M.Phil Maths Syllabus Thiruvalluvar University

I want to do Master of Philosophy in Mathematics from the Thiruvalluvar University so I want to get the syllabus of this course, can you please provide me this?

[Quick Sam]

Well, as you need the syllabus of the Master of Philosophy Mathematics course of Thiruvalluvar University so here I am sharing the same with you
Thiruvalluvar University M.Phil Maths Syllabus
PART I
CORE COURSE I
UNIT-I: RINGS, IDEALS AND MODULES
Rings and ring homomorphisms - Ideals, Quotient rings - Zero-divisors, Nilpotent elements, Units - Prime idelas and maximal ideals - Nilradical and Jacobson radical - Operations on ideals - Extension and contraction - Exercises - Modules and module homomorphisms - Submodules and quotient modules - Operations on submodules - Direct sum and product - Finitely generated modules - Exact sequences - Tensor product of modules - Restriction and extension of scalars - Exactness properties of the tensor product - Algebras - Tensor product of algebras - Exercises.
UNIT-II: RINGS, MODULES OF FRACTIONS AND PRIMARY DECOMPOSITION
Local properties - Extended and contracted ideals in rings of fractions Exercises - Primary Decomposition - Exercises.
UNIT-III: CHIAN CONDITIONS, NOETHERIAN RINGS AND ARTIN RINGS
Chain conditions - Exercises - Primary decomposition in Noetherian rings - Exercises - Artin Rings - Exercises.
UNIT-IV: ABSTRACT INTEGRATION AND LP - SPACES
The concept of measurability - simple functions - Elementary properties of measures - Integration of positive functions - Integration of complex functions - The role played by sets of measure zero - Convex functions and inequalities - LP - spaces
UNIT-V: FOURIER TRANSFORMS AND HOLOMORPHIC FOURIER TRANSFORMS
Formal properties - The Invention Theorem - the Plancheral Theorem - The Banach algebra L1 - Introduction - Two Theorems of Paley and Wiener - Quasi - analytic classes - The Denjoy - Carleman theorem.
TEXT BOOKS:
1. M.F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Addison - Wesley Publishing Company, 1969.

Unit - I Chapter - 1 (pp 1 - 10), Chapter - 2 (pp 17 - 31)
Unit - II Chapter - 3 (pp 36 - 43), Chapter - 4 (pp 50 - 55)
Unit - III Chapter - 6 (pp 74 - 78), Chapter - 7 (pp 80 - 84)
Chapter - 8 (pp 89 - 91)
2. Walter Rudin, Real and Complex Analysis, 3rd Edition, McGraw Hill International, 1986.

Unit - IV Chapter - 1 (pp 5 - 31), Chapter - 3 (pp 61 - 69),
Unit - V Chapter - 9 (pp 178 - 193), Chapter - 19 (pp 371 - 383)
PART I
CORE COURSE II TOPOLOGY AND DIFFERENTIAL EQUATIONS
UNIT-I: FUNDAMENTAL GROUP AND COVERING SPACES
Homotopy - Fundamental group - Covering spaces.
UNIT-II: SIMPLICIAL COMPLEXES
Geometry of Simplicial Complexes - Bary Centric subdivisions - Simplicial approximation Theorem - Fundamental Group of a simplicial Complex.
UNIT-III: LINEAR SYSTEMS
Uncoupled Linear System - Diagonalization - Exponentionals operators - The Fundamental Theorem for linear system - Linear System in R2 - Complex Eigen Values - Multiple Eigen Values - Non Homogeneous Linear System.
UNIT-IV: NON LINEAR SYSTEMS: LOCAL THEORY
Some preliminary concepts & definitions - The Fundamental Existence - Uniqueness Theorem - Dependence on Initial Conditions and Parameters - The Maximum Interval of Existence - The Flow Defined by a Differential Equation.
UNIT-V: NON LINEAR SYSTEMS
Linearization - The Stable Manifold Theorem - Dynamical Systems and Global Existence Theorems - Limit Sets and Attractors
TEXT BOOK(S):
1. I.M. Singer, J.A. Thorpe, Lecture Notes on Elementary Topology and Geometry, Springer - Verlag, New York, 1967.

Unit - I Chapter - 3 (pp 49 - 77)
Unit - II Chapter - 4 (pp 78 - 108)
2. L. Perko, Differential Equation and Dynamical System, Third Edition, Springer - Verlag, New York, 2006.

Unit - III Chapter - 1 (Sections 1.1 to 1.7 and 1.10) (pp 1 - 39, 60 - 63)
Unit - IV Chapter - 2 (Sections 2.1 to 2.5) (pp 65 - 101)
Unit - V Chapter - 2 (Sections 2.6 and 2.7) (pp 101 - 118)
Chapter - 3 (Sections 3.1 and 3.2) (pp 181 - 199)

Sir, I am doing M.phil mathematics in Thiruvalluvar university .so,i want to previous yrs questions paper can you pls kindly provide me this.