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Linear Algebra

By Prof. Pranav Haridas   |   Kerala School of Mathematics
Learners enrolled: 3276
Linear Algebra is a foundational subject in Mathematics which is of fundamental importance in the development of almost every branch of Mathematics, Theoretical Physics and Computer Science. A good understanding of the subject is also crucial to the study of most Engineering disciplines and many problems in Social Sciences. Linear Algebra can be succinctly described as the study of Linear Transformations and its algebraic properties. This course is an introduction to Linear Algebra


INTENDED AUDIENCE : Undergraduate students in various universities.
PREREQUISITES : Nil
INDUSTRY SUPPORT : Almost all engineering based companies
Summary
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Start Date : 27 Jan 2020
End Date : 17 Apr 2020
Exam Date : 25 Apr 2020 IST
Enrollment Ends : 24 Feb 2020
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate



Course layout

Week 1 : Vectors, vector spaces, span, linear independence, bases 
Week 2 : Dimension, linear transformations
Week 3 : Null spaces, range, coordinate bases
Week 4 : Matrix multiplication, Invertibility, Isomorphisms
Week 5 : Coordinate change, products and quotients of vector spaces, duality
Week 6 : Review of elementary row operations, rank, determinants 
Week 7 : Eigenvalues, Eigenvectors
Week 8 : Diagonalization
Week 9 : Characteristic polynomials, inner products and norms
Week 10 : Orthogonal bases, orthognalization, orthogonal complements
Week 11 : Adjoints, normal and self-adjoint operators
Week 12 : Spectral theorem for normal and self-adjoint operators

Books and references

1. Linear Algebra - Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence; fifth edition
2. Linear Algebra - Kenneth Hoffman Ray Kunze; second edition
3. Linear Algebra done right - Sheldon Axler; second edition
4. Lecture notes by Terence Tao

Instructor bio

Prof. Pranav Haridas

Kerala School of Mathematics
The instructor is an Assistant Professor at the Kerala School of Mathematics. His research interests broadly lie in Complex Analysis and more specifically quadrature domains in several complex variables. He is also interested in the study of quasiconformal mappings and Teichmller spaces. He completed his doctoral studies from the Indian Institute of Sciences, Bangalore

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 IIT Madras. 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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