample mass. Assumptions: rapid heat
CVEN 5534: Wastewater Treatment Assignment 1: Due Tuesday, 1/20BACKGROUND In 1905, Pennsylvania passed a law forbidding the discharge of untreated sewage from new sewerage extensions and extensions of existing sewerage systems into streams. The law
AREN 2110: Thermodynamics Midterm 1 Fall 2005_ NameTest is open book and notes. Answer all questions and sign honor code statement: I have neither given nor received unauthorized assistance during this exam. Signed__Remember to show your work
AREN 2110: Thermodynamics Midterm 1 Fall 2004_ NameTest is open book and notes. Answer all questions and sign honor code statement: I have neither given nor received unauthorized assistance during this exam. Signed__Remember to show your work
AREN 2110: Thermodynamics Midterm 2 Fall 2005_ NameTest is open book and notes. Answer all questions and sign honor code statement: I have neither given nor received unauthorized assistance during this exam. Signed__Remember to show your work
AREN 2110: In class exercises 1st Law 1. 7.2 MJ of work is put into a gas at 1 MPa and 150 C while heat is removed at the rate of 1.5 kw. What is the change in internal energy of the gas after one hour? a. 5.7 MJ b. 1.8 MJ c. 8.7 MJ d. 13 MJ 2. One k
FCS Core Learner Outcomes1. Articulate the historical foundation of family and consumer sciences, its evolution over time, its mission, and its integrative focus. 2. Analyze family structures and apply major theoretical perspectives to understand in
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DPD Portfolio Evaluation Format Includes the necessary components in the following order (12 points): Cover sheet in outer `pocket' of the binder. Title page (same as cover sheet) Table of Contents Current resumeFCS 4150Professional goals within
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More About
This Textbook
Overview
This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes
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Video Organizer for Beginning & Intermediate Algebra, 5th Edition
This title is currently out of stock. Please check back for availability.
Description
The Video Organizer encourages students to take notes and work practice exercises while watching Elayn Martin-Gay's lecture series (available in MyMathLab® and on DVD). All content in the Video Organizer is presented in the same order as it is presented in the videos, making it easy for students to create a course notebook and build good study habits! The Video Organizer provides ample space for students to write down key definitions and rules throughout the lectures, and "Play" and "Pause" button icons prompt students to follow along with Elayn for some exercises while they try others on their own.
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Description
From ancient to modern times, mathematics has been fundamental to the development of science, engineering, and philosophy. In this math course, students consider the questions and problems that have fascinated humans across cultures since the beginning of recorded history
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You're bundled against the Arctic chill. You're loaded with equipment. And that big white bear who's just slashed your tires has a toothache. Where is that helicopter? Norbert Rosing leads young readers into the wintry world of the dangerous polar bear, who has good reason to be angry at man's intrusions. Let this National Geographic expert show you the bears' playful side; learn how they make nests for hibernation, why their coats are so white, and how you can help to protect their environment from the effects of global warming.
If you have a TI-84 Plus Graphing Calculator, you have a powerful, sophisticated tool for advanced math. In fact, it's so sophisticated that you may not know how to take advantage of many of its features and functions. That's a good problem to have, and TI-84 Plus Graphing Calculator For Dummies is the right solution! It takes the TI-84 Plus to the next power, showing you how to:
Display numbers in normal, scientific, or engineering notations
Perform basic calculations, deal with angles, and solve equations
Create and investigate geometric figures
Graph functions, inequalities, or transformations of functions
Create stat plots and analyze statistical data
Create probability experiments like tossing coins, rolling dice, and so on
Save calculator files on your computer
Add applications to your calculator so that it can do even more
TI-84 Plus Graphing Calculator For Dummies was written by C.C. Edwards, author of TI-83 Plus Graphing Calculator For Dummies, who has a Ph.D. in mathematics and teaches on the undergraduate and graduate levels. The book doesn't delve into high math, but it does use appropriate math examples to help you delve into:
Using the Equation Solver
Using GeoMaster and its menu bar to construct lines, segments, rays, vectors, circles, polygons, perpendicular and parallel lines, and more
Creating a slide show of transformations of a graph
Using the Inequality Graphing application to enter and graph inequalities and solve linear programming problems
There's even a handy tear-out cheat sheet to remind you of important keystrokes and special menus, And since you'll quickly get comfortable with the built-in applications, there's a list of ten more you can download and install on your calculator so it can do even more! TI-84 Plus Graphing Calculator For Dummies is full of ways to increase the value of your TI–84 Plus exponentially.
Math textbooks can be as baffling as the subject they're teaching. Not anymore. The best-selling author of The Complete Idiot's Guide to Calculus has taken what appears to be a typical calculus workbook, chock full of solved calculus problems, and made legible notes in the margins, adding missing steps and simplifying solutions. Finally, everything is made perfectly clear. Students will be prepared to solve those obscure problems that were never discussed in class but always seem to find their way onto exams. --Includes 1,000 problems with comprehensive solutions --Annotated notes throughout the text clarify what's being asked in each problem and fill in missing steps --Kelley is a former award-winning calculus teacher
The updated guide to the newest graphing calculator from Texas Instruments
The TI-Nspire graphing calculator is popular among high school and college students as a valuable tool for calculus, AP calculus, and college-level algebra courses. Its use is allowed on the major college entrance exams. This book is a nuts-and-bolts guide to working with the TI-Nspire, providing everything you need to get up and running and helping you get the most out of this high-powered math tool.
Texas Instruments' TI-Nspire graphing calculator is perfect for high school and college students in advanced algebra and calculus classes as well as students taking the SAT, PSAT, and ACT exams
This fully updated guide covers all enhancements to the TI-Nspire, including the touchpad and the updated software that can be purchased along with the device
Shows how to get maximum value from this versatile math tool
With updated screenshots and examples, TI-Nspire For Dummies provides practical, hands-on instruction to help students make the most of this revolutionary graphing calculator.
TI-83 Plus Graphing Calculator For Dummies shows you how to:
Perform basic arithmetic operations
Use Zoom and panning to get the best screen display
Use all the functions in the Math menu, including the four submenus: MATH, NUM, CPS, and PRB
Use the fantastic Finance application to decide whether to lease or get a loan and buy, calculate the best interest, and more
Graph and analyze functions by tracing the graph or by creating a table of functional values, including graphing piecewise-defined and trigonometric functions
Explore and evaluate functions, including how to find the value, the zeros, the point of intersection of two functions, and more
Draw on a graph, including line segments, circles, and functions, write text on a graph, and do freehand drawing
Work with sequences, parametric equations, and polar equations
Use the Math Probability menu to evaluate permutations and combinations
Enter statistical data and graph it as a scatter plot, histogram, or box plot, calculate the median and quartiles, and more
Deal with matrices, including finding the inverse, transpose, and determinant and using matrices to solve a system of linear equations
applications you can download from the TI Web site, and most of them are free. You can choose from Advanced Finance, CellSheet, that turns your calculator into a spread sheet, NoteFolio that turns it into a word processor, Organizer that lets you schedule events, create to-do lists, save phone numbers and e-mail addresses, and more.
Get this book and discover how your TI-83 Plus Graphing Calculator can solve all kinds of problems for you.
TI-89 For Dummies is the plain-English nuts-and-bolts guide that gets you up and running on all the things your TI-89 can do, quickly and easily. This hands-on reference guides you step by step through various tasks and even shows you how to add applications to your calculator. Soon you'll have the tools you need to:
Solve equations and systems of equations
Factor polynomials
Evaluate derivatives and integrals
Graph functions, parametric equations, polar equations, and sequences
Create Stat Plots and analyze statistical data
Multiply matrices
Solve differential equations and systems of differential equations
Transfer files between two or more calculators
Save calculator files on your computer
Packed with exciting and valuable applications that you can download from the Internet and install through your computer, as well as common errors and messages with explanations and solutions, TI-89 For Dummies is the one-stop reference for all your graphing calculator questions!Most math and science study guides are a reflection of the college professors who write them-dry, difficult, and pretentious.
The Humongous Book of Trigonometry Problems is the exception. Author Mike Kelley has taken what appears to be a typical trigonometry workbook, chock full of solved problems — more than 750! — and made notes in the margins adding missing steps and simplifying concepts and solutions, so what would be baffling to students is made perfectly clear. No longer will befuddled students wonder where a particular answer came from or have to rely on trial and error to solve problems. And by learning how to interpret and solve problems as they are presented in a standard trigonometry course, students become fully prepared to solve those difficult, obscure problems that were never discussed in class but always seem to find their way onto exams.
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Comment
I only had a chance to look through it briefly, going through the main menu (the links), probably for about 10 minutes or so, and so far it looks pretty useful for a student taking an Algebra course. I looked at the links provided, and it's pretty useful for both student and teachers who want to review the algebraic concepts.
The content is pretty simple to use. Under the main menu, there are links that takes you to the different concepts, which provides an brief explanation about what it is, and then continues on to show examples of how it is used in the math. It takes you from angles and circles all the way to vectors, and although it is not as thorough and detailed like it would be in a textbook, it does provide to be a good reference. They even have math games and riddles for the student to ponder and try out as well.
It's effective as a reference, and maybe a brief study on the concepts before taking it head on in a math course or text. A student can prepare him/herself using this site.
The layout of the site isn't as intuitive as other sights, so it might be a little harder on the eyes to navigate around. But once you've learn to navigate around, it makes it a lot easier for you to bookmark and figure out where to go.
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GIS offers its students a rigorous and challenging mathematics curriculum that is reviewed and updated on a regular basis to keep up with the latest developments in math education.The mathematics curriculum at GIS is aligned with California Mathematics Academic Content Standards. During their years at GIS, students learn skills in the following strands of mathematics: number sense, geometry, measurement, statistics, algebra, probability and problem solving.
Grades K-2
Students in K-2 use Saxon Math, a research-based program that encourages students to develop a deeper understanding of concepts and the ways in which they may be applied. Newly taught concepts are further reviewed through hands-on activities that enable students to make connections, justify answers and communicate their understanding of the material. Students are introduced to new concepts daily, while old concepts are consistently reviewed and practiced throughout the duration of the term. This approach ensures that students develop and retain their understanding of these concepts and are able to apply them in real-world situations.
Grades 3-6
Students in 3rd to 6th grades make use of the Scott Foresman-Addison Wesley mathematics textbook set. This program focuses on developing a clear understanding of concepts and math skills. It also works to enhance questioning strategies, problem-solving skills, and provides students with opportunities to extend their understanding through reading and writing connections. Students are also able to access their textbook online and benefit from additional examples, practice problems, and sample tests. Scott Foresman-Addison Wesley textbooks follow National Council of Teachers of Mathematics (NCTM) standards.
Grade 7-8
7th and 8th graders follow the Prentice Hall Mathematics textbooks for Pre-Algebra and Algebra 1, respectively. This curriculum aims to develop conceptual understanding of key algebraic ideas and skills. Regular and varied skill practice allows students to increase their proficiency and success. Students are also able to make use of online resources that supplement the course, including the homework video tutor, lesson quizzes and chapter tests.
In 8th grade, students are grouped into two levels based on their readiness for Algebra 1. The same material is covered in the two groups, but the pacing, level of support and difficulty are different among the two. Students in Level 1, who complete a review of all Algebra 1 concepts, are ready to take higher-level math courses in high school (i.e. Algebra 2 or Geometry).
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CliffsQuickReview course guides cover the essentials of your toughest classes. Get a firm grip on core concepts and key material, and test your newfound knowledge with review questions. From planes, points, and postulates to squares, spheres, and slopes — and everything in between — CliffsQuickReview Geometry can helpThis is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equationsaredeveloped in this text.A synopsis of the geometry of Banach spaces, aspects... more...
This is the perfect introduction for those who have a lingering fear of maths. If you think that maths is difficult, confusing, dull or just plain scary, then The Maths Handbook is your ideal companion.
Covering all the basics including fractions, equations, primes, squares and square roots, geometry and fractals, Dr Richard Elwes will lead you gently...
From the author of the highly successful The Complete Idiot's Guide to Calculus comes the perfect book for high school and college students. Following a standard algebra curriculum, it will teach students the basics so that they can make sense of their textbooks and get through algebra class with flying colors. more...
Tips for simplifying tricky operations Get the skills you need to solve problems and equations and be ready for algebra class Whether you're a student preparing to take algebra or a parent who wants to brush up on basic math, this fun, friendly guide has the tools you need to get in gear. From positive, negative, and whole numbers to fractions, decimals,... more...
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Undergraduate research in mathematics has become a fundamental part of the mathematics program at many colleges and universities. Number theory is a subject rich with easily stated yet nontrivial problems. This makes it a great source for undergraduate research projects. In this session, we invite presentations about open problems in number theory that are suitable for undergraduate research and/or for joint faculty/student research. We also invite talks that present results concerning these problems. Presentations from elementary, algebraic, analytic, combinatorial, transcendental, and any other branch of number theory are welcome.
Undergraduate research is more popular than ever, and there remains a high demand for open and accessible problems for students to tackle. Combinatorics and graph theory provide an ideal combination of easily stated, but more difficult to solve, problems. We invite presentations about open problems in combinatorics and graph theory suitable for undergraduate research or joint faculty and undergraduate research. Presentations giving results about these types of problems are also welcome.
There are a variety of geometry courses: some take an intuitive, coordinate, vector, and/or synthetic approach; others focus on Euclidean geometry and include metric and synthetic approaches as axiomatic systems; and still others include topics in Euclidean and non-Euclidean geometries and provide opportunities for comparisons and contrasts between the two.
In this session, we invite presentations that address the following questions:
What approaches and pedagogical tools are best?
What are particularly good topics with which to begin geometry courses?
What are some of the most enjoyable proofs to share with students?
What are the best ways in which to explore polyhedra, tessellations, symmetry groups and coordinate geometry?
How can we help students to develop the visualization skills for two and three dimensions as well as to help them to develop the mathematical reasoning skills that are important for studying/exploring/applying geometry at any level?
What are the best ways in which to compare and contrast Euclidean and non-Euclidean geometry?
How can we best convey the beauty of geometry to students?
Presenters are welcome to share interesting applications, favorite proofs, activities, demonstrations, projects, and ways in which to guide students to explore and to learn geometry. Presentations providing resources and suggestions for those teaching geometry courses for the first time or for those wishing to improve/redesign their geometry courses are encouraged.
Undergraduate students in mathematics and statistics departments can assume numerous innovative instructional support roles in addition to the traditional role of grader. They can serve as undergraduate teaching assistants, peer tutors, study session leaders, and statistics lab assistants, to name a few. Assigning undergraduates to these instructional support roles benefits all those involved: undergraduate assistants develop important life and career skills; students receiving the instructional support get additional attention, and have the opportunity to communicate with a peer; and the instructor and the department benefit from the additional help they receive and are able to give students enrolled in their classes more individualized attention.
This session is open to talks aimed to introduce the different ways undergraduates participate in the instructional activities at various institutions. We encourage speakers to include a discussion of the benefits and challenges of their programs and the training/support that students receive while participating in the program. Talks focused on programs based in individual classrooms, as well as those that are department-wide and university-wide are all welcome. We also invite talks focused on improving the efficiency of the more traditional support roles such as grading and common math tutoring.
How does assessment inform the instructor about what students have learned? How can assessment results lead to changes in what content is covered or how it is covered? How can assessment impact what is included in STEM-related degree programs? This session invites presenters to share effective methods for both formative and summative assessment of courses that are part of math-intensive degree programs. Aside from mathematics majors, degree programs of this nature include those in which students take two or more mathematics courses (i.e. economics, business, chemistry,biology, etc.) Talks should include the results of the assessments as well as how those results have been used to make meaningful changes to courses and/or degree programs. The focus of reports should include, but are not necessarily limited to innovative assessment models, ways to analyze assessment results, and course or program improvements based on an implemented assessment program.
This session is dedicated to aspects of undergraduate research in mathematical and computational biology. First and foremost, this session would like to highlight research results of projects that either were conducted by undergraduates or were collaborations between undergraduates and their faculty mentors. Of particular interest are those collaborations that involve students and faculty from both mathematics and biology. Secondly, as many institutions have started undergraduate research programs in this area frequently with the help of initial external funding, the session is interested in the process and logistics of starting a program and maintaining a program even after the initial funding expires. Important issues include faculty development and interdisciplinary collaboration, student preparation and selection, the structure of research programs, the acquisition of resources to support the program, and the subsequent achievements of students who participate in undergraduate research in mathematical and computational biology. The session is also interested in undergraduate research projects in mathematical and computational biology, which are mentored by a single faculty mentor without the support of a larger program.
We seek scholarly papers that present results from undergraduate research projects in mathematical or computational biology, discuss the creation, maintenance, or achievements of an undergraduate research program, or describe the establishment or maintenance of collaborations between faculty and students in mathematics and biology.
In many mathematics classrooms, doing mathematics means following the rules dictated by the teacher and knowing mathematics means remembering and applying these rules. However, an inquiry-based learning (IBL) approach challenges students to create/discover mathematics.
Boiled down to its essence, IBL is a method of teaching that engages students in sense-making activities. Students are given tasks requiring them to conjecture, experiment, explore, and solve problems. Rather than showing facts or a clear, smooth path to a solution, the instructor guides students via well-crafted problems through an adventure in mathematical discovery.
The talks in this session will focus on IBL best practices. We seek both novel ideas and effective approaches to IBL. Claims made should be supported by data (test scores, survey results, etc.) or anecdotal evidence. This session will be of interest to instructors new to IBL, as well as seasoned practitioners looking for new ideas.
