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 Carousel Numbers. A Lead-in to Number Theory - Gary Klatt; Univ. of Wisconsin - Whitewater; The Math Forum A connected series of four problems in elementary number theory that are ideal for discovery learning at several levels. Each problem generates interesting questions and conjectures, and their surprising connections add interest and allow each to shed ...more>> A Catalog of Random Bits - Ivars Peterson (MathLand) Researchers use random numbers for tackling a wide range of problems, from modeling molecular behavior and sampling opinion to solving certain equations and testing the efficiency of algorithms. Such numbers also play crucial roles in a wide variety of ...more>> Center for Mathematical Talent - New York University The Center for Mathematical Talent (CMT) at the Courant Institute of Mathematical Sciences coordinates activities for students in the New York City area who would like more mathematics than is included in the usual mathematics classroom. Freely downloadable ...more>> Chinese Remainder Theorem - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny An explanation and proof, using modular arithmetic, of the Chinese Remainder Theorem, which concerns problems of the following type: There are certain things whose number is unknown. Repeatedly divided by 3, the remainder is 2; by 5 the remainder is 3; ...more>> Classifying Numbers - Math Forum, Ask Dr. Math Common Question A selection of answers to questions about classifying numbers, such as "How are the different types of numbers related?" and "What is a real number?" ...more>> "The Code War" - Beyond Discovery - Dana Mackenzie et al.; National Academy of Sciences PDF of a science article from the Beyond Discovery series that explores the trail of developments in the branch of mathematics known as number theory that led to modern-day encryption techniques. Contents include: Early Ciphers; The Enigma Challenge; ...more>> The Collage Theorem - Cut the Knot!, Alexander Bogomolny To find an IFS whose attractor is "close to" or "looks like" a given set, one must endeavor to find a set of transformations - contraction mappings on a suitable set within which the given set lies - such that the union, or collage, of the images of the ...more>> Collatz 3n+1 Problem Structure - Ken Conrow Pages of observations posted to stimulate further research. ...more>> Collatz Conjecture Calculation Center - Klaas IJntema JavaScript tools to investigate the Collatz problem, as well as general mathematics tools and some recreational mathematics. Some programs are freely downloadable. ...more>> Complete Analysis of the Binary GCD Algorithm - Brigitte Vallée, Université de Caen, France Lecture notes (summary by Cyril Banderier). Introduction; A Ruelle Operator for a Tauberian Theorem; The Other Two Parameters; All Roads Lead to Rome; References. In English. ...more>> Complex Variables (S.O.S. Mathematics) - Dept. of Mathematical Sciences, Univ. of Texas at El Paso An online course: learning units presented in worksheet format review the most important results, techniques and formulas in college and pre-college complex variables. Complex Numbers: Basic Definitions and Arithmetic, The Complex Plane, The Polar Form ...more>> Compound Interest to e and i - Don Cohen (The Mathman) Graphing and exploring simple interest and compound interest. Examples of interest earned on one dollar at 6 percent compounded daily, monthly, quarterly, annually. Patterns, infinite sequence. Sample problems with some answers from Chapter 11 of Don ...more>> The computation of certain numbers using the ruler and compass - Simon Plouffe, Journal of Integer Sequences A method for computing some numbers bit by bit using only the ruler and compass, in particular the construction for arctan(X)/Pi. This method is a spigot algorithm and can be applied to numbers that are constructible over the unit circle and the ellipse. ...more>> Computer Lab Courseware - University of Toronto Courseware to help in the teaching of various mathematical concepts. Most is made up of Mathematica notebooks and packages, but some consists of C programs written to run under X-Windows. A lab manual in TeX beginning with an introduction to UNIX and ...more>> Computing in a Surreal Realm - Ivars Peterson (MathLand) Even among mathematicians, the study of surreal numbers is an obscure pastime. Only a few have occupied themselves in recent years exploring the peculiarities of a number system that includes different kinds of infinities and vanishingly small quantities. ...more>> Computing Minimal Equal Sums Of Like Powers - Jean-Charles Meyrignac A distributed-computing project on equal sums of like powers, for "all those who are fascinated by powers and integers," and the place to look for the current status of the problem. Download and install Euler2000 to