So You Want to Become a Mathematician

These are copious amount of Lecture Note URLs to study Mathematics at graduate level
left in the WWW domain for students. Whatsoever be the number of lecture note URLs,
students are advised to buy and study from standard textbooks as prescribed by their
Lecturers/Professors or as prescribed by their university course and they should also study
via these lecture notes parallely. If you have any idea or suggestion to improve this NOTE
then you are most welcome. BTW as I want to be a VERY GOOD Theoretical Physicist in
future this note is more prejudiced towards any person who wants to become a successful
theoretical physicist. If you find any broken link or if you have any suggestion to improve
this document please mail me ASAP along with the necessary details at
[email protected].

P.S : *DO GO THROUGH THE ENTIRE DOCUMENT*

PLEASE JOIN MY PAGE AT - https://
www.facebook.com/PHMATH
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Real Analysis

1.
2.
3.
4.

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
http://www.indiana.edu/~mathwz/PRbook.pdf

5.
6. http://www.math.louisville.edu/~lee/RealAnalysis/realanalysis.html
7. http://em.fis.unam.mx/~mochan/analisis.html
8. http://www.pages.drexel.edu/~gln22/Lecture%20Notes%20on%20Introductory%20Real%20Analysis.htm
9. http://www.jirka.org/ra/
10. http://www.math.ucla.edu/~tao/245a.1.10f/
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Complex Analysis

1.
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3.
4.
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6.
7.
8.
9.
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http://math.sfsu.edu/beck/papers/complex.pdf
https://www.math.lsu.edu/~neubrand/notes.pdf
http://infohost.nmt.edu/~iavramid/notes/complanal.pdf
http://www.maths.tcd.ie/~dwilkins/Courses/214/
http://math.sfsu.edu/beck/complex.html
http://www.maths.manchester.ac.uk/~cwalkden/complex-analysis/complex-analysis.html
http://www.mth.kcl.ac.uk/courses/cm322.html
http://www.math.ucla.edu/~tao/resource/general/132.1.00w/
http://homepage.ntlworld.com/ivan.wilde/notes/

Vector Analysis

1.
2.
3.
4.
5.
6.
7.

http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx
http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx/
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
http://www.math.umn.edu/~frank/multivar/Fall2003/

8.
9. http://ltcconline.net/greenl/courses/202/202.htm
10. http://dtc.pima.edu/~hacker/vectorcalc/vectorcalc.htm
11. http://www.learnerstv.com/Free-Maths-Video-lectures-ltv452-Page1.htm
12. http://tutorial.math.lamar.edu/Classes/CalcIII/CalcIII.aspx
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Functional Analysis

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3.
4.
5.
6.
7.
8.
9.
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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
http://www.math.ou.edu/~cremling/teaching/ln.html
http://www.math.umn.edu/~garrett/m/fun/
http://math.mit.edu/~rbm/
http://www.uea.ac.uk/~h720/teaching/functionalanalysis/
http://www.e-booksdirectory.com/listing.php?category=47
http://www.freescience.info/go.php?pagename=books&id=1093

Mathematical Analysis

1. http://maths.anu.edu.au/~rennie/Analysis-1.pdf
2. http://cis01.central.ucv.ro/site/Vol1-DifferentialCalculus.pdf
3. http://www.webskate101.com/webnotes/home.htmld/home.html
4. http://www.fen.bilkent.edu.tr/~kocatepe/MATH215LectureNotes.pdf
5. http://www.math.ucdavis.edu/~emsilvia/math127/math127.html
6. http://math.la.asu.edu/~kaz/mat473/12s/
7. http://cs.unitbv.ro/~pascu/analysis.php
8. http://maths.anu.edu.au/~john/lecture_notes.html
9. http://www.e-booksdirectory.com/listing.php?category=34
10. http://www.math.mcgill.ca/jaksic/MATH255.html
11. http://math.swansonsite.com/analysis.html
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Linear Algebra

1.
2.
3.
4.
5.
6.
7.
8.
9.
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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
http://www.numbertheory.org/book/
http://www.ams.sunysb.edu/~andant/ams210-lec.html
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
http://tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspx
http://www.math.ucla.edu/~tao/resource/general/115a.3.02f/

Modern and Classical Analysis

1.
2.
3.
4.
5.
6.
7.
8.
9.
10.