Many students earn degrees in mathematics with little practice in writing and editing. Recognizing the lifelong need of graduates to be able to clearly articulate ideas, institutions are placing a greater emphasis on writing throughout the mathematics curriculum. This session invites presentations describing approaches to incorporating writing and editing into mathematics courses. Presenters are asked to discuss any innovative and original projects, papers and problems that involve both writing and editing in their courses. While contributions detailing any form of mathematical writing are welcome, we are particularly seeking examples and approaches where editing is an essential component. The main goal of this session is to highlight various ways writing and editing have been infused into mathematics curricula and inspire instructors to introduce writing and editing into their courses.
As with all mathematics, recreational mathematics continues to expand through the solution of new problems and the development of novel solutions to old problems. For the purposes of this session, the definition of recreational mathematics will be a broad one. The primary guideline used to determine the suitability of a paper will be the understandability of the mathematics. Papers submitted to this session should be accessible to undergraduate students. Novel applications as well as new approaches to old problems are welcome. Examples of use of the material in the undergraduate classroom are encouraged.
Mathematicians, historians, educators, independent scholars and science writers use the increasingly available corpus of historical mathematical literature to study, understand and elucidate topics mathematical, scientific, historical, intellectual, literary and otherwise. Contributions to this session are case studies in the use of material drawn from the history of mathematics. Speakers describe 1) how they were led to consider this material for their project, 2) how they went about finding, exploring and mining the material, and 3) the impact that the material had on the success or failure of their project.
A math circle is broadly defined as a sustained enrichment experience that brings mathematics professionals in direct contact with pre-college students and/or their teachers. Circles foster passion and excitement for deep mathematics. The SIGMAA on Math Circles for Students and Teachers (SIGMAA MCST) supports MAA members who share an interest in initiating and coordinating math circles.
SIGMAA MCST invites speakers to report on best practices in math circles with which they are or have been associated. Talks could address effective organizational strategies, successful math circle presentations, or innovative activities for students, for instance. Ideally, talks in this session will equip individuals currently involved in a math circle with ideas for improving some aspect of their circle, while also inspiring listeners who have only begun to consider math circles.
The deadline for student papers at MathFest was June 8, 2012 . Every student paper session room will be equipped with a computer projector and a screen. Presenters must provide their own laptops or have access to one. Each student talk is fifteen minutes in length.
MAA Sessions
Students who wish to present at the MAA Student Paper Sessions at MathFest 2012 in Madison must be sponsored by a faculty advisor familiar with the work to be presented. Some funding to cover costs (up to $750) for student presenters is available. At most one student from each institution or REU can receive full funding; additional such students may be funded at a lower rate. All presenters are expected to take full part in the meeting and attend indicated activities sponsored for students on all three days of the conference. Abstracts and student travel grant applications should be submitted at For additional information visit
Pi Mu Epsilon Sessions
Pi Mu Epsilon student speakers must be nominated by their chapter advisors. Application forms for PME student speakers will be available by March 1, 2012 on the PME web site A PME student speaker who attends all the PME activities is eligible for transportation reimbursement up to $600, and additional speakers may be eligible with a maximum $1200 reimbursement per chapter. PME speakers receive a free ticket to the PME Banquet with their conference registration fee. See the PME web site for more details.
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This is a 6 hours video containing 75 solved
problems from 5 different exams (PDF file will be emailed to you). These videos prepare students to
succeed in the algebra exam required in some colleges for placement
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will be prepared to succeed in the placement exam.
You have 3 options in purchasing your video
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Purchase a CD to play on your computer
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users require the DVD version only!
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I'm taking first year calc this coming fall and I'm trying to learn as much as i can now so I'm more prepared this coming fall. Does anyone know of a book that puts topics in plain english (not in math mubojumbo) but is comprehensive at the same time . Thanks in advance for any help you can provide.
If you know your section, you might try contacting your university bookstore to see which textbook your class is using and pick up a copy early. Then you could start reading through it while doing the exercises.
If you'd like something good that's free and online, MIT has one from 1991 that's good:
If you think that math is mumbo-jumbo, then you might consider a review of pre-calculus. Identify the areas where you are having trouble and then study it so that you understand it. My son tutored calculus for over four years and he said that the biggest problem that calculus students had as algebra preparation (trig and logs were a problem too but to a lesser extent). If you don't have the prerequisites down, then you'll get killed unless you're taking a really watered-down course.
YES!!! Calculus the Easy Way, published by Barrons. It is in the study guides section of the bookstore. It's SOO COOL! It's a cross between an adventure story (fairly lame) and a calculus book, where the king's entourage wanders around the kingdom inventing the calculus they need to solve the problems they find. Algebra the Easy Way and Trigonometry the Easy Way are also in this series.
It's also possible to read it for concepts and reasons before you do the math, so you'll understand the point of it all.
MUS also has calculus and I believe Chalkdust does too. I noticed Teach12 also has a calculus dvd set. I have not tried any of these. I did purchase the MUS calculus but had to return it when it was decided that the older kids will remain in public school this next year. (my youngers home school still though).
As someone who just recently went through the lower-division curriculum of math, I find that Calculus by Ron Larson & Bruce Edwards is the best by far for HS to college sophomore level. I'd especially recommend it to someone who is going to try and teach themselves the material. It's not full of proofs but there are proofs you can do if you want. And there are many "applied" problems.
Someone already mentioned it but supplementing with either Khan Academy or MIT is a great way to learn. However, there is a Calculus lecture series done by UCLA that I've used to review this past summer. As for someone seeing the material for the first time, I'd say it's pretty great. Not really otherwise 'cause after two more semesters of Calculus you're like "Yadda yadda yadda. I know, guess I didn't need to review".
It is easy to understand and has the right amount of examples.
I bought the Dummies books before I ever took Calculus and I'd say they were more confusing than anything else I've read. I didn't really like the Calculus the Easy Way when I was in high school just trying to get an idea of what "Calculus" was about. Idk, different strokes for different folks.
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MATH 190 - Real-World Mathematics: A Service-Learning Math Course (4)
Contemporary society is filled with political, economic and cultural issues that arise from mathematical ideas. This service-learning Core mathematics course will engage students in using mathematics as a tool for understanding their world with a focus on the connection between quantitative literacy and social justice.Topics covered will include financial mathematics, voting theory, data representation and statistics.
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The first is Cohen's Precalculus. If you don't remember things like the quadratic formula and trigonometry, then this will cover it all. The new edition seems to have typos, so you might want to look around for an older edition on Amazon. Otherwise, you can't go wrong with Sullivan
, which I have not used but heard good things about. Either one of these is better than Larson that's used in most high schools.
Then for calculus, I recommend Anton's Calculus Early Transcendentals. You may opt to skip chapter 0 if you do all of Cohen. If you still remember things like the quadratic formula, how to factor, distribute, etc., then you can skip Cohen and read the trigonometry review in Anton.
I came to this board looking for the same answer to the exact same question. I'm dropping out of comm to follow my hopeless dream of taking physics! Need to rebuild a solid math foundation to have any hope in hell at getting through four years of calculus and physics classes. I'll take your recommendations. Thanks a lot.
I recommended a few going from basic math to vector calculus (namely, Cohen/Sullivan and Anton). For linear algebra, you can go with Leon (which I've used and found boring, but it gets the job done) or Lay (which I've never used but heard other people say good things about).
One of my friends is a graphics researcher who self-studied from Leon, so it will definitely prepare you even if it's not the most fun book in the world.
I don't know of a single book but if you have a university nearby there is likely some kind of non-university bookstore which does buyback. You can probably find old editions of textbooks to guide you along the way. Pre-algebra and college algebra should be good enough. I'm assuming the college algebra book will include trigonometry, if not then make sure you get a trig book. You can probably skip geometry if you are familiar with areas and volumes of common figures.
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Students are asked to predict what an absolute value graph will look like with given parameters. Then they can use a graphing utility that is on the same page to test their predictions. Feedback is g... More: lessons, discussions, ratings, reviews,...
An interactive applet and associated web page that demonstrate the area of an ellipse.
The major and minor axes can be dragged and the area is continuously recalculated.
The ellipse has a g... More: lessons, discussions, ratings, reviews,...
Students learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, also learning about properties of fractal objects. Parameter: fraction of the segment to be deletedThis applet does symbolic calculation of complex numbers. This means that you can enter integers and fractions for the component values of a complex number (real and imaginary). Values with numbers th... More: lessons, discussions, ratings, reviews,...
This activity allows the user to manipulate the graphs of the conic sections by changing the constants in their respective equations. The equation and variable values are displayed and change as the u... More: lessons, discussions, ratings, reviews,...
With this applet, students study the extrema of the function A cos^2 (t) + B cos(t) + C. A parabola is drawn with student-supplied coefficients and constant, and the unit circle is drawn below, so th... More: lessons, discussions, ratings, reviews,...
The applet manipulates an apparatus that draws a parabola from its definition that the distance from a fixed point called the focus is equivalent to the distance from a fixed line called the directri... More: lessons, discussions, ratings, reviews,...
An interactive applet and associated web page that show the definition and properties of an ellipse.
The applet has a draggable point that shows that the sum of the distances to the foci is a co... More: lessons, discussions, ratings, reviews,...
An interactive applet and associated web page that show the major and minor axes of an ellipse.
The applet has an ellipse whose major and minor axis endpoints can be dragged. As they are dragge
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This book reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly), which is needed to succeed in science courses.
Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields. The recorded lectures are from the Harvard Faculty of Arts and Sciences course Mathematics 122, which was offered as an online course at the Extension School.
Just-In-Time Math is a concise review and summary of the mathematical principles needed by all engineering professionals. Topics covered include differential calculus, integral calculus, complex numbers, differential equations, engineering statistics, and partial derivatives. Numerous example engineering problems are included to show readers how to apply mathematical techniques to a wide range of engineering situations. This is the perfect mathematics refresher for engineering professionals who use such math-intensive techniques as digital signal processing.
Learn how to create a full-length, interactive math lesson with a glossary, equations, illustrative charts and graphs, and a section that tests your students on what they've learned. This course builds on the lessons in iBooks Author for Teachers: Fundamentals and shows teachers how to leverage their existing math material and present it in an engaging digital way. Author Mike Rankin shows you how to import text from Microsoft Word, format your pages, add images and hyperlinks, and even add a useful calculator widget so students can perform calculations right inside the lesson.
Would you be interested in learning how to directly solve even the difficult math questions (in just one step). Learn the handy tricks to verify (double-check) your answer so that you can avoid making those silly calculation errors (thus get that 100% score in your math test) In short, would you like to discover the fastest and easiest way to master maths (from basic to advanced level)?
Number puzzles, spatial/visual puzzles, cryptograms, Sudoku, Kokuro, logic puzzles, and word games like Frame Games are all a great way to teach math and problem-solving skills to elementary and middle school students. In these two new collections, puzzle master Terry Stickels provides puzzles and brain games that range from simple to challenging and are organized by grade level and National Council of Teachers of Mathematics (NCTM) content areas. Each book offers over 300 brain games that will help students learn core math concepts and develop critical thinking skills. The books include a wide range of puzzle types and cover a variety of math topics, from fractions and geometry to probability and algebra.
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examine common algebra-related misconceptions and errors of middle school students. In recent years, success in Algebra I is often considered the mathematics gateway to graduation from high school and success
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An Arithmetic for Upper Grades, while intended chiefly
for pupils of the last two years of the elementary school,
has been arranged to include the work of the sixth grade.
The seventh year portion comprises a simple, but system-
atic, treatment of commercial arithmetic, including per-
centage with its several applications, and" elementary
exercises involving the employment of common business
forms. This is preceded by reviews of fractions and deci-
mals, and is followed by miscellaneous problems, oral and
written.
The eighth year section contains the remaining topics
of the ordinary course, prefaced by a review of compound
denominate numbers and simple measurements. The mis-
cellaneous problems that immediately follow are limited
to the subjects treated in this portion, so as to be available
for use in such schools as teach the seventh and eighth
grades in combined classes alternating the work of each
year.
A scientific treatment of numbers and processes is next
presented, which may be taken up at any stage. The mis-
cellaneous reviews that follow cover all the ground previ-
ously studied.
In many schools whose courses of study require an ad-
vanced text-book in the sixth year, it is customary to begin
the arithmetic work of this grade with the development of
formal definitions, principles, rules, etc. In this case, the
section on numbers and processes should first be taken up,
then the fraction and decimal reviews; followed by the
reviews of compound numbers and measurements.
Areas of Plane Surfaces ; Area of a Polygon ; Area of a
Regular Hexagon ; United States Public Lands ; Circum-
ference and Area of a Circle ; Prisms ; Cylinders ; Pyramids
and Cones ; The Sphere ; Miscellaneous Problems.
1. As a preliminary to the regular percentage work of
the seventh year, it will often be found profitable to give a
short time to the review of fractions, common and decimal.
At intervals throughout the year, a few minutes of an arith-
metic period should be spent in rapid oral reviews, employ-
ing the drills and the sight exercises of this chapter.
Drill Exercises.
Note. The fractions in the answers should be given in their low-
est terms.
2. Add:
1.
l
3
2.
2.
5
3.
4
9
4.
2
5
5.
2
9
6.
4
9
1
3
1
1
9
2
2
9
4
9
7.
2
3
8.
3
5
9.
5
9
10.
1
3
11.
4
5
12.
8
9
1
3
5"
4
9
2
3
•
3
5
5
9
3.
31
14.
41
15.
U 9
16.
H
17.
61
18.
8±
°9
1
• "3
1
5
1
9
1
2
9
4
9
.9.
°3
20.
6f
21.
QA
J 9
22.
6^
u 3
23.
64
5
24.
13|
1
3
2
~5
4
9
2
3
3
5
3
9
2 . - Arithmetic
Add:
'
25.
4!
^3
26.
H
27.
^9
28.
H
29.
8^-
°9
30.
U 9
^3
H
2*
H
n
94
J 9
31.
42
^3
32.
n
33.
»f
34.
^3
35.
n
36.
2*
3 1
^3
H
41
* 9
8f
64
3f
37.
1
4
38.
H
39.
5
8
40.
5 T V
41.
3
8
42.
^4
°9
1
4
1
6
^1
^8
9- 1 -
^12
3
8
2
9
43.
3
1
44.
^12
45.
7
8
46.
Q8
°9
47.
7
1
48.
^T2
°1
Q 5
°T2"
5
8
7
9
Q_9_
°l
71i
' 12
3. Subtract;
13
19
25.
•
4
5
JL
5
2.
7
9
5
9
3.
6f
2
5
4.
8^-
°9
4
9
5.
74
'"5
2!
6.
•
8
8.
6
9.
7
10.
4
11.
6
12.
8
1
1
2
5
5
9
Q2
^3
5*
7^-
1 9
.
8
14.
6
15.
7
16.
9
17.
'6
18.
8
H
H
1^
Q2
H
95
~9
H
20.
H
21.
71
4 9
22.
91
,; 3
23.
6*
24.
8^
°9
if
H
1^
3|
4f
Z 9
.
5
6
26.
7
8
27.
7
9
28.
ItV
29.
9|
30.
8^-
°9
1
6
5
8
4
9
5
1 2
1
8
2
9
4.
Multiply
:
•
l.
ix
2
2.
3x
1
4
3.
iof
4
4.
5
x*
5.
*X
9
6.
17 x
1
8
7.
iof 23
8.
31
x tV
9.
|x
2
10.
3x
2
7
11.
f of
5
12.
7xf
Review of Fractions
Multiply :
13.
H
14. 51
15.
n
16.
9 1
17. 84
2
3
4
5
6
18.
92
2
19. 5f
3
20.
7^
' 8
5
21.
Q2
8
22. 91
7
23.
i°f
2
24.
3
x«
25.
i
8
X 4
26.
6xi
27.
iof
4
28.
6
xi
29.
i
8
Xl6
30.
27xi
31.
lof
6
32.
9
xi
33.
l
8
x20
34.
33 x i
35.
fof
2
36.
3
x|
37.
•5
6
x 3
38.
7x1
39.
f of 15
40.
24
x|
41.
5
8
xl2
42.
3xi
43.
2
44. 51
4
45.
61
u 8
2
46. 7f
3
47- 8,A
6
48.
6
49. 8J
9
50.
Q2
3
51. 4|
4
52. 6|
5
5.
Divide :
l.
2)4 fifths
2.
3)6
sevenths
3
. 4)8 ninths
Note. In dividing i by 2, the pupil may think 2 into 4 fifths, or
i of 4 fifths, or 4 fifths divided by 2. These and the following ex-
amples are placed in the short-division form to lead pupils to refrain,
at times, in written work from changing the mixed number in the
dividend to an improper fraction when the divisor is a whole number.
4.
<)ii
5.
W
6.
m
7.
6)ff
8.
2)44
9.
3)6f
10.
■±M
11.
5)5}
12.
2 )A
13.
31i
14.
4 )i
15.
%
16.
2)12i
17.
3)91
18.
4)161
19.
5)151
Arithmetic
Divide :
20. 6 )181
24. 5)|
28. 4)2j
32. 2)191
36. 2)j
40. 2 )171
44. 6 )431
21. 7 )211
25. 5)21
29. 5)3f
33. 4 )26f
37. 2)11
41. 3 )161
45. 7 )4Qi
22. 8)401
26.
2)1
30.
'6)3*
34.
5)28|
38.
31i
42.
4)191
46.
8)411
23. 9 )631
27. 2)11
31. 7)4j
35. 6 )33f
39. 3)11
43. 5)42|
47. 9 )461
6. Preliminary Exercises.
1. How many baseballs at $ i each can be purchased
for$i? For$l? For $11?
2. 1)1 3. 1)1 4. 1)11 5. 1)2
7. 1)8 8. 1)20 9. 1)6 10. 1)12
How is the quotient obtained in each case ?
