Mathematical Foundations for Machine Learning

By Prof. Ashok Rao, Prof. Arulalan Rajan | IISc Bangalore, NITK Surathkal

Learners enrolled: 1554

ABOUT THE COURSE:

This course will provide a holistic approach to the mathematical foundations for Machine Learning. The course is focussed on developing mathematical ideas, necessary for machine learning applications, through intuitions and visualizations.The course primarily focuses on three important mathematical domains, namely

Linear Algebra
Probabilty and Statistics and
Multivariable Calculus,

on which the ML and data science ideas are built.

INTENDED AUDIENCE: BE/BTech/ME/MTech//BSc/MSc(Maths)/MCA

PREREQUISITES: Basic Mathematics at school and undergraduate level

INDUSTRY SUPPORT: Amazon, Flipkart, Robert Bosch, Qualcomm, Nvidia and Companies that are into Computer vision, Data Science, Robotics and Control

Summary

Course Status :	Upcoming
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Computer Science and Engineering
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	21 Jul 2025
End Date :	10 Oct 2025
Enrollment Ends :	28 Jul 2025
Exam Registration Ends :	15 Aug 2025
Exam Date :	01 Nov 2025 IST
NCrF Level	4.5 — 8.0

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Vectors, Vector Spaces and Subspaces

Week 2: Linear Transformations, eigenvalues and eigenvectors

Week 3: Orthogonality, Projection and Real symmetric matrices

Week 4: Singular value decomposition, Principal Component Analysis, Support Vector Machines and Applications

Week 5: Probability Foundations - From Events to Bayes’ Theorem

Week 6: Random Variables, Moments of Random Variables

Week 7: Jointly Distributed Random Variables, Conditioning of Random variables

Week 8: Limit Theorems, Sample Geometry, Covariance Matrices and Properties

Week 9: Taylor’s series, Partial Derivatives, Chain rule, Gradient, Jacobian, Hessian

Week 10: Matrix Derivatives, Gradient Descent and Stochastic Gradient Descent, Constrained and Unconstrained optimization, Lagrangian, Least Squares and PCA

Week 11: Neural Nets, Perceptron, Back Propagation Algorithm

Week 12: Algorithms for ML - Classification, Clustering and Regression

Books and references

Gilbert Strang,”Introduction to Linear Algebra” Wellesley Cambridge Press, 5th Ed
Gilbert Strang,” Learning from Data”, Wellesley Cambridge Press 2019
Steven M Kay, Intuitive Probability and Random Processes, Springer, 2017
Deisenroth, Mathematics for Machine Learning, Cambridge University Press,
Richard Johnson, Applied Multivariate Statistical Analysis, 6th ed, Pearson Ed, 2015

Instructor bio

Prof. Ashok Rao

IISc Bangalore

Dr. Ashok Rao - Formerly, Head, Network Project, DESE, IISc.

Dr. Ashok Rao is with 30 years of teaching and research experience in the domains of Digital Signal Processing, Linear Algebra, Image Processing, Multimedia and Machine Learning etc. He is a gold medalist from IISc in his MTech degree and holds a PhD from IIT Bombay. He has been awarded Texas Instruments (TI) International DSP Design & Education Award for promoting Excellence in Undergraduate DSP education during 1996-98. He has received Citation from Philips Company for regularly crafting excellent UG students in E & C, in the area of Signal processing & Digital Communication during 96-98.

Prof. Arulalan Rajan

NITK Surathkal

Dr. Arulalan Rajan - Formerly, Assistant Professor, Dept. of E & C Engg, NITK Surathkal

Dr. Arulalan Rajan is a PhD from IISc with interests in Algorithms and Architectures for Signal Processing and Machine Learning, Applied Linear Algebra, Number Theory, Probabilistic ML and Statistics. He has taught courses on Linear Algebra, Matrix Theory and Stochastic Processes during his tenure, between 2013-19 at NITK Surathkal. He has also co-taught the courses on Mathematical Foundations of Machine Learning, Probability Foundations for Machine Learning and Probability, Statistics and Matrix Methods for Machine Learning at the Centre for Continuing Education in the IISc in the last 5 years.

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: November 01, 2025 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

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

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.

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

- NPTEL team