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Computational Mathematics with SageMath

By Prof. Ajit Kumar   |   Institute of Chemical Technology, Mumbai
Learners enrolled: 410
Computational Mathematics with SageMath: This twelve 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, Numerical Methods and basic Linear Programming Problems.  The course will begin with the introduction of basic Python programming language. Next, we shall provide a quick introduction to SageMath software along with plotting 2D and 3D objects. The focus will be on using SageMath to explore topics in Calculus, Applied Linear Algebra, Numerical Method and Linear Programming Problems along with several applications.

INTENDED AUDIENCE
UG and PG students of Mathematics and BE Students, Teachers teaching in UG/PG Level.
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 : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Exam Date : 23 Apr 2022 IST
Category :
  • Mathematics
  • Foundations of Mathematics
  • Algebra
Credit Points : 3
Level : Undergraduate/Postgraduate



Course layout

Week 1:
  • Installation of Python
  • Getting Started with Python
  • Python as an advanced calculator
  • Lists in Python
  • Tuple, Sets and Dictionaries in Python
  • Functions and Branching
Week 2:
  • For loop in Python
  • While loop in Python
  • Creating Modules and Introduction to NumPy
  • Use of NumPy module
  • Python Graphics using MatplotLib
Week 3:
  • Use of SciPy and SymPy in Python
  • Classes in Python - Part 01
  • Classes in Python - Part 02
  • Introduction and Installation of SageMath
  • Exploring integers in SageMath
Week 4:
  • Solving Equations in SageMath
  • 2d Plotting with SageMath
  • 3d Plotting with SageMath
  • Calculus of one variable with SageMath - Part 1
  • Calculus of one variable with SageMath - Part 2
  • Applications of derivatives 
Week 5:
  • Integration with SageMath
  • Improper Integral using SageMath
  • Application of integration using SageMath
  • Limit and Continuity of real valued functions
  • Partial Derivative with SageMath
  • Local Maximum and Minimum
Week 6:
  • Application of local maximum and local minimum
  • Constrained optimization using Lagrange multipliers
  • Working with vectors in SageMath
  • Solving system of linear Equations in SageMath
  • Vector Spaces in SageMath
  • Basis and dimensions of vector spaces in SageMath
Week 7:
  • Matrix Spaces with SageMath
  • Linear Transformations Part 1 with SageMath
  • Linear Transformations Part 2 with SageMath
  • Eigenvalues and Eigenvectors Part 1 with SageMath
  • Eigenvalues and Eigenvectors Part 2 with SageMath
Week 8:
  • Inner Product  Part 1 with SageMath
  • Inner Product  Part 2 with SageMath
  • Orthogonal Decomposition with SageMath
  • Least Square Solution with SageMath
  • Singular Value Decomposition (SVD) with SageMath
  • Application of SVD to image processing
  • Solving System of linear ODE using Eigenvalues and Eigenvectors
Week 9:
  • Google Page Rank Algorithm using SageMath
  • Finding Roots of algebraic and transcendental equations in SageMath
  • Numerical Solutions of System of linear equations in SageMath
  • Interpolations in SageMath
  • Numerical Integration in SageMath
  • Numerical Eigenvalues
Week 10:
  • Solving 1st and 2nd order ODE with SageMath
  • Euler's Method to solve 1st order ODE with SageMath
  • Fourth Order Runge-Kutta Method 
  • RK4 method for System of ODE and Applications
  • Solving ODE using Laplace Transforms in SageMath
Week 11:
  • Introduction to Linear Programming Problems (LPP)
  • Solving Linear Programming Problmes using Graphical Methods
  • Basics Definitions and Results in LPP
  • Theory of Simplex Method
  • Simplex Methods in SageMath - Part 01
  • Simplex Methods in SageMath - Part 02
  • Simplex Methods in Matrix Form
Week 12:
  • Revised Simplex Method in SageMath
  • Two Phase Simplex Method in SageMath
  • Big-M Method in SageMath
  • Duality of Linear Program
  • Dual Simplex Method in SageMath
  • Review and What next in SageMath?

Books and references

1. www.sagemath.org
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
6. Group Theory: An expedition with SageMath, Ajit Kumar and Vikash Bist, Narosa (2021)

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: 23 April 2022 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.

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

- NPTEL team


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