MA1001 · Foundation · 4 credits

Mathematics for Data Science I

Sets, functions, straight lines, matrices, permutations, and a first taste of calculus — the mathematical vocabulary every later course will assume you already speak.

Instructor Prof. Neelesh Upadhye, Prof. Madhavan Mukund & Prof. Sarang S Sane Term Every term Prereq class XII maths

§ 1Calendar

  • Quiz 1—
  • Quiz 2—
  • End-term examination—

§ 2Previous Year Questions

§ 3Resources

Course material9

Notes5

Practice6

Weekly slides3

Books1

TA resources4

MA1001 · Foundation · 4 credits

Syllabus

The official course syllabus, transcribed from the IITM BS Data Science & Applications course booklet.

§ 1Course Description

This course introduces functions - including Linear, Quadratic, Polynomial, Exponential, and Logarithmic - along with Single-Variable Calculus and foundational Discrete Mathematics, including Graph Theory, through numerous examples. This course shall develop the ability to model real-world situations using abstract mathematical structures.

Lectures-Tutorials-Practicals-Credits: 4-0-0-4

§ 2Faculty

  • Prof. Neelesh Upadhye, Department of Mathematics, IIT Madras
  • Prof. Madhavan Mukund, Director, Chennai Mathematical Institute
  • Prof. Sarang S Sane, Department of Mathematics, IIT Madras

§ 3Week-by-week

Week 1: Set theory - number systems, sets and their operations; Relations & functions and their types.

Week 2: Rectangular coordinate system, straight lines - slope, parallel and perpendicular lines, representations, general equations, and straight-line fitting.

Week 3: Quadratic functions - properties, minima, maxima, vertex, and slope; Quadratic Equations.

Week 4: Polynomial algebra - basic arithmetic operations and algorithms; Polynomial graphs - x-intercepts, multiplicities, end behavior, and turning points; Graphing and polynomial construction.

Week 5: Functions - horizontal and vertical line tests; Exponential, composite, and inverse functions.

Week 6: Logarithmic functions - properties, graphs; Exponential and logarithmic equations.

Week 7: Sequence and limits; Function of one variable - graphs and tangents; Limits for sequences and functions; Continuity.

Week 8: Derivatives and critical points - differentiability; Computing derivatives and L'Hôpital's rule - tangents and linear approximation; Local maxima and minima.

Week 9: Integrals of functions of one variable - computing areas (including area under a curve); Relationship between derivatives and integrals.

Week 10: Graph theory - graph representation; Breadth-first search, Depth-first search and their applications; Directed acyclic graphs; Complexity analysis; Topological sorting.

Week 11: Graph Algorithms - longest path, transitive closure, matrix multiplication; Shortest paths (single source and all-pairs); Dijkstra's, Bellman-Ford, and Floyd-Warshall algorithm; Minimum cost spanning trees; Prim's and Kruskal's algorithm

Week 12: Revision