# Mathematics 341: Matrix Analysis and Positivity

## *2018 Spring semester:*
Apoorva Khare

**Course description:** This course explores matrix positivity and
operations that preserve it. These involve fundamental questions that have been
extensively studied over the past century, and are still being studied in the
mathematics literature, including with additional motivation from modern
applications to high-dimensional covariance estimation. The course will bring
together techniques from different areas: analysis, linear algebra,
combinatorics, and symmetric functions.

**Meetings:** Wed Fri 11am – 12:30pm, Mathematics Lecture Hall LH-3

**Midterm:** Friday February 23, in class.

**Pre-requisites:** A course in linear algebra, and a course in calculus/real
analysis.

**List of topics:** See this link (all but one or two sub-topics were discussed, though not in the order in the link).

**Course notes:** Click on this link for the course notes.

## *2017 Autumn semester:*
Apoorva Khare and Gadadhar Misra

- Mathematics 221 is a Core Course in real analysis, for the Integrated
Ph.D. program in IISc Mathematics.

This semester, we will closely follow Rudin's *Principles of
Mathematical Analysis*.

**Course handout:** Click on this
link.

**Homework assignments**

Homework 1
(due by Friday August 25, in TA's office hours or earlier in class)

Homework 2
(due by Friday September 8, in TA's office hours or earlier in class)

Homework 3
(due by Friday September 29, in TA's office hours or earlier in class)

Homework 4
(due by Tuesday October 24, in class)

Homework 5
(due by Tuesday November 7, in class)

Homework 6
(due by Friday November 17, in TA's office hours or earlier in class)

Homework 7
(due by Wednesday December 6, in Instructor's office hours by 4pm, or earlier in class)