2021 Math Camp Syllabus
Office: JMHH 533.1
8/06/2021 - 8/25/2021, MWF, 1:30PM - 3:00PM
The classes will be held over Zoom. Sessions will be recorded for the students who are unable to attend.
Friday, August 27, 2021
Time: 1:30PM - 3:00PM
Sundaram, R., A First Course in Optimization Theory, Cambridge University Press, 1996.
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.
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.
- Elements of Analysis
– Real Number System
– Metric Spaces
– Numerical Sequences in Rn
– Basic Topology
– Continuity and Differentiation
– Gradients and Higher Order Derivatives
– Separation Theorems
– Intermediate and Mean Value Theorems
– Inverse Function Theorem
– Envelope and Implicit Function Theorems
- Elements of linear algebra
– 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
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.
- There will be one final exam on Friday, August 27, 2021. It will cover everything that is discussed in lectures (definitions, theorems, proofs,...).
The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.
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