KTU 2024 Scheme · Semester 2 · Program Core — Information Technology

Discrete Mathematical Structures (PCITT205) Syllabus

Official KTU 2024 Scheme syllabus for Discrete Mathematical Structures, Semester 2, Program Core — Information Technology (Information Technology).

This page compiles APJ Abdul Kalam Technological University's officially published 2024 Scheme syllabus for Information Technology, Semester 2, sourced directly from KTU's official website (ktu.edu.in). Learnizo is an independent online tuition platform and is not affiliated with, endorsed by, or officially connected to APJKTU. The university may revise syllabus content after this page was last updated — always cross-check with the official KTU source for the current, authoritative version.

Course Code

PCITT205

Credits

Teaching Hours

3:1:0:0 (L:T:P:R)

CIE Marks

ESE Marks

Exam Duration

2 Hrs 30 Min

Prerequisites

A sound background in higher secondary school Mathematics

Semester

Semester 2

Course Objective

Students will be able to understand and apply mathematical notations and concepts essential for computing, and to develop and utilize mathematical reasoning and proof strategies to enhance their analytical thinking and creative problem-solving skills.

Module-wise Syllabus

Module 1

11 contact hours

Introduction to Logic: Propositional Logic, Truth tables, Conditional propositions and Logical Equivalence, The laws of Logic, The Principle of Duality, Resolution proofs. Predicates and Quantifiers: Universal quantifier and Existential quantifier, Negation of Quantifiers, The Rule of Universal Specification, The Rule of Universal Generalizations, The implications of Quantifiers.

Module 2

11 contact hours

Fundamental Principles of Counting: The Rules of Sum and Product, Permutations, Combinations, The Binomial Theorem (without proof), Combinations with Repetition, Pigeon Hole Principle, Principle of Inclusion and Exclusion (without proof), Derangements.

Module 3

12 contact hours

Relations, Functions and Algebraic Structures: Sets, Relations, Functions, Equivalence Relations, Posets and Lattices, Hasse Diagrams, Complemented and Distributive lattices, Structured sets for binary operations, Semigroups, Monoids, Groups, Rings, Fields.

Module 4

10 contact hours

Generating Function: Definitions and Examples, Calculation Techniques, Exponential Generating Function. Recurrence Relations: First-order linear recurrence relations with constant coefficients — homogeneous, non-homogeneous solution. Second-order linear recurrence relations with constant coefficients, homogeneous, non-homogeneous solution.

Course Outcomes

CO1Apply logical reasoning and formal methods to construct and verify logical arguments and proofs involving propositions, truth tables, logical equivalence, and quantifiers.
CO2Apply fundamental counting principles, including permutations, combinations, and the pigeonhole principle, to solve problems related to combinatorial analysis and discrete structures.
CO3Describe the concepts of sets, relations, and functions, and recognize the properties and structures of algebraic systems such as lattices, semigroups, monoids, groups, rings, and fields.
CO4Explain the concepts of sets, relations, functions, algebraic structures such as groups and fields, and the methods for solving first and second-order linear recurrence relations using generating functions and other techniques.

Assessment Pattern (CIE: 40 marks, ESE: 60 marks)

Continuous Internal Evaluation (CIE)

Attendance	5
Assignment / Microproject	15
Internal Examination 1 (Written)	10
Internal Examination 2 (Written)	10

End Semester Examination (ESE)

Total 60 marks, 2 Hrs 30 Min. See the official KTU syllabus document for the exact Part A / Part B question pattern for this course.

Textbooks & Reference Books

Textbooks

Discrete and Combinatorial Mathematics: An Applied Introduction — Ralph P. Grimaldi, B.V. Ramana (Pearson, 5th edition, 2007)
Discrete Mathematics with Graph Theory and Combinatorics — T. Veerarajan (Tata McGraw Hill, 1st edition, 2007)

Reference Books

Discrete Mathematics and its Applications — K.H. Rosen (McGraw Hill, 7th edition, 2012)
Discrete Mathematical Structures — D.S. Chandrasekharaiah (PRISM Books, 4th edition, 2012)
Discrete Mathematical Structures with Application to Computer Science — J.P. Tremblay and R. Manohar (Tata McGraw Hill, 2nd edition, 2002)
Discrete Mathematics for Computer Scientists & Mathematicians — Joe L. Mott, Abraham Kandel and Theodore P. Baker (Pearson Education, 2nd edition, 2015)

Frequently Asked Questions

How many credits is KTU Discrete Mathematical Structures (PCITT205)?

4 credits, with 3:1:0:0 (L:T:P:R) teaching hours per week, under the KTU 2024 Scheme.

How many modules are in the PCITT205 syllabus?

4 modules, 44 total contact hours.

What is the CIE and ESE mark split for this course?

CIE (Continuous Internal Evaluation): 40 marks. ESE (End Semester Examination): 60 marks, 2 Hrs 30 Min. Total: 100 marks.

What are the recommended textbooks for PCITT205?

Discrete and Combinatorial Mathematics: An Applied Introduction (Ralph P. Grimaldi, B.V. Ramana); Discrete Mathematics with Graph Theory and Combinatorics (T. Veerarajan).

Is this syllabus specific to one branch, or common to others too?

This Semester 2 course is listed under Program Core — Information Technology at KTU under the 2024 Scheme — check the course header above for which branches it's common to.

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