## M.Tech.(CS) Year I

ISI Kolkata, 2021-2022 Session

**Semester**: First

**Instructor**: Sujata Ghosh

**Meeting Times**: Mondays, Wednesdays 4:15PM - 6:00PM

**First Class**: Monday, October 4

**Location**: Online

[Teaching staff | Course overview | References | Grading | Lecture schedule | Homeworks/Handouts]

## Teaching staff

**Sujata Ghosh**

### Instructor

**Office Hours**: By Arrangement (please send an e-mail)

**Avijeet Ghosh**

### TA

**Office Hours**: By Arrangement (please send an e-mail)

## Course overview

**Course Description**: This course can be considered as an introductory course on different algebraic structures. The focus will be on groups, rings, fields and vector spaces. We will have a brief recapitulation of the concepts of sets, relations and functions at the beginning of the course. Towards the end, we will look into some applications of algebra in computer science. The complete syllabus of the course can be found here.

This course is also about building up mathematical maturity, e.g., how to read and write mathematics, especially mathematical proofs, and how to communicate mathematics.

**Pre-requisites**: There are no pre-requisites for this course.

## References

**Text book**: This main text book for the course is

**Algebra**by Mike Artin.

Some other books which might prove to be helpful are

**A first course in Abstract Algebra**by J.B. Fraleigh, the classic

**Topics in Algebra**by I.N. Herstein,

**Abstract Algebra**by D.S. Dummit and R.M. Foote.

## Grading

Grades will be based on assignments (20%), mid-semester examination (20%), project (10%),
and end-semester examination (50%).

## Lecture schedule

04.10.2021 | Sets, relations, functions: Class notes |

06.10.2021 | Sets, relations, functions (contd.): Class notes |

20.10.2021 | Finite and infinite sets: Class notes |

25.10.2021 | Countable sets: Class notes |

27.10.2021 | Uncountable sets: Class notes |

27.10.2021 | Tutorial 1 (included in the homework set) |

01.11.2021 | Groups and subgroups: Class notes |

03.11.2021 | Cyclic groups and isomorphisms: Class notes |

10.11.2021 | Homomorphisms and isomorphisms: Class notes |

15.11.2021 | Normal subgroups: Class notes |

15.11.2021 | Tutorial 2 (included in the homework set) |

17.11.2021 | Left and right cosets: Class notes |

22.11.2021 | Cosets and quotient groups: Class notes |

24.11.2021 | Product of groups: Class notes |

06.12.2021 | Introduction to rings: Class notes |

08.12.2021 | Tutorial 3 (included in the homework set) |

13.12.2021 | Ideals and quotient rings: Class notes |

15.12.2021 | Polynomial rings: Class notes |

20.12.2021 | Fields and integral domains: Class notes |

22.12.2021 | Quotient rings and isomorphisms: Class notes |

23.12.2021 | Adjoining elements to a ring: Class notes |

02.01.2022 | Tutorial 4 (included in the homework set) |

03.01.2022 | Field extensions: Class notes |

05.01.2022 | Field extensions (contd.): Class notes |

14.01.2022 | Splitting fields: Class notes |

17.01.2022 | Finite fields: Class notes |

## Homeworks/Handouts

Homework 1

(Firm) deadline for submission: October 31, 2021.Homework 2

(Firm) deadline for submission: November 21, 2021.Homework 3

(Firm) deadline for submission: December 12, 2021.Homework 4

(Firm) deadline for submission: January 9, 2022.Homework 5

(Firm) deadline for submission: January 28, 2022.