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 “Introduction to Abstract Group Theory” on NPTEL which first ran during August-October 2018.
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Teaching Assistant(s)

NEELARNAB RAHA

M.Sc. Mathematics

Rahul Hirwani

MSc (Honours)

 Course Duration : Aug-Oct 2019
  View Course
 Syllabus
 Enrollment : 15-May-2019 to 26-Aug-2019
 Exam registration : 01-Jun-2019 to 30-Sep-2019
 Exam Date : 17-Nov-2019, 17-Nov-2019

Enrolled

2175

Registered

200

Certificate Eligible

107

Certified Category Count

Gold

18

Silver

31

Elite

27

Successfully completed

31

Participation

48

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
Introduction to Rings and Fields - Toppers list
Top 1 % of Certified Candidates

SAHEB DNYANESHWAR NAVGHARE 100%

SWAMI RAMANAND TEERTH MARATHWADA UNIVERSITY


Top 2 % of Certified Candidates

KARNAN A 98%

THE GANDHIGRAM RURAL INSTITUTE (DEEMED TO BE UNIVERSITY)

NEHA SHAILESH GOREGAOKAR 98%

St Xaviers College (Autonomous)


Top 5 % of Certified Candidates

M. SIVAGAMI 97%

MANONMANIAM SUNDARANAR UNIVERSITY

SUSHIL DNYANESHWAR MUNESHWAR 95%

SWAMI RAMANAND TEERTH MARATHWADA UNIVERSITY

SMITHA G V 95%

NMAMIT, Nitte

Enrollment Statistics

Total Enrollment: 2175

Registration Statistics

Total Registration : 200

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.