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Mathematics

CONTENTS

General Mathematical Resources 
Puzzles, Problems-of-the-week, 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 cross-references, thousands of figures, hundreds of animated graphics, and about a thousand live Java applets.
http://www.thesaurus.maths.org is a comprehensive math resource, with many java applets to help you visualize mathematical concepts.

Cut The Knot!

An interactive column using Java applets by Alex Bogomolny, part of the Cut-the-knot website.
Math Pages
MathPages.com
Number Theory
Combinatorics
Geometry
Algebra
Calculus & Diff Eqs
Probability & Statistics
Set Theory & Foundations
Reflections on Relativity
History
Physics
Music
Animated Illustrations
Combined List of Articles
Quotations

KöMaL

A mathematical journal for high school students
Ask Dr. Math, http://mathforum.org/dr.math/
(Mostly K-12 math and college algebra in a Q&A format.)
Dr. Gerard Michon, of Numericana Numericana

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


KABOL: Knot a Braid of Links
"Your rough guide to math on the web", a link farm.

KaBoL is a "cool math site of the week" service to the mathematics community provided within Camel by the Canadian Mathematical Society.


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.

The Mathematical Tourist, by Ivars Peterson
Devlin's Angle, by Keith Devlin
Card Colm
,
by Colm Mulcahy
Launchings
, by David Bressoud
Math Games
,
by Ed Pegg, Jr.
How Euler Did It
,
by Ed Sandifer
Math Cha
t, by Frank Morgan
Cut the Knot
,
by Alex Bogomolny
MathTrek, By Ivars Peterson

according to http://www.stetson.edu/~efriedma/mathmagic/  . . . . . .

Great Math Sites: | Geometry Junkyard | Integer Sequences | Mathematician Biographies |
| Numbers With Names | Inverse Calculator | Geometric Dissections |
Recreational Math Sites: | Mike Keith | Harvey Heinz | World of Numbers | Fibonacci |
| GIMPS | Primes | Polyforms | More Polyforms | Soup Kitchen |

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
Latex image
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

Links to Links -- a master table of mathematical links

NRICH.maths.org/  (part of the Millennium Mathematics Project)-- click "Links" to get hundreds of categorized links

  Math Forum Internet News is a newsletter with links to all sorts of math resources

Radio programs

Five Numbers (Zero, Pi, Phi, i, and infinity) -- click the link at the bottom of this page to hear the program (originally broadcast in March, 2002, on BBC Radio4) in Real Audio format.

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 homework-solving 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 Java-based 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 shockwave-enhanced 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 -- shockwave-enhanced 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 problem-solving methods including 3D Plotting Tool, Bar Graph, Brownian Motion Simulator, Bull's-Eye 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

Java-based visualization aids

http://www.thesaurus.maths.org/dictionary/map/word/2098 -- The first Napoleon Point

http://math2.math.nthu.edu.tw/jcchuan/java-sketchpad/jsp.html -- A smorgasbord of java applets for visualizing all sorts of geometric factoids

 

 

Elliptic Curves Franz Lemmermeyer's "Mother of all Elliptic Curves Resources" site.  (Also, see here).

 

Geometry

 

 Geometry Theorems & Problems

 Inca Geometry

Archimedes' Book of Lemmas:Try to solve the Archimedes' problems of geometry (High school Level)

Butterfly Theorem Proof. Puzzle.

Butterfly Theorem Introduction.

Carnot's Theorem

Ceva's Theorem Concurrency

Circles

Clifford's Circle Chain Theorems

Equilic Quadrilateral Five theorems.

Equal Incircles Theorem. Interactive presentation.

Eyeball Theorem

Gergonne Point Theorem

Johnson Theorem

Heron's Formula. Key facts and a purely geometric step-by-step proof

Kurschak's Tile and Theorem

Kurschak's Tile and Theorem. No frames.

Langley Theorem. Adventitious angles.

Menelaus' Theorem. Triangle and transversal line.

Miquel's Pentagram Theorem Proof

Miquel's Pentagram Dynamic Geometry

Monge & d'Alembert Three Circles Theorem I Dynamic Geometry

Monge & d'Alembert Three Circles Theorem II Dynamic Geometry

Morley's Theorem

Nagel Point Theorem Proof

Napoleon's Theorem

Newton's Theorem

Parallelogram&Squares

Pentagons and Pentagrams. Menelaus and Collinearity.

