Mathematics for Physicists

Mathematics for Physicists

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Real Analysis

http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF

http://www.math.harvard.edu/~ctm/home/text/class/harvard/114/07/html/home/course/course.pdf

https://www.math.lsu.edu/~sengupta/4031f06/IntroRealAnalysNotes.pdf

http://www.math.mcmaster.ca/courses/20112012/term1/math721/M721%20Advanced%20Real%20Analysis%20Sept%2028.pdf

 

Complex Analysis

http://math.sfsu.edu/beck/papers/complex.pdf

https://www.math.lsu.edu/~neubrand/notes.pdf

http://infohost.nmt.edu/~iavramid/notes/complanal.pdf 

 

Vector Analysis 

http://www.matthewhutton.com/files/VA%20Notes.pdf

http://www.archim.org.uk/lecturenotes/ia/VC_2000.pdf

http://www.mecmath.net/calc3book.pdf 

http://www.math.caltech.edu/~dinakar/Vector%20Calculus%20Notes.pdf

http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/vcalc.html

 

Functional Analysis 

http://www.maths.lancs.ac.uk/~belton/www/notes/fa_notes.pdf

http://www.uea.ac.uk/~h720/teaching/functionalanalysis/materials/FAnotes.pdf

http://www.ima.umn.edu/~arnold/502.s97/functional.pdf

 

Mathematical Analysis 

http://maths.anu.edu.au/~rennie/Analysis-1.pdf

http://cis01.central.ucv.ro/site/Vol1-DifferentialCalculus.pdfModern and Classical Analysis 

http://www.indiana.edu/~mathwz/PRbook.pdfhttp://www.math.ust.hk/~machiang/391N/Classical_Analysis.pdf

http://www.cems.uvm.edu/~cooke/analysis.pdf

 

Linear Algebra  

http://www.math.byu.edu/~klkuttle/linearalgebra.pdf 

http://www.math.ubc.ca/~carrell/NB.pdf

http://www.math.ucdavis.edu/~linear/linear.pdf 

http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf  

 

Modern and Classical Analysis  

http://yaroslavvb.com/papers/books/Smith-Primer%20of%20Modern%20Analysis-Part3.pdf

http://www.mathematik.uni-bielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/urbano.pdf

http://www.scribd.com/doc/53408614/Introduction-to-Topology-and-Modern-Analysis

http://www.math.ust.hk/~machiang/391N/Classical_Analysis.pdf

http://www.cems.uvm.edu/~cooke/analysis.pdf 

 

Abstract Algebra 

http://www.math.umn.edu/~garrett/m/intro_algebra/notes.pdf 

http://www.math.purdue.edu/~dvb/algebra/algebra.pdf

http://www.math.niu.edu/~beachy/abstract_algebra_2ed/guide/guide.pdf

http://www.math.utoledo.edu/~dbastos/files/algebra.pdf

 

Groups, Rings and Fields 

 http://www.jmilne.org/math/CourseNotes/GT.pdf

 http://www.geometer.org/rubik/group.pdf

 http://www.win.tue.nl/~amc/ow/gpth/reader.pdf

 http://homepages.math.uic.edu/~grizzard/Professional/WCgroup.pdf

 http://www.math.iitb.ac.in/atm/atmt1/jkv.pdf

 http://www3.ntu.edu.sg/home/Frederique/chap2.pdf

 http://www.jmilne.org/math/CourseNotes/CFT310.pdf

 http://www.lorentz.leidenuniv.nl/~vanbaal/FTcourse.html

 http://www.lorentz.leidenuniv.nl/~vanbaal/FTcourse.html 

 

Matroid Theory 

http://www.math.washington.edu/~billey/classes/582/bulletins/wilson.matroids.pdf

http://www.whitman.edu/mathematics/SeniorProjectArchive/2008/hillman.pdf

https://www.math.lsu.edu/~oxley/survey4.pdf 

 

Algebraic Structures 

http://www.maths.qmul.ac.uk/~pjc/notes/algstr.pdf

http://www.math.niu.edu/~beachy/courses/520.html

http://www.cs.ubc.ca/~nickhar/Publications/AlgebraicMatching/AlgebraicMatching.pdf 

 

Symmetries 

http://math.mit.edu/~apost/papers/symmetries.pdf

ftp://ftp.cs.wisc.edu/Approx/symmetries.pdf

http://www.math.ubc.ca/~cass/symmetry.pdf 

http://www.math.umn.edu/~olver/s_/v.pdf 

http://www.math.columbia.edu/~bayer/F03/symmetry/

http://hans.math.upenn.edu/~galois/

 

