SET THEORY AND ALGEBRA
Day 
Date 
Contents 
Slides 
Assignments 
1 
July 2 
No discussion 

Assignment 1 
2 
July 3 
Introduction to Sets, Relations, Functions 


3 
July 4 
Equivalence Relations, Types of Functions 

Assignment 2 

July 5 
No Discussion: Problem solving from GO PDF 


4 
July 17 
Introduction to Groups



5 
July 18 
Groups, Fermat's Little Theorem. Introduction to Ring, Field.
Partial Orders, Lattice. 


MATHEMATICAL LOGIC
Day 
Date 
Contents 
Slides 
Assignments 
1 
July 6 
Propositional Logic, Truth Table, Implications, Validity, Satisfiability 



July 7 
No discussion Problem Solving from GO PDF 


2 
July 8 
First Order Logic  Existential and Universal Quantifiers,
DeMorgan's law, How to check for validity/satisfiability of
FOL statements 


COMBINATORICS
Day 
Date 
Contents 
Slides 
Assignments 
1 
July 9 
Introduction to Combinatorics 


2 
July 10 
Balls & Bins problems  4 Types 
Slide 1 

3 
July 11 
Balls & Bins problems continuation, Stirling's number of second kind 
Slide 2 
Assignment 1 

July 12 
Problem solving from GO PDF 


4 
July 13 
Integer Partition Problem Revisited 

Assignment 2 
5 
July 16 
Generating Functions, how to write a generating function for a given sequence, solution using calculus, generating function for Fibonacci series 


6 
July 17 
Recurrence Relation
 How to solve a recurrence relation recursively
 Number of binary\ternary strings of length n having k consecutive 0's



7 
July 20 
Catalan Number, Recurrence for it, Generating Function Solution, Pigeohole Principle and its generalization. Example problems to be solved from Rosen. 


GRAPH THEORY
Day 
Date 
Contents 
Slides 
Assignments 
1 
Aug 24 
Graph theory Introductiondefinition of graph, simple graph, finite graph, degree of a vertex, isolated and pendant vertices, null graph, subgraph of a graph, walkopen and closed, path, circuit,Euler line, Euler graph, Hamiltonian circuit, Hamiltonian path, examples, Complete graph, tree, eccentricitycentre, spanning tree of graph, connected components of graph, branch, chord, rank and nullity of graph, distance in spanning tree, Cutset  some lemmas 


2 
Aug 25Aug 29 
No discussion, Solve previous year GATE questions 


3 
Aug 30 
Graph colouring chromatic number, matching 
Graph theory 











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