12. f)i 13. 11)11 14. f)| 15. 11)3 16. 1#6
Multiply the divisor and the dividend in each of the five preceding
examples by 2 :
6- i]2J
11. 1)12
17. 3)3 18. 3)3 19. 3)6 20. 3)6
How do the quotients compare in each case ?
21.
)12
7. 1. Divide 12 by If
Proof.
1|)12
x2 x2
3 ^24
8 Ans.
l|x 8 = 12.
2. Divide 21 by f.
Proof.
f)21
x4 x4
28
3)84
28 Ans
x | = 21.
Review of Fractions 5
Note. In mental work it is often convenient to change a fractional
divisor to a whole number by multiplying the divisor by the denomi-
nator of the fraction, the dividend being multiplied by the same num-
ber. Divide the new dividend by the new divisor.
8. Drill Exercises,
Divide :
1. 11)9
6. 21)15
11.
2. 11)15
7. 31)21
12.
3. 11)18
8. 21)27
13.
4. 11)15
9. 31)26
14.
5. 11)20
10. 1|)15
15.
f)12 16. li]7J 21. J)2i
f]12 17. H)8| 22. |)2£
4)12 18. 11)9! 23. |)4J
f)10 19. 1£7J 24. f)5f
|)14 20. 1 1)16| 25. f)6*
9. Oral Problems.
1. A farmer sold 151 cords of wood in January and 10^
cords in February. How many cords did he sell in all ?
2. From a piece of cloth containing 30 yards, 121 yards
are sold. How many yards remain ?
3. A rectangular field is 121 rods long and 1\ rods wide.
How many rods of fence will be needed to inclose it ?
4. How many i-pound packages will 24J pounds of
candv make ?
5. A traveler w r alked 60J miles in 3 days. How many
miles a day did he average ?
6. How many square rods are there in a field 20^ rods
long and 10 rods wide ?
7. Mr. Yates pays % 171 for carpet and $ 201 for furni-
ture. What is the amount of his bill ?
8. How many minutes are there in 1 of a day ?
9. At 60 pounds per bushel, what will J bushel weigh ?
10. How many yards of cloth at $ 11 per yard can be
bought for $12?
6 Arithmetic
10. Written Problems.
1. A boy sold. 16| dozen eggs at one time and 20f dozen
at another time. How many eggs did he sell ?
2. Fin'd the sum of four numbers, two of which are 15 T 4 -
and 19 T 7 5, respectively, the third being equal to the sum of
these two, and the fourth being equal to their difference.
3. Two trains start from the same point and move in
opposite directions, each at the rate of 32i miles per hour.
How far apart are they in 4 hours ? .
4. What is the total weight of 16 barrels of sugar,
averaging 310 J pounds each ?
5. A crop of wheat averaged 121 bushels per acre.
How many acres were required to produce 500 bushels ?
6. How many square rods are there in a rectangular field
160 J- rods by 84 rods ?
7. A train starting at 10.45 a.m. reaches a town 140
miles distant at 2.15 p.m. How many miles per hour does
it average ?
8. If 3 eighths of a number is 147, what is 1 eighth of
the number ? What is the number ?
9. A rectangular lot is 120 feet long. Its width is T 9 7
of its length. How many running feet of fence will be
required to inclose it ? (Make a diagram.)
10. How many gallons are there in 1J barrels of 31^ gal-
lons each ?
11. Sight Exercises.
Note. To accustom the pupils to avoid unnecessary figures, fre-
quent drills in sight and blackboard exercises are important. Pupils
should give orally the answers to the following examples, or should
promptly write the answer to each at a signal, the pupil being ex-
pected to know the answer before beginning to write.
Review of Fractions 7
Add
1. 241 4. 172 7 . 48 5
Q3 Kl Ql
°¥ °4 ^3
2. 42f 5. 8 J- 8. 84|f
8i 36f 9i
3. 931 6. 3f 9. 46f
7| 91* 71
12. Blackboard Exercises.
Note. Pupils are expected to write only the answers to the follow-
ing examples, but time should be allowed them to write the total of
each column as they obtain it. These exercises are designed to show
pupils that it is not always necessary to rewrite the fractions with a
common denominator.
Add :
1. 241 4. 401 7. 471
6} 281 7|
59\ 51 59^
8. 461
81
39 1
2. 47|
5.
48^
181
321
H
7|
3. 841
6.
9Q1
10|
4of
°T<T
.
»i
13. Sight Exercises.
Subtract :
1. 18}
3.
721
H
21
w 6
2. 541
4.
9T1
^' 2
H
6f
401
_ii
801
71
4 3
8
Arithmetic
Subtract :
7.
36i
8.
62 T V
8*
9.
931.
10i
14. Blackboard Exercises,
Subtract :
1. 841
4.
401
7.
631
29£
16#
27|
2. 90 T V
5.
60f
8.
52 T V
261
23|
341
3. 78^
6.
45- 7 -
^1
9.
93|
39f
18f
471
15. Sight Exercises.
Multiply :
i. m
4.
16
7.
101
8
41
12
2. 20|
5.
24 *
8.
12f
9
_?i
7
3. 21f
6.
48
9.
40f
4
«
Ji
_9^
16. Blackboard Exercises.
Multiply :
1. 1241
4.
304£
7.
251^
7
5.
12
8.
10
2. 320f
423f
9<>9 3
8
6.
2
9.
13
3. 621f
516f
2011
5
5
14
Review of Fractions 9
17. Sight Exercises.
Divide :
1. 2 )261 4. 7 )781 7. 6 )67j
2. 3 )39| 5. 8 )17f 8. 5 )51$
3. 4 )36f 6. 9)36-^ 9. 4 )27f
18. Blackboard Exercises.
Divide :
1. 2 )2461 4. 5 )8491 7. 8)6491
2. 3)4591 5. 6 )2731 8. 9 )833|
3. 4 )7231 6. 7 )723f 9. 1 0)537f
19. Written Exercises.
Note. Determine the common denominator by inspection.
Find results :
1. 8i + 7L-fl3f + 42f 3. 28f + 45i + 83| + 96i
2. 26J + 30f + 471 + 56| 4. 351 + 56^ + 971 + 4811
5. 19if + 12| + 24|| + 87|
6. 910f-316 T i- 9. 862|-258f
7. 862|-258| 10. 683^-42311
8. 200-V - 103 T V 11. 7091-357^
To multiply two mixed numbers, reduce them to improper
fractions, multiply the numerators together and the denomina-
tors together, and reduce the resulting fraction, if possible.
In each of these examples the price per yard is obtained by dividing
the total cost by the number of yards: 24^ -r- 2, 30 p -*■ 2^, 6^-e-^,
9?-=-f.
21. Oral Problems.
Note. In solving each of the following problems, the pupils should
first state whether it is an example in multiplication or in division.
They may easily determine this by mentally substituting a whole
number for the traction.
1. A 24-acre field is divided into plots of § acre each.
How many plots are there ?
2. At $J per bushel, find the cost of 56 bushels of
wheat.
3. How many cords of wood in 32 piles containing J
cord each?
Review — Type Problems n
4. If a train goes f mile in a minute, how many minutes
will it take to go 60 miles?
5. A dealer's profit is \ of the cost. What is the cost,
if his profit is $24?
6. How many f-pound packages can be filled from a
36-pound box of tea ?
7. A drover sells § of his herd of 120 cattle. How
many does he sell ?
8. Nine tenths of the pupils of a certain class are pres-
ent. There are 27 present. How many pupils belong to
the class ?
9. If a man can do two fifths of a piece of work in a
day, how long will it take him to do the whole work ?
Number of days = 1 work -f- f work = \ work -f- f work = 5 -f- 2.
10. How long will it take a pipe discharging f gallon per
second to empty a tank containing 60 gallons ?
22. Written Problems.
Note. Before solving the following problems, the required opera-
tion should be indicated in each case by the use of the proper sign.
1. Into how many building sites of f acre each can a
farm of 192 acres be divided ?
Number of sites = 192 A. -=- 1 A.
2. Find the cost of 784 bushels of wheat at $ }f per
bushel.
Cost = $ i| x 784.
3. How many loads, each containing -J cord, are there in
336 cords of wood ?
4. What time will it take a train to go 195 miles at the
rate of f mile a minute ?
5. At 95^ per bushel, how many bushels of wheat can
be bought for $ 142.50 ?
12 Arithmetic
6. How many bushels of wheat at $ i| per bushel can
be bought for $ 1421 ?
7. If it takes J yard of material to make an apron, how
many yards will be required to make 144 aprons ?
8. How many vests can be made from 144 yards of
cloth, if J yard is needed for each ?
9. If three men working together can do ^ + 2*5 + ^V
of a piece of work in a day, how long will they require to
do the whole work ?
10. Find the cost of if acre of land at $ 256 per acre.
11. If a horse eats § bale of hay in a week, how long
will a bale last ? 32 bales ?
12. A farmer sold his farm for f of its cost, which was
14800. What did he receive for it ?
13. A can do J as much work in a day as B. How many
days would he require to do a piece of work that B could
finish in 105 days ?
14. A and B together can do ^- as much work as B alone.
How many days would both working together require to do
a piece of work which B can do in 105 days ?
15. A dealer's profits average ^^ of the cost of the goods
sold. How much does he gain on goods costing $ 275 ?
16. If the weight of roasted coffee is JJ of the weight of
unroasted coffee, how many pounds of the latter will be re-
quired to make 221 pounds of roasted coffee ?
Suggestion. In this problem and in the remaining four, the pupil
may use x as follows :
| 677.169 | 1 |
Prealgebra and Introductory Prealgebra (Basic Math with very early Algebra) and Introductory Algebra (or Beginning Algebra). This engaging prepa... MOREration My Math Lab. Elayn Martin-Gay believes "every" student can succeed and that is the motivating force behind her best-selling texts and acclaimed video program. With Martin-Gay you get 100% consistency in voice from text to video! "Prealgebra and Introductory Algebra 2e "is appropriate for a 2-sem sequence of Prealgebra (Basic Math with very early introduction to algebra) and Introductory Algebra (aka Elementary Algebra). This text was written to help students effectively make the transition from arithmetic to algebra and provide a strong foundation for success in their next, intermediate algebra course. To reach this goal, Martin-Gay introduces algebraic concepts early and repeats them as she treats traditional arithmetic topics, and then further develops their exposure to elementary-level algebra topics." "The material from this text is also available split out into two separate textbooks, "Prealgebra 5e" and "Introductory Algebra 3e, "if you prefer to use split textbooks, rather than one combined textbook for your 2-sem sequence.
Whole Numbers and Introduction to Algebra Tips for Success in Mathematics
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MAED 5030: GEOMETRY AND MEASUREMENTS
An investigative approach to the study of Euclidean, Non- Euclidean and transformation geometry that enriches students knowledge of the concepts, principles and process as it relates to the school curriculum. Students will make conjectures, test and verify properties of geometric figures in the physical world using such tools as the Geometer's Sketchpad. Proof as it relates to geometric concepts and principles will be constructed.... more »
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These challenging books are designed for students with significant mathematical backgrounds, yet it can be appreciated by non-mathematicians; there are no maths formulae. As well as exploring the concepts of transformation and deformation, they introduce the idea of surfaces without thickness or boundary.
Waves, Diffusion and Variational Principles (MS324)
Variational Principles
Four books focus on three areas of applied mathematics. The first explores wave motion using vibrating strings and sound waves as examples. The second describes heat flow and the flow of particles which follow random walks. The third area introduces variational principles and calculus through simple problems.
In recent decades, mathematicians have increasingly employed computer- assisted algebra packages in their calculations. Maple is one of the more popular packages, used to expand functions as series, evaluate sums and integrals, solve differential equations and plot the results of calculations. Books and a CD-ROM introduce computer-assisted algebra techniques using Maple.
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Introducing Expanded Step-by-step Math Solutions
Step-by-step solutions, one of the most popular features for mathematics in Wolfram|Alpha, has just received a dramatic expansion in its functionality! With our new interface, you now have the ability to walk through all of our Step-by-step solutions at your own pace, revealing only one step at a time. Some of our programs will offer to guide you with hints when walking through solutions. And for common math problems, we can even show multiple ways to find the solutions. We are also very excited to introduce three new math content areas that now have Step-by-step solutions: solving equations, rational arithmetic, and verifying trigonometric identities. When you're signed into Wolfram|Alpha, you can use this new feature three times a day. Or, when you upgrade to Wolfram|Alpha Pro, you can use it as many times as you like!
Let's look at a new Step-by-step solution for an integral (one of the more popular math queries we receive). We'll type "integrate cos^2(x)" into Wolfram|Alpha and then click the Step-by-step solution button in the top right of the results page.
To walk through the problem one step at a time, you can click the Next step button, as we have done above. Or if you'd rather see everything at once, click the Show all steps button:
Now let's look at the input (8 * 11) / 3 + 4, which features a Step-by-step solution from one of our brand-new programs. In this walkthrough, you will have the option to use hints to help guide you through the problem:
As you walk through the problem, hints will give you an idea of what comes next. If you'd rather not use the hints, you can click the Hide hints button in the top right. And of course, if you'd like to see all of the steps at once, we can click "Show all steps," as we did in our first example.
The top-right corner of the Step-by-step solutions window has a drop-down menu to let us choose how to solve the problem: use the factor method, complete the square, or use the quadratic formula. Let's try all three and compare:
Again, we see that we have the option to walk through the steps one at a time (using hints if we'd like) or to show all steps at once.
In addition to offering hints and multiple methods to solve a problem, we can now solve equations over the real numbers or over the complex numbers! Let's see this in action by asking Wolfram|Alpha to find the roots of (e^x + 2)(x – 1). When solving over the real numbers, Wolfram|Alpha will show us that (e^x + 2)(x – 1) has only one root; over the complex numbers, Wolfram|Alpha will find the complex roots of this expression.
To see even more of our brand-new functionality, let's ask Wolfram|Alpha to verify a trigonometric identity. To do this, we simply type the identity we wish to prove into Wolfram|Alpha, and it will walk us through our proof one step at a time. For example, let's try the identity (sin(x) – tan(x))(cos(x) – cot(x)) = (sin(x) – 1)(cos(x) – 1):
Here are some more examples for you to explore the scope of Step-by-step solutions.
This gives you a brief overview of what you can do with our new Step-by-step solutions. When you're signed into Wolfram|Alpha, you can use this new feature three times a day. Wolfram|Alpha Pro users receive unlimited access to Step-by-step solutions.
With Wolfram|Alpha's Step-by-step Solutions feature, you can be guided—at your own pace—through a broad range of math problems, from arithmetic and equation solving all the way through integrals and ordinary differential equations. We look forward to expanding our Step-by-step solutions to more areas—please let us know if there are new solutions that you'd like to see!
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Forms Pro is the most in-depth and comprehensive math program ever. (This may get kind of long, so for a quick overview, just read the last two words). With 100+ formulas it is undoubtedly the best math program ever. FormsPro contains everything from a 2-5 VARUABLE EQUATION SOLVER to just about every AREA, LATERAL AREA, SURFACE AREA, VOLUME and PERIMETER formulas that their are. FormsPro also contains many helpful triangle formulas such as the SSS,SAS,SAA,SSA and ASA. Also solves for any side of the PYTHAGOREAN THEROM. Forms Pro has a very neat SLOPES EQUATION for just about everything including being able to find a parrallel and perpendicular line. Also included is a very good X=GRAPHER that solves for all X= equations. FormsPro also has some very helpful conversions, like STANDARD->SLOPE, and SLOPE->STANDARD. New and improved, and it's still ONE PROGRAM, so you don't need to worry about a whole bunch of programes to unarchive and archive. All this and much, much more in a program that is (needless to say) Simply Amazing.
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Prerequisite: acceptable placement score (or ACT math score of at least 28), or at least 3 years of high school algebra and trigonometry with at least a B average, or a grade of C or better in MATH 180. General Education course: G9.
3. Life Values: Students analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems.
(a) Develops an appreciation for the intellectual honesty of deductive reasoning.
(b) Understands the need to do one's own work, to honestly challenge oneself to master the material.
4. Cultural Skills: Students understand their own and other cultural traditions and respect the diversity of the human experience.
(a) Develops and appreciation of the history of calculus and the role it has played in mathematics and in other disciplines.
(b) Learns to use the symbolic notation correctly and appropriately.
NCTM Goals: The NCTM (National Council of Teachers of Mathematics) gives the following set of overall goals for mathematics education in general, which are worth including here, since I think they are such fundamental reasons for studying mathematics.
1. Learn to value mathematics.
2. Learn to reason mathematically.
3. Learn to communicate mathematically.
4. Become confident in your mathematical ability.
5. Become problem solvers and posers.
Course Goals:
1. Students shall develop a solid foundation in the basic concepts and methods of Differential Calculus.
2. Students shall develop problem solving skills.
3. Students shall understand the appropriate use of technological tools in their mathematical work.
Outcomes: This is a list of more specific mathematical outcomes this course should provide. The student shall...
Content:
1. ... demonstrate the knowledge of the theory and methods of Differential Calculus, specifically, limits, derivatives by definition, differentiation formulas, and applications of the derivative.
Problem-Solving:
2. …demonstrate the ability to apply appropriate mathematical tools and methods of novel or non-routine problems.
3. …demonstrate the ability to use various approaches in problem solving situations, and to see connections between these varied mathematical areas.
Technology:
4. …demonstrate the basic ability to perform computational and algebraic procedures using a calculator or computer.
5. …demonstrate the ability to efficiently and accurately graph functions using a calculator or computer.
6. …demonstrate the knowledge of the limitations of technological tools.
