Siyu Heng

• AMCS PhD Student

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.

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 - ADV APPLIED 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 probabilist's lexicon (random variables, independence, etc.). We will then study laws of large numbers, Central Limit Theorem, Poisson convergence and processes, conditional expectations, and martingales. Emphasis is on using these for probability modeling. Application areas include genetics, linguistics, machine learning, agent-based models, statistical physics, and hidden Markov models.

• 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. This course may be taken concurrently with the prerequisite with instructor permission.

• 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

How to Increase Interest in Government Benefits

Americans would be more likely to claim billions in untapped federal aid if they felt psychological ownership over those benefits, according to a new study from Wharton’s Wendy De La Rosa.

Knowledge @ Wharton - 9/14/2021
The Fed, Inflation and Interest Rates: What’s Ahead?

Federal Reserve Chairman Jerome Powell sent “three significant messages” on the U.S. economic outlook in his address last month in Jackson Hole, Wyoming, according to Wharton’s Christina Parajon Skinner.

Knowledge @ Wharton - 9/14/2021
Confronting Ethical and Moral Dilemmas: Don’t Go It Alone

In this Nano Tool for Leaders, Wharton’s G. Richard Shell explains how “the power of two” can help when you are faced with a moral or ethical dilemma at work.

Knowledge @ Wharton - 9/14/2021