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Real Analysis I

By Prof. Jaikrishnan J   |   IIT Palakkad
Learners enrolled: 3174
This is an introductory course on Real Analysis designed for undergraduate students of Mathematics. The only pre-requisite is a knowledge of Calculus at high school level so students of the Sciences or Engineering who want a deeper understanding of Calculus or want to pursue subjects such as Theoretical Physics, Computational Complexity, Statistics, etc. would also benefit from this course.

INTENDED AUDIENCE
UG Students of Mathematics, the Sciences or Engineering
PREREQUISITES 12th Standard Mathematics
INDUSTRIES  SUPPORT     : Google, DeepMind, Microsoft Research
Summary
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Start Date : 14 Sep 2020
End Date : 04 Dec 2020
Exam Date : 20 Dec 2020 IST
Enrollment Ends : 25 Sep 2020
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate

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Course layout

Week 1:Introduction, Set Theory and Logic
Week 2:The Real Numbers as a complete Ordered Field
Week 3:Sequences and Series
Week 4:Sequences and Series continued
Week 5:A Taste of Topology I: Limits and Continuity
Week 6: A taste of Topology II: Compactness
Week 7:A Taste of Topology III: Connected and Perfect sets
Week 8:Differentiation
Week 9:Riemann Integral and the Fundamental Theorem of Calculus
Week 10: Uniform Convergence and Power Series
Week 11:The Elementary Functions
Week 12: Improper Integrals and the Weierstrass Approximation Theorem

Books and references

Analysis I and II by Terence Tao
Mathematical Analysis by Tom Apostol
Understanding Analysis by Stephen Abbott

Instructor bio

Prof. Jaikrishnan J

IIT Palakkad
Jaikrishnan J is an Assistant Professor at IIT Palakkad. He specializes 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: 20 December 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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