 EZ Learning Solutions
EZ Learning Solutions Study Guides are part of a family of study aids designed with a "backtobasics" approach in mind. They are intended for use by students, parents, or teachers, and should be especially useful for the new math curriculum in Ontario.
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 Fred Rickey's History of Mathematics Page  Fred Rickey, Department of Mathematical Sciences, United States Military Academy
Information about courses Rickey and others have taught about the history of mathematics. Historical notes for calculus teachers cover Torricelli's trumpet,
Clepsydra, the history of the brachistochrone, the bridge and the catenary, Cauchy's famous wrong
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 Free Mathematics Books  FreeTechBooks.com
Links to free mathematics books and lecture notes. Mostly in PDF and Postscript format.
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 Game Theory .net  Mike Shor
Lecture notes, text book reviews, and interactive applets and games, print and online tests and quizzes, a section on game theory in pop culture, and links to other resources on the web.
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 A Gentle Introduction to Category Theory  the calculational approach  Maarten M. Fokkinga; Dept. of Computer Science, University of Twente, The Netherlands
Lecture notes introducing some important notions from category theory, in particular adjunctions. Proofs are given in a calculational style, and the (few) examples are taken from algorithmics. Download the full text in postscript format.
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 GoodQuestions Project  Dept. of Mathematics, Cornell University
The GoodQuestions project seeks to improve college calculus instruction by adapting two methods developed in physics instruction — ConcepTests and JustinTimeTeaching. GoodQuestions is a pedagogical strategy that aims to raise the visibility of the
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 Graphics for Complex Analysis  Douglas N. Arnold; Institute for Mathematics and its Applications
A collection of graphical demonstrations of concepts in complex analysis developed for a course at McAllister. Most are animated so that the original curves are continuously deformed into the image curves, and the eye can follow which points move where;
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 Graphics for Complex Analysis (Java version)  Douglas N. Arnold; Institute for Mathematics and its Applications
A collection of graphical demonstrations using Java of concepts in complex analysis developed for a course at McAllister. Most are animated so that the original curves are continuously deformed into the image curves, and the eye can follow which points
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 Graphics for the Calculus Classroom (Java version)  Douglas N. Arnold; Institute for Mathematics and its Applications
Excerpts with Java animations from a collection of graphical demonstrations developed for first year calculus. Includes: Differentials and differences, computing the volume of water in a tipped glass, Archimedes' calculation of pi, how the ball bounces,
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 Helmer Aslaksen
A mathematics professor at the National University of Singapore. Research involves abstract algebra, including the trigonometry of symmetric spaces, and calculations for the Chinese, Islamic, and Indian calculators. Papers about these topics may be
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 Herbert Wilf
Herbert Wilf is a combinatorialist. The entire text of his books generatingfunctionology, A = B, and Algorithms and Complexity may be downloaded in PDF format, as may his "East Side, West Side" lecture notes on combinatorial objects and Maple programming.
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 Herkimer's Hideaway  Sanderson M. Smith, Cate School, Carpinteria, CA
Assignments and readings: a resource for mathematics students and teachers, particularly in the areas of Algebra II, AP Statistics, and Statistics/Finance. See also Smith's Writings and reflections.
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 High School Mathematics  Cem Giray
Site contains lecture notes, exams, quizzes, assignments, challenging problems, curricula (in this case meaning topics of study), and olympiad materials of high school level for teachers and students. Some materials are web pages, some are in PDF format,
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 Historical Tidbits  Paul Golba
Biographical and mathematical information (from an online interactive textbook on Real Analysis by Bert G. Wachsmuth) on Niels Abel, Archimedes, Johann Bernoulli, Bernard Bolzano, Georg Cantor, Augustin Cauchy, Augustus De Morgan, Euclid, Leonhard Euler,
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 Home Page of Andrei Toom, André Toom  Andrei Toom, Department of Statistics, Federal University of Pernambuco, Recife, Brazil
The home page of one of the developers of the ToomCook, or Toom3 algorithm, a method of multiplying two large integers. Toom's Englishlanguage mathematics articles, published in journals such as the Journal of Statistical Physics, include "NonErgodic
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 Homepage of Keith Matthews  Dept. of Mathematics, Univ. of Queensland, Australia
Matthews is a Senior Lecturer whose professional interests are number theory, teaching, and traversing the World Wide Web to uncover things of interest to number theorists for the Number Theory Web. Links to mathematical interests, gateways (mainly mathematical)
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 HyperMath  Carl R. (Rod) Nave; Georgia State University
HyperMath uses concept maps to explore mathematics ideas and applications to physics and astronomy. Originally developed in HyperCard, HyperMath covers the topics of algebra, trigonometry, geometry, vectors, linear algebra, logarithms, exponents, calculus,
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 HyperPhysics  Carl R. (Rod) Nave; Georgia State University
HyperPhysics uses concept maps to explore physics ideas and applications. Originally developed in HyperCard, the networklike environment provides for numerical exploration in the form of active formula and standard problems implemented in Javascript.
