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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- 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    
 2  Aug 25-Aug 29 No discussion, Solve previous year GATE questions    
 3  Aug 30 Graph colouring- chromatic number, matching  Graph theory  
         
         

For more information visit GO Classroom : https://classroom.gateoverflow.in/course/view.php?id=9


 

 

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