7. …demonstrate the ability to work effectively with a CAS, such as DERIVE, to do a variety of mathematical work.
Communication:
8. …use the language of mathematics accurately and appropriately.
9. …present mathematical content and argument in written form.
COURSE POLICIES AND PROCEDURES:
Probably the best single piece of wisdom I can pass on to you as you begin this course is: "Mathematics is not a spectator sport!" You need to view yourself as the LEARNER – and "learn" is an active verb, not a passive verb. I will do what I can to help structure things so that you have an appropriate sequence of topics and a useful collection of problems, but it is up to YOU to DO the problems and to READ the book and THINK ABOUT the topics.
You must develop a system that works for you, but let me suggest that it might include finding a study group or coming to me with your questions or going to tutoring sessions in the learning center. In any case you should expect to spend at least the traditional expectation of 2 hours outside of class for each hour in class – this is important! Class time is for exploring the topics and answering questions you might have, but you simply can't master the material without putting in the time alone to really engage in the mathematics.
We are in the process of phasing in a new textbook and more than ever it is important that you actually READ the BOOK! The authors attempt to force the reader to think about the material and to develop an intuitive sense of what is going on; there is much emphasis on solving problems and much reliance on graphing technology as well as on symbolic manipulation.
HOMEWORK: In a nutshell, working problems is one of the key ways you will learn Calculus. Attending class is important, of course, but without doing problems you will not develop a solid foundation in the material. I will give you daily assignments and will expect that you will do as many as time allows (which I take to be roughly 2 hours per class period). I will not generally collect these assignments but I do see them as testing your understanding and as raising questions for you to ask in class.
LABS: Throughout the course there will be an occasional "lab", a problem set you will work on
EXAMS: There will be exams after each of the 4 chapters we will cover – these will be in two parts, a group practice problem set worth 20 points and then an individual exam worth 80 points, 100 points in total. The final exam will be cumulative and worth 150 points (25 on the group part, 125 on the individual part). By the way, I do not expect you to memorize the various formulas – you are allowed a page of notes for each exam, and you can bring all four pages in for the final exam.
GRADING POLICY: In general I use the rather traditional 90% of possible points for an "A", 80% for a "B", 70% for a "C", and 60% for a "D". I will try to make enough points available in non-test situations that "test-anxiety" should not entirely kill your chances for success, but I am a very firm believer in putting students through the exam experience so that I can see whether you, not your study group, understand the material.
AMERICANS WITH DISABILITIES ACT
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Mathematical concepts such as probability, statistics, geometric constructions, measurement, ratio and proportion, pre-algebra, and basic tests and measurements concepts including interpretation of data. Use of manipulatives in learning mathematical concepts. Only applicable to graduation requirements of elementary education students.
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Cofactor Expansions
In this lesson our instructor talks about cofactor expansions. First, he talks about cofactor expansions and their application. Then he discusses evaluation of determinants by cofactor, inverse of a matrix by cofactor, and list of non-singular equivalences. He ends the lesson by talking about Cramer's Rule.
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Cofactor Expansions
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Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text. Solutions to selected exercises are available from the authors. less
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Course Objectives:† Possessing elementary school certification
in mathematics in the state of Kansas means that you can be called upon to
teach any level of mathematics from first through eighth grade.† This is a large amount of mathematical
material, covering everything from basic arithmetic to algebra and basic
geometry.† The primary purpose of this
course is to give you the mathematical understanding you will need to teach
this material.† The specific course
topics have been chosen to enable you to meet the state guidelines as described
in the Kansas Teacher Licensure Standards.
But learning specific mathematical skills is only
one small part of this course.† Far more
important is learning how a mathematician approaches a problem.† The bulk of the course will emphasize logic
and reasoning rather than the rote memorization of algorithms.† This aspect is, all too often, lost in
traditional classroom presentations of mathematics.† The result is the popular misconception that mathematics is
largely separate from the world at large.†
After all, the amount of numerical computation you are called upon to do
in your day-to-day life is rather small.†
But the reasoning skills you learn in the process of doing mathematics
will serve you well in all aspects of life.
Course Requirements:† Your grade in this course will be
based on several factors.† Homework will
be assigned every other class period and will be collected two class periods
after it is assigned.† Thus, if an
assignment is given on a Monday, it will be collected on Friday.† If it is assigned on Wednesday, it will be
collected the following Monday.† There
will also be two in-class exams during the term, plus a final exam.† It is likely that there will be some quizzes
along the way, but I will never give a pop quiz.† There will also be several writing assignments.† In addition, classroom participation will be
taken into account as well.
Studying Groups:† Most students find it helpful to study with
other class members, and I strongly encourage you to do this.† You are free to work together on homework
assignments, but in the end everyone must hand in his own paper.†
Attendance:† This class moves very quickly, so missing
even one day will entail having to catch up on a substantial amount of
material.† Take this into consideration
if you are considering cutting a particular class period.† Generally, I donít take attendance in a
formal way.† But I will certainly be
aware if you miss a substantial number of class periods and, since class
participation is an important feature of the class, it will adversely affect
your grade.
Textbook Reading:† At the end of each class period I will tell
you the portions of the textbook we will be covering in the next class.† It is expected that you will read the text
before coming to class.† Even if you
find the reading difficult you will be in a much better position to understand
the material in class if you have already seen it once before.† Keep in mind that reading mathematics is
different from reading normal literature.†
Thus, even if the reading assignment is only a few pages long, you might
find that it takes you a substantial amount of time to get through it.† Keep that in mind when you are budgeting
your time.
Final Thoughts:† If you have any special needs, and
medical conditions, etc. that will in any way affect your performance in my
class, let me know as soon as possible.†
Also, if for some reason you will have to be absent for an extended
period of time, again, let me know as soon as possible.† Donít be bashful about coming to office
hours during the term, or talking to me after class.† Ultimately, everything I do at the front of the room is done for
your benefit, so it is important to me that I have your feedback along the way.
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Discrete Math
Discrete mathematics, broadly speaking, is the "study of discrete objects." As opposed to objects that vary smoothly, such as the real numbers, discrete mathematics has been described as the mathematics of countable sets. Because of the absence of an all-encompassing definition, the best way to understand what discrete mathematics entails is to enumerate some of the topics it covers: graph theory, combinatorics, set theory, logic, discrete probability theory, number theory, certain topics in algebra (numerical semigroups and monoids, for instance), discrete geometry, and several topics in game theory.
Of these topics, Princeton offers separate courses on graph theory, combinatorics, logic, discrete geometry, and game theory. Set theory, number theory, probability, and the "discrete" topics in algebra come up in their own right in various other courses, where they can be studied in more depth.
Finally, it should be stated that discrete mathematics is very closely associated with computer science. As a result, many of the topics can be studied as integral parts of either of the two disciplines. In fact, there are a couple of courses offered by Princeton's COS department which are really discrete mathematics courses in disguise. Students majoring in either of the two also often end up taking courses from the other, and as a result there is constant exchange and collaboration between the two departments.
Discrete Math Courses [Show]Discrete Math Courses [Hide] MAT 375: Introduction to Graph Theory
This course, taught by Professor Seymour, serves as the "standard" Princeton introduction to discrete mathematics. The course covers the fundamental theorems and algorithms used in graph theory. Since there is not enough time to build the deeper results in graph theory, the course is based on breadth rather than depth, and therefore goes through a host of topics. These include connectivity, matching, graph coloring, planarity, the celebrated Four Color Theorem, extremal problems, network flows, and many related algorithms which are often of significance to computer science.
Professor Seymour is one of the greatest graph theorists that the world has ever seen, and the course is designed and taught by him; it is, consequently, a unique experience that not many other universities can provide. He uses his own course notes, which have evolved through the last couple of decades, and are notorious for their terse expositions ("Proof: Trivial.") as well as the large amount of material condensed into them. Professor Seymour also recommends Douglas West's classic graph theory textbook, although he rarely consults it after the first lecture.
The course is meant for a wide range of students. Since it assumes no background except with the basics of mathematical reasoning, it is one of the largest departmental courses offered by Princeton Mathematics. Students taking the course range from the mathematics majors who intend to specialize in graph theory to students who need a "theoretical" requirement for their Princeton academic career. A huge contingent of the class is comprised of computer science majors, who are interested in the connections between graph theory and computer science. It is important to note that the course is cross-listed with COS 342, and is therefore also a computer science departmental.
The class starts slowly, but picks up very fast as it goes into more and more material. Although it is almost universally agreed as a "fun" class, doing well can be challenging, since there is a scramble for the higher grades – the class is notorious for yielding medians of 9.8 out of 10 in its weekly problem sets.
The grade is based on eleven problem sets through the semester, and on a ten-problem take-home final exam. The problem sets are instructive, and often end up teaching new material outside of class. Professor Seymour always goes over all the homework problems every week after they are handed in. Collaboration is allowed, and heavily encouraged.
All in all, the course is well-organized, brilliantly taught, and extremely fun and accessible to students of all levels. However, doing well in the course requires hard work and a somewhat substantial time commitment. Collaboration is encouraged and asking the TAs for help is not at all uncommon. MAT 377: Combinatorial Mathematics
This course is taught by Professor van Zwam, and functions as the standard undergraduate introduction to non-graph-theoretic combinatorics. Combinatorics, the theory of "counting," is an indispensable tool and integral component of many areas of mathematics; but more importantly, it has recently, in light of modern research, grown into a fundamental mathematical discipline in its own right. This modern theory relies on deep, well-developed tools, some of which the course gets into. In essence, the course covers over a dozen virtually independent topics illustrating some of the most powerful theorems of modern combinatorics, such as Ramsey Theory, Turan-type theorems, extremal graph theory, probabilistic combinatorics, algebraic combinatorics, and spectral techniques in graph theory.
This course is meant primarily for mathematics majors looking for an introduction to the theory of combinatorics. The class, therefore, is typically much smaller than its "predecessor," MAT 375. Professor van Zwam uses his own notes and supplements them with some of the classic expository texts in combinatorics, such as Peter Cameron's notes or Richard Stanley's book. Students are highly encouraged to take notes during lectures, since they are usually not put up online. Another useful resource is Jacob Fox's notes from the same course, which was taught by him in earlier years.
There are about six problem sets spread evenly through the semester. Each contains about five or six problems, which get steadily more and more challenging. Collaboration, therefore, is an important part of the course. Students have been known to stay up for several nights working on a couple of seemingly impossible problems towards the end. However, this is an effort to introduce students to basic combinatorics research, and is an important part of the course; solutions are discussed in depth after the problems are handed in.
There is a take-home final with six problems, which collectively involve techniques learned throughout the semester. As a recapitulation of these broad techniques, the final is a brilliant but completely reasonable test of what the students are expected to have taken out of the course. Therefore, it is easy to do well on the course as long as a student has attended the lectures and learned the general principles.
An important part of the course is the last two or three weeks, when it departs from the traditional topics taught in similar courses in other universities, and delves into some of the modern research in combinatorics. In particular, the lectures on spectral graph theory and the basic introduction to matroid theory are extremely rewarding, since Professor van Zwam himself is a matroid theorist. There is usually less homework assigned from this part, but the material is wonderfully presented by Professor van Zwam; these last couple of lectures also serve as sufficient background to the graduate course on matroid theory, MAT 595. MAT 378: Game Theory
Professor van Zwam's course on game theory the only class that the mathematics department offers on the subject (there are other classes on game theory offered by other departments). Game theory is the formal mathematical study of strategic decision-making; consequently it deals with a number of scenarios where one person's success depends on others' choices, and therefore choosing the "right" course of action is a complex calculation. Game theory is not entirely a subset of discrete mathematics, since a lot of the more modern results in it are much more continuous in nature; however, given the large discrete component of the discipline, it deserves mention in this category. MAT 584: Incidence Theorems and their Applications
This is Professor Dvir's graduate course on Incidence Theorems and their applications. The titular theorems are a way of formally describing how discrete shapes such as lines, points and various other geometric objects intersect each other. These theorems have recently risen in importance because of their tremendous applications. The course serves as a rigorous introduction to this vast and wonderful theory, proving some of its major results. The course delves into problems such as Szemeredi-Trotter problems ("How many incidences can a set of lines have with a set of points?"), Kakeya problems ("What are the properties of sets in Euclidean space containing line segments in each direction?"), as well as Sylvester-Gallai problems ("Is it possible to have a non-collinear set of points such that a line through any two of them must go through a third?"). The topics covered in this graduate course have far-reaching consequences in some of the most important areas of modern research, such as additive combinatorics, coding theory and computational complexity.
Professor Dvir follows his own excellent notes, which are available on his website. The same page also details some additional readings for the interested reader. The course is aimed primarily at graduate students, although undergraduates with sufficient background in mathematics and computer science are encouraged to try it as well. As with all mathematics graduate courses, the undergraduates have to solve a few problems in order to pass the course, though typically this is more a formality than a stringent requirement.
The course is rewarding but challenging, and any undergraduate student planning on taking it is advised to read up as much background material as possible in order to follow the lectures easily. It also helps to be interested in computer science, as then the motivation behind much of the material becomes evident. MAT 595: Topics in Discrete Mathematics
This graduate topics course is usually offered by Professor Seymour (the matroid theory course has also been offered by Professor van Zwam). The course changes from semester to semester, but is usually one of the three following topics. Matroid Theory: This class is offered by either Professor Seymour or Professor van Zwam, and serves as a rigorous introduction to matroids, which are discrete structures similar to graphs that exhibit properties of rank and linear independence. This theory is young and exciting, and the course covers most of its seminal results in addition to going into current research topics. The instructor's notes are usually used in conjunction with Oxley's classic textbook. Structural Graph Theory – Induced Subgraphs: This course is an introduction to the theory of induced subgraphs, building up gradually to the celebrated 2002 proof of the Strong Perfect Graph Theorem (a graph is perfect if and only if it is a Berge graph). Like its counterpart, the Graph Minors course, this course is about structural graph theory, which is traditionally one of the "hardest" branches of combinatorics, and hence students are expected to be comfortable with long proofs and extremely intricate arguments. Structural Graph Theory – Graph Minors: This course is a fast but intensive run through some of the results of the famous Graph Minors Project of Seymour and Robertson. The course builds up a lot of the theory behind containment relations such as minors, subgraphs, immersions and topological containment, and then goes into structure theorems and many forbidden-minor characterizations. Using pathwidth, treewidth and branchwidth, the course then develops most of the necessary tools for attacking Seymour and Robertson's celebrated Graph Minor Theorem (graphs are well-quasi-ordered under minors), and sketches the proof.
The discrete mathematics graduate course is rewarding in the extreme, since it is taught by the best in the world. Any student planning on taking it, however, should be prepared to put in a lot of time for the problem sets. Some of the homework problems, be warned, have been unsolved and are (still) open.
Another point that should be kept in mind is that knowing the material from MAT 375 is really a pre-requisite to taking this course. The first lecture is sometimes a refresher, but unless a student already knows some standard techniques in graph theory beforehand, even the refresher does not help. This should be kept in mind because of the frenetic nature of the course; it delves into quite advanced material from the second lecture onwards. COS 488: Analytic Combinatorics
This course of Professor Sedgewick's serves as an introduction to one of the most powerful recent techniques in algorithm analysis. The discipline of analytic combinatorics represents many decades of collaboration between Professor Sedgewick and Phillipe Flajolet. Essentially, the course is divided into two halves. In the first half, the course covers techniques from classical combinatorics to tackle "hard" approximation problems that come up in computer science (particularly in the analysis of certain recursion-based algorithms), and then in the second half, it goes into deeper mathematics in order to deal with more general classes of problems by using techniques from complex analysis.
This course is very unique, in that it really is a mathematics class; there is next to no coding, and not much mention of computer science. However, unlike most mathematics classes, it switches gears in the middle, and moves from discrete to continuous mathematics, but with the same end in sight. Not much background is required for the class, though some familiarity with algorithm analysis helps distinctly. Furthermore, a student who knows complex analysis is at a great advantage towards the beginning of the second half of the course. Professor Sedgewick encourages collaboration and is one of the most organized lecturers at Princeton, so the course ends up being accessible to anyone interested in taking it. He is also known to be very generous with his final grades.
Although the "discrete" part of this course is confined to the first half, it is a course worth taking. Professor Sedgewick loves teaching the class, and takes great care to ensure that the content is well understood by everyone. Furthermore, it is useful in simplifying a number of problems that come up a lot in "real-life computer science," and solving them with the aid of the beautiful but counter-intuitive approaches arising from mathematics.
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Elementary and Intermediate Algebra (Hardcover), 1st Edition
This book has been designed to present the material, reinforce major concepts, and test student understanding using a variety of instructional methods and features. The authors had seven objectives in writing this text: 1.) To teach students the language of algebra--how to read, write, speak, and think mathematically (Graphics, examples, and Study Sets throughout text emphasize key phrase and translation); 2.) To use a group of fundamental algebraic concepts as the foundation of the text (introduce equations, variables, problem solving, functions, and graphing in Chapter 1) and constantly reinforce those major concepts of algebra throughout the text (Key Concept feature); 3.) To aid student comprehension and confidence by introducing concepts in one context and revisiting throughout the book in other contexts (coverage of problem solving is one good example); 4.) To gain and keep students' attention through creative applications (See any Applications section in Study Sets), an interactive approach to instruction (Self Checks), and a visually appealing design; 5.) To have top-notch problem sets (purposefully named Study Sets, not Problem or Exercise Sets) that break learning into smaller pieces so that students do not become overwhelmed; 6.) To constantly show how the material being studied can be used to solve real-world problems; 7.) To blend traditional and reform instructional approaches--from vocabulary, practice, and well-defined pedagogy to place an emphasis on problem solving, reasoning, communicating, and technology (Study Sets
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Fundamentals With Elements of Algebra
9780759310001
ISBN:
0759310009
Pub Date: 2002 Publisher: Cengage Learning
Summary: This student-friendly and non-traditional text provides a solid foundation in algebra concepts before introducing signed numbers, helping to build student confidence. Conversational so that students will actually read it, yet mathematically accurate, this text helps students overcome their fear and dislike of mathematics, develops critical thinking and decision-making skills, and prepares them for subsequent courses
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Introduction
This book—which can be used alone, in combination with the LearningExpress publication, Practical Math Success in 20 Minutes a Day, or along with another basic math text of your choice—will give you practice in dealing with whole numbers, fractions, decimals, percentages, basic algebra, and basic geometry. It is designed for individuals working on their own, and for teachers or tutors helping students learn the basics. Practice on 1001 math problems should help alleviate math anxiety, too!
