| Course Category | Credits |
|---|---|
| PC (Programme Core) | 52 |
| PE (Programme Elective) | 15 |
| OE (Open Elective) | 6 |
| Total Graded Credit Requirement | 73 |
| Non-Graded Units (NGU) | Units |
|---|---|
| Total Non-Graded Units | 0 |
| PLO | Outcome |
|---|---|
| PLO 1 | Develop precise analytical thinking and effectively communicate mathematical ideas; cultivate robust logical reasoning and problem-solving abilities necessary for advanced mathematical study. |
| PLO 2 | Demonstrate the ability to independently formulate, analyze, and solve complex problems using appropriate mathematical tools, computational techniques, or statistical methods relevant to their specialization. |
| PLO 3 | Recognize the impact of mathematics in advancing both academic inquiry and industrial innovation, and develop the ability to engage with current developments and future directions in specialized areas through sustained learning and research. |
| Course No. | Course Title | L | T | P | Credits |
|---|---|---|---|---|---|
| MTD6010 | M.Sc. Project Part I | 0 | 0 | 8 | 4 |
| MTD6030 | Cornerstone Project | – | – | – | – |
| MTL5001 | Algebra | 3 | 1 | 0 | 4 |
| MTL5002 | Linear Algebra | 3 | 1 | 0 | 4 |
| MTL5003 | Real Analysis | 3 | 1 | 0 | 4 |
| MTL5004 | Introduction to Computer Programming | 3 | 0 | 2 | 4 |
| MTL5005 | Introduction to Probability | 3 | 1 | 0 | 4 |
| MTL5006 | Ordinary Differential Equations | 3 | 1 | 0 | 4 |
| MTL5007 | Functional Analysis | 3 | 1 | 0 | 4 |
| MTL5008 | Mathematical Programming | 3 | 1 | 0 | 4 |
| MTL5009 | Numerical Analysis | 3 | 1 | 0 | 4 |
| MTL5010 | Measure and Integration | 3 | 1 | 0 | 4 |
| MTL5011 | Statistical Inference | 3 | 1 | 0 | 4 |
| MTL5021 | Professional Ethics in Mathematics | 1 | 0 | 0 | 1 |
| MTL6001 | Complex Analysis | 3 | 1 | 0 | 4 |
| MTL6011 | Discrete Mathematical Structures | 3 | 1 | 0 | 4 |
| Course No. | Course Title | L | T | P | Credits |
|---|---|---|---|---|---|
| MTL6507 | Topology | 3 | 1 | 0 | 4 |
| MTL6632 | Nonparametric Statistical Methods | 2 | 0 | 2 | 3 |
| MTL6777 | Foundations of Statistical Learning | 2 | 0 | 2 | 3 |
| MTL7012 | Computational Methods for Differential Equations | 3 | 0 | 2 | 4 |
| MTL7030 | Fundamentals of Cryptography | 3 | 0 | 2 | 4 |
| MTL7237 | Introduction to Differential Geometry | 3 | 0 | 0 | 3 |
| MTL7239 | Representation Theory of Finite Groups | 3 | 0 | 0 | 3 |
| MTL7244 | Mathematical Theory for Error Correcting Codes | 3 | 0 | 0 | 3 |
| MTL7255 | Algebraic Curves | 3 | 0 | 0 | 3 |
| MTL7257 | Introduction to Algebraic Topology | 3 | 0 | 0 | 3 |
| MTL7258 | Introduction to Differential Topology | 3 | 0 | 0 | 3 |
| MTL7281 | Finite Element Theory and Applications | 3 | 0 | 0 | 3 |
| MTL7455 | Partial Differential Equations | 3 | 0 | 0 | 3 |
| MTL7717 | Fuzzy Sets and Applications | 3 | 0 | 2 | 4 |
| MTL7725 | Stochastic Processes and its Applications | 3 | 0 | 0 | 3 |
| MTL7732 | Financial Mathematics | 3 | 0 | 2 | 4 |
| MTL7735 | Introduction to Number Theory | 3 | 1 | 0 | 4 |
| MTL7736 | Analytic Number Theory | 3 | 0 | 0 | 3 |
| MTL7738 | Commutative Algebra | 3 | 0 | 0 | 3 |
| MTL7741 | Fractal Geometry | 3 | 0 | 0 | 3 |
| MTL7743 | Fourier Analysis | 3 | 0 | 0 | 3 |
| MTL7744 | Applied Harmonic Analysis | 3 | 0 | 0 | 3 |
| MTL7750 | Abstract Harmonic Analysis | 3 | 0 | 0 | 3 |
| MTL7761 | Basic Ergodic Theory | 3 | 0 | 0 | 3 |
| MTL7763 | Introduction to Game Theory | 3 | 0 | 0 | 3 |
| MTL7766 | Multivariate Statistical Analysis | 3 | 0 | 0 | 3 |
| MTL7768 | Graph theory | 3 | 0 | 0 | 3 |
| MTL7770 | Combinatorial Optimization | 3 | 0 | 0 | 3 |
| MTL7783 | Theory of Computation | 3 | 1 | 0 | 4 |
| MTL7799 | Mathematical Analysis in Learning Theory | 3 | 0 | 0 | 3 |
| MTL7848 | Pseudodifferential Operators with Application in PDE | 3 | 0 | 0 | 3 |
| MTL7860 | Linear Algebra II | 3 | 0 | 0 | 3 |
| MTL7890 | Optimization Algorithms | 3 | 0 | 2 | 4 |