Algebraic Topology 

http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf

http://www.maths.tcd.ie/~dwilkins/Courses/421/

http://www.math.muni.cz/~cadek/at/at.pdf

http://arxiv.org/list/math.AT/current  

 

Geometric Topology 

http://www.maths.ed.ac.uk/~aar/books/gtop.pdf

http://fds.oup.com/www.oup.co.uk/pdf/0-19-851597-9.pdf

http://arxiv.org/list/math.GT/current

http://www.math.harvard.edu/~ctm/home/text/class/harvard/99r/03/html/home/course/course.pdf  

 

Gauge Theory(ies)

http://psroc.phys.ntu.edu.tw/cjp/v30/955.pdf

http://www2.warwick.ac.uk/fac/sci/physics/current/teach/module_home/px430

http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf

http://math.ucr.edu/home/baez/qg-winter2005/group.pdf

http://arxiv.org/pdf/hep-th/9910190.pdf 

 

Tensor Analysis 

http://samizdat.mines.edu/tensors/ShR6b.pdf

http://www.math.princeton.edu/~nelson/books/ta.pdf

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050175884_2005173651.pdf

http://assets.cambridge.org/97805216/52278/excerpt/9780521652278_excerpt.pdf 

 

Point Set Topology 

http://www.math.cornell.edu/~hatcher/Top/TopNotes.pdf

http://home.imf.au.dk/marcel/gentop/noter.pdf

http://match.stanford.edu/bump/math171/topology.pdf

http://math.ou.edu/~amiller/4853/TopologyNotes.pdf

http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/blackhl.htm 

 

Number Theory 

http://www.artofproblemsolving.com/Resources/Papers/SatoNT.pdf

http://www.jmilne.org/math/CourseNotes/ANT.pdf

http://wstein.org/ent/ent.pdf

http://www.macalester.edu/~hutchinson/book/chapter4.pdf 

http://www.numbertheory.org/ntw/lecture_notes.html

 

Discrete Mathematics 

http://www.cs.tau.ac.il/~odedr/teaching/discrete_math_fall_2005/dmbook.pdf

http://home.iitk.ac.in/~arlal/book/mth202.pdf

http://www.abstractmath.org/MM/dm.pdf  

 

Non Commutative Geometry 

http://www.math.vanderbilt.edu/~bisch/ncgoa04/talks/masoud_khalkhali.pdf

http://www.claymath.org/library/proceedings/cmip06.pdf

http://alainconnes.org/docs/einsymp.pdf

http://arxiv.org/abs/1005.1174

http://www.math.fsu.edu/~marcolli/NCGindex.html 

 

Discrete Geometry 

http://www.claremontmckenna.edu/pages/faculty/lenny/papers/m149_notes.pdf

http://www.intlpress.com/books/_preview/9781571461919.pdf

http://russell.lums.edu.pk/~cs611s09/lectures.html

http://www.dmg.tuwien.ac.at/gruber/gruber_arbeiten/convex_and_discrete_geometry.pdf

http://geometry.caltech.edu/pubs/GSD06.pdf

 

Differential Geometry 

http://people.uncw.edu/lugo/courses/diffgeom/dg1.pdf

http://www.math.uga.edu/~shifrin/ShifrinDiffGeo.pdf

http://www.astrohandbook.com/ch10/differential_geometry.pdf

http://people.math.gatech.edu/~ghomi/LectureNotes/index.html

http://www.cis.upenn.edu/~jean/gbooks/manif.html

 

Manifolds

http://www.nd.edu/~lnicolae/Lectures.pdf

http://www.math.washington.edu/~lee/Books/Smooth/c01.pdf

http://www.mpfiltricanada.com/pdf/9_manifolds.pdf

http://www.few.vu.nl/~vdvorst/diffgeom1b.pdf

http://www.math.cornell.edu/~hatcher/3M/3M.pdf

 

Ordinary and Partial Differential Equations 

http://www.math.iitb.ac.in/~siva/afs07.pdf

http://www.math.cornell.edu/~bterrell/dn.pdf

http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/ 

http://www-solar.mcs.st-and.ac.uk/~alan/MT2003/PDE/PDE.html 

http://math.berkeley.edu/~evans/

 

Mathematical Methods 

http://nd.edu/~powers/ame.60611/M.pdf

http://www.mpipks-dresden.mpg.de/~jochen/methoden/outline.html

http://www.physics.miami.edu/~nearing/mathmethods/

http://physics.bgu.ac.il/~gedalin/Teaching/Mater/mmp.pdf

http://www.math.leidenuniv.nl/~kooman/problem_setMMP.pdf

http://www.math.umn.edu/~voronov/18.276/

http://infohost.nmt.edu/~iavramid/notes/mathphys.pdf

http://people.uncw.edu/hermanr/phy311/MathPhysBook/index.htm 

 

