Get updates on Eligibility, Admission, Placements Fees Structure
Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The Rings And Modules certification course offers a comprehensive introduction to the two core components of abstract algebra. The course covers fundamental concepts like ring definitions, homomorphisms, and submodule structures. Designed for undergraduates and postgraduates interested in mathematics, it provides a solid foundation for further study or research in algebra.
Split into two six-week segments, the Rings And Modules certification by Swayam delves into Ring Theory and Module Theory. Topics include ideals, quotient rings, module homomorphisms, direct sums, and tensor products. Students will gain essential skills in understanding and analyzing algebraic structures, preparing them for more advanced studies in abstract algebra.
The Highlights
- Elective Online Course
- 12 Weeks Duration
- Offered by IIT Kharagpur
Programme Offerings
- Certificate of completion
- Practical Learning
- Hands-on Experience
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kharagpur |
The Rings And Modules certification fees is free. However, if you want a certificate, you must register and take the proctored exam at designated centers, which is optional and comes with a fee of Rs 1000.
Rings And Modules Certification Fee Structure
Particulars | Total Fees |
Rings And Modules (exam) | Rs 1000/- |
Eligibility Criteria
Academic Qualifications
The Rings And Modules certification course is intended for anyone interested in mathematics and requires prior knowledge of Group Theory and Linear Algebra.
Certification Qualifying Details
To receive the Rings And Modules certification by Swayam, you need a minimum average assignment score of 10/25 and an exam score of 30/75.
What you will learn
After completing the Rings And Modules certification syllabus, you will learn fundamental concepts in modules and rings, which are essential components of abstract algebra. You will gain a deep understanding of ring definitions, properties, and operations, including ideals and quotient rings.
Upon completion of the Rings And Modules training, you will explore the generalization of vector spaces, understanding module homomorphisms, submodule structures, and operations like direct sums and tensor products.
Who it is for
The Rings And Modules online course is suitable for individuals interested in mathematics, particularly those who wish to pursue further studies or research in algebra. This course is particularly relevant for:
Admission Details
Follow these steps to join the Rings And Modules classes:
Step 1: Browse the URL below:
https://onlinecourses.nptel.ac.in/noc23_ma84/preview
Step 2: Click on the “Sign-in/ Register” button
Step 3: Fill out the necessary details and submit the form
The Syllabus
- Introduction to rings, examples, ideals, ring homomorphisms, quotients with examples
- Isomorphism theorems, Prime and maximal ideals, basic properties of ideals, local rings
- Radical ideals, Nil radical, Jacobson radical
- Integral domains, field of fractions, Euclidean Domains, Principal Ideal Domains
- Unique factorization domains, Gauss lemma, Eisenstein’s irreducibility criterion
- Algebraic variety, Weak form of Hilbert’s nullstellensatz
- Introduction to Modules over arbitrary rings, examples, Free modules, submodules, quotient modules, module homomorphisms, direct sums, direct products
- Generators of modules over commutative rings, rank of a free module, Simple modules
- Modules over a PID
- Modules with chain conditions, Noetherian modules, Noetherian rings
- Artinian modules, Artinian rings, Hilbert Basis Theorem
- Tensor product of modules, properties of tensor products
Evaluation process
The Rings And Modules certification offers an optional exam. Your final score is determined by averaging the best 8 out of 12 assignments (25%) and your proctored exam score (75%).
IIT Kharagpur Frequently Asked Questions (FAQ's)
Prerequisites for this course include a solid understanding of Group Theory and Linear Algebra.
The course is divided into two segments: the first six weeks focus on Ring Theory, while the last six weeks cover Module Theory.
By completing this course, you will gain a comprehensive understanding of fundamental concepts in abstract algebra, along with skills in analyzing algebraic structures and operations.
While prior knowledge in Group Theory and Linear Algebra is required, the course is designed for learners interested in mathematics at both undergraduate and postgraduate levels.
Graduates may pursue careers in mathematics research, academia, data science, cryptography, financial analysis, and more, leveraging their strong foundation in abstract algebra.