| MTL8880 | Parameterized Algorithms for NP-hard Problems | 3 | 0 | 0 | 3 |
| Sem | Courses & Baskets | Hrs / week |
NGU | Credits |
|---|---|---|---|---|
| 1 |
MTL5002 Linear Algebra
(3.0-1.0-0.0) 4.00
MTL5003 Real Analysis
(3.0-1.0-0.0) 4.00
MTL5004 Introduction to Computer Programming
(3.0-0.0-2.0) 4.00
MTL5005 Introduction to Probability
(3.0-1.0-0.0) 4.00
MTL5001 Algebra
(3.0-1.0-0.0) 4.00
|
21 | 0 | 20 |
| 2 |
MTL5006 Ordinary Differential Equations
(3.0-1.0-0.0) 4.00
MTL5007 Functional Analysis
(3.0-1.0-0.0) 4.00
MTL5008 Mathematical Programming
(3.0-1.0-0.0) 4.00
MTL5009 Numerical Analysis
(3.0-1.0-0.0) 4.00
MTL5010 Measure and Integration
(3.0-1.0-0.0) 4.00
MTL5021 Professional Ethics in Mathematics
(1.0-0.0-0.0) 1.00
|
21 | 0 | 21 |
| 3 |
MTL6001 Complex Analysis
(3.0-1.0-0.0) 4.00
MTD6010 M.Sc. Project Part I
(0.0-0.0-8.0) 4.00
APE1* (only for specialization)
APE2* (only for specialization)
PE 1
PE 2
OE
(3-0-0) 3
|
21 | 0 | 17 |
| 4 |
MTD6030 Cornerstone Project
(0.0-0.0-6.0) 3.00
APE3* (only for specialization)
APE4* (only for specialization)
PE 3
OE
(3-0-0) 3
PE 4
PE 5
|
21 | 0 | 15 |
| Total | 84 | 0 | 73 | |
Students are required to take a 1-credit course in professional ethics in semester 2. Students choose between MTL5010 Measure and Integration or 5011 Statistical Inference in Semester 2. Students choose between MTL6001 Complex Analysis or MTL6011 Discrete Mathematical Structures in Semester 3.
* APEs refer to recommended additional programme electives required for specialization. The number of APEs varies depending on the choice of open electives as well as whether the student follows a project-intensive or course-intensive track. The credits without brackets shown pertain only to the general M.Sc. programme.
Students have a choice of two PEs or MSc project Part - II in semester 4; eligibility for choosing Major Project-II is CGPA of 7 or higher by the end of the third semester and a grade of A or A- in Project-I. Specialization in Pure Mathematics, Applied and Computational Mathematics, or Statistical, Computing, and Industrial Mathematics requires courses worth 12 credits in one of these areas; courses in OE from the same area also count towards specialization credits (eligibility for specialization is CGPA of 7 or higher by the end of the third semester).
For M.Sc in Mathematics (General Program):
Total Credits: Semester Wise: 20 + 21 + 17 + 15 = 73 credits.
Course-intensive Option: PC = 45, OE = 6, PE = 15, Project = 7.
Project-intensive Option: PC = 45, OE = 6, PE = 9, Project = 13.
There is NO specialization restriction on the choice of PE, OE, and Projects for a general MSc in Mathematics.
For M.Sc in Mathematics with Specialization (Specialization A, Specialization B, or Specialization C):
Total Credits: Semester Wise: 20 + 21 + 23 + 21 = 85 credits (MSc in Mathematics with specialization in A, B, or C)
OR
Total Credits: Semester Wise: 20 + 21 + 20 + 18 = 79 credits (if both OEs are done from Mathematics PEs, then only two APEs are required to be done; however, all four should be within the same specialization)
Course Intensive Program Specializations (85 credits (i) or 79 credits (ii)):
i. PC = 45, Project = 7, OE = 6 (both outside Math), PE = 15, APE* = 12 (all APEs must be from the same Specialization)
OR
ii. PC = 45, Project = 7, PE = 15, OE = 6 (both from Math), APE = 6 (all OEs and APEs must be from the same Specialization)
Project Intensive Program Specialization: (85 credits (iii) or 79 credits (iv))
iii. PC = 45, Project = 7, OE = 6 (both outside Math), PE = 9, ProjectPart 2 = 6, APE = 12 (The APEs and Project -II must be from the same specialization)
iv. PC = 45, Project = 7, Project Part 2 = 6, OE = 6 (both from Math), PE = 9, APE = 6 ( The APEs, OEs, and Project -II must be from the same Specialisation)
*APE: Additional PE (APE courses must be different from PEs and PCs).