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 Integer Jim's Math Squad  Jim Bennett
Creative ways to use art, writing, research, and Internet projects to make math more exciting for students. The Math Squad art projects are yearlong projects; rather than "lesson oriented," they create an "adventure theme" that facilitates math instruction.
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 Interactive Introduction to University Maths  Emma Thomas, The University of Surrey, England
An introduction to matrices and determinants; vectors and 3D planes; and Jordan normal forms. With proofs and examples. Based on the curriculum for first year students pursuing the degree in mathematics from the University of Surrey. Requires Java.
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 An Introduction to Analytic Number Theory  Ilan Vardi, with Cyril Banderier
Lecture notes by Ilan Vardi, IHES, BuressurYvette, December 14, 1998. Introduction; Dirichlet's theorem; The Prime Number Theorem; Chebyshev's bias; references.
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 Introduction to Analytic Number Theory  Noam Elkies
Lecture notes for a course given at Harvard in 1998.
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 Introduction To Cryptography  Lawrie Brown
This site provides a summarization of cryptography, including: definitions of terms, basic concepts, history, techniques, tools, and applications.
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 Introduction to Fractal Geometry  Michael Frame, Benoit Mandelbrot, and Nial Neger
A collection of pages to support a first course in fractal geometry for students without especially strong mathematical preparation. See examples of fractals in the arts, humanities, and social sciences. Learn about selfsimilarity, plane transformations,
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 Introduction to Game Theory: Wining Business in A Competitive Environment  Prof. Hossein Arsham; University of Baltimore
Presents the theory of twoperson, zerosum games. Applications to optimal portfolio selections in investment decisions together with risk assessment are presented.
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 Introduction to Logic and Recursion Theory  Edward Boyden
Notes from a class taught by Prof. Sacks at M.I.T. in the spring of 1998, organized and reinterpreted. Propositional Calculus; FirstOrder Logic; Towards Completeness and Consistency; Recursion Theory – compare this to Sipser’s Computation, Part II; Clarity
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 Introduction to Number Theory  X.D. Jia; Southwest Texas State College
Lecture notes (1996): Factorization of Integers; Congruences; Quadratic Residues; Continued Fractions.
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 John Baez's Stuff  John Baez
The site features the author's column "This Week's Finds in Mathematical Physics," with archives dating back to 1993. "Fun stuff" includes old posts and email on Bayesianism in probability theory and quantum mechanics; some rambling lectures on knot polynomials,
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 John MacFarlane
Papers, books, talks, courses, and other resources by the member of the University of California, Berkeley's Group in Logic and the Methodology of Science and a coorganizer of the Working Group in the History and Philosophy of Logic, Mathematics, and
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 John Olive's Home Page  John Olive, Department of Mathematics Education, The University of Georgia
Course descriptions and requirements for Computers in Mathematics Education and Investigations into the Teaching of Mathematics Grades 712. Recent articles, available online, include Computer Tools for Interactive Mathematical Activity in the Elementary
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 John Taylor's Home Page  John Taylor; University of Brighton
Taylor's other activities include Maple generated animations: vary gradients or intercepts in equations for a straight line, change coefficients of quadratic curves or cubic curves, draw tangents to conics, model a nondifferentiable surface, and construct
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 The Journal of InquiryBased Learning in Mathematics  W. Ted Mahavier, Managing Editor
Classroomtested, professionally refereed, and freely downloadable university course notes intended for course design or independent study. Since the online publication of its first issue, in March of 2007, the Journal of InquiryBased Learning in Mathematics
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 Journal Writing and Investigations  Stephen Cicioni, Manheim Township Middle School
Download PDFs documenting one seventh grade classroom's journal writing and investigations: possible journal entries, yes/no day, cube sticker, words to algebra, absolute value, investigation quiz, lawn mower business, cheapest can, volume of a box, stick
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 KeyedIn Magazine  nelsonthornes.com
Weekly puzzles, quizzes, features of great mathematicians, fun with numbers, and strategy games. An Internet quest and "the serious stuff" offer selfscoring problems. Teacher resources provide links and ideas for each chapter of the Nelson Thornes Key
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 Kolyvagin's Application of Euler Systems to Elliptic Curves  Kedlaya, Osserman; Massachusetts Institute of Technology
A semesterlong seminar studying Kolyvagin's application of Euler systems to elliptic curves (i.e., to the conjecture of Birch and SwinnertonDyer), focused around the expository paper Kolyvagin's Work on Modular Elliptic Curves by Professor Gross. Includes
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 Late Renaissance Thought and the New Universe (Mathematics Across the Curriculum)  Wallace, Sciortino; Dartmouth College
A course taught in the spring of 1997 that examined the Copernican controversy in its historical and social context, and how it influenced and was influenced by contemporary upheavals. The site contains the syllabus and lesson plans for the course.
