Details of each lecture are recorded here in the reverse chronological order.
Click on the theme item for the lecture plan for that section.
Click on the lecture item for suggested additional reading related to it.
- Lecture 00 : Tue, Aug 2, 11-11:50am - Administrative details - (Ashish)
- Missing lectures Aug 3,4,5
Theme 1: Sets, Relations, Functions, Proofs, Logic.
(Jayalal, 11 meetings)
- Lecture 01 : Tue, Aug 9, 11-11:50am - (Jayalal)
References & Additiional Reading :
- Chapter 2 of the reference text
- Lecture 02 : Wed, Aug 10, 10-10:50am - (Jayalal)
Functions, Bijections, Cardinality(pushed to
next lecture)
References & Additiional Reading :
- Chapter 2 of the refernce text
- Lecture 03 : Thu, Aug 11, 8-8:50am - (Jayalal)
Proofs, Proof by picture, Deceiving proofs
References & Additiional Reading :
- Lecture 04 : Thu, Aug 11, 12-12:50pm (for Aug 3) - (Jayalal)
Need of a mathematical proof, Propositions,
Logic
References & Additiional Reading :
- Chapter 2 of the refernce text
- Missing lectures on Aug 12, 15 due to rescheduling.
- Lecture 05 : Tue, Aug 16, 10-10:50am (for Aug 4) - (Jayalal)
Implications, Bi-implication
References & Additiional Reading :
- Lecture 06 : Tue, Aug 16, 11-11:50am - (Jayalal)
References & Additiional Reading :
- Lecture 07 : Wed, Aug 17, 9-9:50am (for Aug 5) - (Jayalal)
Deriving new logical equivalences
References & Additiional Reading :
- Lecture 08 : Wed, Aug 17, 10-10:50am - (Jayalal)
Predicate Logic, Quantifiers, Examples
References & Additiional Reading :
- Lecture 09 : Thu, Aug 18, 8-8:50am - (Jayalal)
Nested Quantifiers, Negations
References & Additiional Reading :
- Lecture 10 : Thu, Aug 18, 12-12:50am (for Aug 12) - (Jayalal)
References & Additiional Reading :
- Lecture 11 : Fri, Aug 19, 6:30pm-7:30pm (for Aug 15) - (Jayalal)
Rules of inference, Deduction
References & Additiional Reading :
Theme 2: Linear Algebra
(Ashish, 15 meetings)
- Lecture 12 : Mon, Aug 22, 11-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 13 : Tue, Aug 23, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 14 : Tue, Aug 23, 11am-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 15 : Wed, Aug 24, 9-9:50am - (Ashish)
References & Additiional Reading :
- Lecture 16 : Wed, Aug 24, 10-10:50am - (Ashish)
Four Fundamental Subspaces
References & Additiional Reading :
- Lecture 17 : Thu, Aug 25, 8-8:50am - (Ashish)
Four Fundamental Subspaces
References & Additiional Reading :
- Lecture 18 : Mon, Aug 29, 11-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 19 : Tue, Aug 30, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 20 : Tue, Aug 30, 11am-11:50am - (Ashish)
References & Additiional Reading :
- TUTORIAL : Lecture 21 : Thu, Sep 1, 8-8:50am - (Ashish)
References & Additiional Reading :
- Lecture 22 : Mon, Sep 5, 11-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 23 : Tue, Sep 6, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 24 : Tue, Sep 6, 11am-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 25 : Wed, Sep 7, 9-9:50am - (Ashish)
References & Additiional Reading :
- Lecture 26 : Wed, Sep 7, 10-10:50am - (Ashish)
References & Additiional Reading :
- QUIZ-I : Lecture 27 : Thu, Sep 8, 8-8:50am - (Ashish)
References & Additiional Reading :
Theme 3: Probablity Theory
(Ashish, 11 meetings)
- Lecture 28 : Wed, Sep 14, 9-9:50am - (Ashish)
References & Additiional Reading :
- Lecture 29 : Wed, Sep 14, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 30 : Thu, Sep 15, 8-8:50am - (Ashish)
References & Additiional Reading :
- Lecture 31 : Mon, Sep 19, 11-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 32 : Tue, Sep 20, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 33 : Tue, Sep 20, 11am-11:50am - (Ashish)
References & Additiional Reading :
- Lecture 34 : Wed, Sep 21, 9-9:50am - (Ashish)
References & Additiional Reading :
- Lecture 35 : Wed, Sep 21, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 36 : Thu, Sep 22, 8-8:50am - (Ashish)
References & Additiional Reading :
- Lecture 37 : Tue, Sep 27, 10-10:50am - (Ashish)
References & Additiional Reading :
- Lecture 38 : Tue, Sep 27, 11am-11:50am - (Ashish)
References & Additiional Reading :
Theme 1 (continued): Proofs and Methods of Proofs, Basic Combinatorics.
(Jayalal, 15 lectures)
- Lecture 39 : Mon, Oct 3, 11-11:50am - (Jayalal)
Back to Proofs and Valid Arguments, Rules of inferences, Notion of a Proof
References & Additiional Reading :
- Lecture 40 : Tue, Oct 4, 11am-11:50am - (Jayalal)
Proofs as subroutines, Mathematical terminologies, lemmas, propositions, theorems.
