Wharton PhD Math Camp - Summer 2024

2024 Math Camp Syllabus 

 

Instructor: 
Xufei Liu
Office: JMHH 533.6
Email: xufei@wharton.upenn.edu

 

Office Hours: 
By appointment

 

Class Time: 
8/02/2024 - 8/23/2024, MWF, 1:30PM - 3:00PM

 

Session Format: 
The classes will be held in person at JMHH F45.

 

Final Exam:
Friday, August 23, 2024
Time: 1:30PM - 3:00PM

 

Suggested Textbook:
Sundaram, R., A First Course in Optimization Theory, Cambridge University Press, 1996.

 

Course Description:
Wharton’s Summer Math Camp covers the basic principles of mathematical analysis, optimization theory and probability theory. The course is meant to introduce the necessary mathematical tools that are needed for a successful completion of the core courses in economics, operations and statistics. The course will cover the first four chapters (plus some materials in the Appendix) in Sundaram’s book as well as materials on probability theory from handouts. The course is also the first part of a two-course sequence. The second part, OIDD 912, will be offered as a regular mini-course during the first quarter of the Fall semester.

 

Prerequisites:
Students are assumed to be familiar with univariate and multivariate calculus. Experience with proofs in mathematics is highly recommended. Exposure to linear algebra is useful yet not required.

 

Course Topics:

• Elements of Analysis

          – Real Number System

          – Metric Spaces

          – Numerical Sequences in Rⁿ

          – Basic Topology

          – Continuity and Differentiation

          – Gradients and Higher Order Derivatives

          – Intermediate and Mean Value Theorems

• Elements of linear algebra

          – Matrices

          – Quadratic Forms

• Optimization Problems in Rⁿ and their Formulation
• Weierstrass Theorem
• Unconstrained Optimization: First and Second-Order Conditions
• Elements of Probability Theory

          – Random Variables

          – Expected Values

          – Conditional Expectation

          – Stochastic Processes

 

Grading Policies:

Course grade is calculated based on the final exam. Students will not receive a letter grade and the course record will not appear on their transcripts. However, individual scores will be notified to each student and to his/her Ph.D. Program Coordinator.

 

Exam Date:

• There will be one final exam on Friday, August 23, 2024.  It will cover everything that is discussed in lectures (definitions, theorems, proofs,...).