participate. ...more>> The Constants and Equations Pages - Jonathan Stott A growing reference resource providing alphabetically listed categories of some of the more important and useful aspects of maths and special sections on numbers, algebra, trigonometry, integration, differentiation, and SI units and symbols, with in addition ...more>> Continued Fractions and Chaos (Organic Mathematics Proceedings) - Robert M. Corless From the Proceedings of the Organic Mathematics Workshop. This paper is meant for the reader who knows something about continued fractions, and wishes to know more about the theory of chaotic dynamical systems; it is also useful for the person who knows ...more>> Continued Fractions With A Calculator (SMILE) - Fred J. Schaal, Lane Tech High School A lesson designed to teach students how to evaluate continued fractions by taking many reciprocals with a calculator. From the Arithmetic section of a collection of almost 200 single concept lessons by the Science and Mathematics Initiative for Learning ...more>> A Course in Number Theory for High School Students - David Garlock For students who have completed algebra, geometry, trigonometry, pre-calculus and calculus and are looking for new challenges. It could also be taken as a summer course or as an independent study in the midst of the traditional math sequence. Download ...more>> Courses I Teach - John Cosgrave; St. Patrick's College, Dublin, Ireland Lecture notes from three courses given at St Patrick's College, Dublin: Maple/Calculus/Analysis; Number Theory; Number Theory and Cryptography. ...more>> Covering Systems, Restricted Sumsets, Zero-sum Problems and Their Unification - Zhi-Wei Sun Three famous topics in combinatorial number theory and a unified theory of them. ...more>> A Creative Encounter of the Numerical Kind: A Webquest for Middle Grades Math Students - Alice Gabbard Students create their own numerals and base four number system for an alien civilization. This web quest features background and evaluation materials, links to state and national standards, and tips for teachers. ...more>> Creative Java Puzzles - J. L. Read, Enchanted Mind Games "good for exercising both sides of the brain." Knight's Tour: pass all the squares of the board with the knight, making only legal moves. Peg Solitaire: Remove all the pegs in the least amount of time, finishing with only one peg in the target hole. ...more>> Curving Beyond Fermat - Ivars Peterson (MathTrek) "When Andrew Wiles of Princeton University proved Fermat's last theorem several years ago, he took advantage of recently discovered links between Pierre de Fermat's centuries-old conjecture concerning whole numbers and the theory of so-called elliptic ...more>> Dana Mackenzie Author of The Universe in Zero Words and The Big Splat, or How Our Moon Came to Be, freelance mathematics and science writer Dana Mackenzie also contributes to the series What's Happening in the Mathematical Sciences published by the American Mathematical ...more>> d'Arbeloff Interactive Math Project - Massachusetts Institute of Technology Java applets, with help documentation, for exploration: Amplitude and Phase, Beats, Complex Exponential, Complex Roots, Convolution (accumulation or flip and drag), Damped Vibration, Damping Ratio, Euler's Method, Forced Damped Vibration, Fourier Coefficients, ...more>> Database of Number Correlations - James Barton Partitionings, prime factorizations, polygonal numbers, and other data about each of the numbers one through one thousand, as well as connections to "various material and occult phenomena." See also Barton's magic square that has interesting prime factor ...more>> David Goodman's Math Links - David Goodman, editor Link listings for a variety of topics, organized by those topics. ...more>> David Marius Bressoud David Bressoud has written several undergraduate textbooks that use physics and the history of mathematics to motivate the study of multi-variable calculus, number theory, real analysis. Other books include A Course in Computational Number Theory and ...more>> David Sumner's Home Page - David Sumner Study guides, exams, quizzes, problem sets, exam review materials, utilities, programs and simulations, syllabi, and other materials for courses such as calculus, sequences and series, graph theory, number theory and cryptography, and probability. The ...more>> Decibels (Math Chat) - Frank Morgan, MAA Online Challenge: The Christian Science Monitor of July 8, 1999, reports that "according to the NRDC, the amount of ambient noise in the ocean may have increased by 10 decibels - in other words, 10-fold - between 1950 and 1975." Is this correct? ...more>> Derek's Daily Math - Derek Orr "Every Number Has a Story to Tell." This blog by an undergraduate at the University of Pittsburgh details number theoretic properties for every day of the calendar year. Orr, a physics and math