cbcs - course outline for 2005-2006 - Madras University

10. SCHOOL OF MATHEMATICS, STATISTICS AND COMPUTER SCIENCE Mathematics, Statistics and Computer Science together constitute a
school with wide scope for interaction aiming at excellence in fundamental
research and applications. The University of Madras is known for its nurturing the genius in
Srinivasa Ramanujan, the great mathematical luminary whose mathematics is
engaging the attention of leading mathematicians even today for its
profoundness and applications. The University department of Mathematics was
created in 1927. The Ramanujan Institute of Mathematics, founded by
Dr.Rm.Alagappa Chettiar came into existence in 1957. In 1967, with the
assistance from UGC it become a Centre of Advanced Study in Mathematics
merging the two units. This centre is now known as the Ramanujan Institute
for Advanced Study in Mathematics (RIASM). The RIASM offers Masters,
M.Phil. and . programmes. An independent Department of Statistics started functioning in 1941
and became a full fledged department of study and research from 1975 under
the leadership of Prof.K.N.Venkataraman. The department offers Masters,
M.Phil and Ph.D. Programmes. The department also offeres M.Sc. Actuarial
Science programme under UGC Innovative programme.
Study of Computer Science in the University began in 1984. An
independent department was instituted in 1995. The Department of Computer
Science concentrates research in the areas of Parallel Algorithms,
Architectures and Applications, Parallel Computing, Computational Geometry
and it too has a well equipped Computer Laboratory. The department
currently offers Master of Computer Applications and programmes. Faculty Dr. P.Thangavel, Ph.D. - Chairperson
RIAS in Mathematics S. Parvathi, Ph.D. - Director and Head
K. Parthasarathy, Ph.D. - Professor
Premalatha
Kumaresan, Ph.D. - Professor
M. Loganathan, Ph.D. - Professor
V. Thangaraj, Ph.D. - Professor
R. Sahadevan, Ph.D. - Professor
G.Balasubramanian, Ph.D. - Professor
G.P.Yuvaraj, Ph.D. - Reader
N.Agarwal Sushama, Ph.D. - Lecturer
Statistics G.Gopal, Ph.D. - Professor and Head
P.Dhanavanthan, Ph.D. - Professor
M.R.Srinivasan, Ph.D. - Professor
T. Anbupalam, Ph.D. - Lecturer
M.R. Sindhumol - Lecturer
K.M.Sakthivel - Lecturer (on contract) Computer Science P.Thangavel, Ph.D. - Professor and Head
S.Gopinathan, M.Sc. - Lecturer
P.L. Chitra, M.C.A. - Lecturer
Sornam, M.Sc., M.C.A. - Lecturer
B.Lavanya - Lecturer
M.Sc. MATHEMATICS M.Sc Mathematics (CBCS) 2007 - 2009. | | | |Credit | |
|Course |Title of the Course |C/E/S |L |T |P |C | |
|Code | | | | | | | |
|Times New|SEMESTER I | | | | | | |
|Roman | | | | | | | |
|C001 |Linear Algebra |C |3 |1 |0 |4 |M.Loganathan |
|C002 |Real Analysis |C |3 |1 |0 |4 |G.P.Youvaraj |
|C003 |Ordinary Differential Equations |C |3 |1 |0 |4 |R.Sahadevan |
|C004 |Computational Mathematical |C |0 |0 |4 |4 |Guest Faculty |
| |Laboratory- I | | | | | | |
| |Elective |E |2 |1 |0 |3 | |
|UOM S 001|Soft Skill* |S | | | |2 | |
| |SEMESTER II | | | | | | |
|C005 |Algebra |C |3 |1 |0 |4 |S.Parvathi |
|C006 |Topology |C |3 |1 |0 |4 |G.P.Youvaraj |
|C007 |Partial Differential Equations |C |3 |1 |0 |4 |Guest Faculty |
|C008 |Seminar |C |3 |1 |0 |4 |Faculty Concerned|
