Math

Mathematical and computer programming oriented approach. Discusses wireframe rendering and ray-tracing.

Software simulation offering straightedge and compass constructions in hyperbolic geometry.

Geometric group theory. Includes a problem list.

University of Utah. Low-dimensional geometry and topology.

Differential geometry, mathematical visualisation.

A monograph aiming to provide a readable introduction to the field of projective geometry and a handy reference for some of the more important equations. HTML, PS or PDF versions.

A set of mathematical environments for computing, visualizing and experimenting with geometric objects; built with the OpenGL/Mesa library and the GTK+ user interface.

Software for interactive geometry in three dimensions. In English, French and German.

Catalogued stars, predicted a planet beyond Uranus as well as the existence of dark stars, investigated Johann Kepler's problem of heliocentricity, and systematized the mathematical functions involved, which now bear his name.

Discusses this early Grecian's discoveries in finding a good approximation of the circumference of the earth, the tilt angle of our planet and a tool for finding prime numbers. Page includes biographical information.

Maintained by Christian Gottschall, Vienna philosophy department.

Includes an introduction to logic and formal systems, revolving around the Mizar proof checker, and a guide to Mizar.

(Hyper)textbook for students in mathematical logic, by Karlis Podnieks.

A closed, moderated, e-mail list for discussing Foundations of Mathematics moderated by Martin Davis. Archive available.

Homepage of a lecture course by Natasha Alechina, with a particular emphasis on topics relevant to computer science, such as bisimulation.

Boise State University - Set theory: New Foundations, automated theorem proving.

Carnegie Mellon University - Model theory, set theory, foundations of logic and mathematics, symbolic mathematical computation.

Queen Mary and Westfield College - Categorical logic and the semantics of programming languages and type theories.

Discussion of David Hilbert's development of this type of logical formalism with emphasis on proof-theoretic methods.

Project to keep the book (also named in the title), describing forms related to the Axiom of Choice and their implications, updated.

Takes as input the specification of a finitely-valued first-order logic and produces a sequent calculus, a natural deduction system, and clause formation rules for this logic.

A generic theorem proving environment developed at Cambridge University (Larry Paulson) and TU Munich (Tobias Nipkow). Includes logic, documentation and free download.

Program understands the different types of lambda expressions, can extract lists of variables (both free and bound) and subterms, and can simplify complicated expressions. Uses Python.

Some biographical sketches of mathematicians, ancient and modern.

A list of all of the important mathematicians working in a given century.

Listings by name, location, and fields of interest. Also includes search function.

Formulae and tables for the number of non isomorphic fields with a fixed signature and Galois group sharing a common discriminant.

Taken by Sean Sather-Wagstaff, Utah, Spring 1999. In PS and PDF formats.

Lecture Notes by Noam Elkies, Harvard, 1998.

Archives of postings to the Number Theory mailing list (NMBRTHRY).

Given a Diophantine equation with any number of unknowns and with rational integer coefficients: devise a process, which could determine by a finite number of operations whether the equation is solvable in rational integers.

Triangles in the Euclidean plane such that all three sides are rational. With tables of Heronian and Pythagorean triples.

Some of conjectures and open problems, compiled at AIM.

A web tool for solving Diophantine equations of the form ax + by = c.

Lecture Notes by Don Rideout, Memorial University of Newfoundland. PDF and Maple worksheets.

By Kenneth Kramer, Queens College (CUNY). Abstract with text in PDF.

Courses in Number Theory at St Patrick's College, Dublin.

An abstract to Henri Darmon's and Bertolini's work, which approaches a p-adic variant of the Birch - Swinnerton-Dyer conjecture, for curves of rank higher than one.

Programme at MSRI, Berkeley; January-May 2014.

Held at the Archives of American Mathematics, Center for American History, University of Texas at Austin.

Unsolved Problems in Number Theory, Logic and Cryptography, with references for further reading.

Members, publications, activities.

Carlos Rivera's collection of problems and puzzles related to prime numbers.

The "Riesel Prime Search" project is searching for primes of the form k·2^n-1, odd k.

Number Theory and Algebraic Geometry Research Group. Members, research interest, seminars.

A European network of 12 working groups from 6 countries.

Number Theory Group. Members, publications, meetings.

KANT is a software package for sophisticated computations in number fields and in global function fields. With KASH you are able to use the powerful KANT V4 functions within a shell.

EIS-Seeker is a libguile-based scheme interpreter devoted to the study of the Encyclopedia of Integer Sequences database. It is intended to help find new relations between sequences. C/Scheme, Posix.

R. Ernvall and T. Metsänkylä. Tables of the pairs (p,k) such that the Fermat quotient q(k) = (k^{p-1}-1)/p vanishes mod p. The tables cover the primes p up to one million and, for each prime, the range 1 < k < p.