An Introduction to smooth Manifolds

By Prof. Harish Seshadri | IISc Bangalore

Learners enrolled: 542

The goal of this course is to introduce the student to the basics of smooth manifold theory. The course will start with a brief outline of the prerequisites from topology and multi-variable calculus.

After the introducion of differentiable manifolds, a large class of examples, including Lie groups, will be presented. The course will culminate with a proof of Stokes' theorem on manifolds.

INTENDED AUDIENCE : Masters and PhD students in mathematics, physics, robotics and control theory, information theory and climate sciences.

PREREQUISITES : Real analysis, linear algebra and multi-variable calculus, topology.

INDUSTRY SUPPORT : Nil

Summary

Course Status :	Completed
Course Type :	Elective
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	18 Jan 2021
End Date :	09 Apr 2021
Enrollment Ends :	01 Feb 2021
Exam Date :	24 Apr 2021 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1 : Review of topology and multi-variable calculus

Week 2 : Definition and examples of smooth manifolds

Week 3 : Smooth maps between manifolds, submanifolds

Week 4 : Tangent spaces and vector fields

Week 5 : Lie brackets and Frobenius theorem

Week 6 : Lie groups and Lie algebras

Week 7 : Tensors and differential forms

Week 8 : Exterior derivative

Week 9 : Orientation

Week 10 : Manifolds with boundary

Week 11 : Integration on manifolds

Week 12 : Stokes Theorem

Books and references

Kumaresan: A course in differential geometry and Lie groups

John Lee: Introduction to smooth manifolds

Loring Tu: An introduction to manifolds

Instructor bio

Prof. Harish Seshadri

IISc Bangalore

I work in Riemannian geometry (Einstein manifolds, Ricci flow, etc) and in questions related to invariant metrics in complex analysis.

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: 24 April 2021 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 8 assignments out of the total 12 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 IISc Bangalore.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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