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
http://brazosfellowship.com/data/cool-ebooks-Lectures-in-Modern-Analysis-and-Applications-III115050.html
http://math.mit.edu/~vwg/
http://www.math.caltech.edu/~2011-12/1term/ma108a/
http://heidedn.over-blog.com/pages/lectures-in-modern-analysis-and-applications-iii-book-downloads8065084.html
http://www.scribd.com/doc/53511463/Lectures-in-Modern-Analysis-and-Applications-II-Lecture-Notes-inMathematics-No-10
http://arxiv.org/abs/math/0604089

11.
12. http://arxiv.org/abs/math.CA/9509223
13. http://arxiv.org/abs/1009.3419
14. http://front.math.ucdavis.edu/math.CA

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Abstract Algebra

1. http://www.math.umn.edu/~garrett/m/intro_algebra/notes.pdf
2. http://www.math.purdue.edu/~dvb/algebra/algebra.pdf
3. http://www.math.niu.edu/~beachy/abstract_algebra_2ed/guide/guide.pdf
4. http://www.math.utoledo.edu/~dbastos/files/algebra.pdf
5. http://www.maths.tcd.ie/~dwilkins/Courses/311/
6. http://www.pages.drexel.edu/~gln22/lecture_notes_on_abstract_algebr.htm
7. http://www.mth.kcl.ac.uk/courses/cm121.html
8. http://www.jmilne.org/math/CourseNotes/
9. http://homepages.warwick.ac.uk/~maseap/teaching/aa/aa.html
10. http://homepages.warwick.ac.uk/~maseap/teaching/aa12/aa12.html
11. http://www.learnerstv.com/Free-Maths-Video-lectures-ltv590-Page1.htm
12. http://user.math.uzh.ch/halbeisen/4students/gt.html
13. http://www.maths.nuigalway.ie/MA416/
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Groups, Rings and Fields

1. http://www.jmilne.org/math/CourseNotes/GT.pdf
2. http://www.geometer.org/rubik/group.pdf
3. http://www.win.tue.nl/~amc/ow/gpth/reader.pdf
4. http://homepages.math.uic.edu/~grizzard/Professional/WCgroup.pdf
5. http://www.math.iitb.ac.in/atm/atmt1/jkv.pdf
6. http://www3.ntu.edu.sg/home/Frederique/chap2.pdf
7. http://www.jmilne.org/math/CourseNotes/CFT310.pdf
8. http://www.lorentz.leidenuniv.nl/~vanbaal/FTcourse.html
9. http://www-thphys.physics.ox.ac.uk/people/JamesBinney/lectures.html
10. http://www.maths.usyd.edu.au/u/bobh/UoS/
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COMBINATORIAL OPTIMIZATION and Matroids ( COMMUTATIVE ALGEBRA )

1. http://users.eecs.northwestern.edu/~nickle/combOpt/index.html
2. http://www.mast.queensu.ca/~ahhoefel/pub/ccas/
3. http://math.mit.edu/~goemans/18433.html
4. http://www.math.washington.edu/~billey/classes/582/bulletins/wilson.matroids.pdf
5. http://www.whitman.edu/mathematics/SeniorProjectArchive/2008/hillman.pdf
6. https://www.math.lsu.edu/~oxley/survey4.pdf
7. http://math.sfsu.edu/federico/Clase/Matroids/lectures.html
8. http://users.eecs.northwestern.edu/~nickle/combOpt/index.html
9. http://www.math.umn.edu/~reiner/Talks/Vienna05/Lectures.pdf
10. http://www.math.uga.edu/~pete/MATH8020.html
11. http://www.math.cmu.edu/users/jcumming/teaching/commalg05/
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Algebraic Structures

