# Teaching

## 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

# While at ISI

## 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)

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

## 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

## 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)

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

## 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)

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

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

Syllabus and References
Homework
Preliminary Homework
Practise problems

## Introduction to Algebraic geometry (Jan-May 2013)

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

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