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Day 1 2 3 Date Contents Slides Assignments July 2 No discussion Assignment 1 July 3 Introduction to Sets, Relations, Functions July 4 Equivalence Relations, Types of Functions Assignment 2 July 5 No Discussion: Problem solving from GO PDF July 17 Introduction to Groups July 18 Groups, Fermat's Little Theorem. Introduction to Ring, Field.  Partial Orders, Lattice.

MATHEMATICAL LOGIC

Day 1    2 Date Contents Slides Assignments July 6 Propositional Logic, Truth Table, Implications, Validity, Satisfiability July 7 No discussion Problem Solving from GO PDF July 8 First Order Logic - Existential and Universal Quantifiers, DeMorgan's law, How to check for validity/satisfiability of  FOL statements

COMBINATORICS

Day 1 2 3 Date Contents Slides Assignments July 9 Introduction to Combinatorics July 10 Balls & Bins problems - 4 Types Slide 1 July 11 Balls & Bins problems continuation, Stirling's number of second kind Slide 2 Assignment 1 July 12 Problem solving from GO PDF July 13 Integer Partition Problem Revisited Assignment 2 July 16 Generating Functions, how to write a generating function for a given sequence, solution using calculus, generating function for Fibonacci series July 17 Recurrence Relation  How to solve a recurrence relation recursively   Number of binary\ternary strings of length n having k consecutive 0's 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  1  2  3 Date Contents Slides Assignments Aug 24 Graph theory- Introduction-definition of graph, simple graph, finite graph, degree of a vertex, isolated and pendant vertices, null graph, subgraph of a graph, walk-open and closed, path, circuit,Euler line, Euler graph, Hamiltonian circuit, Hamiltonian path, examples, Complete graph, tree, eccentricity-centre, spanning tree of graph, connected components of graph, branch, chord, rank and nullity of graph, distance in spanning tree, Cut-set - some lemmas Aug 25-Aug 29 No discussion, Solve previous year GATE questions Aug 30 Graph colouring- chromatic number, matching Graph theory

posted Sep 17, 2018
recategorized Sep 17, 2018 | 459 views
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