Educational Resources

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Mathematics, Puzzles, Problem Solving


Recreational Mathematics

Wikipedia Category: Recreational Mathematics
Listing of Wikipedia articles on various subtopics under "Recreational Mathematics." From Magic Squares and Egyptian Fractions to Rigid Origami and the Jeep Problem.

Wikipedia Category: Mathematical Games
Nim, Clumsy Thief, Dots and Boxes, Spoof, Phutball, Order and Chaos, and Chomp are just some of the mathematical games included in this Wikipedia category.

Martin Gardner
Magician, untrained mathematician, author, and renowned Scientific American columnist, the venerable Mr. Gardner is the dean emeritus of recreational math.



How to Solve It – Georg Polya
The Torah of problem solving. (If Zeitz is Jesus, Polya is Abraham!) This short book is the sine qua non of basic heuristics. A quintessential work on the subject.

The Art and Craft of Problem Solving – Paul Zeitz
A manual for competitive mathematics. Heuristics dissected, with strategies, exercises. PDF copy
here. Instructor's manual here. Detailed MAA review here.

Mathematics for the Million
This one makes just about every list of "best books about mathematics." Lancelot Hogben's 1960 classic about xxx.

The Wonderful World of Mathematics
Another Hogben classic, this one geared toward inspiring a love of math and numbers in children (and their moms and dads).

A wonderful, short work blending basic geometry, epistemology, and sardonic commentary on the British social caste system of the Victorian Era.

Secrets of Mental Math: The Mathemagicians Guide ...
Harvey Mudd math prof and all-around teacher and math nut Arthur Benjamin reveals the secrets of his legendary calculating abilities (that all can emulate).

The I Hate Mathematics Book
The irreverant and creative sides of math are on full display in this classic book for kids who don't like math but are open to changing their minds. Follow-up

Mathematical Puzzles and Diversions
A gem among math popularizer Martin Gardner's typically wonderful works on recreational mathematics. Other favorites
here and here. Complete list here.

Arthur Benjamin
Harvey Mudd prof and human calculator extraordiaire, Dr. Benjamin has to be one of the best math teachers in all of human history. Catch him on YouTube,

Family Math (Equals Series)
Compilation of fun and instructive family math activities for parents with young children by the Lawrence Hall of Science.

Trachtenburg Speed Math
Phenominal system of mental calculation created by a man of rarely gifted intellect, conscience, and courage.

The Joy of X
Accessible look at "recreational mathematics" for those for whom the phrase seems like an cruel oxymoron. No, really. There is joy to be had in math!


Textbook Authors

Mary Dolciani
Dolciani books (especially early ones) are famous for their clarity, plentiful illustrative examples and exercises, and absence of distracting fluff and flash.

Earl Swokowski
The king of calculus textbooks has authored other books covering prerequisites: algebra, trig, precalc. A writing style that's lucid, concise, yet eminently rigorous.

Paul Foerster
The author who steered math textbooks in a new direction beginning in the 1980's. Foerster books are less explicit, more oriented toward real-world problem solving.


Problem Solving

Math for Fun and Glory
Kahn Academy's recreational math site. Wonderful training ground for gifted math students. Videos cover AMC problems, advanced topics, and more.
Great site for sharpening math and science problem solving skills. Short intro courses in a variety of subjects. Weekly problem sets keep problem solvers active.
How to summarize in just two lines? Fully accredited online problem solving school. Beware: You could be buried by an avalanche of resources. Ready? Set? Click.


Student Competitions

AMA: American Mathematical Association
Competitions page of the AMA web site. THE place to start looking into opportunities for gifted young mathematical minds to shine.

The 8th grade level of the American Mathematics Competition (AMC), administered by the AMA. Get full info, sample questions, register, start practicing.

AMC 10/12
The advanced AMC for 10th-12th graders. Everything you need to get started. Add good expert coaching and a ton of practice, and you're set.

AMA Invitationals
The AMA also administers various invitational competitions for students of various ages, like the USA Math Olympiad and Junior Math Olympiad, the AIME, etc.

The Putnam Exam
Think of the Putnam as the Math Olympiad for undergrads. Requires plenty of excess horsepower and high octane. Serious mathematics for future PhDs.



National Puzzler’s League
Premier national organization for word-play puzzlers (palindromes, cryptograms, crossword-type puzzles, cryptic crosswords, anagrams, etc.)

Dash Puzzle Hunts
"DASH is a fun, interactive event where teams of players race to find and solve creative puzzles hidden in different locations in cities all over the world."

Puzzle teams compete on-location to solve intriquing puzzles with mental, physical, and phychological aspects. These events are marathons, not sprints!

MIT Mystery Hunt
"A puzzlehunt competition that takes place on the MIT campus every year, one of the oldest and most complex in the world." Attracts over 2000 puzzlers annually.



Wolfram MathWorld
Hard to argue with the site's billing as "the world's most extensive mathematical resource." If it's mathematical, it's probably here.

Wolfram Functions Site
"Providing the mathematical and scientific community with the world’s largest collection of formulas and graphics about mathematical functions."

Mathematics for Non-Mathematicians
List of favorite math books for a general audience compiled by the math department at Bard College.

Proofs of the Pythagorean Theorem
With proofs too numerous to count, there seems no end to the energy and creativity used to prove perhaps the best known fact of mathematics.

Use Google Search as a Graphing Calculator
Google Search is a powerful and versatile
calculator capable of doing simple and complex calculations, 2D and 3D graphs, unit conversions, more. Cheat sheet here.

Excellent online calculator site. Graphing calculator allows animation sliders, tables, restrictions, regression. FREE non-programmable alternative to the Ti-84 Plus CE.

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