MA2101 : Analysis I (Autumn 2021) | Academic Portal of IISER Kolkata

Details of MA2101 (Autumn 2021)

Level: 2

Type: Theory

Credits: 4.0

Course Code	Course Name	Instructor(s)
MA2101	Analysis I	Soumya Bhattacharya

Syllabus
Real Numbers: Introduction to the real number field, supremum, infimum, completeness axiom, basic properties of real numbers, decimal expansion, construction of real numbers. Sequences and Series: Convergence of a sequence, Cauchy sequences and subsequences, absolute and conditional convergence of an infinite series, Riemanns theorem, various tests of convergence. Point-set Topology of \mathbbR: Open and closed sets; interior, boundary and closure of a set; Bolzano-Weierstrass theorem; sequential definition of compactness and the Heine-Borel theorem. Limit of a Function: Limit of a function, elementary properties of limits. Continuity: Continuous functions, elementary properties of continuous functions, intermediate value theorem, uniform continuity, properties of continuous functions defined on compact sets, set of discontinuities.

Syllabus

Real Numbers: Introduction to the real number field, supremum, infimum, completeness axiom, basic properties of real numbers, decimal expansion, construction of real numbers.

Sequences and Series: Convergence of a sequence, Cauchy sequences and subsequences, absolute and conditional convergence of an infinite series, Riemanns theorem, various tests of convergence.

Point-set Topology of \mathbbR: Open and closed sets; interior, boundary and closure of a set; Bolzano-Weierstrass theorem; sequential definition of compactness and the Heine-Borel theorem.

Limit of a Function: Limit of a function, elementary properties of limits.

Continuity: Continuous functions, elementary properties of continuous functions, intermediate value theorem, uniform continuity, properties of continuous functions defined on compact sets, set of discontinuities.

References
Al-Gwaiz, M.A. and Elsanousi, S.A., Elements of Real Analysis, CRC Press. Apostol, T.M., Mathematical Analysis, Narosa Publishers. Bartle, R.G. and Sherbert, D.R., Introduction to Real Analysis, Wiley. Berberian, S.K., A First Course in Real Analysis, Springer. Denlinger, C.G., Elements of Real Analysis, Jones and Bartlett Publishers. Goldberg, R.R., Methods of Real Analysis, Oxford \& IBH Publishing. Howie, J.M., Real Analysis, Springer-Verlag. Kumar, A. and Kumaresan, S., A Basic Course in Real Analysis, CRC Press. Morrey, C.B. and Protter, M.H., A First Course in Real Analysis, Springer-Verlag. Rudin, W., Principles of Mathematical Analysis, McGraw-Hill.

References

Al-Gwaiz, M.A. and Elsanousi, S.A., Elements of Real Analysis, CRC Press.

Apostol, T.M., Mathematical Analysis, Narosa Publishers.

Bartle, R.G. and Sherbert, D.R., Introduction to Real Analysis, Wiley.

Berberian, S.K., A First Course in Real Analysis, Springer.

Denlinger, C.G., Elements of Real Analysis, Jones and Bartlett Publishers.

Goldberg, R.R., Methods of Real Analysis, Oxford \& IBH Publishing.

Howie, J.M., Real Analysis, Springer-Verlag.

Kumar, A. and Kumaresan, S., A Basic Course in Real Analysis, CRC Press.

Morrey, C.B. and Protter, M.H., A First Course in Real Analysis, Springer-Verlag.

Rudin, W., Principles of Mathematical Analysis, McGraw-Hill.

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	MS	5	Not Allowed
8	MS	7	Not Allowed
9	MS	9	Not Allowed
10	RS	1	Not Allowed
11	RS	2	Not Allowed

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Details of MA2101 (Autumn 2021)

Course Credit Options