Mathematical foundation & computer science (MFCS) Hand-written Notes.

Description

UNIT-I
Mathematical Logic & Boolean Algebra
Statements & Notations, Connectives, Basic concepts of Boolean Algebra, Properties, Boolean
functions (Conjunctive normal form and Disjunctive normal form), Applications of Boolean Algebra
(Switching Circuits and Logic circuits)

UNIT-II
Ordered Structures, Relations & Functions
Tuples, Lists, Strings & Languages, Numerals, Relations, Properties of Relations, Partial order
Relation, Lattices. Functions, Properties of Functions, Composition of Functions, The map function &
some useful functions.

UNIT-III
Construction Techniques & Grammars:
Inductively defined sets, Numbers, Strings, Lists, Cartesian product of sets, Recursive functions and
Procedures, Grammars.

UNIT-IV
Graph Theory
Basic concepts of Graph Theory, Types of graphs, Paths and Circuits, shortest path problems, Trees,
Binary Trees, Spanning tree and minimum spanning tree, Matrix Representation of Graphs(Directed
and Undirected).

UNIT-V
Group Theory & Coding
Basic concepts of Group Theory, Subgroups, Homomorphism & Isomorphism of Groups, Cosets and
Langrage’s Theorem, Elements of Coding Theory, Group codes, Decoding.