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Web Pages
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  This Week's Finds in Mathematical Physics http://math.ucr.edu/home/baez/TWF.html
This is a column written about modern topics in mathematical physics.
  Dimensional Analysis http://www.physics.uoguelph.ca/tutorials/dimanaly/
A simple review of the powerful technique of dimensional analysis.
  Solitons http://www.ma.hw.ac.uk/solitons/
Resources at Heriot-Watt University. Meetings, local and other links.
  Doing Physics with Quaternions http://world.std.com/~sweetser/quaternions/qindex/qindex.html
A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.
  Local Quantum Physics Crossroads http://www.lqp.uni-goettingen.de/lqp/
An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).
  Symplectic Geometries in Quantum Physics and Optics http://arxiv.org/abs/quant-ph/9509002
A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
  Discrete Self-trapping Equation http://www.ma.hw.ac.uk/~chris/dst/
A bibliography in BibTeX format for those interested in discrete nonlinear Schrödinger type equations.
  Klaus Brauer's Soliton Page http://www.usf.uni-osnabrueck.de/~kbrauer/solitons.html
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.
  An Introduction to Noncommutative Geometry http://arxiv.org/abs/physics/9709045
A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
  Mathematical Methods I http://w3.physics.uiuc.edu/~m-stone5/mma/mma.html
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.
  Lectures on Orientifolds and Duality http://arxiv.org/abs/hep-th/9804208
Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
  (UK) North British Mathematical Physics Seminar http://www.maths.ed.ac.uk/NBMPS/
Four seminars are held in rotation every year.
  Intrinsic Localized Modes http://www.lassp.cornell.edu/~sievers/ilm/
Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.
  Holomorphic Methods in Mathematical Physics http://arxiv.org/abs/quant-ph/9912054
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.
  On Mathematics, Mathematical Physics, Truth and Reality http://www.spaceandmotion.com/mathematical-physics/logic-truth-reality.htm
How mathematics exists in the universe and is related to physical reality.
  Complex Geometry of Nature and General Relativity http://arxiv.org/abs/gr-qc/9911051
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.
  Period and energy in one degree of freedom systems http://gfm.cii.fc.ul.pt/people/jrezende/jr_periodenergy1.pdf
An article by Jorge Rezende, University of Lisbon.
  On the Origins of Twister Theory http://users.ox.ac.uk/~tweb/00001/
A new approach pioneered by Roger Penrose, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity.
  Journal on Applied Clifford Algebra http://clifford-algebras.org
Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis on the applications to Physics.
  Twistors- What are they? http://www.compsoc.net/~fedja/twistors/twistors.html
A set of notes introducing spinors and twistors.
  Non Deterministic Approaches http://www.ndaportal.com
NDAPortal.com is a free online repository and community dealing with uncertainty and variability in applied mechanics and engineering that explains the application of probabilistic and possibilistic methods in engineering projects.
  Commutative Hypercomplex Mathematics http://home.comcast.net/~cmdaven/hyprcplx.htm
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.
  Inexplicable Secrets of Creation http://www.secamlocal.ex.ac.uk/~mwatkins/isoc/
Relationships between number theory and physics.
  Hyperreal World http://www.sun-inet.or.jp/~leibniz/math/
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English/Japanese.
  Differential Equations and Oscillations http://www.physics.orst.edu/~rubin/nacphy/ComPhys/DIFFEQ/mydif2/
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.
  Recent Developments in Skyrme Models http://arxiv.org/abs/hep-th/9812148
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 http://physics1.usc.edu/~vongehr/solitons_html/solitons.html
An overview of the classical and quantum theory related to solitons
  Euclidean Geometric Transforms for Physics http://physicstransforms.tripod.com/
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 http://arxiv.org/abs/q-alg/9712005
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
  Topology and Physics http://arxiv.org/abs/hep-th/9709135
An essay by C. Nash on the historical connection between topology and physics.
  Homological Methods in Mathematical Physics http://arxiv.org/abs/math.DG/9808130
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.
  The Dirac Delta Function http://www.ph.ed.ac.uk/~wjh/teaching/Fourier/documents/delta.pdf
A brief introduction to the properties and uses of the Dirac delta function.
  Non Commutative Geometry http://dftuz.unizar.es/~rivero/research/index.html
Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
  Geometry and Duality http://online.itp.ucsb.edu/online/geom/
Lecture notes from the ITP miniprogram on Geometry and Duality

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