Algebra - I
Learn in detail about the fundamental mathematical concepts and theories associated with Algebra with this course.
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Course Overview
The ‘Algebra - I’ online certification program is a core course for the students of mathematics that is focused on delivering the students insights on the foundational concepts of algebra. This free online course is provided by Swayam educational platform in collaboration with the National Programme on Technology Enhanced Learning (NPTEL). The course classes are held online in a virtual environment through videos, lectures, online resources, and assessments. The students of this course will take about twelve weeks to complete the course.
The instructors for this online training program are mathematics faculties from The Institute of Mathematical Sciences in Chennai, Prof. S Viswanath, and Prof. Amritanshu Prasad. The candidates of this mathematics course will gain a comprehensive understanding of the theoretical and practical aspects of algebra in this course.
By the end of this postgraduate level course, the students of the ‘Algebra - I’ training program will be given E-Certificate with the credit points.
The Highlights
- Online mode
- Free training
- Twelve weeks
- Expert faculty
- Credit points
- Certificate
Programme Offerings
- Course Modules
- Online Classes
- Books
- references
- Weekly Assignments
- Final Exam
- Credit Points
- course certificate
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IMSc Chennai |
The applicants should pay the ‘Algebra - I’ certification fee to registrater for the certification exam conducted to qualify them for the certification.
Algebra - I fee structure
Course Fee | Nil |
Exam Registration Fee | Rs 1000 |
Eligibility Criteria
The students interested in applying for the ‘Algebra - I’ online course are required to have prior knowledge of undergraduate-level linear algebra.
Certificate qualifying details
The ‘Algebra - I’ certification by Swayam is given to students who have completed the course, assessments, and the final certification exam with at least a minimum score of 10/25 (25) in the best 8 out of 12 assignments and 30/75(75%) in the exam to make an overall average of 40/100.
What you will learn
The ‘Algebra - I’ certification syllabus is structured for the students to enable them to set a strong foundation with knowledge on the theories and principles of algebra. The students of this course will get familiar with the concepts of group theory, ring theory, module theory, and their applications.
Who it is for
The ‘Algebra - I’ online certification course is designed for the postgraduate level students of mathematics and for the research associates pursuing their Ph.D. The course is also for mathematicians, scientists, and engineers who are keen on developing their knowledge of algebra.
Admission Details
The students who wish to join the ‘Algebra - I’ online training are required to register online through the course website.
Step 1: Find the course page using the link,
https://onlinecourses.nptel.ac.in/noc21_ma71/preview
Step 2: Click on the ‘Sign In-Register’ now option.
Step 3: Fill in the details.
Step 4: Start the course.
Application Details
The candidates registering for the ‘Algebra - I’ certification course should enter their Swayam account details on the registration form if they had already registered or can create a new course account. They can also join the course by using their Google, Facebook, or Microsoft account IDs.
The Syllabus
- Permutation groups
- Group axioms
- Order and conjugacy
- Subgroups
- Group actions
- Homomorphisms
- Isomorphisms
- Quotient groups
- Products
- Orbit counting theorem
- Fixed points
- Sylow's theorems
- Sylow's theorems (continued)
- Free groups
- Generators and relations
- Rings
- Euclidean domains
- Ideals and factorization
- Examples of commutative and non-commutative rings
- Quotients by ideals
- Tensor and exterior algebras
- Modules
- Sums
- Quotients and homomorphisms of modules
- Free modules
- Determinants
- Primary decomposition
- Finitely generated modules and the Noetherian condition
- Smith form
- Structure theorem for finitely generated modules over a PID
- Jordan canonical form
Evaluation process
- The students of this free online certification course will become eligible for the ‘Algebra - I’ certification by Swayam after clearing the end-term proctored exam at the end of the course.
- The students of the course should register and pay online through the course website and write the exam from the allotted exam center.
- The qualifying mark for the certification exam is 30/75(75%).
Instructors
IMSc Chennai Frequently Asked Questions (FAQ's)
The course is conducted for a period of twelve weeks.
The course is provided by Swayam and NPTEL.
Yes, the course classes can be accessed for free.
I will get three credit points for the certification.
You will have to get 10/25 (25%) in the best 8 out of 12 weekly assignments.