What are the best online, college-level mathematics courses?

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Devashish Singh

MIT OCW has a huge collection of undergraduate and graduate level courses in mathematics (and other subjects as well) which includes audio/video lectures, lecture notes, textbooks, assignments, exams and other interactive stuff etc.

Besides that there are a bunch of other online resources listed below:

• Ted Chinburg's Lectures on Algebraic Number Theory

1. Tables of current homework and lecture schedules
2. Tables of current homework and lecture schedules
3. Tables of current homework and lecture schedules

• Lectures by Adrian Banner of Princeton University

1. Calculus I : Calculus I (Princeton University)
2. Calculus II : Calculus II (Princeton University)
3. Calculus III : Multivariable Calculus : Calculus III: Multivariable Calculus (Princeton University)
4. Linear Algebra : Linear Algebra (Princeton University)

• Eugenia Cheng and Simon Willerton of the University of Sheffield, a.k.a. The Catsters' Video Lectures on Category Theory : TheCatsters

• Abstract Algebra lectures by Prof. Benedict Gross, Harvard : Abstract Algebra

• Lectures on Complex Analysis by Tibra Ali (followed by few more lectures on different topics) : Perimeter Institute Recorded Seminar Archive

• Lectures on Complex Analysis by Prof. P. A. S. Sree Krishna : New User Registration

• Lectures by Denis Dalidovich on Variational Calculus and Gaussian Integrals (followed by few more lectures on different topics) : Perimeter Institute Recorded Seminar Archive
• Geometric Representation Theory by John Baez and James Dolan : Geometric Representation Theory Seminar: Fall 2007
• Miles Reid's lectures on Algebraic Geometry and Algebraic Surfaces

1. VOD the MathNet Korea
2. VOD the MathNet Korea

• Videos from Summer School of Clay Mathematics Institute on Arithmetic Geometry (You should have a solid foundation of algebraic geometry in order to comprehend these videos) : Clay Mathematics Institute Summer School 2006 Recorded Lessons

• A mini course on Additive Combinatorics taught at IAS by Boaz Barak, Luca Trevisan, and Avi Wigderson : Page on princeton.edu

• Lectures on Real Analysis by Prof. S.H. Kulkarni, Department of Mathematics, IIT Madras : New User Registration

• Point Set Topology videos :

1. Topology - YouTube
2. General Topology

• Sets, Counting, and Probability by Paul G. Bamberg, Harvard University : Sets, Counting, and Probability

• The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford : Stanford School of Engineering

• Courses by Stephen Boyd at Stanford:

1. Introduction to Linear Dynamical Systems - Stanford School of Engineering
2. Convex Optimization I - Stanford School of Engineering
3. Convex Optimization II - Stanford School of Engineering

• Prof. Gilbert Strang's course on Linear Algebra at MIT : Linear Algebra

• Differential Equations, taught by Arthur Mattuck at MIT : MIT 18.03 Differential Equations - Spring 2006

• Video lectures for elementary differential equations with linear algebra : Differential Equations Videos

• This URL provides video lectures on key concepts of calculus : Calculus Videos

• This URL contains a series of video lectures on Calculus I from University of Missouri - Kansas City : Course - Calculus I with Professor Richard Delaware

• College Algebra taught by Professor Richard Delaware, which consists of 40 video lectures emphasizing the concepts of college algebra : Math 110: College Algebra

• More lectures on Real Analysis by Professor Francis Su Harvey, Mudd College (The video quality of the lectures are poor) :
  http://www.youtube.com/watch?v=s...

• MIT OCW - Calculus Revisited: Multivariable Calculus. This course is a study of the calculus of functions of several variables (vector arithmetic and vector calculus) : Calculus Revisited: Multivariable Calculus

• Very quick graduate Probability Theory : Probability Primer

• Very good webpage for many courses by A. D. Snider : A. David Snider

• Numerical Methods at University of South Florida and Arizona State University : Instructional Videos for Numerical Methods

• ZFC Set Theory (More oriented around Lambda Calculus and Computer Science. Sequence of Lectures is in arbitrary order, in the playlist) :
  http://www.youtube.com/watch?v=x...

