Course Archives    Theoretical Statistics and Mathematics Unit
Course: Algebra II
Level: Postgraduate
Time: Currently not offered
Syllabus
Past Exams


Syllabus: Results on finite groups: permutation groups, simple groups, solvable groups, simplicity of A_n.
Topics like semi-direct product (if not covered in Algebra-I).
Algebraic and transcendental extensions; algebraic closure; splitting fields and normal extensions; separable, inseparable and purely inseparable extensions; finite fields. Galois extensions and Galois groups, Fundamental theorem of Galois theory, cyclic extensions, solvability by radicals, constructibility of regular n-gons, cyclotomic extensions.

Time permitting, additional topics may be selected from:

(i) Traces and norms, Hilbert theorem 90, Artin-Schrier theorem, Galois cohomology, Kummer extension.
(ii) Transcendental extensions; Luroths theorem.
(iii) Real fields: ordered fields, real closed fields, Sturms theorem, real zeros and homomor-phisms.
(iv) Integral extensions and the Nullstellensatz.

Suggested Texts :

1. D.S. Dummit and R.M. Foote, Abstract Algebra, John Wiley (Asian reprint 2003).

2. S. Lang, Algebra, GTM (211), Springer (Indian reprint 2004).

3. M. Nagata, Field theory, Marcel-Dekker (1977).

4. N.S. Gopalakrishnan, University Algebra, Wiley Eastern (1986).

5. N. Jacobson, Basic Algebra, W.H. Freeman and Co (1985).

6. G. Rotman, Galois theory, Springer (Indian reprint 2005).

7. TIFR pamphlet on Galois theory. Top of the page

Past Exams
Midterm
04.pdf 06.pdf 08.pdf 10.pdf 12.pdf 14.pdf 16.pdf
Solution
10.pdf 12.pdf 14.pdf
Semestral
04.pdf 06.pdf 12.pdf 16.pdf
Supplementary and Back Paper
04.pdf 06.pdf

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