MA1003 · Foundation · 4 credits

Mathematics for Data Science II

Vectors, matrices and multivariable calculus, building on the toolkit from MFDS I.

Instructor Prof. Sarang S Sane Term Every term Prereq MA1001

§ 1Calendar

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

§ 2Previous Year Questions

§ 3Resources

Course material10

Notes3

Practice9

Books1

TA resources2

Revision guides3

MA1003 · Foundation · 4 credits

Syllabus

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

§ 1Course Description

This course introduces the fundamental concepts of linear algebra, calculus, and optimization with an emphasis on their applications in machine learning and data science.

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

§ 2Faculty

  • Prof. Sarang S Sane, Department of Mathematics, IIT Madras

§ 3Week-by-week

Week 1: Vectors and matrices; Systems of linear equations; Determinants (Part 1 and 2).

Week 2: Solving linear equations - determinants (Part 3), Cramer's rule, invertible coefficient matrices; Echelon form, row reduction, Gaussian elimination.

Week 3: Vector spaces - introduction, properties; Linear dependence and independence.

Week 4: Basis and dimension - definition, computation of bases; Rank and dimension via Gaussian elimination.

Week 5: Rank and nullity of a matrix; Linear transformations - null space (basis and nullity); Linear mappings and transformations.

Week 6: Linear transformation - matrix representations with ordered bases; Image and kernel; Computation of bases for image and kernel.

Week 7: Equivalent and similar matrices; Affine subspaces and mappings; Inner products, norms, lengths, and angles.

Week 8: Orthogonality and orthonormality; Projections; Gram-Schmidt method; Orthogonal transformations and rotations.

Week 9: Multivariate functions - visualisation; Partial and directorial derivatives; Limits and continuity; Gradient interpretation.

Week 10: Optimization concepts - steepest ascent/descent: Tangent lines and tangent hyperplanes; Critical points.

Week 11: Higher-order partial derivatives; Hessian Matrix; Local extrema in two and three variables; Differentiability of multivariable functions; Review of 'Mathematics for Data Science II'.