Discrete Mathematical Structures BCS405A
Course Code: BCS405A
Credits: 03
CIE Marks: 50
SEE Marks: 50
Total Marks: 100
Exam Hours: 03
Total Hours of Pedagogy: 40H
Teaching Hours/Weeks: [L:T:P:S] 2:2:0:0
Fundamentals of Logic:
Basic Connectives and Truth Tables, Logic Equivalence – The Laws of Logic, Logical Implication – Rules of Inference. The Use of Quantifiers, Quantifiers, Definitions and the Proofs of Theorems.
Properties of the Integers:
Mathematical Induction, The Well Ordering Principle – Mathematical Induction, Recursive
Definitions.
Fundamental Principles of Counting: The Rules of Sum and Product, Permutations, Combinations – The Binomial Theorem, Combinations with Repetition.
Relations and Functions:
Cartesian Products and Relations, Functions – Plain and One-to-One, Onto Functions. The Pigeon- hole Principle, Function Composition and Inverse Functions.
Properties of Relations, Computer Recognition – Zero-One Matrices and Directed Graphs, Partial
Orders – Hasse Diagrams, Equivalence Relations and Partitions.
The Principle of Inclusion and Exclusion:
The Principle of Inclusion and Exclusion, Generalizations of the Principle, Derangements – Nothing is
in its Right Place, Rook Polynomials.
Recurrence Relations: First Order Linear Recurrence Relation, The Second Order Linear
Homogeneous Recurrence Relation with Constant Coefficients.
Introduction to Groups Theory:
Definitions and Examples of Particular Groups Klein 4-group, Additive group of Integers modulo n,
Multiplicative group of Integers modulo-p and permutation groups, Properties of groups, Subgroups,
cyclic groups, Cosets, Lagrange’s Theorem.
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