Computational Commutative Algebra

By Prof. Manoj Kummini | CMI

Learners enrolled: 287

ABOUT THE COURSE:
This is an introductory course in computational commutative algebra. Topics in a typical first course in commutative algebra are developed along with computations in Macaulay2. The emphasis will be on concrete computations, more than on giving complete proofs of theorems.

INTENDED AUDIENCE : Advanced undergraduate / post-graduate students

PREREQUISITES : Introduction to basic theory of rings, modules

Summary

Course Status :	Ongoing
Course Type :	Elective
Duration :	12 weeks
Start Date :	25 Jul 2022
End Date :	14 Oct 2022
Exam Date :	30 Oct 2022 IST
Enrollment Ends :	08 Aug 2022
Category :	Mathematics Algebra
Credit Points :	3
Level :	Undergraduate/Postgraduate

Page Visits

Course layout

Week 1:Introduction: rings and ideals, ring homomorphisms, Hilbert basis theorem, Hilbert Nullstellensatz, introduction to Macaulay2

Week 2:Groebner bases, ideal membership, solving systems of polynomial rings

Week 3:Modules.

Week 4:Associated primes and primary decomposition

Week 5:Associated primes and primary decomposition, ctd.

Week 6:Integral extensions, integral closure, Noether normalization

Week 7:Integral extensions, integral closure, Noether normalization, ctd.

Week 8:Hilbert functions, dimension theory

Week 9:Hilbert functions, dimension theory ctd.

Week 10:Applications to geometry.

Week 11:Homological algebra: depth, Koszul complex

Week 12:Homological algebra: free resolutions, Auslander-Buchsbaum formula

Instructor bio

Prof. Manoj Kummini

CMI

I am an Associate Professor at CMI.My research is in commutative algebra, especially on homological properties of ideals and modules. I got my Ph. D. from Kansas, under the direction of Craig Huneke. In my dissertation, `Homological Invariants of Monomial and Binomial Ideals', I studied numerical invariants of free resolutions.

Course certificate

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 Madras. 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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