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KTU 2024 Scheme · Semester 2 · Common to all Computer Science and its allied branches

Discrete Mathematics (PCCST205) Syllabus

Official KTU 2024 Scheme syllabus for Discrete Mathematics, Semester 2, Common to all Computer Science and its allied branches (Computer Science and Engineering).

This page compiles APJ Abdul Kalam Technological University's officially published 2024 Scheme syllabus for Computer Science and Engineering, 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

PCCST205

Credits

4

Teaching Hours

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

CIE Marks

40

ESE Marks

60

Exam Duration

2 Hrs 30 Min

Prerequisites

None

Semester

Semester 2

Course Objective

To equip students with the ability to analyze and solve problems using discrete mathematical techniques; to give a deeper understanding of mathematical logic, set theory, and proof techniques such as direct proofs, proof by contradiction, and mathematical induction.

Module-wise Syllabus

Module 1

11 contact hours

Sets, Functions, and Relations: sets and subsets, Venn diagrams, set operations, set identities, generalized unions and intersections, the principle of inclusion-exclusion (basic and generalized versions) and applications. Function definition, injections, surjections and bijections, inverse functions, compositions of functions, cardinality of sets, Cantor diagonalization argument. Relations and their properties, composition of relations, n-ary relations, representing relations using matrices, equivalence relations, equivalence classes, partial orderings, Hasse diagrams, maximal and minimal elements, lattices.

Module 2

11 contact hours

Mathematical logic and proofs: propositional logic, applications of propositional logic, propositional equivalences, predicates and quantifiers, nested quantifiers, rules of inference. Introduction to proofs, methods of proving theorems — direct proof, indirect proof (proof by contraposition), proof by contradiction, proof by counterexamples, the pigeonhole principle.

Module 3

11 contact hours

Induction and Recurrences: mathematical induction, weak and strong induction, recursive (inductive) definitions and recurrence relations, modeling with recurrence relations, solving linear recurrence relations (homogeneous and nonhomogeneous), generating functions, using generating functions to solve recurrence relations.

Module 4

11 contact hours

Group theory: groups — definition, examples, and elementary properties, Abelian group, permutation group, subgroup, homomorphisms, isomorphisms, and cyclic groups, cosets and Lagrange's theorem.

Course Outcomes

  • CO1Check the validity of predicates in Propositional and Quantified Propositional Logic using truth tables, deductive reasoning and inference theory on Propositional Logic.
  • CO2Solve counting problems by applying elementary counting techniques — Rule of Sum, Rule of Product, Permutation, Combination, Binomial Theorem, Pigeonhole Principle and Principle of Inclusion and Exclusion.
  • CO3Classify binary relations into various types and illustrate an application for each type of binary relation in Computer Science.
  • CO4Illustrate an application for Partially Ordered Sets and Complete Lattices in Computer Science.
  • CO5Explain Generating Functions and solve First Order and Second Order Linear Recurrence Relations with Constant Coefficients.
  • CO6Illustrate the abstract algebraic systems — Semigroups, Monoids, Groups, Homomorphism and Isomorphism of Monoids and Groups.

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

Continuous Internal Evaluation (CIE)

Attendance5
Assignment / Microproject15
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 Mathematics and its Applications — Kenneth H. Rosen, Kamala Krithivasan (McGraw Hill, 8th edition, 2021)

Reference Books

  • Schaum's Outline of Discrete Mathematics — Marc Lipson, Seymour Lipschutz (McGraw-Hill, 3rd edition, 2021)
  • Discrete Mathematics — Kenneth A. Ross, Charles R.B. Wright (Pearson, 5th edition, 2012)

Frequently Asked Questions

How many credits is KTU Discrete Mathematics (PCCST205)?

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 PCCST205 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 PCCST205?

Discrete Mathematics and its Applications (Kenneth H. Rosen, Kamala Krithivasan).

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

This Semester 2 course is listed under Common to all Computer Science and its allied branches at KTU under the 2024 Scheme — check the course header above for which branches it's common to.

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