syllabus/maths.md

# UNIT I: Mathematical Logic, Sets, Relations, and Functions

## Mathematical Logic:
- Notations, Algebra of Propositions & Propositional functions
- Logical connectives, Truth values & Truth tables
- Tautologies & Contradictions, Normal Forms
- Predicate Calculus, Quantifiers

## Set Theory:
- Sets, Subsets, Power sets, Complement, Union and Intersection
- De Morgan's Law, Cardinality

## Relations:
- Cartesian Products, relational Matrices, properties of relations, equivalence relations

## Functions:
- Injection, Surjection, Bijection, Composition of Functions, Permutations, Cardinality
- Characteristic functions, Recursive definitions, Finite induction

# UNIT II: Lattices & Boolean Algebra

## Lattices:
- Lattices as Algebraic Systems, Sublattices
- Some special lattices: Complement, Distributive, Modular

## Boolean Algebra:
- Axiomatic definitions of Boolean algebra as algebraic structures with two operations
- Switching Circuits

# UNIT III: Groups, Fields, & Rings

## Groups:
- Definition of groups, axioms, permutation groups
- Subgroups, co-sets, normal subgroups, free subgroups
- Grammars, language

## Fields & Rings:
- Definition and structure of fields and rings
- Minimal Polynomials, Irreducible Polynomials
- Polynomial roots & its Applications

# UNIT IV: Graphs

## Graphs:
- Simple Graph, Multigraph & Pseudograph
- Degree of a Vertex, Types of Graphs, Subgraphs, Isomorphic Graphs
- Operations on Graphs, Paths, Cycles, and Connectivity
- Euler and Hamilton Graphs, Shortest Path Problems (BFS, Dijkstra's Algorithm)
- Representation of Graphs, Planar Graphs, Applications of Graph Theory

# UNIT V: Trees

## Trees:
- Definition and properties of trees, pendant vertices in a tree, center of a tree
- Spanning tree, Binary tree, Tree traversal
- Applications of trees in computer science