Mathematical Foundation of Computer Science

Mathematical Foundation of Computer Science Videos, PPTs, lecture notes, assignments, question papers for jntuk, jntuh, jntua, vtu, bput, kiit, vit, anna universities

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Created by Ramanjaneyulu K Last updated Sun, 19-Apr-2020 English


Mathematical Foundation of Computer Science free videos and free material uploaded by Ramanjaneyulu K .

Syllabus / What will i learn?

OBJECTIVES:

- To introduce the students to the topics and techniques of discrete methods and combinatorial reasoning.

- To introduce a wide variety of applications. The algorithmic approach to the solution of problems is fundamental in discrete mathematics, and this approach reinforces the close ties between this discipline and the area of computer science.

UNIT -I:

Mathematical Logic: Propositional Calculus: Statements and Notations, Connectives, Well Formed Formulas, Truth Tables, Tautologies, Equivalence of Formulas, Duality Law, Tautological Implications, Normal Forms, Theory of Inference for Statement Calculus, Consistency of Premises, Indirect Method of Proof. Predicate Calculus:Predicative Logic, Statement Functions, Variables and Quantifiers, Free and Bound Variables, Inference Theory for Predicate Calculus.

UNIT -II:

Set Theory: Introduction, Operations on Binary Sets, Principle of Inclusion and Exclusion, Relations: Properties of Binary Relations, Relation Matrix and Digraph, Operations on Relations, Partition and Covering, Transitive Closure, Equivalence, Compatibility and Partial Ordering Relations, Hasse Diagrams, Functions: Bijective Functions, Composition of Functions, Inverse Functions, Permutation Functions, Recursive Functions, Lattice and its Properties.

UNIT- III:

Algebraic Structures and Number Theory: Algebraic Structures:Algebraic Systems, Examples, General Properties, Semi Groups and Monoids, Homomorphism of Semi Groups and Monoids, Group, Subgroup, Abelian Group, Homomorphism, Isomorphism, Number Theory:Properties of Integers, Division Theorem, The Greatest Common Divisor, Euclidean Algorithm, Least Common Multiple, Testing for Prime Numbers, The Fundamental Theorem of Arithmetic, Modular Arithmetic (Fermat’s Theorem and Euler’s Theorem)

UNIT -IV:

Combinatorics: Basic of Counting, Permutations, Permutations with Repetitions, Circular Permutations, Restricted Permutations, Combinations, Restricted Combinations, Generating Functions of Permutations and Combinations, Binomial and Multinomial Coefficients, Binomial and Multinomial Theorems, The Principles of Inclusion–Exclusion, Pigeonhole Principle and its Application.


UNIT -IV:

Recurrence Relations: Generating Functions, Function of Sequences, Partial Fractions, Calculating Coefficient of Generating Functions, Recurrence Relations, Formulation as Recurrence Relations, Solving Recurrence Relations by Substitution and Generating Functions, Method of Characteristic Roots, Solving Inhomogeneous Recurrence Relations

UNIT -VI:

Graph Theory: Basic Concepts of Graphs, Sub graphs, Matrix Representation of Graphs: Adjacency Matrices, Incidence Matrices, Isomorphic Graphs, Paths and Circuits, Eulerian and Hamiltonian Graphs, Multigraphs, Planar Graphs, Euler’s Formula, Graph Colouring and Covering, Chromatic Number, Spanning Trees, Algorithms for Spanning Trees (Problems Only and Theorems without Proofs).

 OUTCOMES:

- Student will be able to demonstrate skills in solving mathematical problems

-  <!--[endif]-->Student will be able to comprehend mathematical principles and logic

- Student will be able to demonstrate knowledge of mathematical modeling and proficiency in using mathematical software

- Student will be able to manipulate and analyze data numerically and/or graphically using appropriate Software

- Student will be able to communicate effectively mathematical ideas/results verbally or in writing



Curriculum for this course
6 Lessons 00:00:00 Hours
Unit-I
1 Lessons
  • Unit-1 Mathematical Foundation of Computer Science notes
  • Unit-2 Mathematical Foundation of Computer Science notes
  • Unit -3 Mathematical Foundation of Computer Science notes
  • Unit -4 Mathematical Foundation of Computer Science notes
  • Unit -4 Mathematical Foundation of Computer Science notes
  • Unit -6 Mathematical Foundation of Computer Science notes
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