Books, Software, Apps
A list of books, journals, computer software, and apps divided by category is provided below. Please contact us if there are links we should add to these lists.
- Topology and the Language of Mathematics by Chris Cunliffe
- The Art of Problem Solving by Sandor Lehoczky and Richard Rusczyk
- How to Solve It by G. Polya
- The Art and Craft of Problem Solving by Paul Zeitz
Problem solving text by a past coach of the United States IMO team
- Geometry Revisited by H. Coxeter and S. Greitzer
The best book for advanced geometry problem solvers.
- Thinking Mathematics!
A book set with both interesting problems and activites
- The USSR Olympiad Problem Book by N. Chentzov, et al.
Excellent practice for advanced competitions such as the USAMO and IMO. Problems cover non-geometric topics such as number theory, inequalities, complex numbers, and more.
- USA and International Mathematical Olympiads by T. Andreescu & Z. Feng
Problems and solutions from the USAMO & IMO. Written by two coaches of the United States IMO team.
- The Mandelbrot Competition First Five Years by S. Vandervelde
An excellent introduction to mathematical writing for beginning and intermediate problem solvers; contains the Team Tests from the first five years of the Mandelbrot Competition (go to Resources page at the site to learn how to purchase these past tests).
- Challenging Problems in Geometry by A. Posamentier, C. Salkind
- Mathematical Olympiads 1998-1999, Problems and Solutions from Around the World by T. Andreescu & Z. Feng
Problems (some with solutions, some without) from 30 national and regional Olympiads from around the world.
- USA Mathematical Olympiads 1972-1986 Problems and Solutions by M. Klamkin
- The Canadian Mathematical Olympiad
Problems from the Canadian Olympiad from 1969-1993.
- Mathematical Olympiad Challenges by T. Andreescu, R. Gelca, M. Saul
Advanced problems from the coach of the United States IMO team and a producer of ARML.
- The Mathematical Olympiad Handbook by A. Gardiner
Over 300 problems presented with solutions from the British Mathematics Olympiad.
- More Mathematical Challenges: Problems for the UK Junior Mathematical Olympiad by A. Gardiner, T. Gardiner.
Explorations in Mathematics
- What is Mathematics? by R.Courant, H. Robbins, I. Stewart
An excellent resource for advanced problem solvers, as well as for students looking for a new subject to explore. Includes many advanced topics and mathematical techniques.
- Godel, Escher, Bach by Douglas Hofstadter
This Pulitzer Prize winner has inspired many high school students to pursue a career in the maths and sciences.
- Godel's Proof by Ernest Nagel and James R. Newman
This provides an interesting and palatable view into the world of paradoxes and inconsistency.
- Godel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter
This ties together a famous mathematician, artist, and musician while exploring many profound mathematical concepts.
- Journey into Geometries by Marta Sved
A journey through geometrical topics, including projection, inversion, and non-Euclidean gemoetries.
- Problems for Mathematicians, Young and Old by Paul Halmos
Challening problems for budding problem-solvers and starting points for projects in new subjects.
- Mathematical Tourist by I. Peterson
Studies in number theory, chaos, topology, higher dimensions, and more.
- Archimedes' Revenge by Paul Hoffman
Entertaining journey into the world of numbers, shapes, codes, and probabilities.
- Mathematical Carnival by Martin Gardner
Collection of puzzles and explorations.
- In Code: A mathematical journey by Sarah Flannery
A biography of a woman enthusiastically involved in cryptography, computer science, and math in general. A captivating and inspiring book.
- The Code Book by Simon Singh
History of cryptography from ancient Egypt through quantum cryptography.
- The Man Who Loved Only Numbers by Paul Hoffman
Biography of prolific mathematician Paul Erdos, as well as a handful of problems and some history of number theory.
- Fermat's Enigma by Simon Singh
History of Fermat's Last Theorem, including much of the history of number theory.
- Crypto by Steven Levy
Recent history about the battles over cryptography in the private sector and government.
- Journey Through Genius by William Dunham
A walk through math history via some landbreaking proofs.
- History of Mathematics by Boyer
An excellent resource and cited by many other credible math history books.
- The Nothing That Is: A Natural History of Zero by Robert Kaplan
- The Golden Ratio: The story of phi, the world's most astonishing number by Mario Livio
- Mathematician's Apology by G. H. Hardy
Touching auto-biographical account of the life a renowned mathematician. More than mere history,
it vividly portrays the psychology of a brilliant man as his mathematical powers are fading.
- Flatland by E. Abbot
Entertaining fiction about life in two dimensions which doubles as a social satire about Victorian England.
- Flatterland by I. Stewart
Inspired by the classic Flatland, this book introduces modern mathematical topics in a similar way.
- Innumeracy by John Allen Paulos
Entertaining, and a bit frightening, tales of mathematical illiteracy.
- Proofs Without Words and Proofs Without Words, Vol 2 by R. Nelsen
Engaging visual proofs of mathematical theorems and relationships.
- Mathematical Cranks by Underwood Dudley
Amusing stories about amateur mathematicians.
Periodical for gifted students produced by John's Hopkins University's Center for Talented Youth.
- Mathematics & Informatics Quarterly
Problem solving approaches, problems, and informatics information for high school students.
- Crux Mathematicorum with Mathematical Mayhem
Canadian Mathematical Society's Journal for undergraduate and high school students.
Easy-to-use software for producing mathematics notation for documents and the internet. Much of the math you'll find on this site was produced with MathType. li>
- The Geometer's Sketchpad
A dynamic construction and exploration tool for investigating geometry. Most of the geometry diagrams you'll find on this site are produced with the Geometer's Sketchpad.
- Education Program for Gifted Youth
Through EPGY, students have access to multimedia courses in a variety of subjects at levels ranging from kindergarten through advanced-undergraduate.
Students across the world rely on Maplesoft products to help with homework and to complete assignments.
- NCTM Illuminations Activities
- iPad Apps:
- Minds of Math - by IBM, chronological view of math as seen through biographies of some great mathematicians from 1100 to 1950.
- Science 360 - by NSF, science and math topics
- Data Finder 3.0 - statistics by country, topic or indicators; updated frequently by World Bank
- Math - prealgebra, algebra 1, geometry lessons
- IMathematics! - a math dictionary