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 Lecture Notes and Exercises  Paul Garrett
Topics in Algebraic Number Theory: Buildings, BNpairs, Hecke algebras, Geometric Algebra; Automorphic (Modular) Forms, Representations, Lfunctions, Number Theory; Functional Analysis; Abstract Algebra; Complex Analysis; Algebraic Number Theory; Intro
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 Lectures on Probability, Statistics and Econometrics  Marco Taboga
Lectures and exercises on probability theory, statistics, and econometrics. The section entitled "mathematical tools" provides overviews and examples of combinatorics (permutations, dispositions, combinations), sequences, limit of a sequence, the RiemannStieltjes
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 Libro Electrónico de Cálculo Diferencial e Integral II  Prof. Sergio Cangiani  Armando Zabert
Libro Electrónico de Cálculo Diferencial e Integral de la Facultad de Ciencias Exactas de la Universidad Nacional del Nordeste en Argentina. Interfase de Estudio de Calculo Diferencial e Integral II: Conjuntos Puntuales, Continuidad, Derivadas,
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 Linear Algebra  Elmer G. Wiens; Egwald Web Services Ltd.
Illustrated examples of polynomials, vectors, matrices, linear equations, and linear differential equations. Discover the important methods used to decompose a matrix. Use the GramSchmidt process to compute orthogonal vectors. Use singular value decomposition
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 Linear Algebra for Informatics  José FigueroaO'Farrill
Lecture notes and tutorial problems for the Linear Algebra module in Mathematics for Informatics 3 (MAT2mi3/am3i), a course at the University of Edinburgh. Divided into three parts: real vector spaces and their linear maps, subspaces, linear (in)dependence,
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 Living Math!  Julie Brennan
A site dedicated to sharing resources for learning, exploring and enjoying math in a dynamic and holistic manner. The homeschooling author has "... found that math history and literature humanizes math, makes it come alive, and provides the context needed
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 Magical Methods  Magical Methods Enterprises
A source for Vedic mathematics, as developed by Pradeep Kumar. Find examples of arithmetic shortcuts for calculating squares, cube roots, multiplication, and division. Play games such as a calculation speed builder; purchase products to prepare for the
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 Making Learning Real  Nashville State Technical Community College and WGBH Educational Foundatio
Videos, professional development, and other resources for teachers already teaching ProblemBased Case Learning (PBCL) or considering such instruction grounded in realtime workplace situations. PDFs available for free download include a Need to Know
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 Margo Lynn Mankus  Margo Lynn Mankus
Talks include Using Virtual Manipulatives on the Web to Develop Number Sense, Connecting Whole Number Arithmetic to Algebra: HandsOn/Number Sense Activities, and Learning About Nutrition Using the TI73 and the Web. Also, online or downloadable classroom
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 MATA26Y: Calculus Lecture Notes  Friedlander, Rosenthal; University of Toronto at Scarborough College
Lecture notes in .pdf format. Gold Notes: Mathematical Sign Language; Induction; Polynomials and Rational Functions; The Mean Value Theorem for Rational Functions; Approximation of Rational Functions; Solving Polynomial Equations; Asymptotic Behaviour
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 MATH091  Intermediate Algebra: Lecture Notes  Lewis Bornmann; Mesa State College, CO
Slides that cover: Review of Real Numbers; Solving Equations and Inequalities; Graphing Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Relational Expressions; and Rational Exponents, Radicals, and Complex Numbers.
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 Math 629  History Of Mathematics  G. Donald Allen; Texas A&M University
Course notes on the history of mathematics, from The Origins of Ancient Mathematics and the Mathematics of American Indians North of Mexico to the History of Infinity, and the roles played by important mathematicians.
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 Math Alive  Ingrid Daubechies, Princeton University
Materials from a course designed for those who have not had college mathematics but would like to understand some of the mathematical concepts behind important modern applications. Interactive "virtual labs" address cryptography; error correction and
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 mathbabe  Cathy O'Neil
"Exploring and venting about quantitative issues." Blog posts, which date back to June, 2011, have included "KNearest Neighbors: dangerously simple," "Cool math books," "Women in math," "Mathematicians know how to admit they're wrong," and "Why log returns?"
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