Platonic Solids Interactive animation

Poncelet's Theorem

Proposed Problems about congruence of line segments, angles, and triangles.
Key Theorems or Facts to know

Sangaku Problem 1

Sangaku Problem 2

Sangaku Problem 3

Semiperimeter and Incircle

Semiperimeter and Excircles

Semiperimeter, Incircle and Excircles

Seven Circles Theorem

Simson Line

Simson Line: Angle

Steiner's Theorem

100° Isosceles

Triangles

Triangle with the bisectors of the exterior angles. Collinearity.

Triangle and Squares. Fifteen theorems, visual illustrations.

Triangle&Squares 0 Two squares

Triangle&Squares 1 Two squares

Triangle&Squares 2 Two squares

Triangle&Squares 3 Three squares

Triangle with Squares 4 Finsler-Hadwiger Theorem

Triangle with Squares 5: Median and Altitude

Triangle with Squares 6: Four squares

Triangle Centers

Van Aubel's Theorem

Adjacent Angles

Varignon & Wittenbauer

 

 Triangle Centers

Centroid

Orthocenter

Circumcenter

Incenter

Excenter

Apollonius Point

Nine-Point

Gergonne Point See also: Gergonne Point Theorem Proof

Nagel Point See also Nagel Point Theorem Proof

Fermat Point

Napoleon Point

Bevan Point The circumcenter of the excentral triangle. Illustration with animation.

Symmedian (Lemoine) Point

Mittenpunkt Point

Steiner Point

Bevan Point Puzzle

Triangle Centers Word Find Puzzle

 

 Inspiration for Problem Solving

Achieve Your Dreams. Inspirational Poem.

I've Learned Inspirational Poem.

The Road Not Taken Robert Frost's poem about choices and decision making.

If Rudyard Kipling' Poem. Nobel Prize 1907.

If (Spanish version)

If - Math Humor, High School version.

Desiderata Ehrmann's Poem for a way of life.

Desiderata (Spanish) Poema de Ehrmann para una forma de vida.

Raft of the Medusa Free interpretation of Gericault's famous painting with Fractals.

Balsa de la Medusa (Spanish version) Interpretación libre de la famosa pintura de Gericault.

Raft of the Medusa (Traditional Chinese version)

On Children a poem by Kahlil Gibran.

Archimedes & Rhombicuboctahedron  Archimedes "The Geometer"

Experiencing Geometry Poem

Top Ten Reasons to Enjoy Geometry

Euler and his beautiful and extraordinary formula

The Landscape of Geometry Terms

The Landscape of Geometry Terms. No frames.

Machu Picchu and Geometric Art

The Lord of Sipan and Geometric Art

Angkor Wat and Geometric Art

Giza Pyramids and Geometric Art

Vatican City and Geometric Art

Morley's Theorem

Hyperbolic Tessellation and Geometric Art.

Star Wars and Geometric Art.

The Chronicles of Narnia and Geometric Art

The Lord of the Rings and Geometric Art

Geometry Wars and Geometric Art

Torino Games and Geometric Art

Simson Line

Sierpinski Triangle and Machu Picchu with fractals.

Nazca Lines Animation. Mystery on the Desert.

Nazca Lines: The Monkey. Geometric Art.

Kurschak's Tile and Theorem. No frames

Home Introduction

46th Annual Georgia Mathematics Conference 2005

Geometric Art. Table of Content

The School of Athens. Interactive Map.

 

The Landscape of Terms

The Landscape of Academic Disciplines

The Landscape of Books of All Time

The Landscape of the Da Vinci Code

The Landscape of E-Learning

The Landscape of Expert System

The Landscape of Geometry terms

The Landscape of Harry Potter terms. Glossary

The Landscape of Hurricane Katrina terms

The Landscape of Instructional Strategies

The Landscape of Inca Empire

The Landscape of LASER terms

The Landscape of Online Degrees

The Landscape of Scientific Instruments

The Landscape of Syllogism

The Landscape of the New SAT Reasoning Test

The Landscape of the Top Overall Searches

The Landscape of Terms of Environment

The Landscape of Think out of the box

The Landscape of Why Study Geometry?

 

 Home

 Home - Welcome

Recent additions

Recent additions (continuation)

 Home - Introduction

Cuzco Ancient Inca Empire Capital.

Cuzco City Map

Cuzco Panorama View

Cuzco Sacsayhuaman Fortress. Panorama View.

Cuzco Chinchero Panorama View

Machu Picchu Lost City of the Incas.

