By Prof. Dilip P. Patil |
IIT Bombay

Learners enrolled: 454

INTENDED AUDIENCE : BS / BSc / BE / ME / MSc / PhD
PREREQUISITES : Linear Algebra; Algebra – First Course
INDUSTRY SUPPORT : R & D Departments ofIBM / Microsoft Research LabsSAP /TCS / Wipro / Infosys

Week 1 : Prime Factorisation in Polynomial Rings, Gauss’s Theorem

Week 2 : Algebraic Extensions

Week 3 : Group Actions

Week 4 : Galois Extensions

Week 5 : Finite Fields, Cyclic Groups, Roots of Unity, Cyclotomic Fields

Week 6 : Splitting Fields, Algebraic Closure

Week 7 : Normal and Separable Extensions

Week 8 : Norms and Trace

Week 9 : Fundamental Theorem on Symmetric

Week 10 : Proof of the Fundamental Theorem Polynomial, of Algebra

Week 11 : Orbits of the action of Galois group

Week 12 : Inverse Galois Problem

Artin, E. : Galois Theory, University of Notre Dame Press, 2 1944.[2] Artin, M. : Algebra, Prentice-Hall, 1994.[4] Jacobson, N. : Lectures in Abstract Algebra, Vols. I, II & III, D. Van Nostrand Co. Inc.,Princeton, New Jersey, 1966.[5] Jordan, C. : Traité des substitutions et des équations algébraiques, Gautjier-Villars, Paris,1870.[5] B. M. Kiernan, B. M. : The development of Galois theory from Lagrange to Artin, Arch.Hist. Exact Sci. 8 (1971 / 72) 40–54.[6] Lang, S. : Algebra, Graduate Texts In Mathematics, Vol. 211, Springer-Verlag, 3 2002.[6] Steinitz, E. : Algebraische Theorie der Körper, 2nd ed., Chelsea, 1950.[6] van der Waerden, B. L. : Die Algebra seit Galois, Jahresber Deutsch. Math. Verein. 68(1966), 155–165.[7] Weber, H. : Lehrbuch der Algebra, Band I, II, III, Braunschweug 2 1898, 2 1899, 2 1908.

Dilip P. Patil received B. Sc. and M. Sc. in Mathematics from the University of Pune in 1976 and 1978,
respectively. From 1979 till 1992 he studied Mathematics at School of Mathematics, Tata Institute of
Fundamental Research, Bombay and received Ph. D. through University of Bombay in 1989. Currently he is
a Professor of Mathematics at the Departments of Mathematics, Indian Institute of Science, Bangalore. At
present he is a Visiting Professor at the Department of Mathematics, IIT Bombay. He has been a Visiting
Professor at Ruhr-Universitt Bochum, Universitt Leipzig, Germany and several universities in Europe and
Canada. His research interests are mainly in Commutative Algebra and Algebraic Geometry.

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:**30 October 2022** Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

**CRITERIA TO GET A CERTIFICATE**

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay. It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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