SET THEORY AND ALGEBRA
| Day |
Date |
Contents |
Slides |
Assignments |
| 1 |
July 2 |
No discussion |
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Assignment 1 |
| 2 |
July 3 |
Introduction to Sets, Relations, Functions |
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| 3 |
July 4 |
Equivalence Relations, Types of Functions |
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Assignment 2 |
| |
July 5 |
No Discussion: Problem solving from GO PDF |
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| 4 |
July 17 |
Introduction to Groups
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| 5 |
July 18 |
Groups, Fermat's Little Theorem. Introduction to Ring, Field.
Partial Orders, Lattice. |
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MATHEMATICAL LOGIC
| Day |
Date |
Contents |
Slides |
Assignments |
| 1 |
July 6 |
Propositional Logic, Truth Table, Implications, Validity, Satisfiability |
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| |
July 7 |
No discussion Problem Solving from GO PDF |
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| 2 |
July 8 |
First Order Logic - Existential and Universal Quantifiers,
DeMorgan's law, How to check for validity/satisfiability of
FOL statements |
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COMBINATORICS
| Day |
Date |
Contents |
Slides |
Assignments |
| 1 |
July 9 |
Introduction to Combinatorics |
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| 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 |
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| 4 |
July 13 |
Integer Partition Problem Revisited |
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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 |
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| 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
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| 7 |
July 20 |
Catalan Number, Recurrence for it, Generating Function Solution, Pigeohole Principle and its generalization. Example problems to be solved from Rosen. |
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GRAPH THEORY
| Day |
Date |
Contents |
Slides |
Assignments |
| 1 |
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 |
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| 2 |
Aug 25-Aug 29 |
No discussion, Solve previous year GATE questions |
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| 3 |
Aug 30 |
Graph colouring- chromatic number, matching |
Graph theory |
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For more information visit GO Classroom : https://classroom.gateoverflow.in/course/view.php?id=9
