Applications Open now for May 2024 Batch | Applications Close: May 26, 2024 | Exam: Jul 07, 2024

Applications Open now for May 2024 Batch | Applications Close: May 26, 2024 | Exam: Jul 07, 2024

Foundational Level Course

Mathematics for Data Science I

This course introduces functions (straight lines, polynomials, exponentials and logarithms) and discrete mathematics (basics, graphs) with many examples. The students will be exposed to the idea of using abstract mathematical structures to represent concrete real life situations.

by Neelesh Upadhye , Madhavan Mukund

Course ID: BSMA1001

Course Credits: 4

Course Type: Foundational

Pre-requisites: None

What you’ll learnVIEW COURSE VIDEOS

Recall the basics of sets, natural numbers, integers, rational numbers, and real numbers.
Learn to use the coordinate system, and plot straight lines.
Identify the properties and differences between linear, quadratic, polynomial, exponential, and logarithmic functions.
Find roots, maxima and minima of polynomials using algorithmic methods.
Learn to represent sets and relations between set elements as discrete graphs using nodes and edges.
Formulate some common real-life problems on graphs and solve them.

Course structure & Assessments

12 weeks of coursework, weekly online assignments, 2 in-person invigilated quizzes, 1 in-person invigilated end term exam. For details of standard course structure and assessments, visit Academics page.

WEEK 1 Set Theory - Number system, Sets and their operations, Relations and functions - Relations and their types, Functions and their types
WEEK 2 Rectangular coordinate system, Straight Lines - Slope of a line, Parallel and perpendicular lines, Representations of a Line, General equations of a line, Straight-line fit
WEEK 3 Quadratic Functions - Quadratic functions, Minima, maxima, vertex, and slope, Quadratic Equations
WEEK 4 Algebra of Polynomials - Addition, subtraction, multiplication, and division, Algorithms, Graphs of Polynomials - X-intercepts, multiplicities, end behavior, and turning points, Graphing & polynomial creation
WEEK 5 Functions - Horizontal and vertical line tests, Exponential functions, Composite functions, Inverse functions
WEEK 6 Logarithmic Functions - Properties, Graphs, Exponential equations, Logarithmic equations
WEEK 7 Sequence and Limits - Function of One variable - • Function of one variable • Graphs and Tangents • Limits for sequences • Limits for function of one variable • Limits and Continuity
WEEK 8 Derivatives, Tangents and Critical points - • Differentiability and the derivative • Computing derivatives and L’Hˆopital’s rule • Derivatives, tangents and linear approximation • Critical points: local maxima and minima
WEEK 9 Integral of a function of one variable - • Computing areas, Computing areas under a curve, The integral of a function of one variable • Derivatives and integrals for functions of one variable
WEEK 10 Graph Theory - Representation of graphs, Breadth-first search, Depth-first search, Applications of BFS and DFS; Directed Acyclic Graphs - Complexity of BFS and DFS, Topological sorting
WEEK 11 Longest path, Transitive closure, Matrix multiplication Graph theory Algorithms - Single-source shortest paths, Dijkstra's algorithm, Bellman-Ford algorithm, All-pairs shortest paths, Floyd–Warshall algorithm, Minimum cost spanning trees, Prim's algorithm, Kruskal's algorithm
WEEK 12 Revision
+ Show all weeks

Reference Documents / Books

Sets & Functions (VOL 1)


Calculus (VOL 2)




Prescribed Books

The following are the suggested books for the course:

Introductory Algebra: a real-world approach (4th Edition) - by Ignacio Bello

About the Instructors

Neelesh Upadhye
Associate Professor, Department of Mathematics, IIT Madras

Experienced Associate Professor with a demonstrated history of working in the higher education industry. Skilled in Mathematical Modeling, R, Stochastic Modeling, and Statistical Modeling. Strong education professional with a Doctor of Philosophy (Ph.D.) focused in Mathematical Statistics and Probability from Indian Institute of Technology, Bombay.


Madhavan Mukund
Director, Chennai Mathematical Institute

Madhavan Mukund studied at IIT Bombay (BTech) and Aarhus University (PhD). He has been a faculty member at Chennai Mathematical Institute since 1992.His main research area is formal verification. He has active research collaborations within and outside India and serves on international conference programme committees and editorial boards of journals.

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He has served as President of both the Indian Association for Research in Computing Science (IARCS) (2011-2017) and the ACM India Council (2016-2018). He has been the National Coordinator of the Indian Computing Olympiad since 2002. He served as the Executive Director of the International Olympiad in Informatics from 2011-2014.

In addition to the NPTEL MOOC programme, he has been involved in organizing IARCS Instructional Courses for college teachers. He is a member of ACM India's Education Committee. He has contributed lectures on algorithms to the Massively Empowered Classroom (MEC) project of Microsoft Research and the QEEE programme of MHRD.


Other courses by the same instructor: BSCS1001 - Computational Thinking , BSCS2002 - Programming, Data Structures and Algorithms using Python and BSCS2005 - Programming Concepts using Java