See also:

• Science: Math: Applications  (924)
• Science: Math: Topology  (221)

Commutative Hypercomplex Mathematics - A commutative algebra, function theory, and system of analysis is developed for one 4-D variable (not quaternions). It is based upon a commutative group ring and extends all of the properties of the classical complex variables.

Complex Geometry of Nature and General Relativity - A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.

Differential Equations and Oscillations - Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.

Dimensional Analysis - A simple review of the powerful technique of dimensional analysis.

Discrete Self-trapping Equation - A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.

Doing Physics with Quaternions - A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.

Euclidean Geometric Transforms for Physics - A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.

Five Lectures on Soliton Equations - A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.

Geometry and Duality - Lecture notes from the ITP miniprogram on Geometry and Duality

Holomorphic Methods in Mathematical Physics - This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations.

Homological Methods in Mathematical Physics - These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.

Hyperreal World - Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.

Inexplicable Secrets of Creation - Relationships between number theory and physics.

Intrinsic Localized Modes - Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.

An Introduction to Noncommutative Geometry - A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.

Journal on Applied Clifford Algebra - Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis en the applications to Physics.

Klaus Brauer's Soliton Page - Presents a history of J.S.Russell's discovery of solitary waves, and animations of one-, two- and three-soliton solutions to the Korteweg-de Vries equation. Includes an article in PDF format on finding exact solutions to the KdV equation using the method of Backlund transform with the help of Mathematica.

Lectures on Orientifolds and Duality - Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.

Local Quantum Physics Crossroads - An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).

Mathematical Methods I - This site contains the complete lecture notes and homework sets for PHYCS498MMA, a course of mathematical methods for physics given to entering graduate students, and senior undergraduates, at the University of Illinois at Urbana-Champaign.

Non Commutative Geometry - Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.

On the Origins of Twister Theory - A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.

Open Problems in Mathematics and Physics - Links to open problems in mathematics, physics and other subjects.

Period and energy in one degree of freedom systems - An article by Jorge Rezende, University of Lisbon. [PDF]

Recent Developments in Skyrme Models - An introduction by T. Gisiger and M.B. Paranjape to recent, more mathematical developments in the Skyrme model. The aim is to render these advances accessible to mainstream nuclear and particle physicists.

Solitons - An overview of the classical and quantum theory related to solitons

Solitons - Resources at Heriot-Watt University. Meetings, local and other links.

Symplectic Geometries in Quantum Physics and Optics - A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics

This Week's Finds in Mathematical Physics - This is a column written about modern topics in mathematical physics.

Topology and Physics - An essay by C. Nash on the historical connection between topology and physics.

Twistors- What are they? - A set of notes introducing spinors and twistors.

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