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Home / Syllabus / B.E. (Artificial Intelligence and Data Science) / SY BE AI and DS / Semester 3 / Discrete Structures and Graph Theory

B.E. (Artificial Intelligence and Data Science) Discrete Structures and Graph Theory Syllabus - Mumbai University 2026

This is the SY BE AI and DS syllabus under NEP 2020, in force from the academic year 2025-26. The third and fourth years of this degree are still taught on the earlier CBCS REV-2019 'C' Scheme, because the University has published no NEP syllabus for Semesters V to VIII of any engineering branch.

Discrete Structures and Graph Theory.pdf
Semester 3 · SY BE AI and DS · NEP 2020

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Syllabus for Discrete Structures and Graph Theory

Semester 3 · SY BE AI and DS · NEP 2020

Module 0: Prerequisite 1 hours

  • Basic Set Theory, Logical Operators, Truth Tables, Cartesian product, Types of Functions. Basic Algebra and Number Theory, Fundamental Counting Principle, Permutations, Combinations. Graph Basics.

Module I: Crisp Set Theory and Logic 7 hours

  • Set Theory: Sets, Subsets, Universal and Empty Sets, Set Operations, Set Representation, Laws of Set theory. Logic: Propositional Logic, Predicate Logic, Quantifiers (Universal and Existential). Types of Mathematical Proof: Direct proof, Proof by contradiction, Proof by deduction, Proof by cases, Proof by exhaustion, Proof by counterexample, Mathematical induction. Self-learning Topics: PROLOG / LISP programming to create expert system using Propositional and Predicate Logic, Other types of logic and sets.

Module II: Mathematical Relations 8 hours

  • Relations: Definition, Representation of Relations, Properties of Relations, Equivalence Relations, Equivalence Classes, Closures of Relations, Warshall's algorithm. Posets and Lattice: Partial Order Relations, Poset, Hasse Diagram, Chain and Anti chains, Lattice, Types of Lattices, Sub lattice. Self-learning Topics: Practical applications of relations in real life in the field of Database Management, Economics, Social Network, Sports, Medical Diagnosis, Weather, etc.

Module III: Functions 3 hours

  • Functions: Types: Injective, Surjective, and Bijective Functions. Composition, Inverse Functions. Real life applications of Functions. Self-learning Topics: Practical applications of function in Neural Network, Determining risk factors for insurance rates, Taxes and tax brackets, Vending machines, etc.

Module IV: Counting 5 hours

  • Pigeonhole Principle, Inclusion-Exclusion Principle. Recurrence relations, Solving recurrence relations Self-learning Topics: Applications of Recurrence Relations – Analysis of recursive algorithms in computing. Combinatorial Problem Solving – Using counting techniques in probability and decision-making.

Module V: Algebraic Structures 7 hours

  • Algebraic structures with one binary operation: Semi group, Monoid, Groups, Subgroups, Abelian Group, and Cyclic group. Algebraic structures with two binary operations: Ring. Self-learning Topics: Error Correcting codes.

Module VI: Graph Theory 8 hours

  • Types of graphs, Graph Representation, Sub graphs, Operations on Graphs, Walk, Path, Circuit, Connected Graphs, Disconnected Graph, Components, Homomorphism and Isomorphism of Graphs, Euler and Hamiltonian Graphs, Planar Graph, Cut Set, Cut Vertex, Real life applications of Graph Theory. Self-learning Topics: Network Flow Problems – Understanding flow in networks and its optimization. Graph Coloring Applications in Scheduling – Use of graph coloring in timetabling and resource allocation. Optimization Techniques – Application of graphs in shortest path problems, spanning trees, and clustering.

Text Books

  • 1 Susanna S. Epp, "Discrete Mathematics with Applications", 5th Edition, Cengage Publications.
  • 2 Ralph P. Grimaldi, "Discrete and Combinatorial Mathematics", 5th Edition, Pearson Publications.
  • 3 Edgar Goodaire and Michael Parmenter, "Discrete Mathematics and Graph Theory", 3rd Edition, Pearson Publications.

Reference Books

  • 1 Kenneth A. Ross, "Discrete Mathematics", 5th Edition, Pearson Publications.
  • 2 Swapan Kumar Sarkar, "Textbook of Discrete Mathematics", 9th Edition, S. Chand Publications.
  • 3 Bernad Kolman, Robert Busby, Sharon Cutler Ross, Nadeem-ur-Rehman, "Discrete Mathematical Structures", 6th Edition, Pearson Education.
  • 4 T. Veera Rajan, "Discrete mathematics with Graph Theory and Combinatorics", McGraw Hill Publications.
  • 5 C. L. Liu "Elements of Discrete Mathematics", second edition 1985, McGraw-Hill Book Company. Reprinted 2000

Online References

  • Sr. No. Website Name
  • 1 https://nptel.ac.in/courses/106106094
  • 2 https://nptel.ac.in/courses/106108227
  • 3 https://nptel.ac.in/courses/106106183
  • 4 https://nptel.ac.in/courses/106103205
  • 5 https://nptel.ac.in/courses/111107058

Reproduced from the University of Mumbai syllabus for B.E. (Artificial Intelligence and Data Science), item 6.20 (N), under NEP 2020, in force from the academic year 2025-26. Wording, module numbering and hours are as printed in that syllabus.

The complete syllabus

This subject is cut from the University circular for its year. Open a document here if you want the whole thing rather than a single subject.

PDF B.E. Artificial Intelligence and Data Science - First Year, Semester I and II - NEP 2020 - Item 7.7 (R-A) NEP 2020, Semesters I and II, in force from 2024-25 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Second Year, Semester III and IV - NEP 2020 - Item 6.20 (N) NEP 2020, Semesters III and IV, in force from 2025-26 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Third Year, Semester V and VI - CBCS REV-2019 C Scheme - Item 6.42 (R) CBCS REV-2019 'C' Scheme, Semesters V and VI, in force from 2022-23 Read full PDF Read
PDF B.E. Artificial Intelligence and Data Science - Fourth Year, Semester VII and VIII - CBCS REV-2019 C Scheme - Item 6.12 (N) CBCS REV-2019 'C' Scheme, Semesters VII and VIII, in force from 2023-24 Read full PDF Read
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