Educational Resources
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, 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
Superenthusiastic YouTube calculus teacher provides
excellent lessons on intergration and other topics of
interest to calculus students. Highly recommend!

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 allaround 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. Followup
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 NonMathematicians
List 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 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 realworld 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.
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
Fullyaccredited problem solving school offering *superb*
mathematics programs, courses, books, and other resources
for kids in grades 212. Ready? Set? Click!

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 10th12th 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.

Groups
National Puzzler’s
League
Premier national organization for wordplay puzzlers
(palindromes, cryptograms, crosswordtype 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 onlocation 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
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 13,
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 nonprogrammable alternative to the Ti84 Plus CE.
GeoGebra
Great site for doing math online. Tools for CAS, geometry,
graphing, 3D, and AR support tinkering/discovery, text,
drawing, tables, documents. Byebye graph pad!
Mathwords
Handy math encyclopedia/glossary listing
formulas/definitions along the standard algebracalculus
sequence. Clear, concise, understandable
explanations/examples.
Copyright
© 2006Present: Christopher R. Borland. All Rights
Reserved.