CONTENTS
General Mathematical Resources
Puzzles, Problemsoftheweek, etc.
Factoids and Oddities
Worksheets, Example sheets
Abstract Algebra, Topology, Set Theory
Calculus

Eric Weisstein's Mathworld
(previously known as the Concise Encyclopedia of Mathematics) has (as of
Aug 1, 2005) 12,325
entries (more than one myriad),
hundreds of thousands of crossreferences, thousands of figures, hundreds
of animated
graphics, and about a thousand live
Java applets. 

Cut The Knot!
An interactive column using Java applets
by Alex Bogomolny, part of the Cuttheknot
website. 

A mathematical journal for high school students 

Final
Answers on Numericana
by Dr._{ }Michon.
Many
basic and advanced scientific questions answered within days.
Ask Gerard any question. Some answers are posted here.
Currently
(on 1/26/2008), that's over 820 articles. 
Link Farms
MAA  www.maa.org
 The Mathematical Association of America 
Click "Publications",
and then look for the section called Web / Electronic. There
you'll find these MAA
Online Columns.
by Ivars Peterson
, by Keith Devlinby Colm Mulcahy by David
Bressoudby Ed Pegg, Jr.by Ed Sandiferby Frank Morganby Alex Bogomolny
By Ivars Peterson

according to http://www.stetson.edu/~efriedma/mathmagic/
. . . . . .
Solvers
Helpful Internet Computing Websites
quickmath.com uses Mathematica to
solve, simplify, and graph,
and so does
 Here are some tips for using Wolfram's
Integrator from David Loeffler:
With a bit of ingenuity you can use Wolfram's
integrator for definite integrals too. If you embed a definite integral
inside a vacuous indefinite integral, it will evaluate the definite
integral first. For example if you enter Integrate[Exp[y^2],
{y,0,Infinity}] into the box, it will try and evaluate
and return x times the value of the integral in the middle, which is
just 1/2 Öp.
You can put any expression you like, not necessarily an integral,
inside: feed it Sum[1/(n^2 + a^2),{n,0,Infinity}], for example. Just as
long as what you're giving it doesn't involve x, you're fine.
Prime
Factorization Machine does just what it says.
Dario Alpern's page, Factorization
using the Elliptic Curve Method does it faster!
Inverse Symbolic
Calculator turns a number into the formula that generated that
number!
Plouffe's Inverter also turns
a number into the formula that generated that number!
Fibonacci
Calculator gives exact values of Fibonacci Numbers, Lucas Numbers,
and "Rabbit" numbers. (linked from here)
Letter Puzzle Solvers
The Cryptarithmetic
Puzzle Solver solves problems like LIP+LIP=KISS
and THREE+THREE+F0UR=ELEVEN
The Alphametic
Puzzle Solver also solves such problems

Help for Math students
SAT preparation and more
Mathactive.com  test
preparation, tutoring, and distance learning for mathematics
NRICH.maths.org/  click
"ask NRICH" to access the web board
mcraefamily.com/MathHelp/ is
Graeme's math website
algebra.com is yet another
homeworksolving mathboard
purplemath.com is a resource for
algebra students
mnemo.nu a brand new (as of
9/27/2002) discussion board website from some foreign country
www.mathematics.0catch.com/
asks for a donation in return for help with math or physics homework
www.cms.livjm.ac.uk/cmsjkung/index11.htm
is an experimental Javabased math tutor.
www.hotmath.org provides free solutions for actual math homework problems in many popular algebra, geometry, and calculus textbooks
physicsforums.com has a number
of free forums, including one on mathematics.
Anne Bell's Recommendations
www.cia.gov/cia/ciakids/codegame/index.html
 Break the secret code
http://mathforum.org/alejandre/magic.star
 Like a magic square, except it's a star
www.aplusmath.com/games/index.html
 Flashcards, worksheets, java programs
www.nottingham.ac.uk/education/number
 Fun facts about the number of today's date
www.cookwithlyle.co.uk  A
shockwaveenhanced resource for kids
www.bbc.co.uk/education/schools/digger
 English, Math, and Science for kids up to age 11
www.cadburylearningzone.co.uk/maths/index_content.htm
 math for kids
www.funbrain.com/ofm/index.html
 escape the haunted house by solving math puzzles
www.learningplanet.com/sam/ff/index.asp
 shockwaveenhanced Fraction Frenzy
www.mathscats.com/explore/multiplicationtable.html
 not found on 6/16/2002
www.funbrain.com/linejump/index.html
 arithmetic facts using a number line

