Lecture hours: |
Mon 10:30am -- 11:25am, Tue 11:30am -- 12:25pm, Thu 08:30am -- 09:25am |
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Office hours: | Wed 11:00am -- 12:30pm | |
Location: | KReSIT SIC 301 | |
Instructor: | Nutan Limaye (firstname[AT]cse[DOT]iitb[DOT]ac[DOT]in) | |
Teaching Assistants: |
Hemant Kumar Adil
(hemant[DOT]adil[AT]gmail)
Khushraj Madnani (khush250[AT]gmail) Naman Mishra (firsnamelastname[AT]gmail) Pratik Patre (pblastname[AT]gmail) |
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Week 1
What is a proof? What are propositions? Proof methodsWeek 2
There is a bijection from N x N to N. There is no bijection between N and all subsets of N [Cantor, 1891]. Let A, B be two sets. If there is an injective map from A to B and another injective map from B to A then there is a bijection from A to B. [Schröder-Bernstein] Relations and types of relations.Week 3
Properties of equivalence classes and partial orders. Basics of counting: count one object in order to count the other, double counting. Approximating n! -- Striling's approximation, Counting the numner of labelled trees.Week 4
Computing the n-th Fibonacci number using generating functions Computing the n-th catalan number using generating functions. Recurrence for triagulating a convex polygon, the number of derrangement.