UM-DAE Centre for Excellence in Basic Sciences

Course structure for the M. Sc. (Integrated) Mathematics streamdownload

Semester I

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
101 Biology I [2+1] 3
C101 Chemistry I [2+1] 3
M101/100 Mathematics I [2+1] 3
P101 Physics I (Mechanics & Thermodynamics) [2+1] 3
G101 Computer Basics [2+1] 3
H101 Communication Skills [2+1] 3
    Lab Hours per Week Credits
PL101 Physics Laboratory [4] 2
CL101 Chemistry Laboratory [4] 2
BL101 Biology Laboratory [4] 2
GL101 Computer Laboratory [4] 2
    Semester Credits 26

 

Semester II

Subject CodeSubjectContact Hours Per Week
(Theory+Tutorials)
Credits
 B201  Biology II [2+1] 3
 C201  Chemistry II [2+1] 3
 M201/200  Mathematics II [2+1] 3
 P201  Physics II (Optics, Electricirty & Magnetism) [2+1] 3
 G201
 Electronics and
 Instrumentation
[2+1] 3
 G202
 Glimpses of Contemporary
 Sciences
[2+1] 3
     Lab Hours per Week  Credits
 PL201  Physics Laboratory [4] 2
 CL201  Chemistry Laboratory [4] 2
 BL201  Biology Laboratory [4] 2
 GL201  Electronics Laboratory [4] 2
    Semester Credits  26

 

Semester III

Subject codeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
M301 Foundations [3+1] 4
M302 Analysis I [3+1] 4
M303 Algebra I [3+1] 4
M304 Discrete Mathematics [3+1] 4
M305 Computational Mathematics I [3+1] 4
 H301
 World Literature
[2+0] 2
H302 History and Philosophy of Science [2+0] 2
    Semester Credits 24

 

Semester IV

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
 M401  Analysis II
[3+1] 4
 M402
 Algebra II
[3+1] 4
 M403  Elementary Number Theory
[3+1] 4
 M404  Topology I
[3+1] 4
 G401
 Statistical Techniques and
 Applications
[3+1] 4
    Lab Hours per Week  Credits
 GL401
 Computational Laboratory and
 Numerical Methods
[4] 2
   Semester Credits   26

 

Semester V

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
 M501  Analysis III
[3+1] 4
 M502  Algebra III
[3+1] 4
 M503  Topology II
[3+1] 4
 M504  Graph Theory
[3+1] 4
 G501
 Earth Science and Energy &
 Environmental Sciences
[3+1] 4
 PM501
 Numerical Analysis
[3+1] 4
    Lab Hours per Week  Credits
 PML501  Numerical Methods Laboratory
[4] 2
    Semester Credits 26

 

Semester VI

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
 M601  Analysis IV
[3+1] 4
 M602  Algebra IV
[3+1] 4
 M603 Di erential Geometry & Applications
[3+1] 4
 M604
Di erential Equations & Dynamical Systems
 Applications
[3+1] 4
 M605
Probability Theory
 Dynamical Systems
[3+1] 4
 PM601 Special Functions and Applications [3+1] 4
 H601  Ethics of Science and IPR [2+0] 2
    Semester Credits 26

 

Semester VII

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
 M701  Functional Analysis
[3+1] 4
 M702  Commutative Algebra
[3+1] 4
 M703
Stochastic Analysis
[3+1] 4
 M704
 Partial Differential Equations
[3+1] 4
 M705
 Representation Theory of Finite
 Groups
[3+1] 4
 MPr701
 Project
[3+1] 4
    Semester Credits 24

 

Semester VIII

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
 M801  Fourier Analysis
[3+1] 4
 M802
 Algebraic Number Theory
[3+1] 4
 M803
 Algebraic Topology
[3+1] 4
 M804 Di erential Topology
[3+1] 4
 M805 Computational Mathematics III [3+1] 4
 MPr801  Project - 6
    Semester Credits  26

 

Semester IX

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
MPr901 Project - 24
    Semester Credits 24

 

Semester X

Subject CodeSubjectContact Hours per Week
(Theory+Tutorials)
Credits
ME100* Elective* [3+1] 4

 

Minimum credits required: 240

Electives

Electives taught in previous years

  1. Advanced Commutative Algebra & Applications.
  2. Advanced Di erential Topology.
  3. Advanced Numerical Techniques.
  4. Coding Theory & Cryptography.
  5. Combinatorics & Enumeration.
  6. Financial Mathematics.
  7. Fractals & Applications.
  8. Graph Theory.
  9. Introduction to Ergodic Theory.
  10. Lie Groups & Geometry
  11. Quantum Computing.
  12. Topics in Algebraic Geometry.

Other possible electives

  1. Advanced Algebraic Topology & Applications.
  2. Advanced Di erential Geometry & Applications.
  3. Algebraic curves.
  4. Analytic number theory.
  5. Class eld theory.
  6. Combinatorial Design Theory.
  7. Econometrics.
  8. Elliptic curves.
  9. Finite Fields & Applications.
  10. Fluid Mechanics.
  11. Geometric algebra.
  12. Homological Algebra & Applications.
  13. Industrial Mathematics.
  14. Introduction to algebraic groups.
  15. Mathematical Applications to Engineering.
  16. Mathematics & Nano Technology.
  17. Modular forms.
  18. Operator Theory.
  19. Perturbation Theory.
  20. Wavelet Analysis & Applications.

Address

UM-DAE Centre for Excellence in Basic Sciences
Health Centre, University of Mumbai,
Vidyanagari Campus, Kalina, Santacruz (East), Mumbai 400098, India.
Phone: 91-22-26524983
Fax: 91-22-26524982
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About Us

CBS was set up by the Department of Atomic Energy and the University of Mumbai in 2007. CBS offers a 5 year integrated MSc program in Basic Sciences, with undergraduate teaching embedded in a postgraduate and research environment, for students who have completed 10+2 schooling or its equivalent.