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Courses » Modern Algebra

Modern Algebra

ABOUT THE COURSE

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

None

INDUSTRY SUPPORT – LIST OF COMPANIES/INDUSTRY THAT WILL RECOGNIZE/VALUE THIS ONLINE COURSE

None

1251 students have enrolled already!!

COURSE INSTRUCTOR



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 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

SUGGESTED READING

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


MORE DETAILS ABOUT THE COURSE
Course url: https://onlinecourses.nptel.ac.in/noc16_cs15
Course duration : 8 Weeks
Start date and end date of course: 18 July, 2016 - 09 September, 2016
Dates of exams : 18 Sep 2016 &  25 Sep 2016
Time of exam : 2pm - 5pm
Final List of exam cities will be available in exam registration form.
Exam registration url - Will be announced shortly
Exam Fee: The online registration form has to be filled and the certification exam fee of approximately Rs 1000(non-Programming) needs to be paid.

CERTIFICATE

E-Certificate will be given to those who register and write the exam. Certificate will have your name, photograph and the score in the final exam. It will have the logos of NPTEL and IIT Kanpur.

It will be e-verifiable at nptel.ac.in/noc.