MFCS Lecture Notes Jntuk R16 2-1 CSE,IT

Mathematical Foundations of Computer Science

OBJECTIVES:

• To introduce the scholars to the topics and techniques of separate ways and
combinatorial reasoning.
• To introduce a large style of applications. The recursive approach to the answer of
problems is prime in separate arithmetic, and this approach reinforces the shut
ties between this discipline and also the space of engineering.

UNIT -I:

Mathematical Logic: Propositional Calculus: Statements and Notations, Connectives, Well
Formed Formulas, Truth Tables, Tautologies, Equivalence of Formulas, Duality Law,
Tautological Implications, traditional Forms, Theory of logical thinking for Statement Calculus,
Consistency of Premises, Indirect methodology of Proof. Predicate Calculus:Predicative Logic,
Statement Functions, Variables and Quantifiers, Free and certain Variables, logical thinking 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 alphabetic character, 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, algorithmic Functions, Lattice and its Properties.

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UNIT- III:

Algebraic Structures and variety Theory: pure mathematics Structures:Algebraic Systems,
Examples, General Properties, Semi teams and Monoids, similarity of Semi teams and
Monoids, Group, Subgroup, Abelian group, similarity, isomorphy, Number
Theory:Properties of Integers, Division Theorem, the best common measure, Euclidean
Algorithm, Least integer, Testing for Prime Numbers, the elemental Theorem of
Arithmetic, standard Arithmetic (Fermat’s Theorem and Euler’s Theorem)

UNIT -IV:

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

II Year – I Semester
L T P C
4 0 0 3

UNIT -V:

Recurrence Relations: Generating Functions, operate of Sequences, Partial Fractions,
Calculating constant of Generating Functions, return Relations, Formulation as
Recurrence Relations, determination return Relations by Substitution and Generating Functions,
Method of Characteristic Roots, determination nonuniform return Relations

UNIT -VI:

Graph Theory: Basic ideas of Graphs, Sub graphs, Matrix illustration of Graphs:
Adjacency Matrices, Incidence Matrices, similarity Graphs, methods and Circuits, Eulerian and
Hamiltonian Graphs, Multigraphs, tabular Graphs, Euler’s Formula, Graph Colouring and
Covering, Chromatic variety, Spanning Trees, Algorithms for Spanning Trees (Problems solely
and Theorems while not Proofs).

OUTCOMES:

• Student are going to be ready to demonstrate skills in determination mathematical issues
• Student are going to be ready to comprehend mathematical principles and logic
• Student are going to be ready to demonstrate data of mathematical modeling and
proficiency in victimization mathematical computer code
• Student are going to be ready to manipulate and analyze information numerically and/or diagrammatically victimization
appropriate computer code
• Student are going to be ready to communicate effectively mathematical ideas/results verbally or in
writing

TEXT BOOKS:

1.Discrete Mathematical Structures with Applications to engineering, J. P. Tremblay
and P. Manohar, Tata McGraw Hill.

1. components of separate Mathematics-A laptop orientating Approach, C. L. Liu and D. P.
   Mohapatra, 3rdEdition, Tata McGraw Hill.
2. separate arithmetic and its Applications with Combinatorics and Graph Theory, K. H.
   Rosen, seventh Edition, Tata McGraw Hill.
   REFERENCE BOOKS:
3. separate arithmetic for laptop Scientists and Mathematicians, J. L. Mott, A. Kandel,
   T.P. Baker, second Edition, novice Hall of India.
4. separate Mathematical Structures, BernandKolman, Robert C. Busby, Sharon dealer
   Ross, PHI.
5. separate arithmetic, S. K. Chakraborthy and B.K. Sarkar, Oxford, 2011.

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