| |Elective |E |2. |1 |0 |3 | |
|UOM S 002|Soft Skill* |S | | | |2 | |
| |SEMESTER III | | | | | | |
|C009 |Complex Analysis |C |3 |1 |0 |4 |Guest Faculty |
|C010 |Measure & Integration theory |C |3 |1 |0 |4 |Premalatha |
| | | | | | | |Kumaresan |
|C011 |Probability theory |C |3 |1 |0 |4 |V.Thangaraj |
|C012 |Computational Mathematical |C |3 |1 |0 |4 |R.Sahadevan |
| |Laboratory-II | | | | | | |
| |Elective |E |2 |1 |0 |3 | |
| |Elective |E |2 |1 |0 |3 | |
|UOM S 003|Soft Skill* |S | | | |2 | |
|UOM I 001|Internship** |S | | | |2 | |
| |SEMESTER IV | | | | | | |
|C013 |Advanced Analysis |C |3 |1 |0 |4 |K.Parthasarathy |
|C014 |Differential Geometry |C |3 |1 |0 |4 |Premalatha |
| | | | | | | |Kumaresan |
|C015 |Functional Analysis |C |3 |1 |0 |4 |Sushama Agrawal |
| |Elective |E |2 |1 |0 |3 | |
| |Elective |E |2 |1 |0 |3 | |
|UOM S 004|Soft Skill* |S | | | |2 | |
Note: Compulsory Components for Postgraudate Programmes
Core Courses - 60 Credits minimum
Elective Courses - 18 Credits minimum
Soft Skill Courses - 08 Credits minimum
Internship - 02 Credits
Total - 88 Credits minimum
Elective Courses Offered by the RIASM
|Course |Title of the Course |C/E/|Credits |Faculty |
|Code | |S/ | | |
| | |SS | | |
| | | |L |T |P |C | |
|MSI E001 |Discrete Mathematics |E |2 |1 |0 |3 |Guest Faculty |
|MSI E002 |Number Theory and |E |2 |1 |0 |3 | Guest Faculty |
| |Cryptography | | | | | | |
|MSI E003 |Programming and Soft |E |1 |1 |1 |3 |Guest Faculty |
| |Computations | | | | | | |
|MSI E004 |Computer Based Numerical |E |1 |1 |1 |3 |Guest Faculty |
| |Methods | | | | | | |
|MSI E005 |Lie Algebras |E |2 |1 |0 |3 |Guest Faculty |
|MSI E006 |Stochastic Processes |E |2 |1 |0 |3 |V.Thangaraj |
|MSI E007 |Representation Theory of Finite|E |2 |1 |0 |3 |S.Parvathi |
| |Groups | | | | | | |
|MSI E008 |Graph Theory |E |2 |1 |0 |3 |M.Loganathan |
|MSI E009 |Lie Groups of Transformations |E |2 |1 |0 |3 |R.Sahadevan |
| |and | | | | | | |
| |Ordinary Differential Equations| | | | | | |
|MSI E010 |Lie Groups of Transformations |E |2 |1 |0 |3 |R.Sahadevan |
| |and | | | | | | |
| |Partial Differential Equations | | | | | | |
|MSI E011 |Potential Theory in Rn |E |2 |1 |0 |3 |Premalatha |
| | | | | | | |Kumaresan |
|MSI E012 |Linear Lie groups |E |3 |0 |0 |3 |K.Parthasarathy |
|MSI E013 |Banach Algebras and Operator |E |3 |0 |0 |3 |Agrawal Sushama |
| |theory | | | | | |N. |
|MSI E014 |Algebraic Number Theory |E |2 |1 |0 |3 |S.Parvathi |
|MSI E015 |Mathematical Theory of |E |2 |1 |0 |3 |G.P.Youvaraj |
| |Electromagnetic Waves | | | | | | |
|Self-Study Courses |
|MSI S001 |Algebraic Theory of Numbers |SS |0 |4 |0 |4 |S.Parvathi |
|MSI S002 |Algebraic Topology |SS |0 |4 |0 |4 |M.Loganathan |
|MSI S003 |Financial Calculus |SS |0 |4 |0 |4 |V.Thangaraj |
|MSI S004 |Fuzzy Analysis |SS |0 |4 |0 |4 |N.Agrawal Sushama|
|MSI S005 |Harmonic Function Theory |SS |0 |4 |0 |4 |Premalatha |
| | | | | | | |Kumaresan |
|MSI S006 |Introduction to Fractals |SS |0 |4 |0 |4 |K.Parthasarathy |
|MSI S007 |Lie Groups and Lie Algebras |SS |0 |4 |0 |4 |K.Parthasarathy |
|MSI S008 |Probability on Abstract Spaces |SS |0 |4 |0 |4 |V.Thangaraj |
|MSI S009 |Quantum Computations |SS |0 |4 |0 |4 |V.Thangaraj |
|MSI S010 |Quantum Groups |SS |0 |4 |0 |4 |S.Parvathi |
P.G.DI