Discrete Mathematical Structures

Lecturer: Prof. Kamala Krithivasan
College/University: Indian Institute of Technology Madras

1. Propositional Logic (First Part)
   
2. Propositional Logic (Second Part)
   
3. Predicates and Quantifiers (First Part)
   
4. Predicates and Quantifiers (Second Part)
   
5. Logical Inference
   
6. Resolution Principles and Application to PROLOG
   
7. Methods of Proof
   
8. Normal Forms
   
9. Proving Programs Correct
   
10. Sets
    
11. Induction
    
12. Set Operations on Strings over Alphabet
    
13. Relations
    
14. Graphs (First Part)
    
15. Graphs (Second Part)
    
16. Trees
    
17. Trees and Graphs
    
18. Special Properties of Relations
    
19. Closure of Relations (First Part)
    
20. Closure of Relations (Second Part)
    
21. Order Relations
    
22. Order and Relations and Equivalence Relations
    
23. Equivalence Relations and Partitions
    
24. Functions (First Part)
    
25. Functions (Second Part)
    
26. Functions (Third Part)
    
27. Permutations and Combinations (First Part)
    
28. Permutations and Combinations (Second Part)
    
29. Permutations and Combinations (Third Part)
    
30. Generating Functions (First Part)
    
31. Generating Functions (Second Part)
    
32. Recurrence Relations (First Part)
    
33. Recurrence Relations (Second Part)
    
34. Recurrence Relations (Third Part)
    
35. Algebras (First Part)
    
36. Algebras (Second Part)
    
37. Algebras (Third Part)
    
38. Finite State Automaton (First Part)
    
39. Finite State Automaton (Second Part)
    
40. Lattices

Linear Algebra

Lecturer: Prof. W. Gilbert Strang
College/University: Massachusetts Institute of Technology (MIT)

1. The Geometry of Linear Equations
   
2. Elimination with Matrices
   
3. Multiplication and Inverse Matrices
   
4. Factorization into A=LU
   
5. Transposes, Permutations, and Spaces Rⁿ
   
6. Column Space and Nullspace
   
7. Solving Ax=0: Pivot Variables, special Solutions
   
8. Solving Ax=b: Row Reduced Form R
   
9. Independence, Basis, and Dimension
   
10. The Four Fundamental Subspaces
    
11. Matrix Spaces
    
12. Graphs, Networks, and Independence Matrices
    
13. Review
    
14. Orthogonal Vectors and Subspaces
    
15. Projections onto Subspaces
    
16. Projection Matrices and Least Squares
    
17. Orthogonal Matrices and Gram-Schmidt
    
18. Properties of Determinants
    
19. Determinant Formulas and Cofactors
    
20. Cramer's Rule, Inverse Matrix, and Volume
    
21. Eigenvalues and Eigenvectors
    
22. Diagonalization and Powers of A
    
23. Differential Equations and e^At
    
24. Markov Matrices and Fourier Series
    
25. Review
    
26. Symmetric Matrices and Positive Definiteness
    
27. Complex Matrices; Fast Fourier Transform
    
28. Positive Definite Matrices and Minima
    
29. Simliar Matrices and Jordan Form
    
30. Singular Value Decomposition
    
31. Linear Transformation and Their Matrices
    
32. Change of Basis; Image Compression
    
33. Review
    
34. Left and Right Inverses; Pseudoinverses
    
35. Review