Recreational Mathematics
Wikipedia Category: Recreational Mathematics
Listing of Wikipedia articles on various topics 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, 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 around. Catch him on YouTube here. Check out his books here.
3Blue1Brown
Grant Sanderson’s superb animated math channel celebrating the art/science of mathematics. For mathophiles, mathletes, and wannabees. Favorite episodes here, here.
Black Pen Red Pen
Super-enthusiastic YouTube calculus teacher provides excellent lessons on integration and other topics of interest to calculus students.
Books
The Art and Craft of Problem Solving
The Bible for competitive mathematics by Paul Zeitz. Heuristics, strategies, exercises. PDF copy here. Instructor's manual here. Detailed MAA review here.
How to Solve It
Ace Stanford professor Georg Polya's 1945 book is the premier work on mathematical problem solving. A quintessential, must-read treatment of 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 oppressive British social class system of the Victorian Era.
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 book 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
Compilation of fun and instructive family math activities for parents by the Lawrence Hall of Science. Simple program gives ordinary adults ideas for generating kids' interest in math.
Mathematics for Non-Mathematicians
"Idiosyncratic annotated bibliography" of favorite math books for a general audience compiled by the math department at Bard College.
Textbook Authors
Mary Dolciani
Dolciani books (especially early ones) are famous for their clarity, plentiful 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, and rigorous.
Paul Foerster
Author who first steered math textbooks toward applied mathematics in the 1980's. Foerster books aim to be more relevant, and are oriented toward real-world problem solving.
Problem Solving
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. See Wiki here.
Student Competitions
International Mathematical Olympiad
The most prestigious mathematics competition in the world, and oldest of the international science contests (since 1959). See here for basic information, and here for YouTube videos.
The Putnam Exam
Think of the Putnam as the Math Olympiad for undergrads. Requires plenty of excess horsepower and high octane. For serious mathematicians on their way to grad school, only.
MAA: Mathematical Association Of America
Competitions page of the MAA 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 MAA. Get full info, sample questions, register, and start practicing.
AMC 10/12
The advanced AMC for 10th-12th graders. Everything you need to get started. Add plenty of natural talent, expert coaching, and a ton of practice, and you're all set.
More U.S. Competitions
Other math contests are held across the country to test the mettle of math students. Click here for information on 25 high school matches and here for 10 tests geared to grades 3-5.
Puzzling
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.
Other
Mathematics on YouTube
There's no shortage of excellent math channels on YouTube devoted to problem solving. My current favorites are: Presh Talwalkar, Math Avenue, SyberMath, and PreMath.
AP Calculus Exams
Official College Board pdf covers both tests. Wiki info here. Excellent Magoosh AB and BC guides here, here, here.
Integral Calculator and Derivative Calculator
Mathbots calculate definite integrals, antiderivatives, and 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” summaries and other excellent math study resources.
Proofs of the Pythagorean Theorem
With proofs too numerous to count, there seems to be no end to the energy and creativity devoted to proving the best known fact of basic mathematics in new and ingenious ways.
Wolfram MathWorld
Hard to argue with the site's billing as "the world's most extensive mathematical resource." For professionals and enthusiasts alike.
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, and more. Cheat sheet here.
Desmos
Powerful online graphing calculator allows animation sliders, tables, restrictions, regression, more. Free non-programmable alternative to the Ti-84 Plus CE. Standard on the dSAT.
GeoGebra
Tools for CAS, geometry, graphing, 3D, AR support tinkering/discovery, text, drawing, tables, and specialized math documents..
Mathwords
Handy math encyclopedia/glossary listing formulas and definitions taught in the standard algebra-calculus sequence. Clear, concise, understandable explanations and examples.
Wikipedia Category: Recreational Mathematics
Listing of Wikipedia articles on various topics 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, 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 around. Catch him on YouTube here. Check out his books here.
3Blue1Brown
Grant Sanderson’s superb animated math channel celebrating the art/science of mathematics. For mathophiles, mathletes, and wannabees. Favorite episodes here, here.
Black Pen Red Pen
Super-enthusiastic YouTube calculus teacher provides excellent lessons on integration and other topics of interest to calculus students.
Books
The Art and Craft of Problem Solving
The Bible for competitive mathematics by Paul Zeitz. Heuristics, strategies, exercises. PDF copy here. Instructor's manual here. Detailed MAA review here.
How to Solve It
Ace Stanford professor Georg Polya's 1945 book is the premier work on mathematical problem solving. A quintessential, must-read treatment of 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 oppressive British social class system of the Victorian Era.
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 book 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
Compilation of fun and instructive family math activities for parents by the Lawrence Hall of Science. Simple program gives ordinary adults ideas for generating kids' interest in math.
Mathematics for Non-Mathematicians
"Idiosyncratic annotated bibliography" of favorite math books for a general audience compiled by the math department at Bard College.
Textbook Authors
Mary Dolciani
Dolciani books (especially early ones) are famous for their clarity, plentiful 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, and rigorous.
Paul Foerster
Author who first steered math textbooks toward applied mathematics in the 1980's. Foerster books aim to be more relevant, and are oriented toward real-world problem solving.
Problem Solving
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. See Wiki here.
Student Competitions
International Mathematical Olympiad
The most prestigious mathematics competition in the world, and oldest of the international science contests (since 1959). See here for basic information, and here for YouTube videos.
The Putnam Exam
Think of the Putnam as the Math Olympiad for undergrads. Requires plenty of excess horsepower and high octane. For serious mathematicians on their way to grad school, only.
MAA: Mathematical Association Of America
Competitions page of the MAA 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 MAA. Get full info, sample questions, register, and start practicing.
AMC 10/12
The advanced AMC for 10th-12th graders. Everything you need to get started. Add plenty of natural talent, expert coaching, and a ton of practice, and you're all set.
More U.S. Competitions
Other math contests are held across the country to test the mettle of math students. Click here for information on 25 high school matches and here for 10 tests geared to grades 3-5.
Puzzling
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.
Other
Mathematics on YouTube
There's no shortage of excellent math channels on YouTube devoted to problem solving. My current favorites are: Presh Talwalkar, Math Avenue, SyberMath, and PreMath.
AP Calculus Exams
Official College Board pdf covers both tests. Wiki info here. Excellent Magoosh AB and BC guides here, here, here.
Integral Calculator and Derivative Calculator
Mathbots calculate definite integrals, antiderivatives, and 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” summaries and other excellent math study resources.
Proofs of the Pythagorean Theorem
With proofs too numerous to count, there seems to be no end to the energy and creativity devoted to proving the best known fact of basic mathematics in new and ingenious ways.
Wolfram MathWorld
Hard to argue with the site's billing as "the world's most extensive mathematical resource." For professionals and enthusiasts alike.
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, and more. Cheat sheet here.
Desmos
Powerful online graphing calculator allows animation sliders, tables, restrictions, regression, more. Free non-programmable alternative to the Ti-84 Plus CE. Standard on the dSAT.
GeoGebra
Tools for CAS, geometry, graphing, 3D, AR support tinkering/discovery, text, drawing, tables, and specialized math documents..
Mathwords
Handy math encyclopedia/glossary listing formulas and definitions taught in the standard algebra-calculus sequence. Clear, concise, understandable explanations and examples.