# Bachelor of Science (Research)

**Source**: https://bs-ug.iisc.ac.in/course-structure/mathematics
**Parent**: https://bs-ug.iisc.ac.in/

Bachelor of Science (Research) • Major

# Mathematics

## Basic Structure

The Mathematics major focuses on the core areas of modern mathematics, including algebra, analysis, topology, and geometry. The program is designed to develop rigorous mathematical thinking and problem-solving skills, preparing students for research in pure and applied mathematics. All students are required to complete a minimum of 131 credits to qualify for the Bachelor of Science (Research) degree.

| Basic Course (Sem 1-3) | Engineering (Sem 2-3) | Humanities (Sem 1-6) | Major and Project | Minor (Optional) | Electives (Assortment Courses) | Total |
| --- | --- | --- | --- | --- | --- | --- |
| 40 | 6 | 9 | 51 | 15 | 10 - 25 | 131 |
|  | | | | 25\* | |

NOTE:

1. **\*Students not opting for a minor** should fulfil 25 credits of assortment courses.
2. To be eligible for a minor, a student should fulfil 15 credits from the minor pool.
3. Excess credit(s) from any pool will be counted towards assortment credits.

## Semester-wise Course Requirements

To view the common shared curriculum (Semesters 1-3), please [click here](https://bs-ug.iisc.ac.in/course-structure/shared-curriculum).

Semester 4Semester 5Semester 6Semester 7Semester 8

| Course Code | Course Name | Instructor | Credits |
| --- | --- | --- | --- |
| UM 204 | Introduction to Basic Analysis | [Muna Naik](https://math.iisc.ac.in/2023/10/31/newfaculty-muna.html) | 3:1 |
| UM 205 | Introduction to Algebraic Structures | [Abhishek Banerjee](https://math.iisc.ac.in/~library/abhishek-banerjee.html) | 3:1 |
| - | [Humanities \*\*](https://bs-ug.iisc.ac.in/assets/Humanities%20Courses.%20.pdf)/Elective | - | 9:12 |
| Reduced Load | | | 15-17 |
| Enhanced Load | | | 15-21 |

Note:

\*\*

Humanities:

**A.** Humanities courses cannot be dropped in both semesters IV and V.

**B.** Students must complete 9 credits in humanities pool by the end of six semester.

### Recommended Course Load

| Semester | Criteria | Credits |
| --- | --- | --- |
| I | Student needs to register for a fixed number of credits | 18 |
| II | No CGPA and TGPA requirements | Min.: 17 and Max.: 21 |
| III | No CGPA and TGPA requirements | Min.: 17 and Max.: 21 |
| IV | CGPA < 8.0 | Min.: 15 and Max.: 17 |
| CGPA ≥ 8.0 | Min.: 15 and Max.: 21 |
| V to VIII | CGPA < 8.0 or Preceding term TGPA < 8.0 | Min.: 16 and Max.: 18 |
| CGPA ≥ 8.0 or Preceding term TGPA ≥ 8.0 | Min.: 16 and Max.: 21 |

## Suggested Core Electives:

Below is the list of core electives available for students majoring in Mathematics. These electives are offered by various departments under the relevant Sciences Department.

**Note:**

**January–April Semester:** Select courses offered in the January intake. These courses are designed for students beginning their studies at the start of the year.

**August–December Semester:** Select courses offered in the August intake, suitable for students starting in the second half of the year.

January - April SemesterAugust - December Semester

| Course Code | Title | Credits | Instructors |
| --- | --- | --- | --- |
| MA 235 | Introduction to Differentiable Manifolds | 3:0 | Subhojoy Gupta |
| MA 218 | Number Theory | 3:0 | Shaunak Deo |
| MA 220 | Representation Theory of Finite Groups | 3:0 | R Venkatesh |
| MA 222A | Topics in Measure Theory | 3:0 | Arka Mallick |
| MA 237 | Introduction to Tilings | 3:0 | Subhojoy Gupta |
| MA 262 | Introduction to Stochastic Processes | 3:0 | Arvind Ayyer |
| MA 305 | Lie Groups and Lie Algebras | 3:0 | Muna Naik |
| MA 319 | Algebraic Combinatorics | 3:0 | Digjoy Paul / Arvind Ayyer |
| MA 321 | Analysis III | 3:0 | A K Nandakumaran |
| MA 326 | Fourier Analysis | 3:0 | Kalachand Shuin / E. K. Narayanan |
| MA 336A | Introduction to Stochastic Finance | 3:0 | Srikanth K. Iyer |
| MA 340 | Advanced Functional Analysis | 3:0 | E. K. Narayanan |
| MA 376 | Extremal Combinatorics | 3:0 | Hiranya Kishore Dey / Arvind Ayyer |
| MA 379 | Linear Algebraic Groups | 3:0 | Radhika Ganapathy |
| MA 347A | Topics in Finite Element Methods | 3:1 | Thirupathi Gudi |

## Continuing Master's Degree

Students have the option to continue for the **Master of Science (MS) degree** after completing four years of the Bachelor of Science (BS).

View 5th Year RequirementsHide 5th Year Requirements

#### Mandatory Courses

| Course Code | Course Name | Term |
| --- | --- | --- |
| MA 389A (1:0) | Seminar on topics in mathematics I | AUG |
| MA 389B (1:0) | Seminar on topics in mathematics II | JAN |
| MA 213 (3:1) | Algebra II | JAN |
| MA 222 (3:1) | Analysis II | JAN |

#### Soft Core Requirement

Students must complete **any 3 courses** from the list below:

MA 223 (3:0): Functional Analysis

MA 232 (3:0): Intro to Algebraic Topology

MA 242 (3:0): Partial Differential Equations

MA 361 (3:0): Probability Theory

MA 235 (3:0): Intro to Differentiable Manifolds

MA 220 (3:0): Rep. Theory of Finite Groups

MA 312 (3:0): Commutative Algebra

MA 313 (3:0): Algebraic Number Theory

MA 262 (3:0): Intro to Stochastic Processes

MA 321 (3:0): Analysis III

#### Remaining Credits

13 Credits Requirement

The remaining **13 credits** could be comprised of:

- Master’s projects A & B
- Courses offered by any department
- A combination of projects and courses