MTH 308 : Groups and Fields

• Instructor : Tanusree Khandai

• Class Timings: 10:00-10:55 AM , Monday, Tuesday, Thursday

• Tutorials will be conducted 10:00 to 10:55 AM on Fridays.

• Problem sheets will be given every Thursday. These will be discussed during the tutorial in the following week.

• Every 2 weeks, there will be a 10 minutes quiz at the beginning of the Tutorial. The quizzes will be based on the problem sheets that

have alrea: dy been solved/discussed during the tutorials.

• Office Hours: 4-5 PM Tuesday and Thursday (Kindly email me in case you wish to meet during the office hours.)

• Components of grading :

  • • Best 3 quizzes out of the total number of quizzes taken will be considered . This will constitute 15% of the total marks.

    • First and Second Mid sem exams will be out of 20 and 30 marks respectivelyThey will constitute 15% and 20% marks of the total.

    • End Sem exams will constitute 40% of the total marks.

    • Project + Viva. This will constitute 10% of the total marks.

• Exam Dates :

  • • 7.2.22 ( 9-10 AM ): 1st Mid Semester Exam

    • 10.3.22 (9-10 AM) : 2nd Mid Semester Exam

    • 21.4.22 (9 AM-12 PM) : End Semester Exam

• Regarding the Projects

  • • By 28.1.2022 a list of project topics will be given. Since there are 20 students, you can choose to form 3 or 4 member groups to work on a particular project.

• • Project report has to be submitted by 31st March 2022. As a team you will have to give a 10 minute project presentation and it will be followed by viva of the group members. The presentations and the vivas will be scheduled on 2nd and 3rd April, 2022 between 2-5pm.

• References for the Course

  • • Artin, Algebra

    • Herstein, Topics in Algebra

    • Armstrong, Groups and Symmetry

    • Hungerford, Algebra

Classes : *

• Jan 6 : IntroductioNotesn to Groups Notes

• Jan 10 : Subgroups Notes

• Jan 11 : LagrangNotese's Theorem, Cosets of a subgroup in a group Notes

• Jan 13 : Normal Subgroups, Quotient groups Notes

• Jan 17 : Homomorphisms Notes

• Jan 18 : Cayley'sThm, First Isomorphism Thm Notes

• Jan 20 : Isomorphism Theorems Notes

• Jan 24 : Group Actions Notes

• Jan 25 : Group action contd Notes

• Jan 27 : Class Equation and Application Notes

• Jan 28 : Direct Product, Permutation Group Notes

• Jan 31 : Permutation Group Notes

• Feb 1 : Sylow's 1st Theorem Notes

• Feb 3 : Sylow's Theorem Notes

• Feb 10 : Dihedral Group Notes

• Feb 11: Groups of Order 8 Notes

• Feb 14 : Sylow's Theorem, Introduction to Free Groups Notes

• Feb 15 : Free Groups Notes

• Feb 17 : Free Groups Notes

• Feb 21 : Free Groups Notes

• Feb 22 : Finitely generated abelian groups Notes

• Feb 24 : Subgroups of finitely generated abelian groups Notes

• Feb 28 : Finitely generated abelian groups Notes

• Mar 3 : Finitely generated abelian groups Notes

• Mar 7 : Nilpotent groups Notes

• Mar 21 : Fields.introduction Notes.

• Mar 24 : Field extensions Notes

• Mar 25: Field Extensions Notes

• Mar 28: Algebraic Extensions Notes

• Mar 29 : Isomorphism of simple algebraic extensions Notes

• Mar 31 : Splitting Field Notes

• Apr 4 : Separable Extensions Notes

Assignments & Related Notes

Quiz & Midsem Questions