1.
2.
3.
4.
5.
6.
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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
http://homepage.lnu.se/staff/psvmsi/2MA105.html
http://www.math.niu.edu/~beachy/courses/520.html
http://www.ma.huji.ac.il/~sefil/TA/2005/struct/struct.html

Symmetries

1.
2.
3.

http://math.mit.edu/~apost/papers/symmetries.pdf
ftp://ftp.cs.wisc.edu/Approx/symmetries.pdf
http://www.math.ubc.ca/~cass/symmetry.pdf

4.
5.
6.
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http://www.math.columbia.edu/~bayer/F03/symmetry/
http://hans.math.upenn.edu/~galois/

Algebraic Topology

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3.
4.
5.
6.
7.
8.
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http://www.math.umn.edu/~olver/s_/v.pdf

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
http://math.ucr.edu/home/baez/algebraic_topology/
http://ocw.mit.edu/courses/mathematics/18-906-algebraic-topology-ii-spring-2006/lecture-notes/
http://www.ams.org/bookstore/pspdf/gsm-35-prev.pdf
http://math.berkeley.edu/~auroux/215Bs12/

Geometric Topology

1. http://www.maths.ed.ac.uk/~aar/books/gtop.pdf
2. http://fds.oup.com/www.oup.co.uk/pdf/0-19-851597-9.pdf
3. http://arxiv.org/list/math.GT/current
4. http://www.math.harvard.edu/~ctm/home/text/class/harvard/99r/03/html/home/course/course.pdf
5. http://www.wfu.edu/~parslerj/math733/note.html
6. http://www.tylerclark12.com/blog/resources-for-students/course-notes/geometric-topology-course-notes/
7. http://www.math.rutgers.edu/~sferry/ps/geotop.pdf
8. http://www.math.ucdavis.edu/~deloera/MISC/BIBLIOTECA/trunk/MacPherson/MacPherson4.pdf
9. http://www.math.harvard.edu/~lurie/937.html
10. http://www.msp.warwick.ac.uk/agt/2012/12-01/b024.xhtml
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Gauge Theory(ies)

1.
2.
3.
4.
5.
6.
7.
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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
http://www.scholarpedia.org/article/Gauge_theories
http://arxiv.org/abs/math-ph/9902027

Tensor Analysis

1.
2.
3.
4.
5.
6.

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
http://www.teorfys.uu.se/people/minahan/Courses/SR/tensors.pdf
http://kolxo3.tiera.ru/M_Mathematics/MC_Calculus/MCta_Tensor%20calculus,%20forms/
Shapiro%20I.L.%20Lecture%20notes%20on%20vector%20and%20tensor%20algebra%20and%20analys
is%20(draft,%202004)(89s)_MCta_.pd
http://arxiv.org/pdf/math/0403252.pdf

7.
8. http://www.win.tue.nl/~rvhassel/Onderwijs/Tensor-ConTeX-Bib/Translated_Tensor.pdf
9. http://www.math.odu.edu/~jhh/counter2.html
10. http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/documents/Tensors_TM2002211716.pdf
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Point Set Topology

1.
2.
3.
4.

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

5.
6.
7.
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http://www.tylerclark12.com/blog/resources-for-students/course-notes/point-set-topology-course-notes/
http://www.millersville.edu/~bikenaga/topology/topology-notes.html

Number Theory

1.
2.
3.
4.
5.
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http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/Mathematical_Thinking/blackhl.htm

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

1.
2.
3.
4.
5.

