CSE401 / Mathematics

Syllabus

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Y2S4-CSE401-BTECH-CSE-IT-SYLLABUS.pdf

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References:

[⤓] Schaum-'s_Outline_Discrete_Mathematics

Resources

M1: Sets, Relations and Functions

[⤓] CSE401-MATHS-M1-SHORT-NOTES

[ ▶︎ ] Sets, Relations and Functions

[ ▶︎ ] Types of Set & Cardinality

[ ▶︎ ] Venn Diagram & Multi Set

[ ▶︎ ] Inclusion-Exclusion-Principle

[ ▶︎ ] Domain, Range, Diagraph, Relation-Matrix

[ ▶︎ ] Types of Relations

[ ▶︎ ] Partial Order Set - POSET

[ ▶︎ ] Types of Function

CSE401 - MODULE 1 - STRUCTURED SYLLABUS

• Sets

  • Definition of sets

  • Subsets

  • Power sets

  • Set operations and set identities

  • Upper and lower bounds of a set

  • Least upper bound (lub)/supremum

  • Greatest lower bound (glb)/infimum

• Relations

  • Definition of relations

  • Properties of binary relations

  • Operations on binary relations

  • Closures

  • Partial ordering

  • Equivalence relations

  • Matrix representation of relations

• Functions

  • Definition and properties of functions

  • Composition of functions

  • Inverse functions

  • Unary, binary, and n-ary operations

  • Characteristic function

  • Permutation function

  • Composition of cycles

• Growth of Functions

  • Big Theta notation

  • Little o notation

  • Big O notation

  • Big Omega notation

M2: Fundamental Principal of Counting

[⤓] CSE401-MATHS-M2-SHORT-NOTES

[ ▶︎ ] Recurrence Relation + Pigeonhole Principle

[ ▶︎ ] Permutations

[ ▶︎ ] Combinations

[ ▶︎ ] Discrete Probability

[ ▶︎ ] Conditional + Baye's Theorem

[ ▶︎ ] Rule of Sum & Product - Binomial Coefficient & Identities

CSE401 - MODULE 2 - STRUCTURED SYLLABUS

• Fundamental Principles

  • Basic counting principles

• Permutations and Combinations

  • Permutations

  • Combinations

  • Combinatorial identities

• Advanced Counting Techniques

  • Principle of Inclusion and Exclusion (PIE)

  • Pigeonhole Principle

  • Pascal’s triangle

• Recurrence Relations

  • Definition of recurrence relations

  • Solution methods for linear, first-order recurrence relations with constant coefficients

M3: Logic

[ ▶︎ ] LOGIC-Proof-by-Math-Induction

[ ▶︎ ] LOGIC-Proposition+Statement

[ ▶︎ ] LOGIC-Tautology+Contingency+Contradiction

[ ▶︎ ] LOGIC-Normal-Forms-DNF+CNF

[ ▶︎ ] LOGIC-Method-of-Proof

[ ▶︎ ] LOGIC-Quantifiers

CSE401 - MODULE 3 - STRUCTURED SYLLABUS

• Propositional Logic

  • Propositions and logical operations

  • Conditional statements

  • Equivalences

  • Tautologies and contradictions

  • Normal forms

  • Theory of inference

• Predicate Calculus

  • Predicates

  • Statement functions

  • Free and bound variables

  • Universal and existential quantifiers

  • Universal specifications

• Methods of Proof

  • Direct proof

  • Proof by contradiction

  • Principle of Mathematical Induction

M4: Lattices & Boolean Algebra

[ ▶︎ ] LATTICES

[ ▶︎ ] PLAYLIST on SOP + POS (Boolean Algebra)

CSE401 - MODULE 4 - STRUCTURED SYLLABUS

• Partially Ordered Sets and Lattices

  • Partially ordered sets

  • Lattices

  • Lattices as algebraic structures

  • Sublattices

  • Direct product

  • Homomorphisms

• Boolean Algebra

  • Definitions and examples

  • Subalgebra

  • Boolean functions

  • Representation and minimization of Boolean functions

M5: Graphs & Trees

[ ▶︎ ] GRAPH-Important-Definitions

[ ▶︎ ] GRAPH-Matrix-Representation

[ ▶︎ ] GRAPH-Isomorphism

[ ▶︎ ] GRAPH-Eulerian+Hamiltonian-Graph

[ ▶︎ ] GRAPH-Handshaking-Lemma+Planar-Graph

[ ▶︎ ] TREE-Basic-Terminologies

[ ▶︎ ] TREE-Spanning-Tree

[ ▶︎ ] TREE-Circuits+Cutsets

CSE401 - MODULE 5 - STRUCTURED SYLLABUS

• Graphs

  • Definition and properties of graphs

  • Degree

  • Connectivity

  • Paths

  • Cycles

  • Subgraphs

  • Isomorphism

  • Eulerian and Hamiltonian walks

  • Graph coloring

• Trees

  • Definition and properties of trees

  • Spanning trees

  • Fundamental circuits

  • Cut-sets

  • Cut-vertices

• Matrix Representations

  • Incidence matrix

  • Adjacency matrix

Notes

MidTerm

[⤓] CSE401-MATHS-M1-MidTerm-SHORT-NOTES

[⤓] CSE401-MATHS-M2-MidTerm-SHORT-NOTES

EndTerm

[⤓] CSE401-Discrete-Maths-All-M-Qs-VIDEO-SCRENSNAP

[⤓] CSE401-PROBABLE-QS-4xPYQ-ANALYSIS

[⤓] CSE401-PROBABLE-QS-4xPYQ-ANSWERS

Qs-Mapping-Document-For-Selectable-Copying:

Qs-Mapping-Document-For-Selectable-Copying

Question Directory

[⤓] QUESTION-BANK_CSE401-DISCRETE-MATHS

Assignment Questions

[⤓] Assignment-1 CSE 401

Previous Year Questions

[⤓] Y2S4-CSE401-MATHS-MidTerm-PYQ-APR25

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun17

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun18

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun19

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun21

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun22

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun23

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun24

[⤓] Y2S4-CSE401-Maths-EndTerm-PYQ-Jun25

External Sources

[ ▶︎ ] Sets, Relations and Functions

[ ▶︎ ] Permutation, Combination & Mathematical Induction

[ ▶︎ ] Pigeonhole Principle

[ ▶︎ ] Recurrence Relation

[ ▶︎ ] PLAYLIST on SOP + POS (Boolean Algebra)

[ ▶︎ ] PLAYLIST on Discrete Mathematics

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