Machu Picchu and Geometric Art

Machu Picchu Map Interactive with zoom.

Machu Picchu and Sierpinski Triangle.

Machu Picchu Condor's Eye View

Inca Trail to Machu Picchu Panorama View

Inca Trail to Machu Picchu

Inca Trail to Machu Picchu: Huinay Hayna

Inca Quipu Data Structure.

Nazca Lines One of humanity's mysteries.

Nazca Lines Animation. Mystery on the Desert.

Nazca Lines: The Monkey. Geometric Art.

Nazca Lines: The Condor bird. Puzzle: 40 pieces of birds tessellation.

Nazca Lines: The Spider, Puzzle: 44 pieces in a tri-dove style of piece.

The Lord of Sipan King Tutankhamen of the Americas

The Lord of Sipan and Geometric Art

The Lord of Sipan and Spiderman Gold Necklace

Caral: the oldest civilization in the New World Peru opens Caral ruins to tourists.

Inca City on Mars? South Polar Region on Mars. NASA Mariner 9.

About Peru Lima, Cuzco, Machu Picchu, Nazca Lines, Titicaca Lake, Biosphere reserves, Amazon River, Paracas, and more.

Geometry and Cultures

Inca Music

Sierpinski Triangle and Machu Picchu fractal illustration with animation

Sierpinski Triangle and Machu Picchu Puzzle.

The Stone of twelve angles Puzzle: 22 pieces of polygons.

Machu Picchu Puzzle: 41 pieces of polyominoes.

The Lord of Sipan Puzzle: 22 pieces of polygons.

The Lord of Sipan: Spiderman Puzzle: 50 pieces of circles.

Inca Quiz. Ten questions in random order.

 

 Quizzes

SAT Math Section 6 Shuffle order.

SAT Math Section 6 Sequential order.

Geometry SAT Techniques 1.

Geometry SAT Techniques 2.

Math Crossword.

Geometry jokes Crossword

Geometry jokes I Matching exercise.

Geometry jokes II Matching exercise.

Geometry Proofs Jokes Matching exercise.

Inca Quiz. Ten questions in random order.

Geometry Quotes Quiz. Five questions in random order.

The Seven Habits Matching exercise.

The Seven Habits - Principles Matching Exercise.

The Seven Habits Games at Quizlab.com.

Geometry Quiz at Quizlab.com.

 

 Puzzles

The Stone of twelve angles Puzzle: 22 pieces of polygons.

Machu Picchu Puzzle: 41 pieces of polyominoes.

Bevan Point Puzzle.

Butterfly Theorem Puzzle.

Ceva's Theorem Puzzle.

Equal Incircle Theorem

Euler's Formula Puzzle: 55 pieces of six star.

Morley's Theorem - Puzzle 22 pieces of polygons.

Nazca Lines: The Condor bird. Puzzle: 40 pieces of birds tessellation.

Nazca Lines: The Monkey Puzzle

Nazca Lines: The Spider, Puzzle: 44 pieces in a tri-dove style of piece.

Nagel Point Puzzle: 22 pieces of polygons.

Newton's Theorem Puzzle: 50 pieces of circles.

Pentagons & Pentagrams: 96 pieces of triangles.

Sierpinski Triangle and Machu Picchu Puzzle.

The Lord of Sipan Puzzle: 22 pieces of polygons.

The Lord of Sipan: Spiderman Puzzle: 50 pieces of circles.

The Raft of the Medusa. Puzzle: 91 pieces of a lizards tessellation.

The Raft of the Medusa (Traditional Chinese version). Puzzle: 91 pieces of a lizards tessellation.

The Raft of the Medusa (Spanish version). Puzzle: 91 pieces of a lizards tessellation.

The Road Not Taken Robert Frost's poem. Puzzle 48 pieces of USA map.

 

 Quotes

Archimedes: diagram

Aristotle: Limit

Banach: mathematician

Cocteau: freedom

Coxeter: exploring

Crelle: triangle

Descartes: reasoning

Dürer: art

Euclid: royal road

Fermat: Last theorem

Fontenelle: elegant

Freud: visualizing

Galileo: The Universe

Hobbes: Pythagoras

Ibn Khaldun: Intellect

Kepler: God

Lafayette: Liberty

Lagrange: Algebra

Leonardo: proof

Lincoln: Euclid

Mandelbrot: fractals

Newton: principles

Pappus: bees

Pedersen: skill

Pythagoras: music

Plato: eternal

Plutarch: Archimedes

Poincaré: natural selection

Polya: elegance

Pushkin: inspiration

Regiomontanus: triangle

Riemann: proofs

Thales of Miletus

Valéry: similar figures

Voltaire: no sects

Wittgenstein: contradict

Shortest Distance

 

  World News

Teamgeist - the 2006 FIFA World Cup official

Tattooed mummy puzzles scientists in Peru.