A
re you frightened of mathematics? You're not alone. By the time I was nine, I had developed a full-blown phobia. In fact, my most horrible moments in grade school took place right before an arithmetic test. My terror—and avoidance—lasted well into adulthood, until the day I landed a job with a social service agency and was given the task of figuring budgets, which involved knowing how to do percentages. I might just as well have been asked to decipher the strange squiggles incised on the nose-cone of an alien spaceship. I decided I'd better...
[continues]
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What do you do when your child brings you an Algebra problem that he just can't solve? The book has the answer key, but how did they get to that point. "Ugh," you exclaim as you realize that it is well over 20 years since you even did Algebra. Now what?
Algebra 1 Solved!, published by Bagatrix, may be just the medicine that the doctor
ordered. This is not a curriculum but an amazing software tool that will help
your student successfully get through his curriculum when trouble points hit.
The software was designed as a homework helper. Its major point that is marketed is that your child can enter in her Algebra problems and see actual step by step solutions. Each of the topics that are covered in Algebra 1 curricula is contained within the software by topic. No need to just start at the beginning. The user interface allows the student to select the topic that they are struggling with and go directly to it. Your son or daughter can even have the computer generate example problems associated with the topic being reviewd. There is also a built in glossary that better explains the definition and concept of the topics selected.
Upon beginning the application, the user creates a notebook that will hold his work or opens a notebook that work was already begun in. Because the user is creating the notebook, each notebook can be labeled to correspond to the number of the lesson in the student's math curriculum, the date that the work is being done, or one notebook can be created for the full year's worth of problems. It is completely up to the student. The notebook categorizes work into four folders: problems, graphs, tests, and documents.
Upon needing help solving a problem, the student would click on the problem button on the toolbar or on the problem folder. A toolbox of algebraic symbols appears making it easy to enter those problems with proper nomenclature. Once the problem is entered, the student clicks on the answer button and then sees how the problem is solved step by step. The computer may prompt the student to specify which variable to solve for. If enough information was entered within the equations provided to solve for the variables, the graphing function of the program becomes enabled. Buttons on the toolbars are only enabled as they apply within the context of the student's work. If the user goes to Tools-Options, he can also set whether to see step by step solutions, explanations, or just the answer.
The application is very valuable in its graphing capabilities. The student may enter more than ten equations into the user interface to have plotted on the graph paper in the center of the screen. Color coding of each equation makes interpreting the graph very user friendly.
In addition to the software's usefulness as a problem set assistant, it also auto-generates tests on any of the algebraic topics contained in the database. Within the test generator, the user can specify the number of problems and level of difficulty. This can then be printed as a paper copy or be answered on screen using a multiple choice selection. If the multiple choice, on-screen test format is chosen the computer will grade the student's work when he is finished.
The document folder can be used to generate custom assignments, quizzes, tests, handouts, or for the student to make notes to himself. The quick insert tool is available so that proper math notation and symbols can be used in creating these documents.
This mom would give this product a thumbs up, especially if one of your concerns in homeschooling through high school is the fear in teaching higher level math. Bagatrix, Inc. continues this product line through Algebra 2, Trigonometry, and Calculus. The CD case that the software ships with states that it is compatible with Windows 2000/XP/2003. We have a Windows Vista, 64-bit system and did not run into any installation issues, except for the optional loading of a particular version of the .NET framework which is not compatible with our version of windows. This did not affect the functionality of the software at all.
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Chapter
1: The Language of Algebra (Page 31) Deduction
and Induction
Read and learn about topics such as the discipline of logic, the structure of argument, recognizing arguments, deductive inferences, inductive inferences, and truth and validity.
Chapter 3: Addition and Subtraction Equations
(Page 111) Arithmetic
Sequences Explicit definition of a sequence, finding the sum of a sequence,
and the recursive definition of a sequence are covered on this page.
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I'm getting really bored in my math class. It's simplify radical expression calculator, but we're covering higher grade syllabus. The topics are really complicated and that's why I usually sleep in the class. I like the subject and don't want to drop it, but I have a real problem understanding it. Can someone help simplify radical expression calculator class will be the best one.
Hello, just a year ago, I was stuck in a similar situation. I had even considered the option of dropping math and selecting some other subject. A colleague of mine told me to give one last chance and gave me a copy of Algebra Buster. I was at comfort with it within few minutes. My ranks have really improved within the last year.
inequalities, like denominators and adding matrices were a nightmare for me until I found Algebra Buster, which is truly the best math program that I have come across. I have used it through many math classes – Algebra 2, College Algebra and Remedial Algebra. Just typing in the algebra problem and clicking on Solve, Algebra Buster generates step-by-step solution to the problem, and my math homework would be ready. I highly recommend the program.
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Buy print & eBook together and save 40%
Description
Theory and application of a variety of mathematical techniques in economics are presented in this volume. Topics discussed include: martingale methods, stochastic processes, optimal stopping, the modeling of uncertainty using a Wiener process, Itô's Lemma as a tool of stochastic calculus, and basic facts about stochastic differential equations. The notion of stochastic ability and the methods of stochastic control are discussed, and their use in economic theory and finance is illustrated with numerous applications.
Quotes and reviews
@from:R. Kihlstrom @qu:This book will almost certainly become a basic reference for academic researchers in finance. It will also find wide use as a textbook for Ph.D. students in finance and economics. @source:Mathematical Reviews
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McGraw-Hill Math Grade 2 by Editors McGraw-Hill
Now students can bring home the classroom expertise of McGraw-Hill to help them sharpen their math skills! McGraw-Hill's Math Grade 2 helps your elementary Know It!" features reinforce mastery of learned skills before introducing new material "Reality Check" features link skills to real-world applications "Find Out About It" features lead students to explore other media "World of Words" features promote language acquisition Discover more inside: A week-by-week summer study plan to be used as a "summer bridge" learning and reinforcement program Each lesson ends with self-assessment that includes items reviewing concepts taught in previous lessons Intervention features address special-needs students
Comment on McGraw-Hill Math Grade 2 by Editors McGraw-Hill
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Vibrant color photographs and simple sentences introduce students to a variety of graphs. Students will love learning about graphs while improving their reading skills. This series meets both math and reading standards.
Vibrant color photographs and simple sentences introduce students to a variety of graphs. Students will love learning about graphs while improving their reading skills. This series meets both math and reading standards.
This comprehensive new edition has been developed specifically for the Australian Curriculum. Covering all the content and requirements of the Year 9 curriculum this accessible text has also been written to cater for a wide range of ability levels
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What's inside... Feature Math and Science Magnet Prepares Students for Algebra and Beyond What's New
Math and Science Magnet Prepares Students for Algebra and Beyond Algebra is an important foundation for building the critical thinking skills we need for solving everyday problems. Picture yourself at the local video rental store getting ready to pay for your selection. The clerk tells you that you have a choice of paying a $25 annual membership fee, plus $1.50 per rental, or paying no membership fee and $2.75 per rental. Would you have imagined that an understanding of algebra and linear equations could help you decide which is the better deal? Or perhaps you have a job offer that requires you to move across the country from Buffalo, N.Y. to San Francisco, Calif., but you would have to cover the cost of gas for approximately 2600 miles in a moving van. If the national average for gasoline is $3.25 per gallon, how much money would you need to save to cover the cost of the move? Would you have believed that when you learned to solve algebraic expressions it would help you find the answer to this unknown variable, too?
There is concern throughout the country that many American students lack the knowledge and skills necessary to succeed in algebra. Those students may not only have greater difficulty solving some of the "real world" problems listed above, but they also may need remedial course work in college and may have a lesser chance of becoming the next generation of American scientists, inventors, and engineers. And with research showing that students who complete Algebra II in high school are more than twice as likely than students with less mathematical preparation to earn a 4-year college degree, we must ensure that students are ready to tackle the more advanced mathematics courses in high school and beyond.
To compete in the 21st century global economy, proficiency in mathematics is crucial. To help ensure our nation's future competitiveness and economic viability, President George W. Bush created the National Mathematics Advisory Panel in April 2006. The Panel was charged with making recommendations on the best use of scientifically based research to advance the teaching and learning of mathematics. During the past two years, the Panel held meetings around the country, reviewed more than 16,000 research studies, received public testimony from 110 individuals, and considered written commentary from numerous organizations and individuals. In addition, the Math Panel conducted, in partnership with the National Opinion Research Center (NORC), a national survey of Algebra I teachers to determine what practices will best prepare American students to succeed in algebra. On March 13, 2008, the 24 expert panelists, including educators, cognitive psychologists, and leading mathematicians, released a report with actionable steps, containing 45 findings and recommendations on numerous topics. Some of these topics included instructional practices, materials, professional development for teachers, learning processes, assessments and research policies, and mechanisms. The report calls for students to attain a strong foundation in basic mathematical skills and for Americans to redefine how they view mathematics, shifting from a belief that particular people cannot learn mathematics to a belief that hard work and effort can pay dividends in achievement.
Some of the report's key findings include: 1.) there should be a systematic progression in mathematics curricula from pre-kindergarten through eighth grade with an emphasis on student mastery of each step; 2.) it is critical to understand and be able to work with fractions (including decimals, percents, and negative fractions), for such proficiency is foundational for algebra; 3.) it is crucial for students to demonstrate quick recall of computational facts if they are to be successful in mathematics; 4.) a student's effort in the learning process is an important factor to ensuring achievement; and 5.) teachers must have a strong understanding of mathematics both prior to and beyond the level they instruct, if students are to succeed.
The K J Clark Middle School of Mathematics, Science & Technology in Chickasaw, Ala., is a magnet school that provides a curriculum rich with many of these recommendations, and the school is producing impressive results for its students. Clark offers a rigorous and relevant mathematics curriculum with a multitude of hands-on activities to get students excited about learning. As the National Math Panel report recommends, the school's approach is systematic and emphasizes conceptual understanding, computational fluency, and problem-solving skills.
Under the leadership of Principal Dianne McWain, a 2007 U.S. Department of Education Terrell H. Bell award recipient, fourth through eighth grade students throughout the Mobile County are being prepared to succeed in mathematics and science in high school and beyond. McWain notes, "We accelerated learning a few years ago. Now our students are so much better prepared. We integrate mathematics into the curriculum everyday and in every class."
The mathematics program allows students to see what is important, according to Math Department Chair Julie Boren. For example, in one algebra class, the students work in groups as they tackle a question involving which one of three candidates won the school's student council election, and by how many votes. "They know we are not going to skip the word problems just because they are difficult. We meet challenges head-on," she said.
The school prepares students for algebra by providing a "core plus" curriculum. The "core plus" takes place in grades four through six, during which time the mathematics instructors teach the grade level county curriculum but add skills from the next grade level as well. By accelerating instruction, all seventh grade students are prepared for the foundations of algebra and all eighth grade students are taught Algebra I for high school credit. Clark also offers geometry for more advanced eighth graders. "We add skills in the sixth and seventh grade that students may need to ensure they take and pass Algebra I in eighth grade," said Boren.
Clark also offers an after-school tutoring program, an in-house tutoring program that removes students from their scheduled classes to obtain extra help, and one-on-one sessions during class with the teacher to ensure that all students, even those who are struggling initially, succeed in the rigorous math program. "It is critical that our students be competitive - it opens doors for them so they can take calculus and upper level math in high school," Boren asserts.
Student enrollment at Clark is determined by a lottery in which there are no academic requirements for admission other than passing the grade the student is in at the time of application. Students come to Clark from parochial or private schools and as many as 60 public elementary schools across the county. The students also arrive with very different backgrounds and levels of academic ability. Teachers work collaboratively to bridge the gap between students' initial levels of knowledge and experience and Clark's standards of proficiency required for promotion.
The U.S. Department of Education named Clark a No Child Left Behind (NCLB) Blue Ribbon School in 2007 in part because it is a high achieving school regardless of its student demographic. Although 58 percent of Clark's student population consists of those from disadvantaged backgrounds, all students have improved their performance on state assessments. Beginning in 2003, Clark began disaggregating information on student performance, in alignment with NCLB's accountability measures and focus on data to drive instruction. By looking at the data on student performance, Clark was able to identify subgroups of students that were not performing as well as the school average and implemented strategies detailed in its Title I School Improvement Plan to close the achievement gap. The data showed that the subgroups that needed more attention were their black students and students eligible for free and reduced-priced lunch. Clark faculty members worked diligently to address the educational needs of those students, and data from the 2006 SAT-10 and Alabama Reading and Mathematics Test (ARMT) showed the progress students had made; on those tests there was little difference between the scores of students in the "black" and "free and reduced-priced lunch" subgroups and students in any other subgroup. In some instances, students in the "free/reduced lunch" subgroup outperformed students in the "paid lunch" group and black students outperformed non-black students.
High-performing schools often share similar characteristics. For example, teachers work collaboratively; there are numerous opportunities for professional development; and data drives instruction and further assessment. All of these characteristics are present at Clark, where teachers use a hands-on approach to address the learning needs of all students. Most importantly, the school's faculty has high expectations, an approach that is paying off for teachers and students.
Teacher Knowledge Is Critical
Consistent with the Math Panel's recommendation that teachers must know in detail the mathematical content they are responsible for teaching and its connections to other important mathematics, Clark aims to increase its teachers' knowledge of math to positively influence student achievement. The district provides in-service training for teachers, and Clark's Math Chair Boren encourages her teachers to be active in professional organizations. Recently some teachers took an online course on differentiating learning strategies and used the strategies to help students use their strengths to master concepts. Clark also sends some teachers to conferences sponsored by the National Council of Teachers of Mathematics (NCTM). Those teachers share what they learn with others at departmental meetings. Principal McWain explains that opportunities for professional development abound at Clark. "We are always on the cutting edge. We try to think outside the box. We incorporate this into the curriculum by giving students new techniques and strategies to succeed. The teachers work cooperatively together-including rewriting and enhancing the curriculum."
Clark aims to increase their students' knowledge with each grade level. A good example of early work with the foundations of algebra is apparent in fourth grade when students study fractions. The fourth grade goal is to expose students to equivalent fractions and basic operations with fractions of like denominators. Some of the activities in the classroom might include making fraction bars and grids, and the elementary teachers use different colors with the bars and grids to help students "see" the fractions.
In fifth grade classes, students use operations with like and unlike denominators. Teachers also expose students to canceling when multiplying fractions and putting fractions in lowest terms. Operations with mixed numbers also are introduced, and by the end of fifth grade, teachers expect students to be proficient with operations with fractions of like denominators and to be able to find equivalent fractions. The sixth graders are expected to master these skills, in addition to changing fractions to decimals and then changing decimals to percents. In the "core plus" curriculum, teachers begin the process of teaching students to work with positive and negative fractions and mixed numbers early. In the seventh grade, students aim to master these skills.
Typical classrooms use a hands-on approach to help students understand key concepts. All of the teachers use games with fractions and white boards in the classroom to encourage students to be proficient. Sixth grade math teacher Angela Rocker said that her students enjoy "Fraction Face-Off," in which a small group of students will be given a fraction problem and race to get the correct answer. The winner of the game will face a new group of challengers. Students use white boards to check for understanding. All of the students in the class are required to do a specific problem and hold up their answer on the boards. According to Boren, "This is a quick way to make sure that all students are focused and understand how to complete the problem. Our students enjoy using these boards!"
Parents also see the advantage of Clark's approach to math. As one parent remarked, "My daughter doesn't even realize she's learning math. They integrate it throughout all the subjects and it's important because we can use it at home in real situations, like sewing skirts for our theater group and determining the circumference of the waists without a pattern. They also have everything a parent needs for the tools to help their child and for the child to work and get whatever they want in life."
