Course Name: Introduction to Algebraic Geometry and Commutative Algebra

Course abstract

Algebraic geometry played a central role in 19th century math. The deepest results of Abel, Riemann, Weierstrass, and the most important works of Klein and Poincar/’e were part of this subject. In the middle of the 20th century algebraic geometry had been through a large reconstruction. The domain of application of its ideas had grown tremendously, in the direction of algebraic varieties over arbitrary fields and more general complex manifolds. Many of the best achievements of algebraic geometry could be cleared of the accusation of incomprehensibility or lack of rigour. The foundation for this reconstruction was (commutative) algebra. In the 1950s and 60s have brought substantial simplifications to the foundation of algebraic geometry, which significantly came closer to the ideal combination of logical transparency and geometric intuition. Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry. In algebraic number theory, the rings of algebraic integers in number fields constitute an important class of commutative rings — the Dedekind domains. This has led to the notions of integral extensions and integrally closed domains. The notion of localization of a ring (in particular the localization with respect to a prime ideal leads to an important class of commutative rings — the local rings. The set of the prime ideals of a commutative ring is naturally equipped with a topology — the Zariski topology. All these notions are widely used in algebraic geometry and are the basic technical tools for the definition of scheme theory — a generalization of algebraic geometry introduced by Grothendieck.


Course Instructor

Media Object

Prof. Dilip Patil

Dilip P. Patil received B. Sc. and M. Sc. in Mathematics from the University of Pune in 1976 and 1978, respectively. From 1979 till 1992 he studied Mathematics at School of Mathematics, Tata Institute of Fundamental Research, Bombay and received Ph. D. through University of Bombay in 1989. Currently he is a Professor of Mathematics at the Departments of Mathematics, Indian Institute of Science, Bangalore. At present he is a Visiting Professor at the Department of Mathematics, IIT Bombay. He has been a Visiting Professor at Ruhr-Universit?ƒÂ¤t Bochum, Universit?ƒÂ¤t Leipzig, Germany and several universities in Europe and Canada. His research interests are mainly in Commutative Algebra and Algebraic Geometry.
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Teaching Assistant(s)

No teaching assistant data available for this course yet
 Course Duration : Jan-Apr 2021

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 Syllabus

 Enrollment : 18-Nov-2020 to 25-Jan-2021

 Exam registration : 15-Jan-2021 to 12-Mar-2021

 Exam Date : 25-Apr-2021

Enrolled

435

Registered

4

Certificate Eligible

1

Certified Category Count

Gold

0

Silver

0

Elite

0

Successfully completed

1

Participation

1

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 8 out of 12 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 Algebraic Geometry and Commutative Algebra - Toppers list

Enrollment Statistics

Total Enrollment: 435

Registration Statistics

Total Registration : 4

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.