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
http://www.scribd.com/doc/7736026/Lecture-Notes-in-Discrete-Mathematics
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-forcomputer-science-fall-2005/

● Non Commutative Geometry
1. http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Ring_theory.html
2. http://www.math.miami.edu/~ec/book/
3. http://arxiv.org/abs/hep-th/9711162
4. http://www.alainconnes.org/docs/book94bigpdf.pdf
5. http://www.alainconnes.org/docs/bookwebfinal.pdf
6. http://arxiv.org/abs/math/0408416
7. http://arxiv.org/abs/math/0506603
8. http://www.matem.unam.mx/~micho/papers/qgeom.pdf
9. http://xstructure.inr.ac.ru/x-bin/subthemes3.py?level=2&index1=-173391&skip=0
10. http://www.math.vanderbilt.edu/~bisch/ncgoa04/talks/masoud_khalkhali.pdf
11. http://www.claymath.org/library/proceedings/cmip06.pdf
12. http://alainconnes.org/docs/einsymp.pdf
13. http://arxiv.org/abs/1005.1174
14. http://www.math.fsu.edu/~marcolli/NCGindex.html
15. http://arxiv.org/abs/hep-th/9701078/www.math.utexas.edu/~benzvi/GRASP/lectures/NCconf.html
16. http://imperium.lenin.ru/~kaledin/math/tokyo/
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1.
2.
3.
4.
5.
6.
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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
http://yvettehba.over-blog.com/pages/downloads-lectures-on-discrete-geometry-book-7899864.html

Differential Geometry

1.
2.
3.
4.
5.

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://www.cis.upenn.edu/~jean/gbooks/manif.html
http://people.math.gatech.edu/~ghomi/LectureNotes/index.html

6. http://www.wisdom.weizmann.ac.il/~yakov/Geometry/
7. http://www.cs.elte.hu/geometry/csikos/dif/dif.html
8. http://ocw.mit.edu/courses/mathematics/18-950-differential-geometry-fall-2008/lecture-notes/
9. http://www.matematik.lu.se/matematiklu/personal/sigma/Geometry-on-web.html
10. http://people.hofstra.edu/Stefan_Waner/diff_geom/tc.html
11. http://www1.maths.leeds.ac.uk/pure/geometry/
12. http://math.stanford.edu/~conrad/diffgeomPage/
13. http://www.maths.adelaide.edu.au/michael.murray/teaching_old.html
14. http://virtualmathmuseum.org/Surface/a/bk/curves_surfaces_palais.pdf
15. http://virtualmathmuseum.org/gallery4.html
16. http://www.wisdom.weizmann.ac.il/~yakov/scanlib/hicks.pdf
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Manifolds

1. http://www.nd.edu/~lnicolae/Lectures.pdf
2. http://www.math.washington.edu/~lee/Books/Smooth/c01.pdf
3. http://www.mpfiltricanada.com/pdf/9_manifolds.pdf
4. http://www.few.vu.nl/~vdvorst/diffgeom1b.pdf
5. http://www.math.cornell.edu/~hatcher/3M/3M.pdf
6. http://ocw.mit.edu/courses/mathematics/18-965-geometry-of-manifolds-fall-2004/lecture-notes/
7. http://www.math.cornell.edu/~sjamaar/classes/3210/notes.html
8. http://ocw.mit.edu/courses/mathematics/18-965-geometry-of-manifolds-fall-2004/lecture-notes/
9. http://ocw.mit.edu/courses/mathematics/18-966-geometry-of-manifolds-spring-2007/lecture-notes/
10. http://www.math.columbia.edu/~neumann/preprints/budfinal.pdf
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Ordinary and Partial Differential Equations

1.
2.
3.
4.
5.
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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

1.
2.
3.
4.
5.
6.
7.
8.
9.
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http://www.math.iitb.ac.in/~siva/afs07.pdf

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
http://arxiv.org/abs/1203.4558

Algebraic Surfaces

1.
2.
3.
4.
5.
6.
7.

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-spring2008/lecture-notes/
http://homepages.warwick.ac.uk/~masda/surf/ParkC/
http://ocw.mit.edu/courses/mathematics/18-727-topics-in-algebraic-geometry-algebraic-surfaces-spring2008/lecture-notes/
http://math.stanford.edu/~vakil/02-245/
http://math.stanford.edu/~vakil/725/course.html

8. http://www.fen.bilkent.edu.tr/~franz/LN/LN-algeo.html
9. http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf
10. http://ocw.mit.edu/courses/mathematics/18-726-algebraic-geometry-spring-2009/lecture-notes/
11. http://www.math.rice.edu/~hassett/teaching/465spring02/465lec.html
12. http://math.stanford.edu/~vakil/0506-216/
●

