UNIQUE SERIES AKTU Syllabus
BBC202

Discrete Mathematics

L-T-P3-1-0 Credits4 Session2025-26 TypeTheory
Appears in 1 semester

BCA · Sem 2 (Core)

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Syllabus

5 units · 40 lecture hours
Unit1

Unit 1: Set Theory

8 hrs

Definition of sets, Venn Diagrams, proofs of some general identities on sets. Relation: Definition, types of relation, composition of relations, Pictorial representation of relation, equivalence relation, partial ordering relation. Function: Definition, type of functions, one to one, into and onto function, inverse function, composition of functions, recursively defined functions.

Unit2

Unit 2: Mathematical Induction

8 hrs

Piano’s axioms, Mathematical Induction Discrete Numeric Functions and Generating functions, Simple Recurrence relation with constant coefficients, Linear recurrence relation without constant coefficients.

Unit3

Unit 3: Algebraic Structures

8 hrs

Properties, Semi group, Monoid, Group, Abelian group, Properties of group, Subgroup, Cyclic group, Cosets, Permutation groups, Homomorphism, Isomorphism and Automorphism of groups.

Unit4

Unit 4: Propositional Logic

8 hrs

Preposition, First order logic, Basic logical operations, Tautologies, Contradictions, Algebra of Proposition, Logical implication, Logical equivalence, Normal forms, Inference Theory, Predicates and quantifiers.

Unit5

Unit 5: Posets, Hasse Diagram and Lattices

8 hrs

Introduction, Ordered set, Hasse diagram of partially ordered set, Isomorphic ordered set, Well ordered set, Properties of Lattices and complemented lattices.

Course Outcomes (COs)5 outcomes

After completion of the course student will be able to:

  1. CO1Use mathematical and logical notation to define and formally reason about basic discrete structures such as Sets, Relations and FunctionsK1, K2
  2. CO2Apply mathematical arguments using logical connectives and quantifiers to check the validity of an argument through truth tables and propositional and predicate logicK2, K3
  3. CO3Identify and prove properties of Algebraic Structures like Groups, Rings and FieldsK3, K4
  4. CO4Formulate and solve recurrences and recursive functionsK3, K4
  5. CO5Apply the concept of combinatorics to solve basic problems in discrete mathematicsK1, K3

Suggested Readings

  1. Tremblay J.P. and Manohar R., “Discrete Mathematical Structures with Application to Computer Science”, Tata McGraw Hill.
  2. Lipschutz S. and Lipson M., “Discrete Mathematics”, Tata McGraw Hill.
  3. Rosen K.H., “Discrete Mathematics and its Applications”, Tata McGraw Hill.
  4. Sarkar S.K., “A Textbook of Discrete Mathematics”, S. Chand Publishing.
  5. Sharma J.K., “Discrete Mathematics’, Trinity Press.
  6. Gill N.S. and Dixit J.B, “Digital Design & Computer Organization”, University Science Press.

Official AKTU syllabus

This subject is on page 12 of the original AKTU PDF.

Official AKTU syllabus PDF ↗