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B.Sc. (Data Science) Discrete Mathematics Syllabus - Mumbai University

This is the FY BSc Data Science syllabus under NEP 2020, in force from the academic year 2024-25. 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 Mathematics Syllabus.pdf
Vocational skill course · Semester 2 · FY BSc Data Science · 2 credits · 50 marks

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Syllabus for Discrete Mathematics

Vocational skill course · Semester 2 · FY BSc Data Science · 2 credits · 50 marks

Module I

  • 1. Functions: Definition of function; Domain, co-domain, range of a function; Examples of standard functions such as identity and constant functions, absolute value function, logarithmic and exponential functions, flooring and ceiling functions; Injective, surjective and bijective functions; Composite and inverse functions. 2. Relations: Definition and examples of relation; Properties of relations, Representation of relations using diagraphs and matrices; Equivalence relation; Partial Order relation, Hasse Diagrams, maximal, minimal, greatest, least element, Lattices. 3. Recurrence Relations: Definition and Formulation of recurrence relations; Solution of a recurrence relation; Solving recurrence relations- Back tracking method, Linear homogeneous recurrence relations with constant coefficients; Homogeneous solution of linear homogeneous recurrence relation with constant coefficients; Particular solution of non-linear homogeneous recurrence relation with constant coefficients; 4. General solution of non-linear homogeneous recurrence relation with constant coefficients; Applications- Formulate and solve recurrence relation for Fibonacci numbers, Tower of Hanoi, Intersection of lines in a plane, Sorting Algorithms.

Module II

  • 1. Counting Principles: Basic Counting Principles (Sum and Product Rule); Pigeonhole Principle (without proof) - Simple examples; Inclusion Exclusion Principle (Sieve formula) (without proof); Counting using Tree diagrams. 2. Permutations and Combinations: Permutation without and with repetition; Combination without and with repetition; Binomial numbers and identities: Pascal Identity, Vandermonde‟s Identity, Pascal triangle, Binomial theorem (without proof) and applications; Multinomial numbers, Multinomial theorem (without proof) and applications. 3. Languages, Grammars and Machines: Languages and Grammars – Introduction, Phase structure grammar, Types of grammar, derivation trees; Finite-State Machines with Output; Finite-State Machines with No Output 4. Regular Expression and Regular Language. 10 Text Books 1. Applied Combinatorics by Alan Tucker 2. Norman L. Biggs, Discrete Mathematics, Revised Edition, Clarendon Press, Oxford 1989. 3. Discrete Mathematics: An Open Introduction by Oscar Levin 4. Combinatorics to Topics, techniques, Algorithms by Peter J. Cameron. 5. Foundations in Discrete Mathematics: K.D. Joshi, New Age Publication, New Delhi. 11 Reference Books 1. "Discrete Mathematical Structures" by Shanker G Rao 2. "Discrete Mathematics and its Applications" by Kenneth H Rosen 3. “Discrete Mathematical Structures" by J P Chauhan 4. “Discrete Mathematical Structures" by Subramaniyan 5. “Discrete Mathematics: SemyourLipschutz, Marc Lipson, Schaum‟s out lines, McGraw- Hill Inc. 12 Internal Continuous Semester End Examination: 60% Assessment: 40% 13 Continuous Evaluation through: Format of Question Paper: External Class test of 1 of 15 marks Examination (30 Marks)– 1 hr duration Class test of 2 of 15 marks Average of the two: 15 marks Quizzes/ Presentations/ Assignments: 5 marks Total: 20 marks 14 Format of Question Paper: (Semester End Examination : 30 Marks. Duration:1 hour) Q1: Attempt any two (out of four) from Module 1 (15 marks) Q2: Attempt any two (out of four) from Module 2 (15 marks)

Text Books

  • 1 Applied Combinatorics by Alan Tucker
  • 2 Norman L. Biggs, Discrete Mathematics, Revised Edition, Clarendon Press, Oxford 1989.
  • 3 Discrete Mathematics: An Open Introduction by Oscar Levin
  • 4 Combinatorics to Topics, techniques, Algorithms by Peter J. Cameron.
  • 5 Foundations in Discrete Mathematics: K.D. Joshi, New Age Publication, New Delhi.
  • 1 "Discrete Mathematical Structures" by Shanker G Rao
  • 2 "Discrete Mathematics and its Applications" by Kenneth H Rosen
  • 3 “Discrete Mathematical Structures" by J P Chauhan
  • 4 “Discrete Mathematical Structures" by Subramaniyan
  • 5 “Discrete Mathematics: SemyourLipschutz, Marc Lipson, Schaum‟s out lines, McGraw- Hill Inc.

Reproduced from the University of Mumbai syllabus for B.Sc. (Data Science) under NEP 2020, in force from the academic year 2024-25. 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 2024 25 DS SEM I & II NEP NEP 2020 syllabus, in force from 2024-25 Read full PDF Read
PDF 2023 24 BSc Data Science Sem V & VI Earlier Choice Based syllabus, still set for ATKT candidates Read full PDF Read
PDF 2021 22 BSc Data Science Sem III & IV Earlier Choice Based syllabus, still set for ATKT candidates Read full PDF Read
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