Mathematics Video Lectures Full Courses
This course is a rigorous analysis of the real numbers, as well as an introduction to writing and communicating mathematics well. Topics will include: construction of the real numbers, fields, complex numbers, topology of the reals, metric spaces, careful treatment of sequences and series, functions of real numbers, continuity, compactness, connectedness, differentiation, and the mean value theorem, with an introduction to sequences of functions. It is the first course in the analysis sequence, which continues in Real Analysis II. Taught through Rudin's Principles of Mathematical Analysis. So it's awesome.
Lecture 1: Constructing the rational numbers. Lecture 2: Properties of Q. Lecture 3: Construction of R. Lecture 4: The Least Upper Bound Property. Lecture 5: Complex Numbers. Lecture 6: The Principle of Induction. Lecture 7: Countable and Uncountable Sets. Lecture 8: Cantor Diagonalization, Metric Spaces. Lecture 9: Limit Points. Lecture 10: Relationship b/t open and closed sets. Lecture 11: Compact Sets. Lecture 12: Relationship b/t compact, closed sets. Lecture 13: Compactness, Heine-Borel Theorem. Lecture 14: Connected Sets, Cantor Sets. Lecture 15: Convergence of Sequences. Lecture 16: Subsequences, Cauchy Sequences. Lecture 17: Complete Spaces. Lecture 18: Series. Lecture 19: Series Convergence Tests. Lecture 20: Functions - Limits and Continuity. Lecture 21: Continuous Functions. Lecture 22: Uniform Continuity. Lecture 23: Discontinuous Functions. Lecture 24: The Derivative, Mean Value Theorem. Lecture 25: Taylor's Theorem. Lecture 26: Ordinal Numbers, Transfinite Induction.
Topics in Contemporary Mathematics
Mathematics of Finance
Introduction to Finite Mathematics with Applications
Elements of Calculus
Calculus for Life and Management Sciences
Applied Differential Equations I
Have fun with these!
- Free Mathematics Video Courses
(Includes discrete mathematics, algebra, linear algebra, mathematics problems, differential equations, math methods for engineers)
- More Mathematics and Theoretical Computer Science Video Lectures(Includes algebra, elementary statistics, applied probability, finite mathematics, trigonometry with calculus, mathematical computation, pre-calculus, analytic geometry, first year calculus, business calculus, mathematical writing (by Knuth), computer science problem seminar (by Knuth), dynamic systems and chaos, computer musings (by Knuth) and other Donald E. Knuth lectures)
- Mathematics Video Lectures(Includes course practice of mathematics and lots of mathematics seminar videos in applied maths, geometry/topology, liquid flow and string theory)
- Even More Mathematics Video Lectures
(Includes Steven Skiena's discrete mathematics, convex optimization, fourier transform, linear dynamical systems, keio university math video archive, monty hall problem and imo problems)
- Latest Mathematics Video Lectures
(Includes: calculus, vector calculus, tensors, the most important concepts of mathematics, basic mathematics, numerical methods, p=np problem, randomness, fractals and splines, lectures from advanced institute for study and a video on indian super 30 mathematics school)