The syllabus of the course applicable for students admitted from 2013 onwards is available in the Kerala University website as a PDF file at this link:http://www.keralauniversity.ac.in/images/Downloads3/msc_maths_colleges_2013.pdf .

**Text Books**

COMPLEX ANALYSIS – I

Text: John. B. Conway, Functions of Complex Variables, Springer-Verlag, New York, 1973.

(Indian Edition: Narosa)

References:

1. L.V. Ahlfors, Complex Analysis, Mc-Graw Hill (1966) **Check price here.**

2. S. Lang, Complex Analysis, Mc-Graw Hill (1998) **Check price here.**

FUNCTIONAL ANALYSIS – 1

Text: B.V Limaye, Functional Analysis (2 nd Edition) **Check price here.**

References:

1. Dunford M and J.T Schwarz, Linear Operators Part 2, Wiley. **Check price here.**

2. Taylor A.E, Introduction to Functional Analysis, Wiley. **Check price here.**

3. G.F. Simmons, Topology and Modern Analysis, Mc Graw Hill. **Check price here.**

COMPLEX ANALYSIS – II

Text: John. B. Conway, Functions of Complex Variables, Springer-Verlag, New York, 1973

(Indian Edition: Narosa) **Check price here.**

References:

1. L.V. Ahlfors, Complex Analysis, Mc-Graw Hill (1966) **Check price here.**

2. W. Rudin, Real and Complex Analysis, Mc-Graw Hill. **Check price here.**

FUNCTIONAL ANALYSIS – II

Texts: 1) B.V Limaye, Functional Analysis (2 nd Edition) **Check price here.**

2) G.F. Simmons, Topology and Modern Analysis, International Student Edition,

Mc Graw Hill Ltd, New Delhi. **Check price here.**

References:

1. Dunford M and J.T.Schwarz, Linear Operators Part 2 , Wiley . **Check price here.**

2. Taylor A.E, Introduction to Functional Analysis, Wiley **Check price here.**

AUTOMATA THEORY (Elective)

Text: J.E. Hoporoft and J.D. Ullman, Introduction to Automata Theory Languages and

Computation, Narosa, 1999. **Check price here.**

References

1. G.E Revesz , Introduction to Formal Languages **Check price here.**

2. P.Linz , Introduction to Formal Languages and Automata, Narosa 2000 **Check price here.**

3. G.Lallment, Semigroups and Applications **Check price here.**

PROBABILITY (Elective)

Texts:

(1) Laha R.G and Rohtagi V.K ,“ Probability Theory”, JohnWiley, New York ( 1979)s **Check price here.**

(2) Johnson N.L and Kotz,S “Distributions in Statistics: Discrete Distributions”, John Wiley,

New York ( 1969)s **Check price here.**

(3) Johnson N.L, and Kots.S “ Distributions in Statistics: Continuous Univariate Distributions”,

Vol 1 and 2 ,John Wiley, New York ( Paperback, 1970) s **Check price here.**

References:

(1). Ash R.B- “Basic Probability Theory”, John wiley, New York (1970)

(2). Bhat B.R-“Modern Probability Theory: An Introduction Text Book”, Wiley Eastern

(Second Edition) 1985

(3). Gnedenko B.V-“The Theory of Probability” , Mir Publishers Moscow (1969)

(4). Luckacs.E-“Characteristic Functions”, Hafner, New York (Second Edition, 1970)

(5). Luckacs. E- “Stochastic Convergence”, Academic Press (Second Edition, 1975)

(6). Johnson N.L, Kots,S and Balakrishnan.N-“Continuos Univariate Distribution”,

Vol.1 and 2 , John Wiley, New York (Second Edition, 194 vol.1 1995 Vol.2)

(7). Johnson N.L, Kots.S and Kemp A.W-“Univariate Discrete Distributions”,

JohnWiley, New York” Second Edition 1992)

OPERATIONS RESEARCH (Elective)

Texts: 1) Ravindran, Philips, Solberg, Operations Research, Principles and Practice, Second

Edition, John Wiley & Sons. **Check price here.**

2) K. V. Mital, C. Mohan. Optimization Methods in Operations Research and Systems

