Siyu Heng

Siyu Heng
  • AMCS PhD Student

Contact Information

  • office Address:

    433 Jon M. Huntsman Hall,
    3730 Walnut Street,
    Philadelphia, PA 19104


Past Courses


    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.


    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.


    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.


    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.


What Contributes Most to Consumer Financial Distress?

New research coauthored by Wharton’s Benjamin Keys looks at the roles geographic location and individual characteristics play in the financial struggles of consumers.

Knowledge @ Wharton - 2020/04/10
When Will the Jobs Return?

Industries such as leisure and hospitality might bounce back sooner than others, but lower demand suggests more layoffs could be on the way, say experts at Wharton.

Knowledge @ Wharton - 2020/04/7
What the COVID-19 Curve Can Teach Us about Climate Change

Much like flattening the curve on COVID-19, the world must act now to lessen the cumulative effects of climate change, says Wharton’s Howard Kunreuther.

Knowledge @ Wharton - 2020/04/7