## Details of MA1201 (Spring 2020)

 Level: 1 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA1201 Mathematics II Shirshendu Chowdhury

Syllabus
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
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.ProgrammeSemester NoCourse 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