Mathematics, Puzzles, Problem Solving
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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, Martin Gardner did as much as anyone to popularize recreational math.
Arthur Benjamin
Harvey Mudd prof and human calculator extraordinaire, Dr. Benjamin has to be one of the best math teachers in all of human history. Catch him on YouTube, here.
3Blue1Brown
Grant Sanderson’s superb animated math channel celebrating the art/science of mathematical proof. For mathophiles, mathletes, wannabees. More here, here.
Black Pen Red Pen
Super-enthusiastic YouTube calculus teacher provides excellent lessons on intergration and other topics of interest to calculus students. Highly recommend!
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Books
The Art and Craft of Problem Solving – Paul Zeitz
A bible for competitive mathematics. Heuristics dissected, with strategies and exercises. PDF copy here. Instructor's manual here. Detailed MAA review here.
How to Solve It – Georg Polya
Polya's short book is the sine qua non of basic mathematical problem solving. A quintessential work on the subject.
Mathematics for the Million
Makes nearly every list of "best books about mathematics." Lancelot Hogben's classic (first published in 1937) explores the role of math in human society.
Flatland
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 for all to emulate.
The I Hate Mathematics Book
The irreverent and creative sides of math are on full display in this classic work for kids who don't like math but are open to changing their minds. Follow-up here.
Mathematical Puzzles and Diversions
A gem among math evangelist Martin Gardner's typically wonderful works on recreational mathematics. Other favorites here and here. Complete list here.
Family Math (Equals Series)
Compilation of fun and instructive family math activities for parents with young children by the Lawrence Hall of Science.
Mathematics for Non-Mathematicians
List of favorite math books for a general audience compiled by the math department at Bard College.
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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 rigorous.
Paul Foerster
The author who steered math textbooks in a new, more relevant, applied direction in the 1980's. Foerster books are oriented toward real-world problem solving.
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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.
brilliant.org
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.
artofproblemsolving.com
Fully-accredited problem solving school offering *superb* mathematics programs, courses, books, and other resources for kids in grades 2-12. Ready? Set? Click!
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Student Competitions
AMA: American Mathematical Association
Competitions page of the AMA web site. Super good place to begin looking into opportunities for gifted young mathematical minds to shine.
AMC 8
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 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.
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Groups
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."
Shinteki
Puzzle teams compete on-location to solve intriguing puzzles with mental, physical, and psychological aspects. These events are marathons, not sprints.
MIT Mystery Hunt
"A puzzle hunt 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.
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Other
AP Calculus Exams
Official College Board pdf covers both tests. Wiki info here. Excellent Magoosh AB and BC guides here, here, here (search for cogent, concise articles on key topics).
Integral Calculator and Derivative Calculator
Mathbots calculate definite integrals, antiderivatives, derivatives showing all steps! Graph/compare f, f'. Common analytic methods and special functions supported.
Paul’s Online Notes
Comprehensive course notes for algebra, trig, calculus 1-3, differential equations ... plus “Cheat Sheet” summary pages and other excellent math study resources.
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.
Wolfram MathWorld
Hard to argue with the site's billing as "the world's most extensive mathematical resource."
Wolfram Functions Site
"Providing the mathematical and scientific community with the world’s largest collection of formulas and graphics about mathematical functions."
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.
Desmos
Excellent online calculator site. Graphing calculator allows animation sliders, tables, restrictions, regression. FREE non-programmable alternative to the Ti-84 Plus CE.
GeoGebra
Great site for doing math online. Tools for CAS, geometry, graphing, 3D, and AR support tinkering/discovery, text, drawing, tables, documents. Bye-bye graph pad!
Mathwords
Handy math encyclopedia/glossary listing formulas/definitions along the standard algebra-calculus sequence. Clear, concise, understandable explanations/examples.
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