Discrete Mathematics (MCA)

Sets, relations, functions, logic, combinatorics, recurrence relations, graphs, trees and algebraic structures.

6 महीनेअवधि 5Chapters26टॉपिक

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सिलेबस · पाठ्यक्रम

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01Unit 1: Sets, Relations & Functions 5 टॉपिक

Sets, operations and Venn diagrams
Power set and Cartesian product
Relations: reflexive, symmetric, antisymmetric, transitive
Equivalence relations and partitions
Functions: one-one, onto, bijection, inverse and composition

02Unit 2: Logic 5 टॉपिक

Propositions and logical connectives
Truth tables, tautology and contradiction
Logical equivalence; converse, inverse and contrapositive
Rules of inference
Predicates and quantifiers

03Unit 3: Combinatorics & Recurrence Relations 6 टॉपिक

Sum and product rules
Permutations and combinations
Pigeonhole principle
Inclusion-exclusion principle
Linear recurrence relations with constant coefficients
Generating functions

04Unit 4: Graphs & Trees 5 टॉपिक

Graph terminology and types
Degree and handshaking theorem
Paths, circuits, Euler and Hamiltonian graphs
Graph representation: adjacency matrix and list
Trees, spanning trees and minimum spanning tree

05Unit 5: Algebraic Structures & Lattices 5 टॉपिक

Partial order relations and Hasse diagrams
Lattices
Boolean algebra and its laws
Groups, subgroups and cyclic groups
Rings and fields

परिचय

आप यह कर पाएँगे

Use sets, relations and functions, and test properties of relations
Apply propositional and predicate logic and rules of inference
Solve counting problems using permutations, combinations and the pigeonhole principle
Solve linear recurrence relations
Use graph and tree concepts: degree, paths, Euler and Hamilton graphs, spanning trees
Explain posets, lattices, Boolean algebra and algebraic structures such as groups

यह किसके लिए है

MCA students of Semester 1 (AKTU)
Students who need the mathematical base for data structures, algorithms and theory of computation

आपको क्या चाहिए

Graduation (BCA / B.Sc / B.Com / B.A) with Mathematics at 10+2 or graduation level (MCA admission)
Class 12 level algebra

सवाल

Which syllabus is followed?

The AKTU (Dr. A.P.J. Abdul Kalam Technical University, Lucknow) MCA syllabus of Discrete Mathematics (Semester 1). If your own university's syllabus differs, the centre follows your university syllabus and units.

Is Discrete Mathematics difficult for non-maths graduates?

With regular practice it is manageable; the trainer solves many examples from each unit and previous AKTU papers.

How will I be tested?

Unit-wise MCQ tests and a final paper at semester level, plus practice on short and long answer questions from previous university papers.