Course Archives Theoretical Statistics and Mathematics Unit
Course: Algebra III
Instructor: B Sury
Room: G26
Level: Undergraduate
Time: Currently offered
Syllabus
Past Exams


Syllabus: (Rings and Modules) Ring homomorphisms, quotient rings, adjunction of elements. Polynomial rings. Chinese remainder theorem and applications. Factorisation in a ring. Irreducible and prime elements, Euclidean domains, Principal Ideal Domains, Unique Factorisation Domains. Field of fractions, Gauss's lemma. Noetherian rings, Hilbert basis theorem. Finitely generated modules over a PID and their representation matrices. Structure theorem for finitely generated abelian groups. Rational form and Jordan form of a matrix.

Evaluation:
Midterm Exam 30 marks
Assignment 20 marks
Final Exam 50 marks
Total 100 marks


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Past Exams
Midterm
02.pdf 03.pdf 05.pdf 06.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf
Solution
09.pdf
Semestral
02.pdf 03.pdf 05.pdf 06.pdf 07.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf
Solution
09.pdf
Supplementary and Back Paper
05.pdf 06.pdf 07.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 17.pdf

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[ Semester Schedule ][ SMU ] [Indian Statistical Institute]