## 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 |
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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 |
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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 | 3 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |