## Core courses

**Mathematics:** Analysis and Linear Algebra I, II, Probability and Statistics, Basic Analysis, Introduction to Algebraic Structures.

**Computing:** Algorithms and Programming, Introduction to Computer Systems, Discrete Mathematics, Data Structures and Algorithms, Automata Theory and Computability, Introduction to Numerical Methods.

**EECS:** Introduction to Electronics and Electrical Engineering, Introduction to AI and ML.

**Breadth Soft Core: **12 credits from a selection of Physics, Chemistry, Biology, Material Science, Earth and Environmental Science subjects.

**Humanities:** 9 credits.

## Soft Core Courses

The soft core consists of the Mathematics and Computing streams. Students have to take at least 6 credits in each stream from the specified lists of courses. Students have to take at least 21 credits from the list of soft core courses. Courses from the list of soft core courses can also be taken as electives.

For details on each of these Mathematics Courses, please click on each course.

- MA 212 Algebra I
- MA 218 Number Theory
- MA 219 Linear Algebra
- MA 232 Introduction to Algebraic Topology
- MA 200 Multivariable Calculus
- MA 222 Measure and Integration
- MA 223 Functional Analysis
- MA 224 Complex Analysis
- MA 231 Topology
- MA 235 Introduction to Differential Manifolds
- MA 241 Ordinary Differential Equations
- MA 242 Partial Differential Equations
- MA 262 Introduction to Stochastic Processes
- MA 361 Probability Theory

For details on these Computing Courses, please click here.

- E0 205 Mathematical Logic and Theorem Proving
- E0 206 Theorist’s Toolkit
- E0 207 Program Analysis and Verification
- E0 209 Principles of Distributed Software
- E0 220 Graph theory
- E0 224 Computational Complexity Theory
- E0 225 Design and Analysis of Algorithms
- E0 228 Combinatorics
- E0 230 Computational Methods of Optimization
- E0 235 Cryptography
- E0 244 Computational Geometry and Topology
- E0 248 Theoretical Foundations of Cryptography
- E0 259 Data Analytics

- E0 265 Convex Optimization and Applications
- E0 267 Soft Computing
- E0 270 Machine Learning
- E0 272 Formal Methods in Software Engineering
- E1 213 Pattern Recognition and Neural Networks
- E1 222 Stochastic Models and Applications (3:0)
- E1 244 Detection and Estimation
- E1 251 Linear and Nonlinear Optimization
- E1 254 Game Theory
- E1 277 Reinforcement Learning

- E2 201 Information Theory
- E2 202 Random Processes
- E2 232 TCP/IP Networking
- E2 230 Network Science and Modelling

- DS 211 Numerical Optimization
- DS 221 Introduction to Scalable System
- DS 250 Multigrid Methods
- DS 256 Scalable Systems for Data Science
- DS 284 Numerical Linear Algebra
- DS 289 Numerical Solution to Differential Equations
- DS 291 Finite Elements: Theory and Algorithms,
- DS 294 Data Analysis and Visualization
- DS 295 Parallel Programming
- DS 301 Bioinformatics

- HE 384 Quantum Computation

## Study Tracks

The programme structure encourages interested students to pursue a study track should they wish to do so. Here is an indicative list of study tracks and their corresponding courses.

## Suggested Electives

- MG 201 Economics, MG 265 Data Mining, MG 221 Applied Statistics, MG 226 Time Series Analysis and Forecasting, MG 258 Financial Instruments and Risk Management.
- PH 204 Quantum Mechanics, PH 202 Statistical Mechanics, Electromagnetic theory, Computational Photonics, Basics of Quantum Information.
- BC 302 Current Trends in Drug Discovery, Applied Bioinformatics.
- ME 286 Numerical methods for partial differential equations.
- EC 201 Theoretical and Mathematical Ecology, EC 303 Spatial and Stochastic Dynamics in Biology.
- NE 250 Entrepreneurship, Ethics and Societal Impact.
- Stochastic Approximation, Random Topology and Geometry, Topological Data Analysis.
- Machine Learning for Geosciences, Data Analytics, Applied Statistics, Computational Epidemiology, Foundations of Robotics, Computational Robotics, Computational Physics, Multivariate Analysis for Machine Learning, Mathematical Biology, Linear and Integer Programming, Network Optimization.

## Projects

- Sem 7 & 8: Independent Study/Research Experience project (ISP)* (8 credits).
- Sem 8: Research/Industry project* (16 credits).
- Project availability is subject to the student finding a supervisor.
- Faculty or Research Groups can advertise projects and students can apply and be selected.
- Students will be encouraged to carry out project work in the industry.

## Semester-wise Course Requirements

For details on these courses, please click here.

Course | Credits |

UM 101 Analysis and Linear Algebra I | 3:0 |

UE 101 Algorithms and Programming | 2:1 |

UH 101 Ways of Knowing | 2:0 |

Any two of: UB101 Biology I UC101 Physical Chemistry UP101 Physics I | 2:1+2:1 |

Total | 14 |

Course | Credits |

UM 102 Analysis and Linear Algebra II | 3:0 |

UE 102 Electrical and Electronics Engg | 2:1 |

UMC 102 Computer Systems | 2:1 |

Any one of: UB102 Biology II, UC102 Inorganic Chemistry, UP102 Physics II (Elec-Mag-Optics), UES 200 Earth & Env | 2:1/2:0 |

UMC 103 Discrete Mathematics | 2:0 |

UH 102 Ways of Seeing | 2:0 |

Total | 16 |

Reduced Load: drop one course other than UM 102, UMC 102, UMC 103 | 13-14 |

Course | Credits |

UM 201 Probability and Statistics | 3:0 |

UMC 201 Data Structures & Algo | 3:1 |

UMC 202 Numerical Methods | 3:1 |

Any one of: UP201 Physics III, UB201 Biology III, UC201 Chemistry III, UMT200 Materials | 2:1/2:0 |

UH 201 Ways of Doing | 2:0 |

Total | 15-16 |

Reduced Load: drop one course other than UM 201, UMC 201, UMC 202 | 13-14 |

Course | Credits |

UM 204 Analysis | 3:1 |

UM 205 Algebraic Structures | 3:1 |

UMC 203 AI and ML | 3:1 |

UMC 205 Automata and Computability | 3:1 |

UH 203 Folk Arts | 1:0 |

Total | 17 |

Reduced Load: drop one course | 13-16 |

Enhanced Load | 17-21 |

Course | Credits |

UH 301 Journalism for Scientists | 1:0 |

Softcore/ Electives | 16 |

Total | 17 |

Normal | 17-19 |

Enhanced Load | 17-23 |

Course | Credits |

UH 302 Governance | 1:0 |

Softcore/ Electives | 16 |

Total | 17 |

Normal | 17-19 |

Enhanced Load | 17-23 |

Course | Credits |

ISP I / Softcore/ Electives | 8 |

Softcore/Electives | 8 |

Total | 16 |

Normal | 12-16 |

Enhanced Load | 16-23 |

Course | Credits | |

UMC 402 ISP II / Electives (8) + Electives (8) OR UMC 403 Project Project (16) | 16 | |

Total | 16 | |

Normal | 12-16 | |

Enhanced Load | 16-23 |

All students must complete a total of at least 128 credits comprising courses and other components like projects, as specified in the course requirements above. The course load for the first semester is fixed. Each subsequent semester has a “Normal”, “Reduced” and “Enhanced” course load, as specified in Table 1. Based on their CGPA and previous-term TGPA, students must register for an appropriate course load as specified in Table 2 below. In Semesters II and III, only courses listed in Sems I to IV can be credited towards an Enhanced load. Any deviation from the recommended load will be allowed only with the permission of the Dean.

**Recommended Course Load**

Criteria | Course Load |

CGPA ≤ 6.0 AND Prev-TGPA ≤ 5.5 | Reduced (in Sems II to IV), Normal (in Sems V to VIII) |

6.0 < CGPA < 8.0 OR 5.5 < Prev-TGPA < 8.0 | Normal (in Sems II to VIII) |

CGPA ≥ 8.0 AND Prev-TGPA ≥ 8.0 | Enhanced (in Sems II to VIII) |