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Details of MA3102 (Autumn 2021)

Level: 3 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA3102 Algebra I Swarnendu Datta

Syllabus
Groups: Definition of groups, subgroups, group homomorphisms and isomorphisms, normal subgroups, quotient groups, Lagrange's theorem, isomorphism theorems, direct sum of abelian groups, direct products, group as symmetries, free group (if time permits).

Group Action: Group actions, conjugacy classes, orbits and stabilizers, class equations.

Symmetric Groups: Symmetric groups, simple groups, simplicity of An with n>4.

Sylow's theorems: Three theorems of Sylow, classification of finitely generated abelian groups.

Prerequisite
Mathematics pre-major or instructor's consent

References


  1. Artin, M., Algebra, Prentice-Hall.

  2. Dummit, D.S. and Foote, R.M., Abstract Algebra, Wiley.

  3. Fraleigh, J.B., A First Course in Abstract Algebra, Narosa Publishers.

  4. Gopalakrishnan, N.S., University Algebra, New Age International.

  5. Herstein, I.N., Topics in Algebra, Wiley.

  6. Hungerford, T.W., Algebra, Springer-Verlag.

  7. Malik, D.S., Mordeson, J.M. and Sen, M.K., Fundamentals of Abstract Algebra, McGraw-Hill.


Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Core
2 IP 3 Not Allowed
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 3 Not Allowed
7 MS 5 Core
8 MS 7 Elective
9 MS 9 Elective
10 RS 1 Elective
11 RS 2 Elective

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