Graphing and solving utilities
Links
to several dozen problemsolving methods including 3D Plotting Tool, Bar Graph, Brownian Motion Simulator, Bull'sEye Shot, Calculator, Computing a Summation, Curve Fit, Definite Integrals, Diffusion Simulator, Elastic collision, Elastic collision (2:1 ratio), Factoring a Polynomial, Gas under a piston, Grade Manager, Implicit Differentiation, Integration, Kepler's laws, Laboratory Report Writer, Limits, Limits & Derivative Tools, Multiplication Table, Osmosis Simulator, Pie Graph, Polynomial Addition, Polynomial Multiplication, Projectile motion, Regression Analysis, Solar system, Solids of Revolution, Solving a System of Equations, Solving a Polynomial Equation, Tangent Lines, and Weight & Measure
Javabased visualization aids
http://www.thesaurus.maths.org/dictionary/map/word/2098
 The first Napoleon Point
http://math2.math.nthu.edu.tw/jcchuan/javasketchpad/jsp.html
 A smorgasbord of java applets for visualizing all sorts of geometric
factoids

Geometry


Minimum Spanning Circle 
Martin: Suppose that you have a set of points in a plane
such that no point is more than a distance d from any other point. What is
the radius of the smallest circle that is guaranteed to enclose all of the
points?
Graeme: http://www.cs.brown.edu/people/tor/java/mec/
gives an efficient algorithm (using the farthest point Voronoi Diagram) for finding the minimal enclosing circle
(a.k.a. minimal spanning circle, MSC). This page has a wonderful
Java applet that lets you see the spanning circle in real time as you move
the points around.
Martin: From considering three points that form the sides of an equilateral
triangle, it follows that the radius must be a least equal to the radius
of the circumscribing circle, (sqrt(3)/3)d.
Will the point set always fit into this equilateral triangle?
Graeme: Martin, although there are points outside the equilateral
triangle whose distance from the vertices of the triangle is d, these
points are still inside the circumscribed circle.
Imagine an equilateral triangle with arcs of radius d centered at each of
the vertices of the triangle. This is a "rounded triangle" which
contains all the points in a set with a maximum distance of d between any
pair of points.
Playing with the java app, I couldn't make a bigger spanning circle than
the one that circumscribes an equilateral triangle with sides of length d. Graeme
continues: The "rounded triangle" is properly called a Reuleaux
Triangle, consisting of the vertices of an equilateral triangle together
with three arcs of circles, each circle having center at one of the
vertices and endpoints, the other two vertices.
The Reuleaux Triangle, T, has the largest known "magic constant"
m(T) for any plane figure, which is about m(T)=0.66753. The "magic
constant", also known as the "dispersion number" or
"rendezvous value" gives a measure of the normalized (that is,
divided by the diameter) average distance separating points in the set.
http://pauillac.inria.fr/algo/bsolve/constant/magic/magic.html
has more info. 
http://www.best.com/~ii/math/ch/
The Continuum Hypothesis: In 1877 Cantor hypothesized that the
number of real numbers is the next level of infinity above
countable infinity. Since the real numbers are used to represent a
linear continuum, this hypothesis is called "the Continuum
Hypothesis" or CH.
http://www.ii.com/ and its mirror, http://www.best.com/~ii/
Infinite Ink is dedicated to writing, teaching, and publishing about math, science, computing, and philosophy.
Infinite Ink focuses on writing,
teaching, and promoting public
discussion about:
 Foundations of Mathematics
and Science including
logic, set theory, physics, and the uses of infinity.
  Computing including the
Internet, intranets,
group work, groupware,
Unix, and Unix
philosophy.
  Philosophy of science,
mathematics, religion, and the infinite. I want to do philosophy
that is careful but more accessible than most of what is published
in academic philosophy
journals these days. I agree with Charles
Daniels (University of Victoria) as quoted by Bas
van Fraassen in The
Scientific Image who said:
It is always easy to tell whether people are doing
good philosophy: they are if they are laughing.


Work Sheets, Example Sheets, Help for kids, etc.
University of Cambridge
Department of Applied Mathematics and Theoretical Physics
Mathematics
Examples, Lecture Notes and Specimen Exam Questions and Natural Sciences
Tripos Mathematics examples
Example sheets for the following topics:
Algebra and Geometry
Differential Equations
Vector Calculus
Dynamics
Complex Methods
Quantum Mechanics
Electromagnetism
Special Relativity
Fluid Dynamics
Numerical Analysis
Dynamical Systems
Further Complex Methods
Classical Dynamics
Cosmology
Partial Differential Equations
Asymptotic Methods
Integrable Systems
Principles of Quantum Mechanics
Applications of Quantum Mechanics
Statistical Physics
Electrodynamics
General Relativity
Fluid Dynamics II
Waves
Numerical Analysis
Introductory Sheet
NST IA Mathematics I, II, and III
NST IB Mathematical Methods I, II, and III


We have
thousands of FREE worksheets, most subjects. The thematic units
and treasure hunt are especially popular. 