Discovering a proof. Some applicable methods : direct proof
References & Additiional Reading :
- Lecture 41 : Wed, Oct 5, 10-10:50am - (Jayalal)
Indirect Proof : Proof by contraposition and example
References & Additiional Reading :
- Lecture 42 : Mon, Oct 10, 11-11:50am - (Jayalal)
Proof by contradiction : Pigeon Hole Principle and other examples
References & Additiional Reading :
- TUTORIAL 4 Lecture 43 : Tue, Oct 11, 10-10:50am - (Jayalal)
Topic: Proofs and Methods of Proofs
References & Additiional Reading :
- Lecture 44 : Tue, Oct 11, 11am-11:50am - (Jayalal)
Principle of Mathematical Induction, validity, introductory example
References & Additiional Reading :
- Lecture 45 : Wed, Oct 12, 10-10:50am - (Jayalal)
All horses are of the same color - pitfalls in inductions proofs,
Survivor in a knife fight game - Creativitiy in induction
References & Additiional Reading :
- Lecture 46 : Thu, Oct 13, 8-8:50am - (Jayalal)
Strong induction, Examples : Factorisation, Triangulation
References & Additiional Reading :
- Lecture 47 : Mon, Oct 17, 11-11:50am - (Jayalal)
Basic Counting : Sum rule, generalised sum rule, Product rule, generalised product rule
Inclusion-Exclusion Principle
References & Additiional Reading :
- Lecture 48 : Tue, Oct 18, 11am-11:50am - (Jayalal)
Pigeon Hole Principle revisited, Application of PHP
References & Additiional Reading :
- Lecture 49 : Wed, Oct 19, 10-10:50am - (Jayalal)
More applications of PHP, Permutations, Basic Counting
References & Additiional Reading :
- QUIZ-II Lecture 50 : Thu, Oct 20, 8-8:50am - (Jayalal)
References & Additiional Reading :
- Lecture 51 : Mon, Oct 24, 11-11:50am - (Jayalal)
Combinations, related identities. Double counting as a proof technique.
References & Additiional Reading :
- Lecture 52 : Tue, Oct 25, 11am-11:50am - (Jayalal)
More applications of double counting, Recurrence relations
References & Additiional Reading :
- Lecture 53 : Thu, Oct 27, 8-8:50am - (Jayalal)
Linear Homogeneous Recurrence Relations - Distinct roots case, examples
References & Additiional Reading :
- Lecture 54 : Mon, Oct 31, 11-11:50am - (Jayalal)
Linear Homogeneous Recurrence Relations - Higher Mutiplicities of roots, general form
References & Additiional Reading :
- Lecture 55 : Tue, Nov 1, 8-8:50am - (Jayalal)
Linear Non-homogeneous Recurrence Relations, Examples
Solving non-linear ones by substitution
References & Additiional Reading :
- TUTORIAL 5 Lecture 56 : Wed, Nov 2, 9-9:50am - (Jayalal)
References & Additiional Reading :
- Lecture 57 : Wed, Nov 2, 10-10:50am - (Jayalal)
Generating Functions method
References & Additiional Reading :
Theme 4: Formal Models of Computation
(Jayalal, 14 lectures)
- Lecture 58 : Thu, Nov 3, 8-8:50am - (Jayalal)
Computation, Modeling computation, Finite Automaton,
Formal definition, Regular Languages.
References & Additiional Reading :
- Lecture 59 : Tue, Nov 8, 10-10:50am - (Jayalal)
Formal proof of acceptance : simple and complicated examples
References & Additiional Reading :
- Lecture 60 : Tue, Nov 8, 11am-11:50am - (Jayalal)
Closure under Boolean operations
References & Additiional Reading :
- Lecture 61 : Wed, Nov 9, 9-9:50am - (Jayalal)
Limitations of Finite Automata, Pumping Lemma, Examples
References & Additiional Reading :
- Lecture 62 : Wed, Nov 9, 10-10:50am - (Jayalal)
Automata as classifiers, Myhill-Nerode Relations
References & Additiional Reading :
- Nov 10 - Institute Holiday.
- Lecture 63 : Mon, Nov 14, 11-11:50am - (Jayalal)
Myhill-Nerode Theorem, Applications for proving limitations of FAs
References & Additiional Reading :
- Lecture 64 : Tue, Nov 15, 10-10:50am - (Jayalal)
2-DFAs, Turing Machines, The model, examples
References & Additiional Reading :
- Lecture 65 : Tue, Nov 15, 11am-11:50am - (Jayalal)
References & Additiional Reading :
- Lecture 66 : Wed, Nov 16, 9-9:50am - (Jayalal)
Universal Turing Machines and Diagonalisation
References & Additiional Reading :
- Lecture 67 : Wed, Nov 16, 10-10:50am - (Jayalal)
Halting Problem is Undecidable
References & Additiional Reading :
- Tutorial 6 Lecture 68 : Thu, Nov 17, 8-8:50am - (Jayalal)
References & Additiional Reading :
- Lecture 69 : Thu, Nov 17, 12-12:50pm - (Jayalal)
References & Additiional Reading :
Statistics : 69 meetings, 62 lectures, 5 Tutorials, 2 Quizes
Notice that the lecture plan is prepared in advance based on some rough
estimate about the pace of lecture. It may vary in the actual implementation.
Last updated on Sat Nov 26 12:21:37 IST 2011