U.S. Secretary of Education Margaret Spellings announced a new pilot program under No Child Left Behind (NCLB) aimed at helping states differentiate between underperforming schools in need of dramatic interventions and those that are closer to meeting the goals of NCLB. As part of the new pilot program, states that meet the four eligibility criteria may propose a differentiated accountability model. These eligibility criteria are based on the "bright line" principles of NCLB. (March 18)
During testimony before the U.S. House Committee on Education and Labor hearing on "Ensuring the Availability of Federal Student Loans," Secretary Margaret Spellings launched a new brochure, Federal Aid First, a resource for students and families that encourages them to maximize more affordable Federal student aid options before pursuing other options. To access the brochure and additional information about federal student aid, please visit (March 14)
Education Secretary Spellings announced the release of the final report of the National Mathematics Advisory Panel, and the findings were passed unanimously at the panel's meeting at Longfellow Middle School in Falls Church, Va. The panel reviewed the best available scientific evidence to advance the teaching and learning of mathematics and stressed the importance of effort, algebra, and early math education. (March 13)
Secretary Spellings joined Intel Chairman Craig Barrett to honor Intel Science Talent Search (STS) finalists. STS is America's oldest and most prestigious high school science competition. The top prize this year went to Shivani Sud of Durham, N.C, who developed a model that analyzed the specific "molecular signatures" of tumors from patients with Stage II colon cancer. She used this information to identify patients at higher risk for tumor recurrence and propose potentially effective drugs for treatment. (March 13)
Following a visit to Van Duyn Elementary School in Syracuse, N.Y., where Secretary Spellings highlighted progress toward NCLB goals in New York and across the nation, she joined Representative Jim Walsh (R-NY) and school officials at an education roundtable to discuss the state's accountability plan, standards, and assessments. She also discussed the new tool recently released by the Department known as Mapping New York's Educational Progress 2008. (March 10)
Continuing the dialogue on NCLB and priorities for 2008, Secretary Spellings convened an education roundtable at the West Virginia State Capitol Building with Congresswoman Shelley Moore Capito (R-WV), First Lady of West Virginia Gayle Manchin, West Virginia State Superintendent Steve Paine, and state education leaders and policymakers. She also visited Saint Albans High School in Saint Albans, W.V., and delivered remarks recognizing the progress of the school's students under NCLB. (March 7)
Secretary Spellings continued her national tour to discuss No Child Left Behind (NCLB) in North Carolina, where she addressed the North Carolina State Board of Education in Raleigh and discussed how the federal government can support and facilitate further academic gains made by the state's students under the law. She also participated in a roundtable with educators and school administrators. (March 5)
Secretary Spellings delivered remarks at the Reading First State Directors Conference and declared that with the help of the Reading First program, there have been dramatic gains in student and school achievement. She called on Congress to restore funding for the program to $1 billion, as requested in the President's fiscal year 2009 budget. (March 6)
The March edition of Education News Parents Can Use featured the work of the National Mathematics Advisory Panel and included a discussion about the Panel's final report and how its findings will lead to more effective math instruction in classrooms nationwide. The show also spotlighted what the Department and other key partners are doing to promote math and science literacy through the American Competitiveness Initiative and showcased the work of high-performing schools around the country that are excelling in math education and effectively implementing the Panel's recommendations. To find out more about the program, visit the Education News Parents Can Use Web site. The archived webcast of the show may be viewed online at (March 18)
Applications for the Teaching Ambassador Fellowship positions at the Department are due April 7, 2008. These positions offer highly motivated and innovative public school teachers the opportunity to contribute their knowledge and experience to the national dialogue on education. For more information go to the Teacher Fellowship Web site.
From the Office of Innovation and Improvement
The Full Service Community Schools (FSCS) Program is recruiting peer reviewers for its upcoming grant competition. This program encourages coordination of educational, developmental, family, health, and other services through partnerships between public elementary and secondary schools and community-based organizations and public or private entities. Grants are intended to provide comprehensive educational, social, and health services for students, families, and communities. To obtain additional information or to submit resumes, contact the program at [email protected], using the subject "Reviewer Information."
American History
Students at Henry E. Lackey High School in southern Maryland have developed one of the most comprehensive oral history projects of black life in the region. Students interviewed several of the region's oldest black residents and are creating an hour-long DVD that will be aired during Charles County's 350th anniversary celebration this summer. The project is one of several recent efforts to expand students' knowledge about the black population in Maryland's oldest counties. (March 6)
Elizabeth R. Varon, distinguished lecturer with the Organization of American Historians (OAH), writes in the OAH Newsletter about her experience visiting teachers who participate in the OII-funded Teaching American History (TAH) Program in Rockford, Ill. She notes, "The first thing that struck me was the dedication of the 60 or so teachers who were willing to give up their Saturdays… for a day of intensive collaboration." The Rockford Public School system is in its last year of a fiscal year 2004 TAH grant. (February 2008)
Arts Education
March is Arts in the Schools Month, and to bring attention to the importance of the arts in K-12, the American Association of School Administrators is putting the arts at "center stage" in its March edition of The School Administrator. Among the journal edition's features available to online readers are perspectives on the role of the arts in fostering innovation and the acquisition of skills needed in a knowledge-based economy, stories of schools and districts keeping the arts strong as part of leaving no child behind, and suggestions for policy leaders about the complete curriculum. (March 2008)
The Art of Collaboration: Promising Practices for Integrating the Arts and School ReformPDF (1.53 MB) is a new research and policy brief from the Arts Education Partnership. The brief describes promising practices for building community partnerships that integrate the arts into urban education systems. The publication resulted from a roundtable discussion among the directors of eight demonstration sites that are participating in The Ford Foundation's Integrating the Arts and Education Reform Initiative. (March 24)
Findings from studies by neuroscientists and psychologists at seven universities are helping scientists understand how arts instruction might improve general thinking skills. Learning, Arts, and the Brain, a Dana Consortium report on arts and cognition, does not provide definitive answers to the "arts-makes-you-smarter" question, but it does dispute the theory that students are either right- or left-brained learners. It also offers hints on how arts learning might relate to learning in other academic disciplines. (March 2008)
Charter Schools
Synergy Charter Academy in South Los Angeles was named Charter School of the Year at this year's California Charter School Conference. Caprice Young, former president of the Los Angeles Unified School Board who is now chief executive of the California Charter Schools Association, said, "[Synergy Charter] should be credited with not only closing the achievement gap, but eliminating it." The school was the highest-performing school in South Los Angeles in 2006 and 2007, and was named a National Charter School of the Year last year by the Center for Education Reform. (March 3)
Students in South Carolina might be interested in a new virtual charter school that will open this fall. South Carolina Connections Academy will be the state's first virtual charter school, and will enroll 500 students in its online K-12 program. Connections Academy, a company that runs schools enrolling 10,000 students in 14 other states, will manage the new school. (March 3)
The Center for Education Reform (CER), a Washington-based education reform advocacy group, recently ranked each state based on the strength of its charter school laws and found significant differences among the states. For example, Minnesota had the strongest charter laws in the country, while Mississippi had the weakest. Each state received a letter grade, "A" through "F," based on criteria developed by CER. (Feb. 13)
As charter schools across the nation gear up for lotteries, the National Alliance for Public Charter Schools is offering a free PDF (168 KB) "Charter School Lottery Day Tool Kit." Lottery days can present opportunities to: draw media attention to the demand for quality charters; create awareness among families of school choice, and create an opportunity for charters to communicate their success. Charter school staff can use the tool kit to create their own lottery day event. Materials on preparation, messaging, recruitment, media outreach, timelines, and costs are included. (February 2008)
Closing the Achievement Gap
Each year since the 2005 National Education Summit and the founding of the American Diploma Project (ADP) Network, Achieve has issued an annual report based on a 50-state survey of efforts to close the "expectations gap" between high school requirements and the demands of colleges and employers. Closing the Expectations Gap 2008 reveals that while a majority of states have made closing the expectations gap a priority, some states have moved much more aggressively than others. (February 2008)
Education Reform
Publicschoolinsights.org is a new online resource aimed at building a sense of community among individuals who are working at the local level to strengthen their public schools. The site also features a variety of success stories from U.S. schools and districts that have adopted effective strategies for addressing key challenges in education. (March 2008)
Mathematics and Science
Nearly three out of five U.S. teens (59 percent) do not believe their high school is preparing them adequately for careers in technology or engineering, according to the 2008 Lemelson-MIT Invention Index, an annual survey that gauges Americans' attitudes toward invention and innovation. The good news is that 72 percent believe technological inventions or innovations can solve some of the world's most pressing problems, such as global warming and water pollution. Sixty-four percent of those surveyed are confident that they could invent the solutions. (Jan. 16)
Raising Student Achievement
Fifty-nine exemplary middle schools across the country have been
named "Schools to Watch" as part of a recognition program developed by the National Forum to Accelerate Middle-Grades Reform. Each school was selected by state leaders for its academic excellence, responsiveness to the needs and interests of young learners, and commitment to helping all students achieve to high levels. In addition, each school has made a commitment to assessment and accountability to bring about continuous improvement, teachers who work collaboratively, and strong leadership. (March 14)
A nonprofit organization has launched a national campaign called "Ready by 21" that will work to help youth become better prepared for college, work, and life. Run by the Forum for Youth Investment, the initiative is intended to help state and local leaders improve education and social services during the first two decades of children's lives. The initiative urges leaders to work together on interrelated problems such as drug use, teenage pregnancy, and school dropouts. (March 2008)
Legislation under consideration in Maryland and many other states is intended to ease the transition for students whose parents serve in the military. These students change schools an average of six to nine times between kindergarten and 12th grade. A proposed PDF (341 KB) multi-state compact supported by the Pentagon is intended to reduce the complications involved with these school transfers. (March 2008)
California students who fail to earn a high school diploma before they turn 20 years old cost the state $46.4 billion over the course of their lives. Each year, about 120,000 students in the state drop out. The high cost associated with these dropouts is related to greater rates of unemployment, crime, and dependence upon welfare and state-funded medical care, as well as lost tax-revenues, according to a report from the California Dropout Research Project. (February 2008)
Teacher Quality and Development
Attrition would be lessened if schools offered new teachers more support and guidance, according to an Alliance for Excellent Education PDF (93.9 KB) issue brief. The report found that teachers who graduated from very selective colleges, or who had high SAT scores, were more likely to leave the teaching profession before retirement or transfer to higher-performing schools. (February 2008)
Charter Schools A mayoral change in Indianapolis, the only city nationwide in which the mayor's office authorizes charter schools, has not changed support for that city's 17 charter schools. The new mayor, Greg Ballard, voiced strong support for the charter movement created by his predecessor, Bart Peterson, at a recent conference of charter school leaders. The charter schools, according to Mayor Ballard, are in no danger, and they offer an important choice for parents and a way to improve education in the city.
[More—Indianapolis Star] (Feb. 22)
The proposition that teacher quality is a more important variable than class size and other factors will be put to the test next school year, when the Equity Project, a new charter middle school in New York City, is slated to open. Its creator and first principal, Zeke Vanderhoek, plans to pay the school's expected teachers $125,000 annually, plus potential bonuses based on school-wide achievement. Because that is nearly twice as much as the average teacher in the city earns, the experiment will no doubt garner more than just local attention. For their high salaries, Equity Project teachers will work a longer day and year and will accept some duties that fall to administrators in other schools.
[More—The New York Times] (March 7) (free registration required)
Mathematics and Science Two members of the USA Today's 2007 All-USA Teacher Team find ways to inspire their high school students in economics and mathematics. An economics teacher at the California Academy of Math and Science, where many students are the children of Asian or Hispanic immigrants, taps into students' creativity. The teacher uses techniques such as student playwriting to illustrate economic principles to semester-long assignments in which students develop a proposed start-up company. In College Park, Ga., at Benjamin Banneker High School, 63 percent of students are eligible for free- or reduced-priced meals, and many students already have children of their own or wear ankle bracelets that allow law enforcement officials to monitor their movements. It is at this school that one teacher has inspired his students to learn advanced mathematics and use education as a tool to improve their lives. The school's pass rate on the state graduation exam has jumped from 85 percent to 95 percent between 2005 and 2006.
[More—USA Today] (Feb. 25) and [USA Today] (March 3)
In search of answers to the question of why students in Scandinavia scored high on the latest Program for International Student Assessment (PISA), a U.S. delegation led by the Consortium for School Networking (CoSN) toured Finland, Sweden, and Denmark, where educators cited "autonomy, project-based learning, and nationwide broadband Internet access as keys to their success."
[More—ESchool News] (March 3)
Achievement in mathematics and science, rather than more general barometers of education attainments, are critical to the international economic performance of the U.S., according to a new study by professors at Stanford and the University of Munich. Reported in the spring issue of Education Next, the research supports the conclusion that "if the U.S performed on par with the world's leaders in science and math, it would add about two-thirds of a percentage point to the gross domestic product."
[More— Wall Street Journal] (March 3)
Interest in an international robotics competition among Minneapolis schools and the community's technology sector has flourished over the past two years, from two student teams competing in 2006 to 54 teams this year. For Inspiration and Recognition of Science and Technology (FIRST) is a catalyst for both public and private investments in science and technology programs in high schools, not only in Minneapolis, but across the state of Minnesota. Driving the investment among such private-sector contributors as Medtronic, Boston Scientific, and the 3M Foundation is a desire to encourage future engineers. The Minnesota Department of Education has increased its funding for science, technology, engineering, and mathematics (STEM) initiatives statewide as well, providing more than $4 million to school districts between 2006 and 2008.
[More—Minneapolis Star-Tribune] (March 4)
Raising Student Achievement An analysis of recently released College Board data on Advanced Placement tests by Education Week found that while more students are taking the exams, the "percentage of exams that received [the passing score of at least] a three…has slipped from about 60 percent to 57 percent." College Board spokesperson Jennifer Topiel, while noting that test scores often decline with increases in the number of test takers, observed, "Students should not be placed into AP classes without better preparation." The analysis also revealed a widening gap over the past four years between black and white students earning at least a three on the exams.
[More—Education Week] (Feb. 14) (paid subscription required)
First-year results of a federally supported study of two reading interventions for struggling adolescent readers indicate increases in proficiency, but not enough to get students to grade level in a single year. Research firm MDRC conducted the study of the Reading Apprenticeship Academic Literacy and Xtreme Reading programs, with support from the U.S. Department of Education's Institute of Education Science. It is the first of three reports under the Enhanced Reading Opportunities Study. Researchers plan to follow the 9th grade students involved in the two interventions through 11th grade.
[More—Education Week] (Feb. 14) (paid subscription required)
A majority of American parents believe that their children have the "right amount" of homework, according to the findings of a poll commissioned by MetLife. Parents, teachers, and students were surveyed concerning time spent on homework as well as the perceived value of it. Clear majorities of both students (77 percent) and teachers (80 percent) said homework is important or very important. In addition, three quarters of the more than 2,000 K-12 students surveyed reported that they had adequate time to complete their assignments.
[More—Education Week] (Feb. 15) (paid subscription required)
More than 10,000 preschool-aged youngsters in Dallas are expected to benefit from a city-sponsored early reading preparation program that is modeled on Ready to Read. With support from an $8 million grant from the Wallace Foundation, the Dallas Public Library will manage the "Every Child Ready to Read @ Dallas" program, which will focus on parents, teachers, day-care providers, and others in the city who work with young children. In announcing the new program, Dallas Mayor Tom Leppert said, "Everything revolves around reading," and indicated the city's annual costs for the new program will be less than $600,000, with the Wallace Foundation grant helping for the next three years.
[More—The Dallas Morning News] (Feb. 22)
Researchers from the Centers for Disease Control and Prevention (CDC) believe that physical education may be linked to academic achievement. This belief is based on a national study of students' reading and mathematics test scores and the students' degree of involvement in physical education between kindergarten and fifth grade. According to the CDC researchers, the connection was most notable for girls receiving the highest levels of physical education (more than 70 minutes per week), who scored consistently higher on the tests than those who received less than 35 minutes a week in physical education. The study is available online in the Journal of American Public Health.
[More—USA Today] (March 5)
School Improvement Standards for school leaders, originally drafted in the mid-1990s and used or adapted by more than 40 states, have been revisited and revised by a panel of experts convened by the National Policy Board for Educational Administration and managed by the Council of Chief State School Officers. The revised Interstate School Leaders Licensure Consortium (ISLLC) standards, which guide the preparation, licensure and evaluation of principals and superintendents, were approved last December. The two-year revision process was supported by the Wallace Foundation, which made the investment, according to its director of education programs, because "there's a lot more known now from the research in terms of understanding what leaders do to impact teaching and learning…"
[More—Education Week] (Feb. 27) (paid subscription required)
A $5 million grant from the Michael & Susan Dell Foundation will enable Dallas educators to have instant access to students' academic records from preschool through high school graduation. The plans for an eventual mega-database of student academic information and other related data will begin with a planned "data warehouse" pilot phase next school year. The new system will provide a "one-stop shop" for local educators and help the Dallas Independent School District with its goal of spotting weaknesses in academic performance under its Dallas Achieves reform plan.
[More—The Dallas Morning News] (Feb. 27)
Houston will have its first public Montessori middle school thanks to the perseverance of the parents of Wilson Elementary, an elementary school currently based on the instructional approach pioneered by Maria Montessori more than a century ago. Parents raised more than $345,000 over five years to expand the current school to grades seven and eight. The 25 seats in the school's inaugural seventh grade will be open to students from several public and private Montessori elementary schools in the area.
[More—The Houston Chronicle] (Feb. 27)
Pay-for-performance initiatives continue to attract the attention of local and national press. The National Center on Performance Incentives released its study of the Texas Educator Excellence Grant program, the largest merit-pay plan in the nation. Texas education department officials were reportedly pleased with the first year's results and the study's findings. An examination of The Teacher Advancement Program (TAP), launched six years ago by the Milken Foundation and with 180 participating schools nationwide produced uneven results, with TAP elementary schools doing better than comparison schools in test-score gains, but those at the middle and high school levels lagging behind their non-TAP counterparts.
[More— The Dallas Morning News] (Feb. 29) [Education Week] (March 3) (paid subscription required)
For more than two decades, Project STAR, a study of class size in Tennessee, has informed thinking about the policy issue of class-size reduction. Now, a Northwestern University professor's review of the study's data is questioning whether there is evidence that reducing class size reduces achievement gaps between groups of students. According to the study's author, the longitudinal data provides weak or no evidence that lower-performing students benefited more than others from small classes.
[More—The Washington Post] (March 10) (free registration required) and [Education Week] (Feb. 21) (paid subscription required)
Teacher Quality and Development Can a single set of standards for accrediting teacher-education institutions be developed? This is the question that a new task force of the American Association of Colleges of Teacher Education (AACTE) will seek to answer this spring. Task force members include representatives of the two national accrediting entities – the longstanding National Council for Accreditation of Teacher Education (NCATE) and the relatively new Teacher Education Accreditation Council (TEAC). While the two entities take very different approaches to granting their seals of approval, AACTE's board of directors is hopeful that the task force can agree on a single set of standards.