major, also maintains a list of "Interesting Propositions/Theorems ...more>> Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n - Thien Do; Westmoore High School, Oklahoma City, OK Using methods of congruences, the author shows that if p = 3 there is only one positive solution (1,2), and if p is any other odd prime not congruent to 7 mod 8, there are no solutions. Introduction; Methodology; Conclusions; Further Works; Acknowledgements; ...more>> Diophantine geometry in characteristic p: a survey - José Felipe Voloch An article that appeared in Arithmetic Geometry, F. Catanese, ed., Symposia Mathematica XXXVII, Cambridge Univ. Press, 1997, pp. 260-278. Introduction; Curves; Abelian varieties and their subvarieties; Diophantine Approximation in characteristic p; Omitted ...more>> Diophantine m-tuples - Andrej Dujella; Zagreb Introduction to Diophantine m-tuples, i.e., sets with the property that the product any two distinct elements is one less than a square. Diophantine quintuple conjecture, sets with the property D(n), connections with Fibonacci numbers, rational Diophantine ...more>> Discovering the Art of Mathematic - Fleron, Julian, et al. Resources to help mathematics faculty teach the subject to liberal arts and humanities undergraduates by actively involving them in authentic mathematical experiences that "provide meaningful cognitive and metacognitive gains, and nurture healthy and ...more>> Dividing by 0 - Math Forum, Ask Dr. Math FAQ Why can't you divide by 0? Why is 0/0 "indeterminate" and 1/0 "undefined"? Why is dividing by zero "illegal"? ...more>> Divisibility Criteria - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny A definition of some divisibility criteria, and their derivation from modulo arithmetic, with links to related pages. ...more>> Divisor Plot - Jeffrey Ventrella "We hear of primes described as the 'building blocks' of all numbers. Let's turn that concept on [its] head. Instead, let's think of primes as the negative spaces behind complex objects. Imagine a series of picket fences stacked in front of each other. ...more>> Dot Patterns and Sierpinski Gasket - Cut the Knot!, Alexander Bogomolny How many ways are there to define the Sierpinski gasket (also, the Sierpinski triangle)? The author has counted a respectable 9 but would be happy to learn of more. An applet with rows of digits or circles with colors corresponding to the digits shows ...more>> Draft version of MSC2000 - European Mathematical Society (EMS) The proposed revision of the 1991 Mathematics Subject Classification (MSC), the classification used by the two reviewing journals Mathematical Reviews (MR) and Zentralblatt für Mathematik (Zbl) since the beginning of 1991. MSC2000 is the result of ...more>> Dr. Alfred Posamentier - Education Update, Inc. Blog by the Dean of Education at Mercy College (New York). Posamentier's Posts, which date back to August, 2010, have included "A Power Loop," "The Unusual Number Nine," "The Irrepressible Number 1," "Enriching Mathematics Instruction, Rather than Teaching ...more>> Duke University Math Union - Jadrian Miles The Duke University Math Union (DUMU) writes and hosts the annual Duke Math Meet. Download PDFs of problems and solutions from meets dating back to 1998. ...more>> Educational Interests - Keith Lynn See, in particular, Lynn's Math Modeling Project, which features Java applets to produce quadratic and sine examples; and Dynamics Project, on the Julia and Mandelbrot sets. ...more>> Egyptian Fractions - David Eppstein Links to algorithms for Egyptian fractions, transcriptions of network conversations, and many other relevant sites. ...more>> Elementary Math Enrichment - Beth Schaubroeck Free mathematics enrichment materials for accelerated 4th and 5th graders. The 70 lessons, grouped into 12 different units, include solutions and teacher guides: Ancient Mathematics (Mayan math, in base 20; and Egyptian math, which lacks zero), Baseball ...more>> Elementary Number Theory - Michael Filaseta; University of South Carolina Lecture notes from a course taught in fall of 1997 - class notes are available in postscript format. A graph compares Li(x), Pi(x), and x/log(x). ...more>> The Elementary Pre-service Teachers Mathematics Project - Suzanne Chapin, Principal Investigator Improving pre-service elementary teachers' mathematical knowledge for teaching (MKT). The Elementary Pre-service (EMP) Teachers Mathematics Project has developed dozens of lessons and corresponding support materials — including video, PowerPoint ...more>> Elliptic Curves - Stéfane Fermigier A collection of links on research articles on elliptic curves and related topics (applications, modular forms, Fermat's Last Theorem). Algorithmic applications; Modular forms aspects; L-curves; High rank curves; Heights. Bibliographies. Some papers in ...more>>
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