Course Name: Introduction to Rings and Fields

Course abstract

This course will cover basics of abstract rings and fields, which are an important part of any abstract algebra course sequence. We will spend roughly the 4-5 weeks on rings. We will begin with definitions and important examples. We will focus cover prime, maximal ideals and important classes of rings like integral domains, UFDs and PIDs. We will also prove the Hilbert basis theorem about noetherian rings. The last 3-4 weeks will be devoted to field theory. We will give definitions, basic examples. Then we discuss extension of fields, adjoining roots, and prove the primitive element theorem. Finally we will classify finite fields.


Course Instructor

Media Object

Prof. Krishna Hanumanthu

Krishna Hanumanthu is an associate professor of mathematics at Chennai Mathematical Institute (CMI). He studied BSc and MSc in CMI during 1998-2003 and did his PhD in mathematics at University of Missouri during 2003-2008. He joined CMI as a faculty member in 2011 after working for 3 years at University of Kansas. His main areas of research are algebraic geometry and commutative algebra. He has been teaching for almost 15 years and taught introductory courses on abstract algebra (including courses on rings and fields) many times. He also taught a course on ?¢â‚¬Å“Introduction to Abstract Group Theory?¢â‚¬Â? on NPTEL which first ran during August-October 2018.
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Teaching Assistant(s)

No teaching assistant data available for this course yet
 Course Duration : Jan-Mar 2021
  View Course
 Syllabus
 Enrollment : 18-Nov-2020 to 25-Jan-2021
 Exam registration : 15-Jan-2021 to 12-Feb-2021
 Exam Date : 21-Mar-2021

Enrolled

1247

Registered

120

Certificate Eligible

83

Certified Category Count

Gold

7

Silver

21

Elite

38

Successfully completed

17

Participation

22

Success

Elite

Silver

Gold




Legend

AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75 AND FINAL SCORE >=40
BASED ON THE FINAL SCORE, Certificate criteria will be as below:
>=90 - Elite + Gold
75-89 -Elite + Silver
>=60 - Elite
40-59 - Successfully Completed

Final Score Calculation Logic

  • Assignment Score = Average of best 6 out of 8 assignments. Final Score(Score on Certificate)= 75% of Exam Score + 25% of Assignment Score.
    Note:
    We have taken best assignment score from both Jan 2020 and Jan2021 course
Introduction to Rings and Fields - Toppers list

RAMASAMY CT 98%

Alagappa Government Arts College

DEEPAK JOY 97%

CENTRAL UNIVERSITY OF KERALA

JISNA JOHNSON 94%

CENTRAL UNIVERSITY OF KERALA

APURVA RAI 94%

INDIAN INSTITUTE OF TECHNOLOGY,KHARAGPUR

BIYA THOMAS 91%

CENTRAL UNIVERSITY OF KERALA

ASWIN RANGASAMY VENKATESAN 91%

ASHI PAUL 91%

DEPARTMENT OF MATHEMATICS, CENTRAL UNIVERSITY OF KERALA

Enrollment Statistics

Total Enrollment: 1247

Registration Statistics

Total Registration : 120

Assignment Statistics



Assignment

Exam score

Final score

Score Distribution Graph - Legend

Assignment Score: Distribution of average scores garnered by students per assignment.
Exam Score : Distribution of the final exam score of students.
Final Score : Distribution of the combined score of assignments and final exam, based on the score logic.