[More—Education Week] (Feb. 21) (paid subscription required)
The burgeoning field of online learning has launched its first voluntary national standards that will help policymakers and practitioners judge the credibility and worthiness of virtual teaching and online course work. Released last month by the North American Council for Online Learning, the standards address such topics as teacher prerequisites and licensure, technology skills, and subject matter proficiency, as well as instructional issues like online interaction, intellectual property rights, and learning assessments and program evaluations.
[More—Education Week (Feb. 29) (paid subscription required)
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Thompsons Calculus?re the starter, the playbook is in your hands, you...
...During the last century comprehension lesson/s usually comprised students answering teachers' questions, writing responses to questions on their own, or both. There is not a definitive set of strategies, but common ones include summarizing what you have read, monitoring your reading to make sure... design of parts and assemblies.
...My I...
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If you enjoy Maths and feel confident with the work you have met so far at GCSE, then you should seriously consider Maths AS or A Level. It is a demanding and challenging subject but it can be an extremely rewarding one if you are prepared ...
Wakefield City Campus
GCSE Maths is required by Higher Education establishments and many employers. If you struggled with Maths at school, this course will develop your number skills and help you to gain that vital qualification.
...
Castleford Campus
Wakefield City Campus
Did you just miss the UMS score required to give you that all-important Grade C in Maths? Don't despair - this intensive revision course will help you to pass with flying colours in the November re-sits.
By the end of your course, you will be able to work with complex functions and understand how to calculate forces in mechanics. You will cover topics such as geometry, calculus, trigonometry and algebra and gain the ability to manipulate fi...
A LEVEL MATHEMATICS WITH STATISTICS
Level: AS and A2 (Full)
This A level course builds on work covered in GCSE Maths at Higher Level, so you need to be familiar with all the mathematics at this level, and your skills should beAn essential subject for all students, IGCSE Mathematics is a fully examined course which encourages the development of mathematical knowledge as a key life skill, and as a basis for more advanced study. The syllabus aims to build students'...
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Does somebody here know anything about ti calculator function inverse matrix program? I'm a little lost and I don't know how to finish my algebra project about this topic. I tried reading all tutorials about it that could help me answer my math problems but I still don't get. I'm having a hard time answering it especially the topics radicals, factoring and converting decimals. It will take me days to answer my algebra homework if I can't get any assistance. It would really help me if someone can suggest anything that can help me with my algebra homework.
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Murderous Maths107135","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.49,"ASIN":"140710716X","isPreorder":0},{"priceBreaksMAP":null,"buyingPrice":4.49,"ASIN":"1407107119","isPreorder":0}],"shippingId":"1407107135::zm7ZSp%2BN5mXjWCwVllYdRAq868rDr25AwN6B7lOunjIfsl%2Ftiuzg3Sd%2Bwno9ceKqbEUgwh1kc5%2FeJ0ezZ9458lNDLTEcrhj5,140710716X::ds2RIYYZsCVOvnf8PzVw6V1J60JuhC82m8O%2Bg6va4xtVVIYGdAdqsYkUfMuEcQFqhykQR2Z9B8iahV9zCnHekKvU8rZQjkUb,1407107119::PbV1n0AVsNs9%2Bl8%2FnI%2BdqsWNRnm%2FyQUOg%2FwiQ%2BntDDvH9PQViqGCFQE10of0%2Bk68TFU%2BAUbHP9dXPbEdEclFiZexe4OkgRC The secret weapon 2. What is algebra? 3. The Slaught-o-Mart equations 4. The father of algebra 5. Packing, unpacking and the panic button 6. The mechanics of magic 7. The Murderous Maths testing laboratory 8. The bank clock 9. Axes, plots and the flight of the loveburger 10. Double trouble 11. The zero proof
written in a variety of fonts in the usual Kjartan Poskitt entertaining style, e.g.:-
'You haven't seen me before and, after this book, I hope for your sake we never meet again, because I'm dangerous to be seen with. In fact, just to be safe, before you read on check there's no one looking over your shoulder. All clear? Right then, here's the situation. Maths is one long fierce battle in which we're all being attacked by an army of different problems. Luckily, most of them are little sums that you can solve in your head. Then for the really tough sums, you can bang the numbers into a calculator and read off the answer. But sometimes you have to do sums and you aren't told what the numbers are! How can you put a number into a calculator when you don't know what it is? What do you do when you're facing the UNKNOWN? It's usually a job for ...... the Phantom X..........'
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Wouldn't it be great if there were a statistics book that made histograms, probability distributions, and chi square analysis more enjoyable than going to the dentist? Head First Statistics brings this typically dry subject to life, teaching you everything you want and need to know about statistics through engaging, interactive, and thought-provoking material, full of puzzles, stories, quizzes, visual aids, and real-world examples.
Whether you're a student, a professional, or just curious about statistical analysis, Head First's brain-friendly formula helps you get a firm grasp of statistics so you can understand key points and actually use them. Learn to present data visually with charts and plots; discover the difference between taking the average with mean, median, and mode, and why it's important; learn how to calculate probability and expectation; and much more.
polynomials.
Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive it off the lot? Can you really afford an XBox 360 and a new iPhone? Learn how to put algebra to work for you, and nail your class exams along the way.
Wouldn't it be great if there were a physics book that showed you how things work instead of telling you how? Finally, with Head First Physics, there is. This comprehensive book takes the stress out of learning mechanics and practical — aThis completely revised Fourth Edition of the book, appropriate for all engineering under-graduate students, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications. The book focuses clearly on teaching students numerical methods and in helping them to develop problem-solving skills.
A distinguishing feature of the present edition is that it provides references to MATLAB, IMSL and Numerical Recipes program libraries for implementing the numerical methods described in the book. Several exercises are included to illustrate the use of these libraries.
Additional worked examples and exercises have been added for better appreciation and understanding of the material. Answers to some selected exercises have been provided.
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Error Patterns in Comput your students learn about mathematical operations and methods of computation, they may adopt erroneous procedures and misconceptions, despite your best efforts. This engaging book was written to model how you, the teacher, can make thoughtful analyses of your student's work, and in doing so, discover patterns in the errors they make. The text considers reasons why students may have learned erroneous procedures and presents strategies for helping those students. You will come away from the reading with a clear vision of how you can use student error patterns to gain more specific knowledge of their strengths on which to base your future instruction. Book jacket.
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Algebra I is a class that introduces the mathematical branch of Algebra. Working with Real Numbers, Solving Equations and Problems, Polynomials, Factoring Polynomials, Fractions and their applicational use, Introduction to Functions, Systems of Linear Equations, and Inequalities are among the first topics learned about in this class.
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Short description
Presents MATLAB both as a mathematical tool and a programming language, giving an introduction to its potential and power. This book illustrates the fundamentals of MATLAB with many examples from a wide range of familiar scientific and engineering areas. It includes coverage of Symbolic Math and SIMULINK. It highlights common errors and pitfalls.
Long description
This is the essential guide to MATLAB as a problem solving tool. This text presents MATLAB both as a mathematical tool and a programming language, giving a concise and easy to master introduction to its potential and power. The fundamentals of MATLAB are illustrated throughout with many examples from a wide range of familiar scientific and engineering areas, as well as from everyday life. The new edition has been updated to include coverage of Symbolic Math and SIMULINK. It also adds new examples and applications, and uses the most recent release of Matlab. Features of this title include: new chapters on Symbolic Math and SIMULINK provide complete coverage of all the functions available in the student edition of Matlab; more exercises and examples, including new examples of beam bending, flow over an airfoil, and other physics-based problems; a bibliography that provides sources for the engineering problems and examples discussed in the text; and, a chapter on algorithm development and program design. In this book, common errors and pitfalls are highlighted. It provides extensive teacher support on: solutions manual, extra problems, multiple choice questions, PowerPoint slides. It features companion website for students providing M-files used within the book.
Product details
Publisher:
Academic Press
ISBN:
9780123748836
Publication date:
October 2009
Length:
236mm
Width:
191mm
Thickness:
20mm
Weight:
821g
Edition:
4th edition
Pages:
391
Illustrated:
True
Review
This book provides an excellent initiation into programming in MATLAB while serving as a teaser for more advanced topics. It provides a structured entry into MATLAB programming through well designed exercises. - Carl H. Sondergeld, Professor and Curtis Mewbourne Chair, Mewbourne School of Petroleum and Geological Engineering, University of Oklahoma This updated version continues to provide beginners with the essentials of Matlab, with many examples from science and engineering, written in an informal and accessible style. The new chapter on algorithm development and program design provides an excellent introduction to a structured approach to problem solving and the use of MATLAB as a programming language. - Professor Gary Ford, Department of Electrical and Computer Engineering, University of California, Davis For a while I have been searching for a good MATLAB text for a graduate course on methods in environmental sciences. I finally settled on Hahn and Valentine because it provides the balance I need regarding ease of use and relevance of material and examples. - Professor Wayne M. Getz, Department Environmental Science Policy & Management, University of California at Berkeley This book is an outstanding introductory text for teaching mathematics, engineering, and science students how MATLAB can be used to solve mathematical problems. Its intuitive and well-chosen examples nicely bridge the gap between prototypical mathematical models and how MATLAB can be used to evaluate these models. The author does a superior job of examining and explaining the MATLAB code used to solve the problems presented. - Professor Mark E. Cawood, Department of Mathematical Sciences, Clemson University This has proved an excellent book for engineering undergraduate students to support their first studies in Matlab. Most of the basics are covered well, and it includes a useful introduction to the development of a Graphical User Interface. - Mr. K
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,... read moreVector Geometry by Gilbert de B. Robinson Concise undergraduate-level text by a prominent mathematician explores the relationship between algebra and geometry. An elementary course in plane geometry is the sole requirement. Includes answers to exercises. 1962Projective Geometry by T. Ewan Faulkner Highlighted by numerous examples, this book explores methods of the projective geometry of the plane. Examines the conic, the general equation of the 2nd degree, and the relationship between Euclidean and projective geometry. 1960Product Description:
, much more. Includes over 500 exercises.
Reprint of A Course for Geometry for Colleges and Universities, Cambridge University Press, Cambridge, England, 1970
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Intermediate 2 Maths Course Notes - Leckie (Paperback)
Specifically designed to support Intermediate 2 students, this text is divided into three units for a succinct approach to topics assessed in Units 1, 2 and 3 of the exam. New formulae and problem-solving methods are explained step-by-step to reinforce knowledge and understanding and enable students to review what they have learned in class. All topics are accompanied by questions with worked examples to allow students to assess their learning and to target areas of weakness for exam success. In addition, the comprehensive topic index supports quick and easy reference in the approach to exams. (Applications of Maths is not covered by this title.)
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In Practise
mode, the students solve questions by performing their own calculations. If
they don't know what to do, they can request a companion to make a
suggestion or a calculation step. Aplusix automatically verifies the students'
calculations and the completion of questions.
In Test
mode,
students work for 30 minutes without any feedback. At the end of
the test, they get a score and can enter Self-correcting mode.
In Self-correction
mode, students review their own work.
Correct and incorrect calculations are clearly marked and they can see whether they have completed
the question or not. They can correct their calculations with the same level of feedback
as in Practise mode, including the use of companions.
In Review mode, students review their work. Correct and incorrect calculations are
clearly marked and they can see whether they have completed the question or not.
A replay system is also available to them.
Many exercises, covering most aspects of the Number and Algebra strands of the UK National Curriculum
and a lot of the algebraic content of Foundation and Higher GCSE, allow to practise, understand,
and become efficient: numerical calculations, expansions and simplifications, factorising,
solving equations and inequalities, simultaneous equations.
In addition to the provided exercises, it is possible to do homework and to practise with exercises
given by the teacher (e.g. from textbooks or worksheets).
Scientific
experiments led in several countries, under the control of
mathematical education researchers, have shown that with Aplusix
students work more, become
self-confident and independent,
and improve their skills.
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Systems of Equations Unit PlanThis 92 page unit plan includes 11 days of lessons on Solving Linear Systems by graphing, substitution, and elimination with multiplication. Also included are special types of linear systems. Each daily plan includes a warm up and the notes / worksheets / activities for the day. There is a quiz and a final assessment. Answer keys for everything are included!
Don't need a full unit plan? Purchase just the resources instead!
Compressed Zip File
Be sure that you have an application to open this file type before downloading and/or purchasing.
2313.99 KB | 92
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Eric Robinson
Above all else, mathematics is a way of thinking. Eric Robinson, the director of COMPASS*--an NSF-sponsored program to implement new secondary mathematics curricula-- talks about the real-world advantages that students gain by learning to think with math concepts.
Why was COMPASS established?
In our efforts to improve the mathematics experience for pre-college students, there has been a realization that change needed to occur in all areas of the classroom: the way math was taught, what math was taught, what students were expected to be doing, what students were expected to get out of their mathematical experience, and how students were assessed.
So, our purpose is to provide support and advice to schools and districts as they implement mathematics education reform, and particularly to help them consider and implement mathematics curricula that reflect this new approach to mathematics education. COMPASS focuses on five high school, multi-year curricula that were developed with funds from the National Science Foundation and which support the vision of school mathematics set forth by the National Council of Teachers of Mathematics.
In what ways have the goals of mathematics education changed?
For one thing, we live in a new age. A strong understanding of mathematics that goes beyond computation is not just for future college math majors in today's world. It is important for all school students. Society is much more dependent on mathematics. Math affects almost every career--sometimes subtly and sometimes very apparently.
Let's look back a bit at the Industrial Age. If you worked on an assembly line, you were given a certain process and you just did the process over and over again. The world is not like that anymore. What we need, in the business world as well as in the professional world of mathematicians, scientists and engineers, is people who able to deal with open-ended situations, problems that are non-routine, and problems that aren't very well formulated. People have to be creative about their solutions, and draw on a variety of different sources to solve problems.
The mathematics curriculum needs to train students to do those things. It's not good enough to be able to solve just template problems. It's creative stuff. It's in a world that is changing almost every 24 hours in terms of what tools we have to work with and, what information and how quickly we get that information.
Maybe we should clarify what is meant by the term "mathematics"?
Well, there are several ways to talk about what mathematics is.
Certainly, it is a collection of facts. For example, all isosceles triangles have equal base angles.
It also contains a collection of operations, algorithms and procedures where, if you follow a certain sequence of computational steps, you get a guaranteed answer.
But to me, as a mathematician, far more important than any of those is that mathematics is a way of thinking. It's a method of inquiry.
More than once I've heard students say "I don't understand what they want me to do, but tell me what to do and I'll do it." They might have had the ability to do the procedures or memorize the facts, but they didn't have the ability to see where their facts were important, when to do the procedures or what the procedures meant.
To me, that's the antithesis of mathematics. The whole idea of doing mathematics is figuring out how to approach a problem. And then, of course, you have to have the ability to do some procedures. We do have to know how to do the computations---sometimes facilitated by the use of technology. But being able to do computations alone doesn't mean we know mathematics.
Doing mathematics includes lots of things. It can include looking at specific examples, trying to find patterns or making comparisons to situations that we already understand. It includes making conjectures. It includes figuring out how simpler situations work and seeing if we can then generalize to more complicated situations. It includes being able to abstract mathematical properties out of real situations. And it includes being able to reason logically.
Real mathematics requires all of these things. It requires mucking along, as well as knowing immediately what to do in some cases. But I know with too many students there's been a tendency to look at a problem and then, if there isn't an understanding of what to do immediately, they skip the problem and ask the teacher the next day. We're not helping kids build in a sense of persistence or build in a sense of exploration that they're going to need to have to solve problems in the real world.
Is there other evidence that indicated a need for change?
Other evidence includes the Second International Mathematics and Science Study and the Third International Mathematics and Science Study. Both of them showed clearly that, internationally, we weren't competing well.
There was also the problem that students were leaving the study of mathematics in droves. As soon as students reached a level where mathematics was no longer required, half of them would quit. Then, the next year, half of the ones who were left would quit. And so on.
That trend of course is exactly contrary to increased need for mathematical ability in society. We were funneling everybody into mathematics courses at the beginning of school and getting a very, very small residue of those who would pursue it beyond high school.
For a whole variety of reasons we had to do better. Some of these reasons I have already mentioned. Others include the need to update the mathematical content of our courses and incorporate the use of new technology that allows us to examine mathematical concepts on a deeper level as well as utilize mathematical tools that remain primarily theoretical without the use of technological computational power. And so early in the 1990's the National Science Foundation put out a call for proposals to update the mathematics curriculum, incorporating not only a more complete approach to learning mathematics, but also based on the knowledge we had gained about how students learn and effective ways to teach.
And the result was?
The result was the development of new comprehensive curriculum materials at elementary, secondary and high school levels.
At the time, at the high school level, by and large across the country schools were committed to an algebra, geometry, advanced algebra, pre-calculus sequence. But when you look at how math is used in the real world, very often real world problems come without the content nicely separated like that.
A problem often can involve algebra and geometry and maybe some probability.
So, with the NSF support, out came high school level programs of three-year length or four-year length in which algebra, geometry and so on were intermixed.
These programs focus on mathematics as a process of reasoning, of thinking. They develop concepts so that there's an understanding of why, rather than simply being able to compute. Students develop a deeper mathematical understanding. And also they develop a deeper way to apply mathematics, such in as multi-step problems. These programs require students to synthesize ideas. And they require students to use math concepts and skills in places other than at the end of the chapter in which they're discussed.
What else was different about these materials?
