Books, Software, Apps

Mu Alpha Theta

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.

Problem Solving

  • 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

Problem Sets

  • 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.

Math History

  • 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

Miscellaneous Books

  • 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.

Journals

Software

  • MathType
    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.
  • Maplesoft
    Students across the world rely on Maplesoft products to help with homework and to complete assignments.

Apps

  • 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