Worksheets

Basics
Simplifying
Multiplication
Exponents

Advanced Simplifying
Negative Exponents
Factoring

Index
with Sample Problems


Everything Else

Math
Resources
Advertisers

algebra.help




Some web sites that offer "distance learning
courses" are
http://www.sosmath.com/
(This one has some good tutorials on various math topics.)
http://members.home.net/jimwenk/Algebra.htm
PowerPoint presentations designed by a school teacher to help algebra students.
brokenlinkhttp://joshua.smcvt.edu/linalg.html">Linear
Algebra
by
Jim Hefferon
brokenlinkhttp://joshua.smcvt.edu/math.html">Mathematics
Saint Michael's College
Colchester, Vermont USA 05439
My text linear algebra, which is free for downloading, is
described here. It covers the material of any undergraduate first linear
algebra course. You can use it either as a main text, or as a supplement
to another text, or for independent study. 

Applied Complex Variables
(Math 552  Fall 2000) 

Singular Integral Operators, LittlewoodPaley Theory, and
Wavelet Approximation
(Math 758S  Spring 2000) 

Maximal Operators, LittlewoodPaley Theory, and Wavelets
(Math 758L  Fall 1999) 

Honors Vector Calculus(Math 241, Spring 1999) 

Calculus I (Math 141, Fall 1998) 

Analysis II (Math 555, Spring 1998)
Topics include:
 Introduction to Metric Spaces 
 Special Functions (exponential, logarithmic, trignometric functions, ...and their inverses) 
 Infinite series (convergence tests) 
 Sequences and Series of functions (for example, C[a,b] is a complete metric space.) 
 Interchange of Limit Operations 
 RiemannStieltjes Integration 
 Weierstrass Approximation Theorem 
 Picard Fixed Point Theorem 
 Existence/Uniqueness of ODE 
 Ascoli's Theorem 
 Fourier Series and Existence/Uniqueness of solutions of elliptic and parabolic PDE. 


Analysis I (Math 554, Fall 97)
The topics will include:
 Countable and uncountable sets, principle of induction, the real numbers, order, least upper bounds, the Archimedian property and completeness. 
 Sequences of real numbers, monotone sequences, convergence, subsequences, the BolzannoWeierstrass property and compactness. 
 Topology of the real numbers: open and closed sets, the HeineBorel theorem and compactness,
connectedness. 
 Continuous functions and their properties, intermediate and extreme value theorems, uniform continuity, monotone functions and inverses. 
 Differentiation, the chain rule, Rolle's theorem and the Mean Value Theorem, L'Hospital's rule. 
 The Riemann integral, its properties, and the Fundamental Theorem of Calculus. 


Vector Calculus (Math 241, Spring 97) 

Nonlinear Optimization (Math 524, Fall 96) 

Analysis I (Math 554, Spring 96) 

brokenlinkhttp://www.stg.brown.edu/~rog/GS99/">
General Mathematics Resources
Number Theory and Mathematical Proof Resources
Combinatorics and Probability Resources
 The
Chance Project (includes several online courses)
  Introduction
to Probability (at Dartmouth;;;;;;;;;;;;;;;; this site includes an good
introductory probability text and links to some wonderful applets).
  weber.u.washington.edu/~rogerrr/stat/index.html, no longer exists, was Probability
Tutorial (at the University of Washington)
  brokenlinkhttp://staff.feldberg.brandeis.edu/~petera/cchs/probability/MainPage.html">Probability
Lessons (at Brandeis)
  The Combinatorial Object
Server (parts still under construction, but very cool)
  Dictionary
of Combinatorics (Joe Fields' online edition)
  brokenlinkhttp://www.math.uga.edu/~andrew/Binomial/index.html">Arithmetic
properties of Binomial Coefficients (at University of Georgia 
rather advanced but very interesting) 

brokenlinkhttp://www.entropia.com/primenet/status.shtml">PrimeNet Server is the
server that hands out assignments to people (like Graeme) who volunteer their computers to
search for Mersenne Primes. You can look here to see more information, including the
names of the "top producers". GraemeMcRae is usually among the 100^{th}
to 500^{th} top producers. 
PI 3.14159265358979323846264338327950288...
http://oldweb.cecm.sfu.ca/organics/papers/borwein/paper/html/paper.html
Eve
Astrid Andersson's pi trivia game. Learn interesting facts such as
pi/4 = 4*arctan 1/5  arctan 239. Oops! I gave away one of the
answers  see if you can get a perfect score now! 
