Theorem of the Day

Web Links for Mathematical Subjects

For convenience, more than anything else, I tend to group the theorems of the day into somewhat artificial categories, combinatorial theory, group theory, etc. For consistency I have done the same here, presented in alphabetical order; probably many of the links would fit happily into many or all of these categories.

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.

Anonymous Tripod site: a very nicely presented compilation of Pascal's Triangle things.

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.

Geometry and Trigonometry

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

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

Gonçalo L. Fonseca's History of Economic Thought site has a nice Mathematics Appendix covering the standard mathematics behind economics.

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

Statistics and Probability

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

Topology

The Mathematics Appendix to Gonçalo L. Fonseca's History of Economic Thought covers fixed point theorems.

Women in Mathematics

Theorems of the Day by women mathematicians are listed here; the 2008 calendar "12 Theorems by Women Mathematicians" is available from the shop.

European Women in Mathematics has links to most related organisations: the Association for Women in Mathematics, in the US; Femmes-et-Maths in France; in the UK, the relevant committee of the London Mathematics Society (click on‘Activities’). 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; another collection by Larry Riddle; and Marie A. Vitulli’s Women in Math project. Another top site: Mums in 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;
• More To Life Than Shoes.