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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 ‘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

Mathematical skillStatistical skillsKnowledge of Applied statistics

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

ScientistResearch AssociateMathematician

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%).