Discrete Structures and Theory of Logic (B.Tech)

Sets, relations, functions, algebraic structures, lattices, propositional and predicate logic, graphs.

6 महीनेअवधि 5Chapters30टॉपिक

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01Unit 1: Sets, Relations, Functions and Proof Methods 6 टॉपिक

Sets, combination of sets, multisets, ordered pairs, set identities
Relations: operations, properties, composite relations, closure
Equivalence relations and partial orders
Functions: types, composition, inverse, growth of functions
Mathematical induction and its variants
Proof by contradiction and counter-example

02Unit 2: Algebraic Structures 6 टॉपिक

Algebraic structures and their properties
Groups, subgroups and order of an element
Cyclic groups and cosets
Lagrange's theorem and normal subgroups
Permutation and symmetric groups, homomorphism
Rings, integral domains and fields

03Unit 3: Lattices and Boolean Algebra 6 टॉपिक

Partially ordered sets and Hasse diagrams
Lattices: bounded, complemented, distributive, modular and complete
Boolean algebra: axioms and theorems
Algebraic manipulation of Boolean expressions
Simplification using Karnaugh maps
Logic gates and digital circuits

04Unit 4: Propositional and Predicate Logic 6 टॉपिक

Propositions, connectives and well-formed formulas
Truth tables, tautology, contradiction and satisfiability
Algebra of propositions and normal forms
Theory of inference
Predicates, quantifiers and their negation
Inference theory of predicate logic

05Unit 5: Trees, Graphs, Recurrence and Combinatorics 6 टॉपिक

Trees, binary trees and binary search trees
Graph terminology, representation, multigraphs and bipartite graphs
Planar graphs, isomorphism and homeomorphism
Euler and Hamiltonian paths, graph colouring
Recurrence relations and generating functions
Sum and product rules, permutations and combinations, pigeonhole principle

परिचय

आप यह कर पाएँगे

Use set operations, relations and functions and prove set identities
Prove statements by mathematical induction, contradiction and counter-example
Identify groups, subgroups, rings and fields and apply Lagrange's theorem
Work with posets, lattices and Boolean algebra and simplify functions with K-maps
Test logical validity using truth tables, inference rules and quantifiers
Apply graph theory, recurrence relations, permutations, combinations and the pigeonhole principle

यह किसके लिए है

B.Tech Computer Science & Engineering, Information Technology students of Semester 3 (AKTU)
Students of other universities studying the same subject who want unit-wise coaching

आपको क्या चाहिए

Class 12 mathematics (sets, functions, permutations and combinations)

सवाल

Which syllabus does the Discrete Structures and Theory of Logic course follow?

It follows the AKTU (Dr. A.P.J. Abdul Kalam Technical University, Lucknow) B.Tech syllabus for Discrete Structures and Theory of Logic. If your own university's syllabus differs, the centre follows your university syllabus.

Will this help in the university examination?

Yes. Teaching is unit-wise as per the AKTU scheme, with previous-year question practice, MCQ tests and doubt sessions before the semester exam.

Is this subject mostly theory or numericals?

Both. Proofs and definitions are asked along with numericals on relations, groups, lattices, logic, graphs and counting.