Specialization A: Pure Mathematics
| Sl. No | Course No. | Course Title |
|---|---|---|
| 1 | MTL6507 | Topology |
| 2 | Analysis | |
| 3 | MTL7735 | Introduction to Number Theory |
| 4 | MTL7736 | Analytic Number Theory |
| 5 | MTL7737 | Algebraic Number Theory |
| 6 | MTL7741 | Fractal Geometry |
| 7 | MTL7237 | Introduction to Differential Geometry |
| 8 | MTL7257 | Introduction to Algebraic Topology |
| 9 | MTL7258 | Introduction to Differential Topology |
| 10 | MTL7738 | Commutative Algebra |
| 11 | MTL7744 | Applied Harmonic Analysis |
| 12 | MTL7743 | Fourier Analysis |
| 13 | MTL7799 | Mathematical Analysis in Learning Theory |
| 14 | MTL7239 | Representation Theory of Finite Groups |
| 15 | MTL7751 | Symbolic Dynamics |
| 16 | MTL7731 | Introduction to Chaotic Dynamical Systems |
| 17 | MTL7761 | Basic Ergodic Theory |
| 18 | MTL7030 | Fundamentals of Cryptography |
| 19 | MTL7244 | Mathematical Theory for Error Correcting Codes |
| 20 | Operator Theory | |
| 21 | MTL7356 | Lie Algebras |
| 22 | MTL7256 | Lie Groups |
| 23 | MTL8854 | Interpolation and Approximation |
| 24 | MTL7255 | Algebraic Curves |
| 25 | Advanced Applied Analysis | |
| 26 | MTL7246 | Combinatorics |
| 27 | MTL7455 | Partial Differential Equations |
| 28 | MTL7273 | Wavelets and Applications |
| 29 | Advanced Matrix Theory | |
| 30 | Fixed Point Theory and Applications | |
| 31 | MTL7750 | Abstract Harmonic Analysis |
| 32 | MTL7848 | Pseudodifferential Operators with Application in PDE |
Specialization B: Applied and Computational Mathematics
| Sl. no | Course Code | Course Title |
|---|---|---|
| 1 | MTL7455 | Partial Differential Equations |
| 2 | MTL7146 | Methods of Applied Mathematics |
| 3 | MTL7012 | Computational Methods for Differential Equations |
| 4 | MTL8251 | Applied Numerical Analysis |
| 5 | MTL7793 | Numerical methods for Hyperbolic PDE |
| 6 | Advanced Matrix Theory | |
| 7 | MTL795 | Numerical methods for PDE |
| 8 | MTL7273 | Wavelets and Applications |
| 9 | MTL7743 | Fourier Analysis |
| 10 | Advanced Applied Analysis | |
| 11 | MTL7350 | Data Structures for Applied Mathematics |
| 12 | Numerical Linear Algebra | |
| 13 | MTL8854 | Interpolation and Approximation |
| 14 | MTL7281 | Finite Element Theory and Applications |
| 15 | Introduction to Machine Learning | |
| 16 | MTL7799 | Mathematical Analysis in Learning Theory |
| 17 | MTL8305 | Modern Methods in Partial Differential Equations |
| 18 | MTL7848 | Pseudodifferential Operators with Application in PDE |
Specialization C: Statistics, Computing and Industrial Mathematics
| Sl. No | Course Code | Course Title |
|---|---|---|
| 1 | MTL6777 | Foundations of Statistical Learning |
| 2 | MTL7350 | Data Structures for Applied Mathematics |
| 3 | MTL6632 | Nonparametric Statistical Methods |
| 4 | MTL7778 | Bayesian Statistics and Modelling |
| 5 | MTL7766 | Multivariate Statistical Analysis |
| 6 | Time Series Analysis | |
| 7 | Introduction to Machine Learning | |
| 8 | Data Mining | |
| 9 | MTL7890 | Optimization Algorithms |
| 10 | MTL7717 | Fuzzy Sets and Applications |
| 11 | MTL7763 | Introduction to Game Theory |
| 12 | MTL7732 | Financial Mathematics |
| 13 | Actuarial Mathematics | |
| 14 | Markov Decision Processes | |
| 15 | MTL7725 | Stochastic Processes and Its Applications |
| 16 | MTL7733 | Stochastics of Finance |
| 17 | Probability Theory | |
| 18 | MTL7768 | Graph Theory |
| 19 | Graph Algorithms | |
| 20 | MTL7783 | Theory of Computation |
| 21 | Advanced Graph Theory | |
| 22 | MTL7742 | Analysis and Design of Algorithms |
| 23 | MTL7246 | Combinatorics |
| 24 | Complexity Theory | |
| 25 | Advanced Algorithms | |
| 26 | MTL7070 | Combinatorial Optimization |
| 27 | MTL7018 | Computational and Combinatorial Geometry |
| 28 | Numerical Linear Algebra | |
| 29 | MTL7799 | Mathematical Analysis in Learning Theory |
| 30 | MTL8880 | Parameterized Algorithms for NP-hard Problems |