Celestial Find at Ancient Andes

Boca Raton High students and Geometry

Japanese Find New Nazca Lines In Peru.

Machu Picchu and Yale University.

Peru: from the art of the Chavin to the Incas. 3,000 years of Peruvian art on show in Paris.

Humans Hard-wired for Geometry

Baby Got Math

Recent additions

Awards

 

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.

 

 

Orthogonal Circles, and Inversion Geometry From Doctor Math, Orthogonal Circles
From Mathworld, Orthogonal Circles, Inversion
From Cut-the-knot, Inversion: Reflection in a Circle
Paul Kunkel's Inversion Geometry

 

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:
 
bulletFoundations of Mathematics and Science including logic, set theory, physics, and the uses of infinity.
 
bulletComputing including the Internet, intranets, group work, groupware, Unix, and Unix philosophy.
 
bulletPhilosophy 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.

HS Unlimited Worksheets 

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

http://freeworksheets.com/

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

http://www.algebrahelp.com/

Lessons

Basic Algebra Concepts Simplifying
Advanced Simplifying Factoring
Descriptions and Sample Problems

Calculators

Equations Expressions: Functions Numbers Fractions
Other
Index with Descriptions

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.

History of Mathematics Page.

Mathematical Challenge Problems

* Denotes a problem which has not yet been solved.

  1. Finding the Axis of a Parabola with Compass and Straightedge
  2. The Steinmetz Problem: Evenly Distributing Points on the Unit Interval
  3. Triangles Having the Same Perimeter and Area
  4. Prime Factors of a Large Number
  5. No Empty Row or Column
  6. Cyclic Quadrilaterals
  7. My Bank Account Balance
  8. Filling Rectangles and Boxes with Trominoes and Tetrominoes*
  9. Sum the Product of the Nonzero Digits
  10. Sharing the Beads*

Problems from the 98-99 academic year

  1. Bracing Figures with Unit Rods
  2. Number of Regions Determined by n Rectangles
  3. An Ant on a Grid
  4. Expected Time Until an Ace
  5. A Cryptarithm
  6. Spreading Points on the Platonic Solids
  7. Sums of Squares of Consecutive Integers
  8. Nesting Various Platonic Solids
  9. Circles Orthogonal to Two Given Circles
  10. Drawing a Parallel Line with a Straightedge

Problems from the 97-98 academic year

  1. Nine Digits with No Three Repeated
  2. Knight Moves
  3. Factoring One Million
  4. Three Squares
  5. Bug on a Square
  6. Attacking Hyperqueens*
  7. Wrapping a Package
  8. Tower of Exponents
  9. Tiling with Dominoes
  10. Harmonic Squares in a Rectangle*
  11. Lewis Carroll's Right Triangles
  12. Lewis Carroll's Diagram Tracing
  13. Area of a Subtriangle
  14. The Initial Digits of a Square Root

Problems from the 96-97 academic year

  1. A Cryptarithm
  2. MATHEMATICS Paths
  3. Four Circles
  4. How Many Tetrahedra?
  5. An Erdös Problem
  6. Aces and Kings
  7. 444...444
  8. Squares by Concatenation
  9. Four Points on a Circle
  10. GCD Equals Difference
  11. Attacking Queens
  12. A Broken Calculator
  13. Five Spheres
  14. Triangles from 100 Rods
  15. Triangles from 100 Rods, part 2
  16. Variation on Fermat
  17. U-pentacubes
  18. Rotating Squares on a Checkerboard
  19. Checkerboard Patterns
  20. Area of a Triangle
  21. Twin Perfect Squares
  22. Unfolding a Cube
  23. Four Letter Words
  24. A Continuation of #23
  25. Three Circles and a Tangent Line
  26. A Checkerboard Turned 45 Degrees
  27. A Cryptarithmic Tableau