Algebraic Surfaces 

http://arxiv.org/abs/alg-geom/9602006

http://www-math.sp2mi.univ-poitiers.fr/~sarti/corso_Perego.pdf

http://ocw.mit.edu/courses/mathematics/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring-2008/lecture-notes/ 

 

Banach Algebras( and Spaces )

http://www.maths.tcd.ie/~levene/442C/?notes

http://www.math.ucsd.edu/~bdriver/240A-C-03-04/240_lecture_notes.htm

http://matematicas.univalle.edu.co/~juancamg/Banach2.pdf

http://www.math.ucdavis.edu/~hunter/book/ch5.pdf 

http://homepage.ntlworld.com/ivan.wilde/notes/fa1/fa1.pdf

http://www.imsc.res.in/xmlui/handle/123456789/168

 

Linear Dynamical systems/Chaotic dynamical Systems and Fractals

http://www.stanford.edu/~boyd/ee263/reader/ee263_course_reader.pdf

http://www.ams.jhu.edu/~ers/book.pdf

http://catdir.loc.gov/catdir/samples/cam033/2001052863.pdf

http://ipht.cea.fr/Pisp/stephane.nonnenmacher/notesSD-en.pdf

http://ifts.zju.edu.cn/~xingangwang/Course2010/download/Yorke-chaos.pdf

http://www.brotherstechnology.com/docs/fractals.pdf

http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/World_of_Fractal.pdf

http://www.fractovia.org/art/pdf/nature_or_fractals.pdf

http://homepages.warwick.ac.uk/~masdbl/dimension-total.pdf

http://classes.yale.edu/fractals/Aut11/Aut11DailyNotes.html 

 

 

Set Theory, Logic And Probability

http://www.comp.nus.edu.sg/~fstephan/settheory.pdf

http://www.math.toronto.edu/weiss/set_theory.pdf

http://www.scribd.com/doc/25318637/Set-Theory-Lecture-Notes

http://www.math.ucla.edu/~ineeman/223s.1.11s/

http://people.umass.edu/partee/NZ_2006/Set%20Theory%20Basics.pdf

http://homepages.math.uic.edu/~marker/math512/dst.pdf

http://www.math.psu.edu/simpson/notes/logic.pdf

http://www.math.umn.edu/~jodeit/course/ACaRA01.pdf

http://www.cs.utexas.edu/~vl/teaching/388Lnotes.pdf

http://www.algebraworkbench.net/download/n41main.pdf

http://www.maths.qmul.ac.uk/~pjc/notes/prob.pdf

http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf

http://homepages.uconn.edu/~rib02005/lecture.html

 

 

 

Lie Groups and Lie Algebras 

http://www.math.sunysb.edu/~kirillov/mat552/liegroups.pdf

http://www.worldscibooks.com/etextbook/6462/6462_chap00.pdf

http://math.berkeley.edu/~anton/written/LieGroups/LieGroups.pdf

http://www.math.columbia.edu/~khovanov/lgroups/

http://arxiv.org/abs/math-ph/0005032

 

Geometric Representation Theory and Graph Theory 

http://www.math.columbia.edu/~khovanov/resources/

http://www.math.harvard.edu/~gaitsgde/267y/catO.pdf

http://math.ucr.edu/home/baez/qg-fall2007/

http://users.utu.fi/harju/graphtheory/graphtheory.pdf

http://homepages.warwick.ac.uk/~masgax/notes.pdf

http://john.fremlin.de/schoolwork/graph/index.html

http://www.cs.elte.hu/~karolyi/GT/index.html 

 

Some more important links 

http://tgd.wippiespace.com/public_html/tgdclass/tgdclass.html#rgflow

http://www.math.miami.edu/~dsolis/notes.html

http://www.maths.cam.ac.uk/studentreps/res/notes.html

http://www.damtp.cam.ac.uk/user/examples/

http://www.puremaths.info/video-lectures-in-mathematics/

http://freescienceonline.blogspot.in/2006/06/free-mathematics-video-courses.html

http://freescienceonline.blogspot.in/2008/10/more-free-mathematics-video-courses.html

http://freescienceonline.blogspot.in/2009/10/mathematics-video-lectures.html

http://freescienceonline.blogspot.in/2009/01/calculus-video-lectures-bonus-basic.html

http://freescienceonline.blogspot.in/2006/09/mathematics-video-lectures.html

http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra 

http://archim.org.uk/index.php

 

Thanks Physics de Pristine