TEW - Linear Algebra, Real Analysis & Group Theory (2023)

Speakers and Syllabus

Name of the Speaker with affiliation	No. of Lectures	Detailed Syllabus
Prof. Anuradha Garge University of Mumbai		Group Theory: Polya Theory and Matrix Decompositions Symmetry group & group actions. Burnside’s Lemma and applications Polya’s theorem and applications to counting. Key lemma and applications in other disciplines. Matrix decompositions: Polar, Cartan, etc
Prof. Harsha Hutridurga IIT Bombay		Real Analysis: From real numbers to functions Sequences and series of real numbers Continuity and Differentiability of real-valued functions of a real variable Convergence of sequences and series of functions, power series Analysis in action: some applications to differential equation
Rekha Santhanam IIT Bombay		Linear Algebra: Matrices and Linear Transformations Correspondence between matrices and linear transformations between finite dimensional vector spaces, behaviour under various matrix operations. Matrix of a transformation: when is it “nice”? Consequence of change of bases. Polynomials satisfied by a transformation, minimal, characteristic polynomials. Diagonalizability and Jordan-Canonical form.

Prerequisites:

The participants are expected to be familiar with the content covered in the following:

Name of the tutors:

Full forms for the abbreviations of speakers and tutors:

Speakers:
1. Prof. Anuradha Garge (AG)
2. Prof. Harsha Hutridugra (HH)
3. Prof. Rekha Santhanam (RS)

Tutors:
1. Arusha C. (AC)
2. Omkar Javadekar (OJ)
3. Priyanka Aroda (PA)

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