Problems from the 95-96 academic year

  1. A Diophantine System
  2. Second Diophantine Variation
  3. Third Diophantine Variation
  4. Final Diophantine Variation
  5. Friday the 13th
  6. January 1st
  7. Counting Rectangles
  8. Counting Squares
  9. Counting Rectangles (a variation)
  10. A Skewed Rectangle
  11. The Post Problem
  12. Weakly Prime Numbers
  13. Friday the 13th (revisited)
  14. Probabilistic Liars
  15. Point in a Tetrahedron
  16. Splitting a Sum
  17. Splitting a Sum (a variation)
  18. Perfect Powers
  19. Tilted Squares
  20. A Sum of Cubes
  21. A Sum of Fourth Powers
  22. Painting a Cube
  23. Parallelepipeds
  24. Circles in a Triangle
  25. Sums of Consecutive Integers
  26. Card Stacks

Back to the Challenge Problems

Back to the Math Department Homepage.

Frequently Asked Questions in Mathematics

bulletIntroduction
bulletWhy a list of Frequently Asked Questions?
bulletFrequently Asked Questions in Mathematics?
bulletFundamentals
bulletAlgebraic structures
bulletMonoids and Groups
bulletRings
bulletFields
bulletOrdering
bulletWhat are numbers?
bulletIntroduction
bulletConstruction of the Number System
bulletConstruction of N
bulletConstruction of Z
bulletConstruction of Q
bulletConstruction of R
bulletConstruction of C
bulletRounding things up
bulletWhat's next?
bulletNumber Theory
bulletFermat's Last Theorem
bulletHistory of Fermat's Last Theorem
bulletWhat is the current status of FLT?
bulletRelated Conjectures
bulletDid Fermat prove this theorem?
bulletPrime Numbers
bulletLargest known Mersenne prime
bulletLargest known prime
bulletLargest known twin primes
bulletLargest Fermat number with known factorization
bulletAlgorithms to factor integer numbers
bulletPrimality Testing
bulletList of record numbers
bulletWhat is the current status on Mersenne primes?
bulletFormulae to compute prime numbers
bulletSpecial Numbers and Functions
bulletHow to compute digits of ?
bulletEuler's formula:
bulletWhat is
bulletWhy is ?
bulletName for f(x)^f(x) = x
bulletSome Famous Mathematical Constants
bulletHuman Interest
bulletIndiana bill sets the value of to 3
bulletFields Medal
bulletHistorical Introduction
bulletTable of Awardees
bulletErdos Number
bulletWhy is there no Nobel in mathematics?
bulletInternational Mathematics Olympiad and Other Competitions
bulletWho is N. Bourbaki?
bulletMathematical Trivia
bulletNames of Large Numbers
bulletFamous Problems in Mathematics
bulletThe Four Colour Theorem
bulletThe Trisection of an Angle
bulletWhich are the 23 Hilbert Problems?
bulletUnsolved Problems
bulletDoes there exist a number that is perfect and odd?
bulletCollatz Problem
bulletGoldbach's conjecture
bulletTwin primes conjecture
bulletMathematical Games
bulletThe Monty Hall problem
bulletMaster Mind
bulletAxiom of Choice and Continuum Hypothesis
bulletThe Axiom of Choice
bulletRelevance of the Axiom of Choice
bulletCutting a sphere into pieces of larger volume
bulletThe Continuum Hypothesis
bulletFormulas of General Interest
bulletHow to determine the day of the week, given the month, day and year
bulletSymbolic Computation Packages
bulletFormula for the Surface Area of a sphere in Euclidean N-Space
bulletFormula to compute compound interest.
bulletReferences, General Bibliography and Textbooks
bulletThe Sci.Math FAQ Team
bulletCopyright Notice
bulletAbout this document ...

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.

 

 

Courses, by Robert Sharpley

bullet Applied Complex Variables (Math 552 - Fall 2000)
bullet Singular Integral Operators, Littlewood-Paley Theory, and Wavelet Approximation (Math 758S - Spring 2000)
bullet Maximal Operators, Littlewood-Paley Theory, and Wavelets (Math 758L - Fall 1999)
bullet Honors Vector Calculus(Math 241, Spring 1999)
bullet Calculus I (Math 141, Fall 1998)
bullet Analysis II (Math 555, Spring 1998)

Topics include:

bullet Introduction to Metric Spaces
bullet Special Functions (exponential, logarithmic, trignometric functions, ...and their inverses)
bullet Infinite series (convergence tests)
bullet Sequences and Series of functions (for example, C[a,b] is a complete metric space.)
bullet Interchange of Limit Operations
bullet Riemann-Stieltjes Integration
bullet Weierstrass Approximation Theorem
bullet Picard Fixed Point Theorem
bullet Existence/Uniqueness of ODE
bullet Ascoli's Theorem
bullet Fourier Series and Existence/Uniqueness of solutions of elliptic and parabolic PDE. 
bullet Analysis I (Math 554, Fall 97)