For a long time mathematics educators adopted what I might loosely call the Euclidean approach. If you go back to Euclid's Elements, which was produced about 300 BC, the organization of the information was first, a statement, and then, a rationalization for it. So you had the answer first. Then, you got an understanding of why it worked.
Math education up through the early '80s was very much in the same spirit. Present some mathematical concepts, maybe some definitions, present the justification for those, present certain formulas and then the explanation of those formulas, do some examples of problems, and then practice with problems that were similar to the problems done in the text.
While this way may be an efficient way to present known results, it is not the best way to engage students in mathematical thinking. What we've learned is that it's more effective if you don't present quite so much to the student up front. Now, we try to present the questions before we give the answers so you get the kids' attention and interest. You get them hooked on pursuing understanding. And then you let them figure out how to get an answer. And when the students come up with the approach, they not only have a much better understanding, they retain their understanding better, too.
Retention, by the way, has long been a major problem in US math education. That's why a lot of topics in the US repeated year after year after year, because there was no retention of what was done. Now we have found that we can really improve retention, by putting the development of mathematics in a context that has some meaning for students. Very often, that takes the form of a real world situation. Real world context can be a wonderful way to provide meaning and mental "glue" for mathematical ideas and concepts.
What about the idea that some students will not be as good at developing inquiry skills, and will fall behind?
Well, it's true that some students will go further than others. But what we've seen is that every student can improve his ability to do mathematics and learn mathematics with this approach. Whereas with earlier approaches, students who did not grasp every new definition or procedure as it was presented to them would not be able to keep up at all with subsequent material.
If the curriculum is engaging, students will come along and will use each problem as an opportunity to exercise their ability to think. Their study of mathematics becomes a process of learning what they can do, not what they can't do.
What's supposed to happen as a result of having these new curricula?
Well, I think, personally, it would be wonderful if these five new curricula were adopted in every school across the country. But that is not just a simple matter of changing textbooks. It often requires a lengthy process, because it involves having teachers and other stakeholders really look at their beliefs and assumptions about what kind of mathematical education they want their high school students to get. It requires significant understanding by all concerned of the aspects and ramifications of such change. And it requires district administrative support for professional development of teachers who want to improve the educational experiences of their students in mathematics. Systemic change is not easy.
Of course these five programs are not the only answer--but they represent five different models that demonstrate an approach math education in the way we've been talking about
Some schools are going to transition in slower ways and will more gradually change their curriculum. But generally I do think we are seeing a continuous motion in the direction suggested by the NCTM standards and successful programs in other countries.
Anything else you'd like to say?
Just that I am very encouraged when I look at all the activities at improving mathematics education—including the valuable resource and promise of the Futures Channel. Because, to my mind, we are getting to the root of what mathematics is. In the world that our children are growing up into, we do need clear thinkers, we do need critical thinkers, we do need creative thinkers. And what better place than to develop those skills than in a mathematics classroom?
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To meet the demands of the world in which they will live, students
will need to adapt to changing conditions and to learn independently.
They will require the ability to use technology effectively and
the skills for processing large amounts of quantitative information.
TCT's mathematics curriculum prepares students for their tomorrows.
It equips them with essential mathematics knowledge and skills;
with skills of reasoning, problem solving, and communication; and,
most importantly, with the ability and the incentive to continue
learning on their own.
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Letter to Parents
Math Lab
by Rob Schultz
The purpose of Math Lab is to assist students in strengthening math skills necessary for success in assigned math classes. Various tools, projects, and in-class assignments will be used to support student understanding of math concepts. We will also discuss numerous strategies that students can use in the classroom for taking notes, taking tests, etc.
Algebra 2
by Rob Schultz
Algebra 2 is designed to build on concepts learned in Algebra 1 while continuing to develop mathematical and problem solving skills. Throughout the course, we will explore functions (linear, quadratic, exponential and logarithmic), graphing (with and without a graphing calculator), matrices, and systems of equations.
Scholarship PreCalculus
by Rob Schultz
Scholarship PreCalculus is designed to build on concepts learned in Algebra II while continuing to develop mathematical and problem solving skills. In addition to the function families introduced in Algebra 2, students will explore advanced function families including trigonometric, parametric, and polar functions, as well as conic sections. Basic calculus concepts will be introduced at the end of the year as time permits.
Intro Computer Science
by Rob Schultz
The Intro Computer Science course is designed to serve as a prerequiste to the AP Computer Science course. Students will explore basic programming techniques and object-oriented programming using Alice and the Java programming language.
AP Computer Science
by Rob Schultz
The AP Computer Science course is designed to be comparable to a college/university level, entry year computer science class using the JAVA programming language. Completion of Intro Computer Science or a comparable course is REQUIRED for enrollment in this course!
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Book Description: Following conveniently displayed in the back. This book is for parents of schooled students, homeschooling parents and teachers. Parents of schooled children find that the problems give their children a "leg up" for mastering all skills presented in the classroom. Homeschoolers use the Workbook - in conjunction with the Guide - as a complete Algebra 1 curriculum. Teachers use the workbook's problem sets to help children sharpen specific skills - or they can use the reproducible pages as tests or quizzes on specific topics. Like the Algebra Survival Guide, the Workbook is adorned with beautiful art and sports a stylish, teen-friendly design
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Framework Maths: Year 9: Support Homework Book
Suitable for: Year 9 students following the Framework for Teaching Mathematics in England. Users of Framework Maths.
Homework for every lesson in a handy book
This homework book is written to complement the Support objectives in Year 9, and is especially useful for students using Framework Maths 9S. The convenient format means students do not need to take home the Students' book. The book is exceptional value for money at only £3.99 for 144 pages.
Features
Homework for every lesson with a focus on problem-solving activities
Worked examples where appropriate so that the book is self-contained
Past paper SAT questions at the end of each unit, levelled so you can check students'
progress
Great value for money
"Framework Maths was voted number 1 in a TES survey of top KS3 titles
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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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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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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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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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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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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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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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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.
Regularly:
£33.00 excl Vat
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Use the form below to email a friend about this product.
All required fields are marked with a star (*). Click the 'Submit' button at the bottom of this form to proceed.
| 677.169 | 1 |
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.
1st Edition. Used - Good. Used books do not include online codes or other supplements unless noted. Choose EXPEDITED shipping for faster delivery! h
$57.19 +$3.99 s/h
Good
Extremely_Reliable Richmond, TX
Buy with confidence. Excellent Customer Service & Return policy.
$69.49
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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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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?
| 677.169 | 1 |
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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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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In continuation with the topics studied in Algebra I, it will develop the real number system and will include a study of the complex numbers as a mathematical system. Students will study the ideas of relations and functions and expand the concept of functions to include quadratic, square root, exponential and logarithmic functions, and rational numbers. Emphasis will also be placed on the analysis of conic concepts with labs and the development of additional real life problem solving skills and applications. Emphasis will be placed on the application of concepts and skills introduced in Algebra II. The level of instruction/curriculum will focus on preparing the student for further advanced placement courses.
I will be available for tutoring Tuesdays and Thursdays after school from 3:00 to 4:00.Any changes to tutoring will be announced in class and on the class website.If the posted tutorial times do not work in your schedule be sure to discuss alternatives with me as soon as possible.Other math teachers are also available at other times which are posted in the math hallway.
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This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives.
Common-sense applications of mathematics engage students while underscoring the practical, essential uses of math..
For more information about the title Using and Understanding Mathematics: A Quantitative Reasoning Approach (4th
| 677.169 | 1 |
This course is an in-depth study of functions and a review of algebraic, geometric, and trigonometric principles and techniques. Students investigate and explore the characteristics of linear, polynomial, and trigonometric functions, and use graphing calculators to solve and evaluate various functions, equations, and inequalities.
| 677.169 | 1 |
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Math Workshop
The PPC (Pre-pre-calculus) program is the component of the Math Workshop which reviews your high school algebra in order to bring you up to the level needed for your required or desired M and Q classes.
1. Always read math problems completely before beginning any calculations. If you "glance" too quickly at a problem, you may misunderstand what really needs to be done to complete the problem.
2. Whenever possible, draw a diagram. Even though you may be able to visualize the situation mentally, a hand drawn diagram will allow you to label the picture, to add auxiliary lines, and to view the situation from different perspectives.
The mission of the Wittenberg University Math Workshop is to provide support for students in mastering the mathematical tools and concepts necessary for them to attain the general education learning goal for mathematics as well as the mathematical requirements of their individual educational programs. The workshop strives to teach students to value math, to become confident in their ability to do math, to become mathematical problem solvers, and to learn to communicate and reason mathematically.
The workshop carries out its mission through the following activities:
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Intended for all students in their freshman year of college (with sufficient knowledge in high-school mathematics), this book is organized around eight fundamental mathematical processes: conjecture, logical argumentation, formal demonstration, algorithmic thinking, correspondence, enumeration, limiting processes, and approximation. Topically, the book cuts across several traditional branches of mathematics, including algebra, trigonometry, number theory, and analysis. Both formal demonstrations and problem solving with extensive applications to the physical sciences are stressed throughout. Use of the microcomputer as a working tool is also emphasized throughout the book.
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Appendices
We will now be more careful about analyzing the reduced row-echelon form derived from the augmented matrix of a system of linear equations. In particular, we will see how to systematically handle the situation when we have infinitely many solutions to a system, and we will prove that every system of linear equations has either zero, one or infinitely many solutions. With these tools, we will be able to solve any system by a well-described method.
Consistent Systems
The computer scientist Donald Knuth said, "Science is what we understand well enough to explain to a computer. Art is everything else." In this section we'll remove solving systems of equations from the realm of art, and into the realm of science. We begin with a definition.
Definition CS (Consistent System)
A system of linear equations is consistent if it has at least one solution. Otherwise, the system is called inconsistent.
We will want to first recognize when a system is inconsistent or consistent, and in the case of consistent systems we will be able to further refine the types of solutions possible. We will do this by analyzing the reduced row-echelon form of a matrix, using the value of $r$, and the sets of column indices, $D$ and $F$, first defined back in Definition RREF.
Use of the notation for the elements of $D$ and $F$ can be a bit confusing, since we have subscripted variables that are in turn equal to integers used to index the matrix. However, many questions about matrices and systems of equations can be answered once we know $r$, $D$ and $F$. The choice of the letters $D$ and $F$ refer to our upcoming definition of dependent and free variables (Definition IDV). An example will help us begin to get comfortable with this aspect of reduced row-echelon form.
The number $r$ is the single most important piece of information we can get from the reduced row-echelon form of a matrix. It is defined as the number of nonzero rows, but since each nonzero row has a leading 1, it is also the number of leading 1's present. For each leading 1, we have a pivot column, so $r$ is also the number of pivot columns. Repeating ourselves, $r$ is the number of nonzero rows, the number of leading 1's and the number of pivot columns. Across different situations, each of these interpretations of the meaning of $r$ will be useful.
Before proving some theorems about the possibilities for solution sets to systems of equations, let's analyze one particular system with an infinite solution set very carefully as an example. We'll use this technique frequently, and shortly we'll refine it slightly.
Archetypes I and J are both fairly large for doing computations by hand (though not impossibly large). Their properties are very similar, so we will frequently analyze the situation in Archetype I, and leave you the joy of analyzing Archetype J yourself. So work through Archetype I with the text, by hand and/or with a computer, and then tackle Archetype J yourself (and check your results with those listed). Notice too that the archetypes describing systems of equations each lists the values of $r$, $D$ and $F$. Here we go...
Using the reduced row-echelon form of the augmented matrix of a system of equations to determine the nature of the solution set of the system is a very key idea. So let's look at one more example like the last one. But first a definition, and then the example. We mix our metaphors a bit when we call variables free versus dependent. Maybe we should call dependent variables "enslaved"?
Definition IDV (Independent and Dependent Variables)
Suppose $A$ is the augmented matrix of a consistent system of linear equations and $B$ is a row-equivalent matrix in reduced row-echelon form. Suppose $j$ is the index of a column of $B$ that contains the leading 1 for some row (i.e. column $j$ is a pivot column). Then the variable $x_j$ is dependent. A variable that is not dependent is called independent or free.
If you studied this definition carefully, you might wonder what to do if the system has $n$ variables and column $n+1$ is a pivot column? We will see shortly, by Theorem RCLS, that this never happens for a consistent system.
Sets are an important part of algebra, and we've seen a few already. Being comfortable with sets is important for understanding and writing proofs. If you haven't already, pay a visit now to Section SET:Sets.
We can now use the values of $m$, $n$, $r$, and the independent and dependent variables to categorize the solution sets for linear systems through a sequence of theorems.
First we have an important theorem that explores the distinction between consistent and inconsistent linear systems.
Theorem RCLS (Recognizing Consistency of a Linear System)
Suppose $A$ is the augmented matrix of a system of linear equations with $n$ variables. Suppose also that $B$ is a row-equivalent matrix in reduced row-echelon form with $r$ nonzero rows. Then the system of equations is inconsistent if and only if the leading 1 of row $r$ is located in column $n+1$ of $B$.
The beauty of this theorem being an equivalence is that we can unequivocally test to see if a system is consistent or inconsistent by looking at just a single entry of the reduced row-echelon form matrix. We could program a computer to do it!
Notice that for a consistent system the row-reduced augmented matrix has $n+1\in F$, so the largest element of $F$ does not refer to a variable. Also, for an inconsistent system, $n+1\in D$, and it then does not make much sense to discuss whether or not variables are free or dependent since there is no solution. Take a look back at Definition IDV and see why we did not need to consider the possibility of referencing $x_{n+1}$ as a dependent variable.
With the characterization of Theorem RCLS, we can explore the relationships between $r$ and $n$ in light of the consistency of a system of equations. First, a situation where we can quickly conclude the inconsistency of a system.
Theorem ISRN (Inconsistent Systems, $r$ and $n$)
Suppose $A$ is the augmented matrix of a system of linear equations in $n$ variables. Suppose also that $B$ is a row-equivalent matrix in reduced row-echelon form with $r$ rows that are not completely zeros. If $r=n+1$, then the system of equations is inconsistent.
Next, if a system is consistent, we can distinguish between a unique solution and infinitely many solutions, and furthermore, we recognize that these are the only two possibilities.
Theorem CSRN (Consistent Systems, $r$ and $n$ zero rows. Then $r\leq n$. If $r=n$, then the system has a unique solution, and if $r < n$, then the system has infinitely many solutions.
Free Variables
The next theorem simply states a conclusion from the final paragraph of the previous proof, allowing us to state explicitly the number of free variables for a consistent system.
Theorem FVCS (Free Variables for Consistent Systems completely zeros. Then the solution set can be described with $n-r$ free variables.
We have accomplished a lot so far, but our main goal has been the following theorem, which is now very simple to prove. The proof is so simple that we ought to call it a corollary, but the result is important enough that it deserves to be called a theorem. (See technique LC.) Notice that this theorem was presaged first by Example TTS and further foreshadowed by other examples.
Theorem PSSLS (Possible Solution Sets for Linear Systems)
A system of linear equations has no solutions, a unique solution or infinitely many solutions.
Here is a diagram that consolidates several of our theorems from this section, and which is of practical use when you analyze systems of equations.
Decision Tree for Solving Linear Systems
We have one more theorem to round out our set of tools for determining solution sets to systems of linear equations.
Theorem CMVEI (Consistent, More Variables than Equations, Infinite solutions)
Suppose a consistent system of linear equations has $m$ equations in $n$ variables. If $n>m$, then the system has infinitely many solutions.
Notice that to use this theorem we need only know that the system is consistent, together with the values of $m$ and $n$. We do not necessarily have to compute a row-equivalent reduced row-echelon form matrix, even though we discussed such a matrix in the proof. This is the substance of the following example.
These theorems give us the procedures and implications that allow us to completely solve any system of linear equations. The main computational tool is using row operations to convert an augmented matrix into reduced row-echelon form. Here's a broad outline of how we would instruct a computer to solve a system of linear equations.
Represent a system of linear equations by an augmented matrix (an array is the appropriate data structure in most computer languages).
Convert the matrix to a row-equivalent matrix in reduced row-echelon form using the procedure from the proof of Theorem REMEF.
Determine $r$ and locate the leading 1 of row $r$. If it is in column $n+1$, output the statement that the system is inconsistent and halt.
With the leading 1 of row $r$ not in column $n+1$, there are two possibilities:
$r=n$ and the solution is unique. It can be read off directly from the entries in rows 1 through $n$ of column $n+1$.
$r < n$ and there are infinitely many solutions. If only a single solution is needed, set all the free variables to zero and read off the dependent variable values from column $n+1$, as in the second half of the proof of Theorem RCLS. If the entire solution set is required, figure out some nice compact way to describe it, since your finite computer is not big enough to hold all the solutions (we'll have such a way soon).
The above makes it all sound a bit simpler than it really is. In practice, row operations employ division (usually to get a leading entry of a row to convert to a leading 1) and that will introduce round-off errors. Entries that should be zero sometimes end up being very, very small nonzero entries, or small entries lead to overflow errors when used as divisors. A variety of strategies can be employed to minimize these sorts of errors, and this is one of the main topics in the important subject known as numerical linear algebra.
In this section we've gained a foolproof procedure for solving any system of linear equations, no matter how many equations or variables. We also have a handful of theorems that allow us to determine partial information about a solution set without actually constructing the whole set itself. Donald Knuth would be proud.
| 677.169 | 1 |
Pages
Maths
Mr Robb's Math Videos is a YouTube channel containing 555 videos produced by high school mathematics teacher Bradley Robb. Mr. Robb's videos explain and demonstrate solving problems in Algebra I, Algebra II, and Calculus. Most of the videos are recorded while Mr. Robb is teaching
| 677.169 | 1 |
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