MCA-103 Discrete Mathematical Structure

Note:Examiner will be required to set NINE questions in all. Question Number 1 will consist of total 8 parts (objective type/short-answer type questions) covering the entire syllabus and will carry 24 marks. In addition to the compulsory question there will be four units i.e. Unit-I to Unit-IV. Examiner will set two questions from each Unit of the syllabus and each question will carry 14 marks. Student will be required to attempt FIVE questions in all. Question Number 1 will be compulsory. In addition to compulsory question, student will have to attempt four more questions selecting One question from each Unit.

Total Marks : 100  Theory Paper : 80  Internal Assessment: 20

Time : 3 Hours

Unit-I

Groups and subgroups: Group axioms, Permutation Groups, Subgroups, Cosets, Normal Subgroups, Semi-groups, Free Semi-groups, Modular Arithmetic, Grammars, Language, Regular Expressions, Finite State Machine.

Unit-II

Graphs: Directed and Undirected Graphs, Chains, Circuits, Paths, Cycles, Connectivity, Adjacency and Incidence Matrices, Algorithms for determining Cycle and Minimal paths, Trees ,Polish Notation, Flows in Networks.

Unit-III

Latices and boolean algebra: Relations to partial ordering, Lattices, Hasse Diagram, Axiomatic definition of Boolean Algebra as algebraic structures with two operations, Boolean Functions, Representing Boolean Functions, Switching Circuits, Gate Circuits.

Unit-IV

Finite fields: Definition, Representation, Structure, Integral Domain, Irreducible Polynomial, Polynomial Roots, Splitting Field.

Text Books:

• Alan Doerr And Kenneth Levaseur, Applied Discrete Structures For Computer Science, Galgotia Publications Pvt. Ltd., New Delhi.
• Seymour Lipschutz And Marc Lars Lipson, Discrete Mathematics”, Mcgrraw- Hill International Editions, Schaum’s Series, New York.

Reference Books:

• Olympia Nicodemy, “ Discrete Mathematics ”, Cbs Publisher, Delhi
• C. L. Liu, “Elements of Discrete Mathematics”, Tata Mcgrraw- Hill Publishing Company Limited, New Delhi.
• Bernard Kolman And Robert C. Busby, “Discrete Mathematical Structures For Computer Science”, Prentice- Hall Of India Pvt. Ltd., New Delhi.
• Kenneth G. Rosen, “Discrete Mathematics And Its Applications”, Mcgrraw- Hill International Editions, Mathematics Series, New York.