Analysis, Third Edition, New Age International Publishers, New Delhi. **Check price here.**

Reference:

Hamdy A. Taha, Operations Research, Fifth edition, PHI **Check price here.**

APPROXIMATION THEORY (Elective)

Text: EW Cheney, “Introduction to Approximation Theory”, Mc Graw Hill **Check price here.**

Reference:

P.J Davis. “Interpolation and Approximation”, Blaisdell Publications. **Check price here.**

GEOMETRY OF NUMBERS (Elective)

Text Book: D.D Olds,Anneli Lax and Guiliana P. Davidoff, The Geometry of Numbers,

The Mathematical Association of America 2000 **Check price here.**

References

1. J.W.S Cassells, Introduction to Geometry of Numbers, Springer Verlag 1997 **Check price here.**

2. C.I Siegel, Lectures in Geometry of Numbers, Springer Verlag 1989. **Check price here.**

GRAPH THEORY (Elective)

Text: Gary Chartrand and Ping Zhang , Introduction to Graph Theory, Tata Mc Graw Hill,

Edition 2006 **Check price here.**

References:

1. Bondy J.A and Murthy U.S.R, “Graph Theory with Applications”, the Macmillan Press

Limited. **Check price here.**

2. Hararay F.,”Graph Theory”, Addison-Wesley **Check price here.**

3. Suesh Singh G.,”Graph Theory”, PHI Learning Private Limited **Check price here.**

4. Vasudev.C , ”Graph Theory Applications”. **Check price here.**

5. West D.B,”Introduction to Graph Theory”, PHI Learning Private Limited **Check price here.**

DIFFERENTIAL GEOMETRY (Elective)

Text: John.A. Thorpe, Elementary Topics in Differential Geometry, Springer Verlag **Check price here.**

References:

[1] I Singer and J.A Thorpe, Lecture notes on Elementary Topology and Geometry, Springer-

Verlag **Check price here.**

[2] M Spivak, Comprehensive introduction to Differential Geometry (Vols 1 to 5), Publish or Perish

Boston.

MATHEMATICAL STATISTICS (Elective)

Texts:

(1) Lehmann.E.L “Theory of Point Estimation”, John wiley, New York (1983).

(2) Lehmann.E.L “Testing of Statistical Hypothesis”, John Wiley, New York ( Second Edition 1986)

(3) Randles R.H and Wolf D.A-“Introduction to the Theory of Non Parametric Statistics”, Wiley,

New York (1979)

(4) Kendall, M.G and Stuart. A, ”The Advanced Theory of Statistics”, Vol. 2 Mac Millan , New York

(Fourth Edition 1979)

References:

1) Rohatgi V.K , “ An Introduction to Probability Theory and Mathematical Statistics”, Wiley

Eastern New Delhi ( 1985)

2) Rao, C.L , “ Liner Statistical Inference and Its Applications “, Wiley Eastern ,

New Delhi ( 1974)

3) Mood Ali, Gray Bill Fhardoes D.C” , “Introduction to the Theory of Statistics”, Mc Graw

Hill International, New York ( Third Edition, 1972)

FIELD THEORY (Elective)

Text: Joseph Rotman, Galois Theory, Second Edition, Springer, 1998.

References:

1. Harold M. Edwards, Galois Theory, Springer, 1984.

2. Joseph . A. Gallian, Contemporary Abstract Algebra, 7th Edition, Brooks/Cole.

3. J. B. Fraleigh, A First Course in Abstract Algebra, 7th Edition, PHI.

4. T. W. Hungerford, Algebra, Springer 2005.

5. O. Zariski and P. Samuel, Commutative Algebra, Vol. I, Springer – Verlag

MECHANICS (Elective)

Text: Herbert Gioldstein, Classical Mechanics, Addison Wesley

Reference:

Synge J.L and Griffith B.A, Principles of Mechanics, MC Graw-Hill

THEORY OF WAVELETS (Elective)

Text Book:

Michael Frazier, An Introduction to Wavelets through Linear Algebra, Springer **Check price here.**

References:

Mayor (1993), Wavelets and Operators, Cambridge University Press **Check price here.**

Chui. C( 1992), An Introduction to Wavelets, Academic Press, Boston **Check price here.**

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