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Computational Mathematics with SageMath

By Prof. Ajit Kumar   |   Institute of Chemical Technology, Mumbai
Learners enrolled: 1832
Computational Mathematics with SageMath: This eight week course aims to use SageMath, a Python based free and open source computer algebra system (CAS) to explore concepts in Calculus, Applied Linear Algebra and Numerical Methods. The course will begin with the introduction of basic Python programming language in the first two weeks. Next we shall provide a quick introduction to SageMath software along with plotting 2D and 3D objects. The main focus will be on using SageMath to explore topics in Calculus, Applied Linear Algebra and Numerical Method along with several applications.

INTENDED AUDIENCE
UG and PG students of Mathematics and BE Students, Teachers teaching in Degree colleges.
PREREQUISITES : Basic knowledge of Calculus, Linear Algebra and ODE and Numerical Methods.
INDUSTRIES  SUPPORT     : Any industry dealing with Data Science and Numerical Computations.
Summary
Course Status : Completed
Course Type : Elective
Duration : 8 weeks
Start Date : 18 Jan 2021
End Date : 12 Mar 2021
Exam Date : 21 Mar 2021 IST
Enrollment Ends : 01 Feb 2021
Category :
  • Mathematics
  • Foundations of Mathematics
  • Algebra
Credit Points : 2
Level : Undergraduate/Postgraduate

Page Visits



Course layout

Week 1:
0. Installation  of Python
1. Getting Started with  Python
2. Python as an advanced Calculator 
3. Lists in Python
4. Tuples sets and dictionary in Python
5. Functions and Branching
6. For loop in Python 
7.  While loop in Python
Week 2:
8. Creating Modules and Introduction to NumPy
9. Use of NumPy module
10. Python Graphics using MatplotLib
11. Use of SciPy and SymPy in Python
12. Classes in Python
13. Classes in Python
Week 3:
00. Introduction and Installation of SageMath
14. Exploring integers in SageMath
15. Solving Equations in SageMath
16. 2d Plotting with SageMath
17. 3d Plotting with SageMath
18. Calculus of one variable with SageMath Part 1
19.  Calculus of one variable with SageMath Part 2
Week 4:
20. Applications of derivatives 
21. Integrals in SageMath 
22. Applications of Integrals
23. Partial Derivatives and gradients, jacobians
25. Local maximum-minimum 
26. Application of local maximum and minimum
27 Applications to least square problems
Week 5:
28. Lagrange Multipliers
29. Working with vectors in SageMath 
39. RREF and Solving system of linear Equations
31. Vector Spaces in SageMath
32. Vector Spaces in SageMath (cont..)
33. Linear Transformations with SageMath
34. Linear Transformations with SageMath (cont..)
Week 6:
35. Eigenvalues and Eigenvectors with SageMath
36. Eigenvalues and Eigenvectors with SageMath (cont..)
37. Inner Product Spaces in SageMath
38. Inner Product Spaces in SageMath (cont..)
39. Gram-Schmidt Process and QR-factorization
40. Singular Value Decomposition (SVD)
Week 7:
41 Applications of SVD & Least Square Methods
42. Applications of linear algebra with SageMath
43. Numerical Solution of algebraic equations
44. Numerical Solutions of system linear equations
45. Interpolations
46. Numerical Integration
47. Numerical Integration (Cont..)
Week 8:
48. Numerical Eigenvalues
49. Solving ODE with SageMath
50. Initial Value ODE with SageMath
51. Initial Value ODE with SageMath (cont..)
52. Solving system of ODE
53. Solving ODE with Laplace Transforms
54.  Applications of ODE with SageMath
55. What next with SageMath?

Books and references

2. Mathematical Computation with Sage by Paul Zimmermann available from on http://www.sagemath.org
3. A First Course in Linear Algebra by Robert Beezer available online http://linear.ups.edu/
4. Abstract Algebra: Theory and Applications by Tom Judson and Robert Beezer (http://abstract.ups.edu/)
5. An Introduction to SAGE Programming: With Applications to SAGE Interacts for Numerical Methods by Razvan A Mezei, Springer

Instructor bio

Prof. Ajit Kumar

Institute of Chemical Technology, Mumbai
Dr. Ajit Kumar is an Associate Professor and the Head, Department of Mathematics, Institute of Chemical Technology. He did his Masters and Ph.D. from the University of Mumbai. His current areas of interest are Optimization Techniques, Data Analysis, and Mathematical Pedagogy. He has been a prolific user of various mathematical software such as SageMath, Python, R, Mathematica, MatLab etc. Due to this expertise, he has been invited to give talks on these topics at several national and international events and has conducted numerous training programmes for students and teachers.He has been associated with one of the most popular and significant training programmes in Mathematics known as "Mathematics Training and Talent Search” (MTTS) Programme for the last several years in various capacities. Currently he is the managing trustee of the MTTS TRUST, which organizes all the programmes under the MTTS umbrella.

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: 21 March 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 6 assignments out of the total 8 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.

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

- NPTEL team


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