Unit 1 : Sets, Functions, Sequences and Summations and Relations- What are Set Operations
- Computer Representation of Sets
- Countable and Uncountable Sets
- Principle of Inclusion and Exclusion
- Multisets
- Functions: One-to-one and Onto Functions
- Inverse Functions and Compositions of Function
- Graphs of Functions
- Sequences and Summations: Sequences
- Special Integer Sequences
- Summations; Relations: Properties of Binary Relations
- Equivalence relations and Partitions
- Partial Ordering Relations and Lattices
Unit 2 : Logic and Proofs- Propositional Logic
- Propositional Equivalences
- Use of first-order logic to express natural language predicates
- Quantifiers
- Nested Quantifiers
- Rules of Inference
- Introduction to Proofs
- Proof Methods and Strategies
- Mathematical Induction
Unit 3 : Number Theory- Division and Integers
- Primes and Greatest Common Divisors
- Representation of Integers
- Algorithms for Integer Operations
- Modular Exponentiation
- Application of number theory
Unit 4: Combinatorics/Counting- The Pigeonhole Principle
- Permutations and Combinations
- Binomial Coefficients
- Generalized Permutations and Combinations
- Generating Permutations and Combinations
Unit 5: Graph and Tree- Basic Terminology of Graphs
- Multigraphs and Weighted Graphs
- Paths and Circuits of Graphs
- Eulerian Paths and Circuits of Graphs
- Hamiltonian Paths and Circuits of Graphs
- Shortest Paths of Graphs
- Spanning Trees
- Graph Isomorphism
- Planar Graphs
- Introduction to Trees
- Rooted Trees
- Path Lengths in Rooted Trees.
Unit 6: Recurrence- Recurrence Relations
- Generating Functions
- Linear Recurrence Relations with Constant Coefficients and their solution
