Mathematics Video Lectures for Undergraduates and Graduate

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. -Albert Einstein

• Ted Chinburg's Lectures on Algebraic Number Theory

1. http://www.math.upenn.edu/~ted/620F09/hw-620SchedTab.html
2. http://www.math.upenn.edu/~ted/620S10/hw-621SchedTab.html
3. http://www.refseek.com/directory/educational_videos.html
4. http://www.math.upenn.edu/~ted/721S11/hw-721SchedTab.html

• Lectures by Adrian Banner of Princeton University

1. Calculus I : http://bit.ly/18IN4AE
2. Calculus II : http://bit.ly/19JZFnq
3. Calculus III : Multivariable Calculus : http://bit.ly/1b5XhXK
4. Linear Algebra : http://bit.ly/1b5XtGs

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

• Abstract Algebra lectures by Prof. Benedict Gross, Harvard : http://www.extension.harvard.edu/open-learning-initiative/abstract-algebra

• Lectures on Complex Analysis by Tibra Ali : http://www.perimeterscholars.org/435.html 

• Lectures on Complex Analysis by Prof. P. A. S. Sree Krishna: http://www.youtube.com/playlist?list=PLbMVogVj5nJQ9MLfcY8Q9xArBSUKp-Hbd

• Lectures by Denis Dalidovich on Variational Calculus and Gaussian Integrals : http://www.perimeterscholars.org/461.html 

• Lectures on Abstract Algebra : http://www.youtube.com/playlist?list=PLF379B0552AD17780

• Lecture Videos from the program on Topology and Field Theories : http://www3.nd.edu/~stolz/field_theory_videos.html 

• Lectures on Functional Analysis by Prof. P.D. Srivastava, Department of Mathematics, IIT Kharagpur : http://www.youtube.com/course?list=EC5022A32B9BCFE3E4

• Lectures by Anna Koustouki on Algebra : http://www.perimeterscholars.org/459.html

• Geometric Representation Theory by John Baez and James Dolan : http://math.ucr.edu/home/baez/qg-fall2007/

• Lectures on Distributions and Special Functions, by Dan Wohns : http://www.perimeterscholars.org/462.html

• Algebraic topology by Prof. N. J. Wildberger of the School of Mathematics and Statistics, UNSW : http://www.youtube.com/playlist?list=PL6763F57A61FE6FE8

• Miles Reid's lectures on Algebraic Geometry and Algebraic Surfaces 

1. http://www.mathnet.or.kr/new_VOD/sub1.php?key_s_title=Lectures+on+Basic+Algebraic+Geometry+by+Miles+Reid+%28WCU+project%29
2. http://vod.mathnet.or.kr/sub1.php?key_s_title=Lectures+on+Algebraic+Surfaces+by+Miles+Reid+%28WCU+project%29

• 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) : http://www.uni-math.gwdg.de/aufzeichnungen/SummerSchool/

•  A mini course on Additive Combinatorics taught at IAS by Boaz Barak, Luca Trevisan, and Avi Wigderson : http://www.cs.princeton.edu/theory/index.php/Main/AdditiveCombinatoricsMinicourse 

• Lectures on Real Analysis, from Bilkent University by Prof. Alexandre Gontcharov : http://courses.bilkent.edu.tr/course_videos.php?courseid=12

• Lectures on Real Analysis by Prof. S.H. Kulkarni, Department of Mathematics, IIT Madras : http://www.youtube.com/playlist?list=PLbMVogVj5nJSxFihV-ec4A3z_FOGPRCo-

• Point Set Topology videos :

1. http://www.youtube.com/user/ThoughtSpaceZero#grid/user/F94A6F65866F3F31
2. http://bit.ly/15QrBVP 

• Sets, Counting, and Probability by Paul G. Bamberg, Harvard University : http://www.extension.harvard.edu/open-learning-initiative/sets-counting-probability

• The Fourier Transform and Its Applications, taught by Brad Osgood at Stanford : http://see.stanford.edu/see/lecturelist.aspx?coll=84d174c2-d74f-493d-92ae-c3f45c0ee091

• Courses by Stephen Boyd at Stanford:

1.  Introduction to Linear Dynamical Systems - http://see.stanford.edu/see/lecturelist.aspx?coll=17005383-19c6-49ed-9497-2ba8bfcfe5f6
2. Convex Optimization I - http://see.stanford.edu/see/lecturelist.aspx?coll=2db7ced4-39d1-4fdb-90e8-364129597c87
3. Convex Optimization II - http://see.stanford.edu/see/lecturelist.aspx?coll=523bbab2-dcc1-4b5a-b78f-4c9dc8c7cf7a

