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Swayam Central

An introduction to smooth manifolds.

By Prof. Harish Seshadri   |   IISc Bangalore
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

Learners enrolled: 294

SUMMARY

Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 27 Jan 2020
End Date : 17 Apr 2020
Exam Date : 25 Apr 2020
Enrollment Ends : 03 Feb 2020
Category :
  • Mathematics
  • Level : Postgraduate
    This is an AICTE approved FDP course

    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: 25th April 2020, 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.

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