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Web Links for Mathematical Subjects

A long time ago this page collected most of the sites which I had found helpful in preparing theorem descriptions. By now it would be a huge task to bring it up to date. What is on offer is good (and the links are working, as of September 2012); there just isn't much of it. If anyone has suggestions for inclusion I will be very happy to respond.

Analysis
Binomial and Fibonacci
Combinatorial Theory
Education
Geometry and Trigonometry
Group Theory
History and Philosophy
Logic and Computer Science
Number Theory
Organisations
Statistics and Probability
Topology
Women in Mathematics

Analysis

SOS Maths is a good source of notes, generally on calculus, differential equations and the like.

The UBC Calculus Online site covers basic integration, differential equations and Taylor series very thoroughly.

 

Binomial & Fibonacci

Ron Knott's wonderful compendium of material on the Fibonacci Sequence and the Golden Section.

A very nicely presented compilation of Pascal's Triangle things.

A useful collection of Fibonacci-related links (thanks to Dawn Shultz for this).

 

Combinatorial Theory

Peter Cameron has many fine notes and papers on combinatorics and group theory. He also maintains the Encyclopedia of Design Theory site.

Clement Lam's extended essay on the proof that there exists no projective plane of order 10 is very well written.

Robin Thomas has good notes on many aspects of graph theory, including an excellent description of the Four Colour Theorem and its proof.

 

Education

The Young Child and Mathematics by Juanita V. Copley, published by the National Association for the Education of Young Children

 

Geometry and Trigonometry

Clark Kimberling: home of the Encyclopedia or Triangle Centers etc, as well as some nice biographical studies.

Geometry Step by Step from The Land of the Incas by Antonio Gutierrez (beautifully animated illustrations and proofs from geometry).

John C. Polking's site has some beautiful notes on the geometry of the sphere.

 

Group Theory

Peter Cameron's Permutation Group Resources is the perfect place to start...

 

History and Philosophy

Reinhard Laubenbacher and David Pengelley have a nice project on Teaching with Original Historical Sources in Mathematics.

 

Logic and Computer Science

Dan Hirschberg's site has some nice lecture notes on algorithms, data structures and data compression.

Dale Mayers has created a very nice 'story' which begins with Cantor and ends in a proof of Godel's theorems.

I suppose Ham Richard's E. W. Dijkstra Archive belongs here, although his manuscripts contain gems from many areas.

 

Number Theory

Peter Borwein offers an amazing supply of papers, talks and other things relating to number theory and polynomials.

Eric van Fossen Conrad has a very nice extended essay on Jacobi's Four Square Theorem.

Chris Caldwell maintains a great site devoted to prime numbers, the Prime Pages.

Larry Freeman has a 'blog' on Fermat's Last Theorem which covers lots of ground in many directions.

Timothy Gowers provides many wonderfully-written notes and essays on number theory and combinatorics, as well as on more philosophical topics.

Franz Lemmermeyer, has compiled lists of lecture notes on various aspects of number theory

 

Organisations

The International Center for Scientific Research offers many valuable international listings, e.g. mathematics organisations, people etc.

 

Statistics and Probability

Thayer Watkins has a nice discussion, illustrated by applets, of the Central Limit Theorem.

 

Topology

 

Women in Mathematics

There are many resources at the national and international level (please let me know of omissions):

Association for Women in Mathematics, at the Candadian Mathematical Society, European Women in Mathematics, Femmes-et-Maths, at the London Mathematical Society, International Mathematical Union website

Many university mathematics departments support initiatives (again, please let me know of omissions):

at UC Berkeley, at University of Illinois at Urbana-Champaign, at Metropolitan State University of Denver, at University of Minnesota, at MIT, at Northwestern University, at University of Maryland, at University of Pennsylvania, at Smith College, at University of Waterloo, at University of Wisconsin Madison.

The web has some wonderful individual contributions as well: John J. O'Connor and Edmund F. Robertson’s collection of biographies at the famous MacTutor History of Mathematics; Cathy O'Neil's mathbabe.org; another collection by Larry Riddle; Marie A. Vitulli’s Women in Math project; the Girls Equal organisation. Top science sites include: Mums in Science and Women Rock Science.

There are many non-academic organisations which can support women scientists as professionals, leaders or mentors. For instance:

the International Federation of Business and Professonal Women (BPW International), for instance, and its sister organisations Business and Professional Women UK Limited (BPWUK) and BPW EUROPE.

A good ongoing discussion of femal role models in mathematics can be found here.

Theorems of the Day by women mathematicians are listed here; I have an associated series of calendars "12 Theorems by Women Mathematicians" but this is on hold for the minute while I (slowly) accumulate more theorem descriptions. The 2010 calendar remains available as a free download from the shop. The Bibliography has a women in mathematics section.

 


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