The topics will include:

bullet Countable and uncountable sets, principle of induction, the real numbers, order, least upper bounds, the Archimedian property and completeness.
bullet Sequences of real numbers, monotone sequences, convergence, subsequences, the Bolzanno-Weierstrass property and compactness.
bulletTopology of the real numbers: open and closed sets, the Heine-Borel theorem and compactness, connectedness.
bullet Continuous functions and their properties, intermediate and extreme value theorems, uniform continuity, monotone functions and inverses.
bullet Differentiation, the chain rule, Rolle's theorem and the Mean Value Theorem, L'Hospital's rule.
bullet The Riemann integral, its properties, and the Fundamental Theorem of Calculus. 
bullet Vector Calculus (Math 241, Spring 97)
bullet Nonlinear Optimization (Math 524, Fall 96)
bullet Analysis I (Math 554, Spring 96)

brokenlinkhttp://www.stg.brown.edu/~rog/GS99/">Foundations of Mathematics Course for High School Students
General Mathematics Resources

bulletThe MacTutor History of Mathematics Archives
bulletCRC Concise Encyclopedia of Mathematics
bulletWWW Virtual Library: Mathematics (at Florida State University)
bulletThe Math Forum (at Swarthmore)
bulletThe Geometry Center (at the University of Minnesota)
bulletbrokenlinkhttp://www.math.uga.edu/~ntheory/gateways.html">Mainly Mathematical Gateways (at University of Georgia)
bulletNational Council of Teachers of Mathematics (NCTM) Standards Page (at The Math Forum)

Number Theory and Mathematical Proof Resources

bulletSouthwest Texas State University 
brokenlinkhttp://www.math.swt.edu/~haz/">Donald G. Hazlewood 
brokenlinkhttp://www.math.swt.edu/~haz/math_sess.html">Problem Sets and Notes 
brokenlinkhttp://www.math.swt.edu/~haz/prob_sets/notes/notes.html">Introduction to Number Theory, by X. D. Jia 
brokenlinkhttp://www.math.swt.edu/~haz/prob_sets/notes/node29.html">Quadratic Residues 
bulletLecture notes for course 311 (Abstract algebra), taught at Trinity College, Dublin
Includes:
   Part I: Topics in Number Theory 
   Part II: Topics in Group Theory 
   Part III: Introduction to Galois Theory
bulletNumber Theory Resources On-Line (at the MathArchives)
bulletbrokenlinkhttp://www.math.uga.edu/~ntheory/number_theory.html">Things of Interest to Number Theorists (at the Number Theory Web)
bulletSloane's On-Line Encyclopedia of Integer Sequences (at AT&T)
bulletThe Prime Page
bulletFifteen Proofs of Euler's V-E+F=2 (at the Geometry Junkyard)
bulletReal Analysis (at Seton Hall)

Combinatorics and Probability Resources

bulletThe Chance Project (includes several on-line courses)
bulletIntroduction to Probability (at Dartmouth;;;;;;;;;;;;;;;; this site includes an good introductory probability text and links to some wonderful applets).
bulletweber.u.washington.edu/~rogerrr/stat/index.html, no longer exists, was Probability Tutorial (at the University of Washington)
bulletbrokenlinkhttp://staff.feldberg.brandeis.edu/~petera/cchs/probability/MainPage.html">Probability Lessons (at Brandeis)
bulletThe Combinatorial Object Server (parts still under construction, but very cool)
bulletDictionary of Combinatorics (Joe Fields' on-line edition)
bulletbrokenlinkhttp://www.math.uga.edu/~andrew/Binomial/index.html">Arithmetic properties of Binomial Coefficients (at University of Georgia -- rather advanced but very interesting)

GIMPS -- The Great Internet Mersenne Prime Search

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 100th to 500th top producers.

PI 3.14159265358979323846264338327950288...

Ramanujan, Modular Equations, and Approximations to Pi or How to compute One Billion Digits of Pi

http://oldweb.cecm.sfu.ca/organics/papers/borwein/paper/html/paper.html 

Eve Astrid Andersson, Strange woman with antennae and a green faceEve 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!


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