2024-Spring ST: Brownian motion and Stochastic (MATH719A-01) The course syllabus

1.Course Information

Course No. MATH719A Section 01 Credit 3.00
Category Major elective Course Type Classroom Course prerequisites
Postechian Core Competence
Hours MON, WED / 11:00 ~ 12:15 / MathBldg[206]Lecture Room Grading Scale G

2. Instructor Information

Kim Kunwoo Name Kim Kunwoo Department Dept. of Mathematics
Email address kunwoo@postech.ac.kr Homepage https://sites.google.com/view/kunwookim
Office Office Phone 054-279-2327
Office Hours

3. Course Objectives

In this course, we will learn about various interesting mathematical theories related to Brownian motion, as well as foundational elements of stochastic calculus like stochastic integrals and stochastic differential equations.

4. Prerequisites & require

Prerequisite (Recommended): MATH 531 Probability Theory and MATH 514 Real analysis (or equivalent courses taken or having equivalent knowledge)

5. Grading

TBA

6. Course Materials

Title Author Publisher Publication
Year/Edition		 ISBN

7. Course References

Brownian Motion, Martingales, and Stochastic Calculus – Jean Francois Le Gall
Brownian motion and stochastic calculus – Ioannis Karatzas and Steven E. Shreve
Continuous martingales and Brownian motion – Daniel Revue and Marc Yor
Stochastic differential equations - Bernt Øksendal
Analysis of Stochastic Partial Differential Equations – Davar Khoshnevisan

8. Course Plan

In this course, we aim to cover the following topics in order:
● Gaussian processes and Brownian motion
● Continuous time martingale and semi-martingale
● Stochastic integration and Ito formula
● Brownian motion and partial differential equations
● Stochastic differential equations
● Application to mathematical finance
● Basics of stochastic partial differential equations (if time permits)

9. Course Operation

Lecture and discussion

10. How to Teach & Remark

11. Supports for Students with a Disability

- Taking Course: interpreting services (for hearing impairment), Mobility and preferential seating assistances (for developmental disability), Note taking(for all kinds of disabilities) and etc.

- Taking Exam: Extended exam period (for all kinds of disabilities, if needed), Magnified exam papers (for sight disability), and etc.

- Please contact Center for Students with Disabilities (279-2434) for additional assistance

Copy The course syllabus
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