• Lectures for seven courses are available (Single Variable Calculus, Multivariable Calculus, Differential Equations, Statistical Methods, Fundamentals of Mathematics, Functions of a Complex Variable, and Introduction to Number Theory). Lectures on Precalculus is being developed : Page on latech.edu

• Intro to differential forms (A good foundation of vector calculus is needed ) : http://www.youtube.com/playlist?list=PLB8F2D70E034E9C29&feature=plcp

• Maths and Mathematica - Pedro Vieira (along with some other lectures) : Perimeter Institute Recorded Seminar Archive

• Lectures for Differential Topology

1. Milnor - Differential Topology 01
2. Milnor - Differential Topology 02
3. Milnor - Differential Topology 03

• An extensive lecture series from the same guy who has done the Multi-Linear algebra videos : mlbaker

• Measure and Integration series from NPTEL resources :http://textofvideo.nptel.iitm.ac.in/video.php?courseId=111101005 (Book to be read along with the videos : http://books.google.ie/books?id=CIsOVPm6zE8C&source=gbs_navlinks_s).

• Functional Analysis Lectures by Prof. P.D. Srivastava, IIT Kanpur : New User Registration

• Calculus of Variations (20 lectures) and Integral Equations (20 lectures), by Dr. Malay Banerjee & Prof. D. Bahuguna, IIT Kanpur : http://nptel.iitm.ac.in/courses/...

• Mathematical Logic lectures by Prof. Arindama Singh, IIT Madras : Page on iitm.ac.in

• Some seminars & hardcore video courses on Algebraic Topology : Video lectures for Algebraic Geometry

• This "Physics Forums" thread contains a list of tons of lecture videos, compiled by PF members : Math - A collection of audio/video lectures on mathematics

• Tons of Video lectures which would be of utmost help in case the above list wasn't enough :

1. Audio/video Courses - Mathematics
2. Mathematics - VideoLectures.NET
3. Mathematics video lectures, tutorials & courses
4. MSRI
5. 99 Incredible Open Lectures for Math Geeks - OnlineCollege.org
6. Mathematics Video Lectures
7. Video Lectures in Mathematics
8. Page on umn.edu
9. Video Lectures in Mathematics (mathematicsprof)
10. Best online mathematics videos?
11. Video lectures of mathematics courses available online for free
12. Page on refseek.com
13. NPTEL PHASE 2 - Courses
14. Audio/Video Lectures
15. School of Mathematics

The following is another huge collection of lecture notes available online:

• Real Analysis

1. Page on trinity.edu
2. Page on harvard.edu
3. Page on lsu.edu
4. Page on math.mcmaster.ca
5. Page on indiana.edu
6. Introduction to Real Analysis
7. Page on fis.unam.mx
8. Page on drexel.edu
9. Basic Analysis: Introduction to Real Analysis
10. Page on ucla.edu

• Complex Analysis

1. Page on sfsu.edu
2. Page on lsu.edu
3. Page on nmt.edu
4. Course 214 - Complex Analysis
5. A First Course in Complex Analysis
6. MATH20101 Complex Analysis Lecture Notes
7. Page on kcl.ac.uk
8. Math 132
9. Notes

• Vector Analysis

1. Pauls Online Notes : Calculus I
2. Pauls Online Notes : Calculus II
3. Page on matthewhutton.com
4. Page on archim.org.uk
5. Page on mecmath.net
6. Page on caltech.edu
7. Study Guide for Vector Calculus
8. IT Multivariable Calculus and Vector Analysis
9. Vector Calculus Home Page
10. Wayne Hacker's Vector Calculus Webpage
11. Free Maths Video Lectures
12. Pauls Online Notes : Calculus III

• Functional Analysis

1. Page on lancs.ac.uk
2. Page on uea.ac.uk
3. Page on umn.edu
4. Page on ou.edu
5. Functional Analysis
6. Web page for Richard Melrose
7. Page on uea.ac.uk
8. Functional Analysis
9. http://www.freescience.info/go.php?pagename=books&id=1093

