## Details of MA1201 (Spring 2020)

Level: 1 |
Type: Theory |
Credits: 3.0 |

Course Code | Course Name | Instructor(s) |
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MA1201 |
Mathematics II |
Shirshendu Chowdhury |

Syllabus |
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Part I: Sequences & Series
Sequences: definition, notion of convergence, properties of limit, sandwich Theorem, examples including 1/n, rn, (_1)n, sin(n), n, (_1)nn, c1/n for c > 0. Series: partial sums, definition of convergence, geometric progression, comparison test, telescopic sum, examples including 1/nP. Part II: Linear Algebra in dimensions 2 and 3 Basic material: system of linear equations, elementary operations, linear transformation in R2 and R3. Determinant: definition and its geometric meaning. Rigid motions in R2 & R3: isometry, symmetry of planar objects, distance preserving maps. Eigenvalues: definition and examples including symmetric matrices. Conic sections: examples and properties. Part III: Introduction to Integration Basic material: definition of integral as a Riemann sum, elementary properties: linearity, order preserving, integral of |f | versus modulus of integral. Fundamental Theorem of Calculus: statement and proof for continuous functions, computation of __0^x_f(t)dt for step functions and f (x) = |x|. Further topics: integration by parts, change of variables, Cauchy-Schwarz inequality. Part IV: Set Theory II Finite & infinite sets: countable and uncountable sets, Hilbert's infinite hotel, Russell's barber paradox, power set, sets indexed by another set. Fundamental arguments: Cantor's Theorem, Cantor's diagonalization argument, Schroder-Bernstein Theorem |

References |
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Suggested Texts / Reference Books:
1. Apostol, T.M., Calculus I, Wiley India Pvt Ltd. 2. Apostol, T.M., Calculus II, Wiley India Pvt Ltd. 3. Artin, M., Algebra, Prentice-Hall of India. 4. Barnard, S. and Child, J.M., Higher Algebra, Macmillan. 5. Bartle, R.G., Sherbert, D.R., Introduction to Real Analysis , John Wiley & Sons. 6. Denlinger, C.G., Elements of Real Analysis, Jones & Bartlett Learning. 7. Halmos, P.R., Na_ive Set Theory, Springer 8. Kreyszig, E., Advanced Engineering Mathematics (8th Edition), Wiley India Pvt Ltd. 9. Piskunov, N., Differential and Integral Calculus: Volume 1, CBS. 10. Polya, G., How to Solve It, Princeton University Press. |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 2 | Not Allowed |

2 | IP | 4 | Not Allowed |

3 | IP | 6 | Not Allowed |

4 | MR | 2 | Not Allowed |

5 | MR | 4 | Not Allowed |

6 | MS | 2 | Core |

7 | RS | 1 | Not Allowed |

8 | RS | 2 | Not Allowed |