BHARATHIDASAN UNIVERSITY, TIRUCHIRAPPALLI – 620 024
M.Sc. MATHEMATICS SYLLABUS (ANNUAL PATTERN)
(FOR DISTANCE EDUCATION CANDIDATES ONLY)
(For the candidates admitted from the academic year 2006-2007 batch onwards)
PAPER II - REAL ANALYSIS
Unit I
Basic topology: Finite, Countable sets – Metric spaces - Compact sets – Perfect sets – Connected sets.
Numerical sequences and series, sequences – convergence – subsequences – Cauchy sequences – Upper and Lower limits – some special sequences – Tests of Convergence – Power series – Absolute convergence – Addition and Multiplication
series.
Unit II
Continuity: Limits of functions – Continuous Functions - Continuity and Compactness – Continuity and connectedness – discontinuities – Monotonic functions- Infinite limits and Limit at infinity.
Differentiation: Derivative of real functions – mean value theorems – intermediate value theorems for derivatives – L’ hospital rule – Taylor’s Theorem – differentiation of vector – valued functions.
Unit III
Riemann – Stieltjes integrals: definition and existence – properties – integration and differentiations – Integration of vector valued functions.
Unit IV
Sequence and Series of functions – Discussions of main problem – uniform convergence – Uniform convergence and continuity – Uniform convergence and integration – Uniform convergence and different ion – equi continuous – family of
functions – Stone – Weierstrass theorem.
Unit V
The Lebesgue theory – set functions. Construction of Lebesgue measure – measure spaces – measurable functions – simple functions – integration – comparisons with the Riemann integral – integration of Complex function – function of class L2.
Text Books:
1. Walter Rudin, “Principles of Mathematical Analysis”, Third edition, Mc-Graw Hill,
1976
Unit I: Chapter 2 and 3
Unit II: Chapter 4 and 5
Unit III: Chapter 6
Unit IV: Chapter 7
Unit V: Chapter 11
Books for Reference:
1. T.M. Apostol, “Mathematical Analysis”, Second edition, Addison Wesley publication,
Tokyo 1981.
2. V.Ganapathy Iyer, “Introduction to Real Analysis”, PHI.
M.Sc. MATHEMATICS SYLLABUS (ANNUAL PATTERN)
(FOR DISTANCE EDUCATION CANDIDATES ONLY)
(For the candidates admitted from the academic year 2006-2007 batch onwards)
PAPER II - REAL ANALYSIS
Unit I
Basic topology: Finite, Countable sets – Metric spaces - Compact sets – Perfect sets – Connected sets.
Numerical sequences and series, sequences – convergence – subsequences – Cauchy sequences – Upper and Lower limits – some special sequences – Tests of Convergence – Power series – Absolute convergence – Addition and Multiplication
series.
Unit II
Continuity: Limits of functions – Continuous Functions - Continuity and Compactness – Continuity and connectedness – discontinuities – Monotonic functions- Infinite limits and Limit at infinity.
Differentiation: Derivative of real functions – mean value theorems – intermediate value theorems for derivatives – L’ hospital rule – Taylor’s Theorem – differentiation of vector – valued functions.
Unit III
Riemann – Stieltjes integrals: definition and existence – properties – integration and differentiations – Integration of vector valued functions.
Unit IV
Sequence and Series of functions – Discussions of main problem – uniform convergence – Uniform convergence and continuity – Uniform convergence and integration – Uniform convergence and different ion – equi continuous – family of
functions – Stone – Weierstrass theorem.
Unit V
The Lebesgue theory – set functions. Construction of Lebesgue measure – measure spaces – measurable functions – simple functions – integration – comparisons with the Riemann integral – integration of Complex function – function of class L2.
Text Books:
1. Walter Rudin, “Principles of Mathematical Analysis”, Third edition, Mc-Graw Hill,
1976
Unit I: Chapter 2 and 3
Unit II: Chapter 4 and 5
Unit III: Chapter 6
Unit IV: Chapter 7
Unit V: Chapter 11
Books for Reference:
1. T.M. Apostol, “Mathematical Analysis”, Second edition, Addison Wesley publication,
Tokyo 1981.
2. V.Ganapathy Iyer, “Introduction to Real Analysis”, PHI.
0 comments:
Post a Comment