• Mathematical Analysis

1. Page on anu.edu.au
2. Page on central.ucv.ro
3. Page on webskate101.com
4. Page on bilkent.edu.tr
5. Math 127
6. MAT 473 / Spring 2012
7. Homepage of Mihai Pascu
8. Page on anu.edu.au
9. Mathematical Analysis & Calculus
10. MATH 255
11. math.swansonsite.com

• Linear Algebra

1. http://www.math.byu.edu/~klkuttl...
2. Page on math.ubc.ca
3. http://www.math.ucdavis.edu/~lin...
4. Page on brown.edu
5. ELEMENTARY LINEAR ALGEBRA
6. Linear Algebra Lecture Notes
7. Linear Algebra
8. Pauls Online Math Notes
9. Math 115A

• Modern and Classical Analysis

1. Page on yaroslavvb.com
2. Page on mathematik.uni-bielefeld.de
3. Page on math.ust.hk
4. Page on uvm.edu
5. Page on brazosfellowship.com
6. Victor Guillemin
7. Page on caltech.edu
8. Page on over-blog.com
9. [math/0604089] Montreal Lecture Notes on Quadratic Fourier Analysis
10. [math/9509223] Lecture notes for an introductory minicourse on q-series
11. [1009.3419] Lecture notes on variational models for incompressible Euler equations
12. math.CA Classical Analysis and ODEs

• Abstract Algebra

1. Page on umn.edu
2. Page on purdue.edu
3. Page on niu.edu
4. Page on utoledo.edu
5. Course 311 - Abstract Algebra
6. Page on drexel.edu
7. Page on kcl.ac.uk
8. Course Notes -- J.S. Milne
9. MA136 Introduction to Abstract Algebra
10. MA136 Introduction to Abstract Algebra
11. Free Maths Video Lectures
12. Group Theory
13. RING THEORY (MA416)

• Groups, Rings and Fields

1. Page on jmilne.org
2. Page on geometer.org
3. Page on win.tue.nl
4. Page on uic.edu
5. Page on iitb.ac.in
6. Page on ntu.edu.sg
7. Page on jmilne.org
8. Lecture notes and problem set for a course in Field Theory
9. Lecture notes and problem set for a course in Field Theory
10. lectures
11. Bob Howlett's teaching page

• COMBINATORIAL OPTIMIZATION and Matroids (COMMUTATIVE ALGEBRA)

1. Combinatorial Optimization
2. Page on mast.queensu.ca
3. Page on mit.edu
4. Page on washington.edu
5. Senior Project Archive
6. Page on lsu.edu
7. federico ardila - matroid theory
8. Combinatorial Optimization
9. Page on umn.edu
10. Page on uga.edu
11. Commutative Algebra

• Algebraic Structures

1. Page on qmul.ac.uk
2. Page on niu.edu
3. Page on cs.ubc.ca
4. Page on homepage.lnu.se
5. Page on niu.edu
6. Algebraic Structures 2 (80446)

• Symmetries

1. Page on mit.edu
2. ftp://ftp.cs.wisc.edu/Approx/sym...
3. Page on math.ubc.ca
4. Page on umn.edu
5. Groups and Symmetry
6. Galois Theory Home Page

• Point -Set Topology

1. Page on cornell.edu
2. Page on imf.au.dk
3. Page on stanford.edu
4. Page on ou.edu
5. Black Holes and Point Set Topology
6. Welcome tylerclark12.com - BlueHost.com
7. Notes on Topology

• Algebraic Topology

1. Page on uchicago.edu
2. Course 421 - Algebraic Topology
3. Page on math.muni.cz
4. Algebraic Topology
5. Algebraic Topology
6. Lecture Notes | Algebraic Topology II | Mathematics | MIT OpenCourseWare
7. Page on ams.org
8. Math 215B - Algebraic Topology - Spring 2012

• Geometric Topology

1. Page on ed.ac.uk
2. Page on oup.com
3. Page on harvard.edu
4. Math 733: Geometric Topology
5. Welcome tylerclark12.com - BlueHost.com
6. Page on rutgers.edu
7. Page on ucdavis.edu
8. Topics in Geometric Topology (18.937)
9. Page on warwick.ac.uk

