Free Mathematics Video Courses
This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.
- Video Lectures (Click on the titles of lectures (they dont appear as links, but on click they work as links). Access to lectures restricted to USA only.
This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
Mathematical Problems II
Mathematics originated in the distant past as our ancestors tried to understand the world around them.
First, the course will survey the role that problems and problem-solving have played in the historical development of mathematics.
In Lecture 1 course covers Mesopotomian and Egyptian mathematics
Then the course goes over the basic elements of problem solving:
Models, Abstraction, Conjectures, Hypotheses, Proofs (Heuristic, Rigorous), Generalizations
Mathematical Methods for Engineers I
This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.
Have fun watching these. I have approx. 40 more links of math video lectures to sort.
- 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)
- 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 and various lectures from advanced institute for study.)