I have done Master degree and want to do M.Phil course from Anna University Chennai so can you please provide me the details of eligibility condition and the admission criteria for this course? I have to clear any entrance exam for admission in M.Phil in this University?

The syllabus for M. Phil. Mathematics (FT) Program offered by the Department of Mathematics, Anna University, Chennai is as follows:


MX5101 ALGEBRA AND ANALYSIS

UNIT I MODULES 12
Basic Definitions Quotient Modules Module Homomorphisms Generation of Modules- Direct Sums Free Modules.


UNIT II STRUCTURE OF MODULES 12
Change of scalars Simple Modules - Semi-simple Modules - Structure of Semi-simple Modules Chain conditions The Radical.


UNIT III ABSTRACT INTEGRATION 12
The concept of measurability Simple functions Elementary properties of measures Integration of positive functions Integration of complex functions The role played by the sets of measure zero.


UNIT IV ELEMENTARY PROPERTIES OF HOLOMORPHIC FUNCTIONS 12
Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues.


UNIT V HARMONIC FUNCTIONS 12
The Cauchy-Riemann Equations - The Poisson Integral - The mean value property - Arzela Ascoli Theorem.

OUTCOMES:
The students are capable of handling the advanced topics in algebra. Ability to understand and apply algebraic structures in other area of Mathematics. Students will be knowledgeable on abstract integration. Students will understand the properties of analytic functions and use it to evaluate the integrals. Students will get more idea about harmonic function and its applications.


REFERENCES
1. Elras, M. Stein and Ramishakarchi, Complex Analysis, Princeton University Press, New
Jersey, 2003.
2. Halmos P.R., Measure Theory, Springer, New York, 1974.
3. Lang S., Algebra, Reading Mass., Addisson Wesley, Third Edition, Massachusetts, 2005.
4. Pierce R.S., Associative Algebras, Graduate Texts in Mathematics, Springer Verlag,
NewYork,1982.
5. Royden, H.L., Real Analysis, Macmillan Company, Fourth Edition, New York, 2010. 6. Rudin W., Real and Complex Analysis, Tata Mc-Graw Hill, Third Edition, New York, 2006.


Syllabus M. Phil. Mathematics (FT) Department of Mathematics, Anna University, Chennai

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