• Gauge Theory

1. Page on ntu.edu.tw
2. PX430 Gauge Theories
3. Page on claymath.org
4. Page on ucr.edu
5. Page on arxiv.org
6. Gauge theories - Scholarpedia
7. [math-ph/9902027] Preparation for Gauge Theory

• Tensor Analysis

1. Page on mines.edu
2. Page on princeton.edu
3. Page on nasa.gov
4. Page on cambridge.org
5. Page on teorfys.uu.se
6. Page on arxiv.org
7. Page on win.tue.nl
8. Free Textbook Tensor Calculus and Continuum Mechanics
9. Page on nasa.gov

• Number Theory

1. Page on artofproblemsolving.com
2. Page on jmilne.org
3. Page on wstein.org
4. Page on macalester.edu
5. Online number theory lecture notes and teaching materials

• Discrete Mathematics

1. Page on tau.ac.il
2. Page on iitk.ac.in
3. Page on abstractmath.org
4. Lecture Notes in Discrete Mathematics
5. Mathematics for Computer Science

• Non Commutative Geometry

1. Ring Theory
2. Elements of Abstract and Linear Algebra by Edwin H. Connell
3. Compactification on Tori
4. http://www.alainconnes.org/docs/...
5. http://www.alainconnes.org/docs/...
6. [math/0408416] Very Basic Noncommutative Geometry
7. [math/0506603] Lectures on Noncommutative Geometry
8. Page on matem.unam.mx
9. http://xstructure.inr.ac.ru/x-bin/subthemes3.py?level=2&index1=-173391&skip=0
10. Page on vanderbilt.edu
11. Page on claymath.org
12. Page on alainconnes.org
13. [1005.1174] Notes on "quantum gravity" and non-commutative geometry
14. Noncommutative Geometry
15. [hep-th/9701078] An Introduction to Noncommutative Spaces and their Geometry
16. Non-commutative geometry

• Discrete Geometry

1. Page on claremontmckenna.edu
2. Page on intlpress.com
3. Page on lums.edu.pk
4. Page on tuwien.ac.at
5. http://geometry.caltech.edu/pubs...
6. Page on over-blog.com

• Differential Geometry

1. Page on uncw.edu
2. Page on uga.edu
3. Page on astrohandbook.com
4. Lecture Notes on Differential Geometry
5. Books in Progress
6. Lecture Notes on Differential Geometry
7. Notes for the course in Differential Geometry
8. Notes on Differential Geometry by B. Csikós
9. Lecture Notes | Differential Geometry | Mathematics | MIT OpenCourseWare
10. Geometry and Topology on the Web
11. Page on hofstra.edu
12. Geometry Group

• Manifolds

1. Page on nd.edu
2. Page on washington.edu
3. Page on mpfiltricanada.com
4. http://www.few.vu.nl/~vdvorst/di...
5. Page on cornell.edu
6. Lecture Notes | Geometry of Manifolds | Mathematics | MIT OpenCourseWare
7. Reyer Sjamaar
8. Lecture Notes | Geometry of Manifolds | Mathematics | MIT OpenCourseWare
9. Lecture Notes | Geometry of Manifolds | Mathematics | MIT OpenCourseWare
10. Page on columbia.edu

• Ordinary and Partial Differential Equations

1. Page on iitb.ac.in
2. Page on cornell.edu
3. Differential Equations
4. PDE
5. Lawrence C. Evans's Home Page

• Mathematical Methods

1. http://nd.edu/~powers/ame.60611/...
2. Mathematical Methods - Outline
3. Mathematical Tools for Physics
4. Page on bgu.ac.il
5. Page on math.leidenuniv.nl
6. Course 18.276 Mathematical Methods in Physics
7. Page on nmt.edu
8. Mathematical Physics Lecture Notes
9. [1203.4558] Mathemathical methods of theoretical physics