• Prof. Gilbert Strang's course on Linear Algebra at MIT : http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm

• Differential Equations, taught by Arthur Mattuck at MIT : http://videolectures.net/mit1803s06_differential_equations/

• Video lectures for elementary differential equations with linear algebra : http://www.math.armstrong.edu/faculty/hollis/DEvideos/

• This URL provides video lectures on key concepts of calculus : http://www.online.math.uh.edu/HoustonACT/videocalculus/

• This URL contains a series of video lectures on Calculus I from University of Missouri - Kansas City : http://www.youtube.com/watch?v=CtRAHmeWSC0&lr=1

•  College Algebra taught by Professor Richard Delaware, which consists of 40 video lectures emphasizing the concepts of college algebra : http://www.infocobuild.com/education/audio-video-courses/mathematics/math110-college-algebra-umkc.html

• More lectures on Real Analysis by Professor Francis Su Harvey, Mudd College (The video and audio quality of the lectures are poor) : http://www.youtube.com/watch?v=sqEyWLGvvdw&feature=list_related&playnext=1&list=SP04BA7A9EB907EDAF

• MIT OCW - Calculus Revisited: Multivariable Calculus. This course is a study of the calculus of functions of several variables (vector arithmetic and vector calculus) : http://www.infocobuild.com/education/audio-video-courses/mathematics/calculus-revisited-multivariable-mitocw.html 

• General Topology Lectures : http://www.youtube.com/watch?v=yWi2_H-JUqY&feature=BFa&list=PL00F2E5C8D5D5F18B

• Differential Geometry lectures by Prof. N. J. Wildberger : http://www.youtube.com/playlist?list=PLIljB45xT85DWUiFYYGqJVtfnkUFWkKtP

• Very quick graduate Probability Theory : http://www.youtube.com/watch?v=Tk4ubu7BlSk

• Very good webpage for Partial Differential Equation  : http://ee.eng.usf.edu/people/snider2.html

• Numerical Methods at University of South Florida and Arizona State University : http://nm.mathforcollege.com/videos/

• 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=xalFtiY-JoQ&feature=BFa&list=PLE9C1CAA6D2DB2FBD

• GRASP lecture series from University of Texas at Austin, has tons of lecture videos on many topics : http://www.ma.utexas.edu/users/benzvi/GRASP.html

• 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 : http://www2.latech.edu/~schroder/videos.htm 

• Multi-linear Algebra (Tensor Products, etc.) : http://www.youtube.com/playlist?list=PLB7041DC6FDA5452C ( Pretty good videos ). 

• 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 : http://www.perimeterscholars.org/259.html 

• Lectures for Differential Topology 

1. http://vimeo.com/29434116
2. http://vimeo.com/29434762
3. http://vimeo.com/29436993

• An extensive lecture series from the same guy who has done the Multi-Linear algebra videos : http://www.youtube.com/user/litsky/videos

•  Measure and Integration series from NPTEL resources: http://nptel.iitm.ac.in/courses/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 : http://nptel.iitm.ac.in/courses/111105037/

• 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/111104025/

• Mathematical Logic lectures by Prof. Arindama Singh, IIT Madras : http://nptel.iitm.ac.in/courses/111106052/

• Some seminars & a hardcore video course on Algebraic Topology : http://www.youtube.com/user/arichar6

• This "Physics Forums" thread contains a list of tons of lecture videos, compiled by PF members : http://bit.ly/14hBf5o

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

1. http://www.infocobuild.com/education/audio-video-courses/mathematics/mathematics.html
2. http://videolectures.net/Top/Mathematics/
3. http://freevideolectures.com/Subject/Mathematics
4. http://www.onlinecollege.org/2009/10/19/100-incredible-open-lectures-for-math-geeks/
5. http://freescienceonline.blogspot.in/2006/09/mathematics-video-lectures.html
6. http://www.puremaths.info/video-lectures-in-mathematics/
7. http://www.perimeterscholars.org/317.html (Check the "Mathematical Review" section)
8. http://www.math.umn.edu/~adams/FM500x/
9. http://www.pinterest.com/mathematicsprof/
10. http://www.perimeterscholars.org/396.html (Check the lectures in the "Front End") 
11. http://mathoverflow.net/questions/1714/best-online-mathematics-videos

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