4.5 Mathematical Sciences

MTH405: Homological algebra

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH406: Fourier analysis

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Additional Topics

Recommended Reading

MTH407: Algorithms and complexity

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH408: Riemannian geometry

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH409: Computational methods

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH410: Algebraic topology

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH411: Commutative and homological algebra

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH412: Structure of algebras

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH413: Advanced probability

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH414: Advanced complex analysis

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH415: Enumerative problems in geometry

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH416: Arithmetic of elliptic curves

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline The course aims to introduce elliptic curves and their moduli with an emphasis on curves over finite and number fields. Statements of theorems will be explained in detail and some relevant proofs will be given. Some examples of classical problems that can be studied using elliptic curves will be taken up and the use of the SAGE system to make calculations on elliptic curves will be introduced.

The following advanced topics could also be addressed:

Recommended Reading

MTH418: Fuchsian groups

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH419: Number theory

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH420: Linear operators in Hilbert spaces

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Additional Topics:

Recommended Reading

MTH421: Combinatorial group theory

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Additional Topics

Recommended Reading

Suggested Reading

MTH422: Representations of finite groups

Course Outlie

Recommended Texts

Suggested reading

MTH423: Structure of finite groups

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH424: Introduction to Lie algebras

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH425: Geometric group theory

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH426: Algebraic curves

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

Suggested Reading

MTH427: Introduction to Global Analysis

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Additional Topics

Recommended Reading

Advanced Reading

MTH428: Commutative Algebra and Combinatorics

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Additional Topics

Recommended Reading

MTH601: Topics in algebra

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH602: Topics in topology

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH603: Mathematics seminar course

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline The aim of this course is to make PhD students understand and present technical talks of their interest. Faculty and Mathematics PhD students will meet once a week. Suitable topics will be decided with the mutual consent of the participants. Occasionally visitors of the institute will be asked to give a talk in this course.

MTH604: Homological and commutative algebra

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Homological Algebra

Commutative algebra

Recommended Reading

MTH605: Topics in analysis

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH606: Mathematics seminar course

[Cr:2, Lc:2, Tt:0, Lb:0]

Course Outline

MTH607: Euclidean harmonic analysis

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Additional topics (a subset of the following):

Recommended Reading

MTH608: Algebraic number theory-I

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading

MTH609: Algebraic number theory-II

[Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

Recommended Reading