University of Goa - Department of Maths

Will you please provide me the syllabus of M.Sc. Mathematics offered under Department of Mathematics - Goa University??

Department of Mathematics was established in 2006-07 under Goa University. Goa University was established in 1985 and is currently accredited to the NAAC (National Assessment and Accreditation Council) in India

Facilities:
Audio visual
Computers

Courses Offered
M.Sc. Mathematics
Ph.D Mathematics

Syllabus of M Sc Mathematics –

MATH-101: REAL ANALYSIS
Number of Credits: 4

Prerequisites: Set Theory.
1) Real and Complex Number Systems: Finite sets, Natural Numbers and Induction
Principle, Countable sets, Integers, Rational Numbers, Ordered Field, Complete
Ordered Field, Real Numbers, Dedikind cuts, Complex Numbers. Topology of Euclidean Spaces: Metric Spaces, Euclidean Spaces, Compact Sets,
Perfect sets, Connected sets. (15 hours)

2) Continuity: Continuous Function, Continuity and Compactness, Continuity and
Connectedness, Types of Discontinuities, Monotone Functions, Extended Real Number System, Infinite limits and Limits at Infinity. (15 hours)

3) Differentiation: Mean Value Theorem, Continuity of Derivatives, L’Hospital’s Rule, Derivative of Higher order, Taylor’s Theorem, Differentiation of Vector valued
Functions. (15 hours)

4) The Riemann Stieltje’s Integral: Definition and Existence of the Integral, The
Integral as a limit of Sums, Integration and Differentiation, Integration of Vector
Valued Functions, Functions of Bounded Variation, Properties of Integration,
Rectifiable Curves. (15 hours)

Rest of the syllabus is attached in below file which is free of cost for you

Address:
Goa University
Taleigao, GA 403206 ‎
0832 245 1345 ‎

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Attached Files Available for Download

Goa University M Sc Mathematics Syllabus.pdf (318.3 KB, 28 views)