Banach Algebras( and Spaces )

1.
2.
3.
4.
5.
6.
●

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

1. http://www.stanford.edu/~boyd/ee263/reader/ee263_course_reader.pdf
2. http://www.ams.jhu.edu/~ers/book.pdf
3. http://catdir.loc.gov/catdir/samples/cam033/2001052863.pdf
4. http://ipht.cea.fr/Pisp/stephane.nonnenmacher/notesSD-en.pdf
5. http://ifts.zju.edu.cn/~xingangwang/Course2010/download/Yorke-chaos.pdf
6. http://www.brotherstechnology.com/docs/fractals.pdf
7. http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/World_of_Fractal.pdf
8. http://www.fractovia.org/art/pdf/nature_or_fractals.pdf
9. http://homepages.warwick.ac.uk/~masdbl/dimension-total.pdf
10. http://classes.yale.edu/fractals/Aut11/Aut11DailyNotes.html
●

Set Theory, Logic And Probability

1. http://www.comp.nus.edu.sg/~fstephan/settheory.pdf
2. http://www.math.toronto.edu/weiss/set_theory.pdf
3. http://www.scribd.com/doc/25318637/Set-Theory-Lecture-Notes
4. http://www.math.ucla.edu/~ineeman/223s.1.11s/
5. http://people.umass.edu/partee/NZ_2006/Set%20Theory%20Basics.pdf
6. http://homepages.math.uic.edu/~marker/math512/dst.pdf
7. http://www.math.psu.edu/simpson/notes/logic.pdf
8. http://www.math.umn.edu/~jodeit/course/ACaRA01.pdf
9. http://www.cs.utexas.edu/~vl/teaching/388Lnotes.pdf
10. http://www.algebraworkbench.net/download/n41main.pdf
11. http://www.maths.qmul.ac.uk/~pjc/notes/prob.pdf
12. http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/amsbook.mac.pdf
13. http://homepages.uconn.edu/~rib02005/lecture.html
14. http://www.math.drexel.edu/~jsa33/311.html
15. http://www.math.ucla.edu/~ynm/books.htm
16. http://www.nikipdf.com/freedownload/lecture-1-basic-concepts-of-set-theory-functions-and-relations.html
17. http://ocw.mit.edu/courses/mathematics/18-440-probability-and-random-variables-spring-2011/lecturenotes/

18. http://homepages.uconn.edu/~rib02005/lecture.html
19. http://ocw.mit.edu/courses/mathematics/18-175-theory-of-probability-fall-2008/lecture-notes/
20. http://www.math.psu.edu/simpson/notes/logic.pdf
21. http://www.maths.wits.ac.za/~goranko/ML/ML08.html

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Lie Groups and Lie Algebras

1.
2.
3.
4.
5.
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http://math.berkeley.edu/~anton/written/LieGroups/LieGroups.pdf
http://www.math.columbia.edu/~khovanov/lgroups/
http://arxiv.org/abs/math-ph/0005032

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

List of some ACE books which you should buy

1.
2.
3.
4.
5.
6.
7.
8.
9.

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

Geometric Representation Theory and Graph Theory

1.
2.
3.
4.
5.
6.
7.
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http://www.math.sunysb.edu/~kirillov/mat552/liegroups.pdf

http://www.amazon.com/Favorite-math-books-physics-self-study/lm/R2NCH1NBTUYXBR
http://www.amazon.com/Best-Math-Books/lm/2J1BZG9FH9R8L
http://www.physicsforums.com/showthread.php?t=611953
http://www.librarything.com/series/Mathematics+for+Self-Study
http://www.ocf.berkeley.edu/~abhishek/chicmath.htm
http://en.wikipedia.org/wiki/Undergraduate_Texts_in_Mathematics
http://www.maths.cam.ac.uk/undergrad/admissions/readinglist.pdf
http://en.wikipedia.org/wiki/Graduate_Texts_in_Mathematics (Graduate Level)
http://www.amazon.com/graduate-math-books-algebraic-stand/lm/RW8A044JA4987

