# Essential Mathematics for Machine Learning

By Prof. Sanjeev Kumar, Prof. S. K. Gupta   |   IIT Roorkee
Machine learning (ML) is one of the most popular topics of nowadays research. This particular topic is having applications in all the areas of engineering and sciences. Various tools of machine learning are having a rich mathematical theory. Therefore, in order to develop new algorithms of machine/deep learning, it is necessary to have knowledge of all such mathematical concepts. In this course, we will introduce these basic mathematical concepts related to the machine/deep learning. In particular, we will focus on topics from matrix algebra, calculus, optimization, and probability theory those are having strong linkage with machine learning. Applications of these topics will be introduced in ML with help of some real-life examples.

INTENDED AUDIENCE
UNDERGRADUATE AND POSTGRAUATE STUDENTS OF COMPUTER SCIENCE/MATHEMATICS/DATA SCIENCE…
PREREQUISITES : None
INDUSTRIES  SUPPORT     : Microsoft/Amazon/Intel/…

Learners enrolled: 7219

### SUMMARY

 Course Status : Ongoing Course Type : Elective Duration : 8 weeks Start Date : 14 Sep 2020 End Date : 06 Nov 2020 Exam Date : 19 Dec 2020 Enrollment Ends : 25 Sep 2020 Category : Mathematics Level : Undergraduate/Postgraduate
This is an AICTE approved FDP course

### COURSE LAYOUT

Week 1:LINEAR ALGEBRA BASICS- Vector spaces and subspaces, basis and dimensions, linear transformation, four fundamental subspaces
Week 2:MATRIX THEORY- Norms and spaces, eigenvalues and eigenvectors, Special Matrices and their properties, least squared and minimum    normed solutions
Week 3:MATRIX DECOMPOSITION ALGORITHMS- SVD: Properties and applications, low rank approximations, Gram Schmidt process, polar decomposition
Week 4:DIMENSIONS REDUCTION ALGORITHMS and JCF- Principal component analysis, linear discriminant analysis, minimal polynomial and Jordan canonical form
Week 5:CALCULUS – Basic concepts of calculus: partial derivatives, gradient, directional derivatives, jacobian, hessian, , convex sets, convex functions and its properties
Week 6:OPTIMIZATION – Unconstrained and Constrained optimization, Numerical optimization techniques for constrained and unconstrained optimization: Newton’s method, Steepest descent method, Penalty function method
Week 7:PROBABILITY – Basic concepts of probability: conditional probability, Bayes’ theorem, independence, theorem of total probability, expectation and variance, few discrete and continuous distributions, joint distributions and covariance.
Week 8:SUPPORT VECTOR MACHINES – Introduction to SVM, Error minimizing LPP, concepts of duality, hard and soft margin classifiers

### BOOKS AND REFERENCES

1. W. Cheney, Analysis for Applied Mathematics. New York: Springer Science+Business Medias, 2001.
2. S. Axler, Linear Algebra Done Right (Third Edition). Springer International Publishing, 2015.
3. J. Nocedal and S. J. Wright, Numerical Optimization. New York: Springer Science+Business Media, 2006.
4. J. S. Rosenthal, A First Look at Rigorous Probability Theory (Second Edition). Singapore: World Scientific Publishing, 2006.

### Prof. Sanjeev Kumar

IIT Roorkee
Dr. Sanjeev Kumar is working as an associate professor with Department of Mathematics, IIT Roorkee. Earlier, he worked as a postdoctoral fellow with Department of Mathematics and Computer Science, University of Udine, Italy and assistant professor with IIT Roorkee. He is actively involved in teaching and research in the area of computational algorithms, inverse problems and image processing. He has published more than 55 papers in various international journals conferences of repute. He has completed a couple of sponsored research projects and written several chapters in reputed books published with Springer and CRC press.

### Prof. S. K. Gupta

Dr. S. K. Gupta is an Associate Professor in the Department of Mathematics, IIT Roorkee. His area of expertise includes nonlinear, non-convex and Fuzzy optimization. He has guided three PhD thesis and have published more than 40 papers in various international journals of repute.

### 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: 19 December, 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 Roorkee. It will be e-verifiable at nptel.ac.in/noc
•Only the e-certificate will be made available. Hard copies will not be dispatched.