• Algebraic Surfaces

1. [alg-geom/9602006] Chapters on algebraic surfaces
2. Page on sp2mi.univ-poitiers.fr
3. Algebraic Surfaces | Mathematics | MIT OpenCourseWare
4. Chapters on algebraic surfaces
5. Algebraic Surfaces | Mathematics | MIT OpenCourseWare
6. Math 245A Topics in algebraic geometry: Complex algebraic surfaces
7. Introduction to Algebraic Geometry
8. Lecture Notes Algebraic Geometry
9. Page on mathematik.uni-kl.de
10. Lecture Notes | Algebraic Geometry | Mathematics | MIT OpenCourseWare
11. Math 465 Notes
12. Math 216: Foundations of algebraic geometry 2005-06

• Banach Algebras(and Spaces)

1. Notes - 442C Banach algebras
2. 240 Lecture Notes
3. Page on univalle.edu.co
4. Page on ucdavis.edu
5. Page on ntlworld.com
6. Notes on Banach Spaces: Basic definitions and theorems, and related Topics[MatSciRep:13]

• Linear Dynamical systems/Chaotic dynamical Systems and Fractals

1. Page on stanford.edu
2. Page on jhu.edu
3. Page on loc.gov
4. Page on ipht.cea.fr
5. Page on zju.edu.cn
6. Page on brotherstechnology.com
7. Page on nus.edu.sg
8. Page on fractovia.org
9. http://homepages.warwick.ac.uk/~...
10. Fractal Geometry

• Set Theory, Logic And Probability

1. Page on nus.edu.sg
2. Page on toronto.edu
3. Math 223S, Topics in Set Theory
4. Page on psu.edu
5. Page on umn.edu
6. Page on utexas.edu
7. Page on algebraworkbench.net
8. Page on qmul.ac.uk
9. Page on dartmouth.edu
10. Lecture Notes
11. Math 311: Probability & Statistics I, Spring 2011-2012
12. Yiannis N. Moschovakis Books
13. Page on nikipdf.com
14. Lecture Notes | Probability and Random Variables | Mathematics | MIT OpenCourseWare
15. Lecture Notes
16. Page on mit.edu
17. Page on psu.edu
18. Page on wits.ac.za

• Lie Groups and Lie Algebras

1. Page on sunysb.edu
2. Page on worldscibooks.com
3. Page on berkeley.edu
4. Math G4343-Lie Groups and Representations
5. [math-ph/0005032] An Elementary Introduction to Groups and Representations

• Geometric Representation Theory and Graph Theory

1. Representation theory online resources
2. Page on harvard.edu
3. Geometric Representation Theory Seminar: Fall 2007
4. Page on users.utu.fi
5. Page on warwick.ac.uk
6. Notes on Graph Theory
7. Lecture Notes and Exercises in Graph Theory

• Some more important links

1. Lecture Notes
2. My Lecture Notes
3. Math Olympiad teaching notes
4. Lecture Note Series
5. International Mathematics Olympiad
6. Undergraduate Mathematics Lecture Notes
7. The Free Lecture Notes Page
8. Classes | MIT Mathematics
9. Simpson: Courses
10. http://www.mathematicsgre.com/viewtopic.php?f=1&t=842
11. Tags
12. euclid.ucc.ie - /pages/staff/Mckay/calculus/Rossi/
13. http://www.cacr.caltech.edu/~sea...
14. Calculus Online Book
15. Elementary Calculus
16. http://www.lightandmatter.com/ca...
17. Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
18. Lecture Notes
19. Notes on the Web
20. Mathematics Examples
21. Video Lectures in Mathematics
22. The Archimedeans
23. The Calculus Lifesaver:
24. How to Become a Pure Mathematician (or Statistician)
25. NPTEL PHASE 2 - Courses
26. Barry Mazur Homepage
27. Pure Mathematics
28. Mathematical Institute
29. Page on v5o5jotqkgfu3btr91t7w5fhzedjaoaz8igl.unbsj.ca
30. Durham Pure Mathematics Preprint Series
31. Free Mathematics Books
32. Mathematics - Free E-Books
33. Page on itu.edu.tr
34. Free video lectures,Free Animations, Free Lecture Notes, Free Online Tests, Free Lecture Presentations
35. Math - Video Lectures for Upper-Level Mathematics

[Disclaimer: The above list is not my collection, it was provided by a friend. Apologies for any redundancies.] Thanks Sean Hood for A2A.

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