Some more important links

1. http://tgd.wippiespace.com/public_html/tgdclass/tgdclass.html#rgflow
2. http://www.e-booksdirectory.com/listing.php?category=3
3. http://www.rzuser.uni-heidelberg.de/~hb3/notes.html
4. http://maths.mq.edu.au/~wchen/ln.html
5. http://ocw.mit.edu/courses/mathematics/
6. http://www.math.cmu.edu/~ploh/olympiad.shtml
7. http://www.math.tifr.res.in/~publ/ln/index.html
8. http://www.scribd.com/doc/39062851/9814293547-Olympiad-Courses-1
9. http://olympiads.win.tue.nl/imo/
10. http://www.paultaylor.eu/tripos/
11. http://www.math.wisc.edu/~angenent/Free-Lecture-Notes/
12. http://math.mit.edu/classes/18.095/
13. http://www.math.psu.edu/simpson/courses/
14. http://www.mathematicsgre.com/viewtopic.php?f=1&t=842
15. http://www.math.ucla.edu/~tao/tags.html
16. http://educhoices.org/articles/
Applied_Mathematics_OpenCourseWare_MITs_Free_Online_Undergraduate_Course_on_Applied_Mathemat
ics.html
http://tutorial.math.lamar.edu/Classes/CalcI/CalcI.aspx

17.
18. http://www.pages.drexel.edu/~gln22/Lecture%20Notes%20on%20Calculus.htm
19. http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/

20. http://ocw.mit.edu/courses/mathematics/18-022-calculus-of-several-variables-fall-2010/
21. http://euclid.ucc.ie/pages/staff/Mckay/calculus/Rossi/
22. http://www.cacr.caltech.edu/~sean/applied_math.pdf
23. http://www.understandingcalculus.com/
24. http://www.math.wisc.edu/~keisler/calc.html
25. http://www.lightandmatter.com/calc/calc.pdf
26. http://arxiv.org/abs/1205.0174
27. http://www.math.miami.edu/~dsolis/notes.html
28. http://www.maths.cam.ac.uk/studentreps/res/notes.html
29. http://www.damtp.cam.ac.uk/user/examples/
30. http://www.puremaths.info/video-lectures-in-mathematics/
31. http://freescienceonline.blogspot.in/2006/06/free-mathematics-video-courses.html
32. http://freescienceonline.blogspot.in/2008/10/more-free-mathematics-video-courses.html
33. http://freescienceonline.blogspot.in/2009/10/mathematics-video-lectures.html
34. http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra
35. http://archim.org.uk/index.php
36. http://press.princeton.edu/video/banner/
37. http://hbpms.blogspot.in/
38. http://bengtmn.wordpress.com/?blogsub=confirming#subscribe-blog
39. http://www.nptel.iitm.ac.in/courses.php?disciplineId=115
40. http://www.math.harvard.edu/~mazur/
41. http://www.e-booksdirectory.com/listing.php?category=32
42. http://www.maths.ox.ac.uk/courses/material/
43. http://v5o5jotqkgfu3btr91t7w5fhzedjaoaz8igl.unbsj.ca/~tim/UWOnotes/notes.htm
44. http://maths.dur.ac.uk/pure/preprint.html
45. http://www.e-booksdirectory.com/mathematics.php
46. http://www.e-booksdirectory.com/listing.php?category=3
47. http://web.itu.edu.tr/~delidumanc/math.html
48. http://www.learnerstv.com/
49. http://www.physicsforums.com/showthread.php?t=554150

BIBLIOGRAPHY:
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WIKIPEDIA
GOOGLE
WOLFRAM MATHWORLD
CAMBRIDGE UNIVERSITY LECTURE NOTES
HARVARD UNIVERSITY LECTURE NOTES
MATH OVERFLOW
MATH STACKEXCHANGE
MIT OCW
arXiv.Org
NPTEL

● BLACK INTEGRAL

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