Teaching

Introduction to Algebraic geometry(Jan-May 2025)

References:
(1) Algebraic curves --Fulton
(2) Introduction to commutative algebra --Atiyah and Macdonald
(3) Undergraduate Algebraic Geometry --Miles Reid
(4) Basic algebraic geometry --Shafarevich
(5) Algebraic Geometry --Joe Harris

Syllabus
Homework

While at ISI

Vector Bundles and Characteristic classes for Master's students (Jul-Nov 2024)

Syllabus
References:
(1) Milnor and Stasheff: Characteristic classes
(2) Norman Steenrod: The Topology of Fibre Bundles
(3) I. H. Madsen, J. Tornehave: From Calculus to Cohomology
Homework

Previous Teaching

Algebra II for Master's course (Jan-Apr 2024)

Syllabus and References
Reference online Milne's notes
Homework

Algebra for KSoM Masters' students (Sep-Nov 2023)

References:
(1) M. Artin, Algebra.
(2) D.S. Dummit and R.M. Foote, Abstract Algebra, John Wiley.
(3) K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall of India (1998).
Homework

Numerical Computing (Earlier Computer Science II) for BMath(Jan-Apr 2023)

Syllabus and References
Important Resources
Numerical Methods with MATLAB
GNU Octave Wiki
Tool box: Some pre-written codes
Some useful Exercises
Homework

Introduction to Representation Theory (Aug-Nov 2022)

References:
(1) J.P. Serre: Linear representations of finite groups
(2) W. Fulton and J. Harris: Representation Theory, Part I
BMath Syllabus
MMath Syllabus
Homework

Introduction to Algebraic geometry(Jan-May 2022)

References:
(1) Undergraduate commutative algebra --Miles Reid
(2) Introduction to commutative algebra --Atiyah and Macdonald
(3) Undergraduate Algebraic Geometry --Miles Reid
(4) Basic algebraic geometry --Shafarevich
(5) Algebraic Geometry --Joe Harris

Syllabus
Homework

Introduction to Representation Theory (Sept-Dec 2021)

References:
(1) J.P. Serre: Linear representations of finite groups
(2) W. Fulton and J. Harris: Representation Theory, Part I
Syllabus
Homework

Introduction to Algebraic geometry(Jan-May 2021)

Algebra III for B.Math course (Sept-Dec 2020)

References:
(1) D.S. Dummit and R.M. Foote, Abstract Algebra, John Wiley (Asian reprint 2003).
(2) M. Artin, Algebra.
(3) N. Jacobson, Basic Algebra Vol. I, W.H. Freeman and Co (1985).
Syllabus
Homework
Notes

Topology for B.Math course (Jan-May 2020)

References:
(1) J.R. Munkres, Topology.
(2) J. Dugundji, Topology.
Syllabus
Homework

Linear algebra for M.Math course (Jul-Nov 2019)

References:
(1) M. Artin, Algebra.
(2) D.S. Dummit and R.M. Foote, Abstract Algebra, John Wiley.
(3) S. Lang, Algebra, GTM (211), Springer (Indian reprint 2002).
(4) K. Hoffman and R. Kunze, Linear Algebra, Prentice-Hall of India (1998).
Syllabus
Homework

Algebra II for B.Math course (Jan-Apr 2019)

References:
(1) M. Artin, Algebra.
(2) A.R. Rao and P. Bhimasankaram, Linear Algebra.
Syllabus
Homework

Algebra III for B.Math course (July-Nov 2018)

Algebra II for Master's course (Jan-Apr 2018)

Syllabus and References
Reference online Milne's notes
Homework

Algebra I for Master's course (July-Nov 2017)

Syllabus and References
Homework
Preliminary Homework

Introduction to Algebraic Number Theory for BMath(Jan-May 2017)

References:
(1) Algebraic Number Theory -- G.J. Janusz
(2) Algebraic Number Theory -- Stewart and Tall
(3) Algebraic Number theory -- J. Milnes notes

Syllabus
Homework

Commutative Algebra I for MMath(July-Nov 2016)

References:
(1) Introduction to commutative algebra --Atiyah and Macdonald
(2) Commutative Algebra with a view towards Algebraic Geometry -- David Eisenbud
(3) Undergraduate Algebraic Geometry --Miles Reid

Syllabus
Homework

Computer Science II for BMath(Jan-Apr 2016)

Syllabus and References
Important Resources
Numerical Methods with MATLAB
GNU Octave Wiki
Tool box: Some pre-written codes
Some useful Exercises
Extra homework

Algebra I for BMath(July-Nov 2015)

Syllabus and References
Homework
Practise problems

Algebraic geometry for MMath(Jan-Apr 2015)

References:
(1) Introduction to commutative algebra --Atiyah and Macdonald
(2) Commutative algebra --Matsmura
(3) Algebraic Geometry --Hartshorne
(4) Basic algebraic geometry --Shafarevich
(5) Algebraic Geometry –-Qing Liu

Homework

Algebra I for JRF(Jul-Nov 2014)

Syllabus and References
Homework
Preliminary Homework
Practise problems

Introduction to Algebraic geometry(Jan-Apr 2014)

Algebra I for Master's course (July-Nov 2013)

Syllabus and References
Homework
Preliminary Homework
Practise problems

Introduction to Algebraic geometry (Jan-May 2013)

At Essen

Riemann Surfaces

References:
(1)Forster
(2)Gunning
(3)Narasimhan

At MSU

418H Students

Course Information for Math 418H
Homework for Math 418H

419H Students

Course Information for Math 419H
Homework for Math 419H

309 Students

Course Information for Math 309
Homework for Math 309
Worksheet
Notes

310 Students

Course Information for Math 310
Homework for Math 310

132 Students

Syllabus for Math 132 Section 014
The supplemental exercises and supplemental material that are part of some of the assignments can be obtained by clicking below.

supplemental exercises for Section 2.3.

supplemental exercises for Section 2.4.

supplemental exercises for Section 2.6.

supplemental exercises for Section 3.6.

supplemental exercises for Section 4.7.

supplemental material for Section 3.6.

supplemental material for Section 5.3.

supplemental material for Section 5.6.

254H Students

Course Information for Math 254H

Homework for Math 254H