Swayam Central

# Modern Algebra

By Prof. Manindra Agrawal   |   IIT Kanpur
The course discusses how algebra allows us to abstract out the geometric objects and numbers. This leads to an understanding of fundamental properties of geometry and numbers as well as allows us to manipulate them in ways not possible directly. This has resulted in some of the most remarkable applications of mathematics in real life.

INTENDED AUDIENCE: All undergraduate science and engineering students

PRE-REQUISITES : Nil

Learners enrolled: 1855

### SUMMARY

 Course Status : Ongoing Course Type : Elective Duration : 8 weeks Start Date : 26 Aug 2019 End Date : 18 Oct 2019 Exam Date : 17 Nov 2019 Category : Computer Science and Engineering Level : Undergraduate
This is an AICTE approved FDP course

### COURSE LAYOUT

Week 1: Introduction to abstraction,Introduction to Groups
Week 2: Properties of Finite Groups,Applications of Groups
Week 3: Introduction to Rings,Properties of Finite Rings
Week 4: Introduction to Ideals
Week 5: Properties of Ideals
Week 6: Applications of Ideals and Rings
Week 7: Introduction to Fields
Week 8: Applications of Finite Fields

### BOOKS AND REFERENCES

1) Abstract Algebra: Theory and Applications by Thomas W. Judson, available as PDF at http://abstract.ups.edu/download/aata-20110810.pdf
2) Abstract Algebra by I. N. Herstein

### INSTRUCTOR BIO

Prof. Manindra Agrawal is a computer scientist by training and mathematician by profession, thus allowing him to wear different hats as per convenience. Most of his time is spent in proving, about certain problems of interest, that no one can ever solve them quickly (and deriving pleasure by the look of disappointment on those trying to solve these problems). At times, this quest, rather unexpectedly, results in a quick solution of a problem. He made his name due to one such problem: how to test if a number is prime. As a consequence, he was bestowed with several wards and honors including Shanti Swarup Bhatnagar prize, Godel prize, Fulkerson prize, Infosys prize, and Padma Shri.

### 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: 17 November 2019, 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 6 assignments out of the total 8 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 Kanpur. It will be e-verifiable at nptel.ac.in/noc.
• Only the e-certificate will be made available. Hard copies are being discontinued from July 2019 semester and will not be dispatched