Details of MA2103 (Autumn 2016)
| Level: 2 | Type: Theory | Credits: 2.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA2103 | Foundations I | Asok Kumar Nanda |
| Syllabus |
|---|
| Sets, relations and functions: Basic set operations: Subsets, equality of sets, union of sets, intersection of sets, complement of a set, ordered pairs, cartesian product of sets. Relations: Equivalence relations, equivalence classes. Functions: Domain of a function, range, codomain, surjective functions, injective functions, bijective functions, composition of functions, inverse functions.
Elementary combinatorics: Permutations and combinations, elementary properties. Binomial coefficients: Properties of binomial coefficients, binomial theorem, counting nonnegative integer solutions of certain equations, Bertrand's postulate. Principles of counting: Pigeonhole principle and applications. Inclusion-Exclusion principle and applications. |
| References |
|---|
| 1. Gilbert, W. J., and Vanstone S. A., An introduction to mathematical thinking (Algebra and number systems), Prentice Hall, 2005.
2. DAngelo, J. P. and West, D. B., Mathematical thinking (Problem-Solving and Proofs), (2nd Edition), Prentice Hall, 2000. 3. Ray, S. L., Analysis with an Introduction to Proof, (4th Edition), Prentice Hall, 2005. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MR | 1 | Not Allowed |
| 5 | MR | 3 | Not Allowed |
| 6 | MS ( Mathematical Sciences ) | 3 | Core |
| 7 | RS | 1 | Not Allowed |
| 8 | RS | 2 | Not Allowed |