# Siyu Heng • AMCS PhD Student

## Contact Information

433 Jon M. Huntsman Hall,
3730 Walnut Street,

## Past Courses

• ### MATH104 - CALCULUS I

Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylor's theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus.

• ### MATH509 - ADVANCED ANALYSIS

Continuation of Math 508. The Arzela-Ascoli theorem. Introduction to the topology of metric spaces with an emphasis on higher dimensional Euclidean spaces. The contraction mapping principle. Inverse and implicit function theorems. Rigorous treatment of higher dimensional differential calculus. Introduction to Fourier analysis and asymptotic methods.

• ### MATH546 - ADVANCED PROBABILITY

The required background is (1) enough math background to understand proof techniques in real analysis (closed sets, uniform covergence, fourier series, etc.) and (2) some exposure to probability theory at an intuitive level (a course at the level of Ross's probability text or some exposure to probability in a statistics class). After a summary of the necessary results from measure theory, we will learn the probabist's lexicon (random variables, independence, etc.). We will then develop the necessary techniques (Borel Cantelli lemmas, estimates on sums of independent random variables and truncation techniques) to prove the classical laws of large numbers. Next come Fourier techniques and the Central Limit Theorem, followed by combinatorial techniques and the study of random walks.

• ### STAT101 - INTRO BUSINESS STAT

Data summaries and descriptive statistics; introduction to a statistical computer package; Probability: distributions, expectation, variance, covariance, portfolios, central limit theorem; statistical inference of univariate data; Statistical inference for bivariate data: inference for intrinsically linear simple regression models. This course will have a business focus, but is not inappropriate for students in the college.

• ### STAT930 - PROBABILITY THEORY

Measure theory and foundations of Probability theory. Zero-one Laws. Probability inequalities. Weak and strong laws of large numbers. Central limit theorems and the use of characteristic functions. Rates of convergence. Introduction to Martingales and random walk.

## Knowledge@Wharton The Problem with Heroes

For any leader, the ongoing presence of heroes is both a cause for celebration and a reason for deep concern, because it indicates a failure of the wider system, writes Wharton’s Gregory P. Shea in this opinion piece.

Knowledge @ Wharton - 2020/05/29
The Politics of Pandemics: Why Some Countries Respond Better Than Others

Strong state capacity and low economic inequality are more important than being a democracy when it comes to dealing with health emergencies like pandemics, Wharton research shows.

Knowledge @ Wharton - 2020/05/26
Pulling Through the Pandemic: Advice for Entrepreneurs

Wharton’s Karl Ulrich offers guidance for entrepreneurs trying to make it to the other side of the coronavirus pandemic.

Knowledge @ Wharton - 2020/05/26