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B.E Artificial Intelligence and Machine Learning Discrete Structures and Graph Theory Syllabus - Mumbai University

This is the Second Year AI-ML syllabus under NEP 2020, in force from the academic year 2025-26. The University still sets the earlier Choice Based papers alongside it for ATKT candidates, so check which scheme your exam form names before you revise.

Discrete-Structures-and-Graph-Theory.pdf
Semester 3 · Second Year AI-ML · 3 credits · 100 marks

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Syllabus for Discrete Structures and Graph Theory

Semester 3 · Second Year AI-ML · 3 credits · 100 marks

Module 0: Prerequisite

  • 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

  • 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

  • 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

  • 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

  • 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

  • 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. must be from any other Module randomly selected from all the modules).
  • A total of four questions need to be answered.

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.
  • 1 Kenneth A. Ross, “Discrete Mathematics”, 5 th Edition, Pearson Publications.
  • 2 Swapan Kumar Sarkar, “Textbook of Discrete Mathematics”, 9 th 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

Reproduced from the University of Mumbai syllabus for B.E. (Artificial Intelligence and Machine Learning) under NEP 2020, in force from the academic year 2025-26. Wording is as printed in that syllabus. Module numbering is as printed there too.

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 7.8 (R-A) B.E. (Artificial Intelligence and Machine Learning) Sem I & II (Revised, NEP 2020) NEP 2020 syllabus Read full PDF Read
PDF 6.21 (N) B.E. (Artificial Intelligence and Machine Learning) Sem III & IV (NEP 2020) NEP 2020 syllabus Read full PDF Read
PDF 6.42 (R) B.E. (Artificial Intelligence and Machine Learning) Third Year, Sem V & VI (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read
PDF B.E. (Artificial Intelligence and Machine Learning) Fourth Year, Sem VII & VIII (REV-2019 'C' Scheme) REV-2019 'C' Scheme syllabus Read full PDF Read
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