Mathematical Logic, Set Theory and Combinatorics

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Work in progress: These course notes are actively being written and may contain errors or omissions. If you spot a mistake, please let me know by email.

Course Code: MAT1MN104  ·  Semester: I (Minor)  ·  Credits: 4
Institution: Jamia Nadwiyya Arts and Science College, Edavanna, University of Calicut (CUFYUGP 2024)
Textbook: Thomas Koshy — Discrete Mathematics with Applications, 1/e (Academic Press, 2003)

Complete lecture notes with worked examples, truth tables, and practice problems.

Assessment: Internal 30 marks + External 70 marks (Section A: 3 marks each, ceiling 24; Section B: 6 marks each, ceiling 36; Section C: 10 marks, answer any one of two). A minimum of 15 external marks comes from each of Modules I–IV; Module V is not assessed in the external exam.

Modules

• Module I — Mathematical Logic

  Propositions, conditionals, converse/inverse/contrapositive, logical equivalences, quantifiers, valid arguments

• Module II — Set Theory

  Sets and subsets, operations with sets, the laws of sets, Cartesian product, cardinality

• Module III — Functions and Matrices

  Functions, special functions, floor/ceiling, characteristic functions, matrix addition and multiplication

• Module IV — Combinatorics and Discrete Probability

  Fundamental counting principles, permutations, combinations, discrete probability

• Module V — Open-Ended Topics

  Calculus preview, relations and digraphs, conditional probability, correlation and regression, numerical methods  ·  Not assessed in external exam

Exam Practice

• Class Tests

  Question papers and answer keys for class tests conducted during the course

• Previous Year Questions

  October 2024 — End Semester Examination, full question paper (70 marks) for exam-pattern reference