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Quick Facts

Medium Of Instructions	Mode Of Learning	Mode Of Delivery
English	Self Study	Video and Text Based

Course Overview

The ‘Computational Commutative Algebra’ certification course is an elective course for the students to develop their understanding of the computation of the rings, ideals, and modules with the help of a computer. This course enables students to get an overview of commutative algebra with a focus on the computations and the techniques behind them. This free online training course is provided by the Swayam education portal along with the National Program for Technology Enhanced Learning (NPTEL). The classes for this course are conducted online for a period of twelve weeks.

The students of this program are led by the instructor, Prof. Manoj Kummini from the Chennai Mathematical Institute (CMI). In this course, candidates will get a theoretical and hands-on experience with the computational tool Macaulay2. This program can be downloaded and installed locally or can also be worked with the online version for smaller computations.

The ‘Computational Commutative Algebra’ online training program ensures an E-Certificate and credit points after completing the course and the assessments successfully.

The Highlights

Online mode
Free training
Twelve weeks
Elective program
Credit points
Course certificate

Programme Offerings

videos
Lectures
Weekly Assignments
Course Modules
Final Exam
Certificate
Credit Points

Courses and Certificate Fees

Fees Informations	Certificate Availability	Certificate Providing Authority
INR 1000	yes	CMI Chennai

The candidates of this program will not be expected to pay for the classes but the ‘Computational Commutative Algebra’ certification fee is for registration for the final exam.

Computational Commutative Algebra fee structure

Program Fee	Nil
Exam Registration Fee	Rs. 1,000

Eligibility Criteria

The individuals applying for the ‘Computational Commutative Algebra’ online course should have prior knowledge of the mathematical concepts of rings and modules.

Certificate qualifying details

The students of the ‘Computational Commutative Algebra’ certification course will become eligible for the certificate after finishing the course of study and the assessments with the following scores,

Internal assignments - 10/25(25%) in the best 8 out of 12 assignments.
Final Exam - 30/75(75%).
Overall average - 40/100.

What you will learn

Problem Solving AbilityMathematical skillKnowledge of Algorithms

The classes for this mathematics and algebra certification course are designed with a ‘Computational Commutative Algebra’ certification syllabus to help the students explore the concepts such as computations of rings and ideals algorithmically. The students of this course will get to know about the functions behind the computations. By the end of this program, participants will be familiar with the techniques involved in the Macaulay2 program for computations and will be able to carry out computations even in a different algebraic system. Students will study the rings, ideals, and modules of commutative algebra and can solve problems efficiently.

Who it is for

The ‘Computational Commutative Algebra’ online certification course is aimed at students in the advanced level of their undergraduate course or pursuing their master’s degree in the domain of mathematics and algebra.

Admission Details

The participants applying for the ‘Computational Commutative Algebra’ online training program should register for the course online.

Step 1: Find the course page using the following link,

https://onlinecourses.nptel.ac.in/noc21_ma40/preview

Step 2: Choose the ‘Sign-In/Register’ link.

Step 3: Fill in the details for registration and join the course.

Application Details

The application form for the ‘Computational Commutative Algebra’ course is found on the course page and the students will have to enter their registration details if they already possess a Swayam account or can form a new account with the basic information. Participants can also sign in using their Facebook, Google, or Microsoft account IDs.

The Syllabus

Introduction: rings and ideals
Ring homomorphisms
Hilbert basis theorem
Hilbert Nullstellensatz
Introduction to Macaulay2

Groebner bases
Ideal membership
Solving systems of polynomial rings

Modules

Associated primes and primary decomposition

Associated primes and primary decomposition, ctd.

Integral extensions
Integral closure
Noether normalization

Integral extensions
Integral closure
Noether normalization, ctd.

Hilbert functions
Dimension theory

Hilbert functions
Dimension theory ctd.

Applications to geometry.

Homological algebra: depth
Koszul complex

Homological algebra: free resolutions
Auslander-Buchsbaum formula

Evaluation process

The ‘Computational Commutative Algebra’ certification exam is the end-term proctored exam organized at the allotted exam centers. Students are required to register and pay for the exam through the course website and clear the exam with 75% (30/75) to qualify for the certificate.