**Combinatorics** |
L1- Sum rule and product rule |

L2- Permutations |

L3- Combinations |

L4- Examples of combination problems |

L5- One to one correspondence technique |

L6- Combinations with repetitions of objects |

L7- Permutations of objects, objects are repeated |

L8- Numerical problems related to combinations |

L9- Previous gate questions related to combinatorics |

L10- Principles of mutual exclusion and inclusion |

L11- Derangements |

L12-How to write recurrence relations |

L13-How to solve recurrence relations part 1 |

L14-How to solve recurrence relations part 2 |

**Propositional and First Order Logic** |
L1- Propositional logic -Basics |

L2- Propositional logic- propositional functions, tautology, contradiction, contingency |

L3- Propositional logic-Gate problems related to tautology |

L4- Propositional logic-Equivalences |

L5- Propositional logic-problems related to equivalences |

L6- Propositional logic-validity, satisfiability, logical implication, inference system |

L7- First order logic- How to write First order logic statements |

L8- First order logic-Gate problems related to first order logic statements |

L9- First order logic- equivalences 1 |

L10-First order logic- equivalences 2 |

**Functions** |
L1- Basic stuff about sets, what is function, one to one function |

L2-One to one functions, onto functions |

L3- Bijections, inverse functions, composite functions |

L4- Gate problems related to bijections |

**Relations** |
L1- Properties-reflexive, symmetric, transitive, anti-symmetric, asymmetric, irreflexive |

L2-Equivalence relations |

L3- Equivalence relations, gate problems on equivalence relations |

L4- Reflexive symmetric and transitive closures |

L5- Partial order relations, hasse diagrams |

L6- Lattice-Introduction |

L7- Lattice- Remaining topics |

**Graph Theory** |
L1-Introduction to Graph Theory |

L2- Degree sequence, Connectivity |

L3-Connectivity-cut vertex, cut edge, some questions |

L4- Let us ignore NULL graphs |

L5-connectivity- some gate questions |

L6-Isomorphism |

L7-Isomorphism examples |

L8-Euler, Hamiltonian Graphs |

L9-trees |

L10- forest and some theorems related to connected graphs |

L11-coloring |

L12-Matching |

**Group Theory** |
Introduction to group theory |

Simple theorems on group theory |

Cayley table |

Abelian group |

Cyclic group |

Subgroups |

GATE problems on Groups |