This course intends to provide mathematics preparation for new PhD students.

The materials are based on

• 1. A First Course in Optimization Theory by Rangarajan Sundaram and
• 2. Note on Introductory Point-set Topology by Allen Hatcher.

Lecture 1 (February 2020) -- Lecture 1. Logic and Set Theory 1

Lecture 2 (February 2020) -- Lecture 2. Logic and Set Theory 2

Lecture 3 (February 2020) -- Lecture 3. Topology and Metric Spaces 1

Lecture 4 (February 2020) -- Lecture 4. Topology and Metric Spaces 2

Lecture 5 (February 2020) -- Lecture 5. Linear Algebra

Lecture 6 (February 2020) -- Lecture 6. Functions

Lecture 7 (March 2020) -- Lecture 7. Convexity

Lecture 8 (March 2020) -- Lecture 8. Optimization 1

Lecture 9 (March 2020) -- Lecture 9. Optimization 2

Lecture 10 (March 2020) -- Lecture 10. Stationary Equilibrium