Syllabus (MATHEMATICS)
Course Type: SEC-1
Semester: 1
Course Code: BMTMSEC01T
Course Title: Discrete Mathematics & Graph Theory
(L-P-Tu): 3-0-0
Credit: 3
Practical/Theory: Theory
Course Objective: To be done.
Learning Outcome: Course Outcomes (CO): The whole course will have the following outcomes: Upon successful completion, the students will be able to CO1: apply algorithms based on prime numbers on practical problems. CO2: understand the structure and types of proofs in math
Syllabus:
Unit-I: Discrete Mathematics [Credit: 2, 30 L]
- Set Theory: sets and classes, relations and functions, recursive definitions, posets, Zorn’s lemma, cardinal and ordinal numbers.
- Logic: propositional and predicate calculus, well-formed formulas, tautologies, equivalence, normal forms, theory of inference.
- Combinatorics: permutation and combinations, partitions, pigeonhole principle, inclusion-exclusion principle, generating functions, recurrence relations.
Unit-II: Graph Theory [Credit: 1, 15 L]
Graph Theory: graphs and digraphs, Eulerian cycle and Hamiltonian cycle, adjacency and incidence matrices, vertex colouring, planarity, trees.
Reading References
- R.P. Grimaldi, Discrete Mathematics and Combinatorial Mathematics, Pearson Education, 1998.
- P.R. Halmos, Naive Set Theory, Springer, 1974.
- E. Kamke, Theory of Sets, Dover Publishers, 1950.
- B.A. Davey and H.A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge, 1990.
- Edgar G. Goodaire and Michael M. Parmenter, Discrete Mathematics with Graph Theory, 2nd Edition, Pearson Education (Singapore) P. Ltd., Indian Reprint 2003.
- Rudolf Lidl and Gunter Pilz, Applied Abstract Algebra, 2nd Ed., Undergraduate Texts in Mathematics, Springer (SIE), Indian reprint, 2004.
- S. Santha, Discrete Mathematics (Cengage Learning).
- S Pirzada, An Introduction to Graph Theory, Universities Press.
Basic Features
Undergraduate degree programmes of either 3 or 4-year duration, with multiple entry and exit points and re-entry options, with appropriate certifications such as:
- UG certificate after completing 1 year (2 semesters with 40 Credits + 1 Summer course of 4 credits) of study,
- UG diploma after 2 years (4 semesters with 80 Credits + 1 Summer course of 4 credits) of study,
- Bachelor’s degree after a 3-year (6 semesters with 120 credits) programme of study,
- 4-year bachelor’s degree (Honours) after eight semesters (with 170 Credits) programme of study.
- 4-year bachelor’s degree (Honours with Research) if the student completes a rigorous research project (of 12 Credits) in their major area(s) of study in the 8th semester.
Note: The eligibility condition of doing the UG degree (Honours with Research) is- minimum75% marks to be obtained in the first six semesters.
- The students can make an exit after securing UG Certificate/ UG Diploma and are allowed to re-enter the degree programme within three years and complete the degree programme within the stipulated maximum period of seven years.
