Can you provide me the syllabus for B. Tech./B. Tech (Hon)/Dual Degree (B. Tech - MS) program offered by Indian Institute of Information Technology, Kottayam?

The syllabus for B. Tech./B. Tech (Hon)/Dual Degree (B. Tech - MS) program offered by Indian Institute of Information Technology, Kottayam is as follows:


PROGRAMME

SEMESTER I

IMA 111 Discrete Mathematics [3-1-0-4]

Objectives of the course
• To extend student’s Logical and Mathematical maturity and ability to deal with abstraction
• To introduce most of the basic terminologies used in computer science courses
• To explain and apply the basic methods of discrete mathematics in Computer Science.
• To able to write clear, concise and correct mathematics proofs.
• To solve counting problems involving permutations and combinations and apply Pigeon hole principle
• To understand the basics of graph theory and group theory


Outcomes of the course
• Have knowledge of the concepts needed to test the logic of a program.
• Have an understanding in identifying structures on many levels.
• Be aware of a class of functions which transform a finite set into another finite set which relates to input and output functions in computer science.
• Be able to apply basic counting techniques to solve combinatorial problems
• Acquire ability to describe computer programs in a formal mathematical manner.

Syllabus

Logic: Propositions, negation, disjunction and conjunction, implication and equivalence, truth tables, predicates, quantifiers, rules of inference, methods of proof.

Set theory: definition and simple proofs in set theory, Inductive definition of sets and proof by induction, inclusion and exclusion principle, relations, representation of relations by graphs, properties of relations, equivalence relations and partitions, partial orderings, linear and well-ordered sets.

Functions: mappings, injection and surjections, composition of function, inverse functions, special functions, recursive function theory.

Elementary combinatorics: Counting techniques, pigeonhole principle, recurrence relation, generating functions.

Graph theory: Elements of graph theory, Euler graph, Hamiltonian path, trees, tree traversals, spanning trees.

Algebra: groups, Lagrange’s theorem, homomorphism theorem, rings and fields, structure of the ring Zn and the unit group Zn*, lattice


Textbooks/References
1. Kenneth H. Rosen, Discrete Mathematics and Its Applications, Seventh Edition, Mcgraw-
Hill, 2017.
2. Norman L. Biggs, Discrete Mathematics, Oxford University Press, Second Edition,
2003.
3. J.P. Tremblay, R. Manohar, Discrete Mathematical Structures with applications to Computer Science, McGraw Hill,2017.
4. K.A. Ross, C.R. B. Wright, Discrete Mathematics, 5th Edition, Pearson, 2003.
5. P. B. Bhattacharya, S. K. Jain, S, R. Nagpaul, Basic Abstract Algebra, Second Edition, Cambridge University Press, 2003.
6. J.A. Gallian, Contemporary Abstract Algebra, Ninth Edition, Cengage Learning, 2017.



Syllabus B. Tech. B. Tech (Hon)/Dual Degree (B. Tech - MS) IIIT, Kottayam