Siyu Heng

Siyu Heng
  • PhD Student

Contact Information

  • office Address:

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

Teaching

Past Courses

  • 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.

  • STAT930 - PROBABILITY

    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

Dwindling Brexit Options: What’s the Path Ahead?

A no-deal Brexit has investors rattled, because it could disrupt supply chains and cause economic and political chaos, warn experts.

Knowledge @ Wharton - 2019/01/17
Farewell, John Bogle: A Tribute to the Father of Indexing

John Bogle, the plain-spoken founder of mutual fund giant Vanguard, passed away this week at age 89.

Knowledge @ Wharton - 2019/01/17
Why Social Media Is the New Weapon in Modern Warfare

Authors Peter Singer and Emerson Brooking explain how social media has emerged as a surprising -- and effective -- tool in modern warfare, in their new book.

Knowledge @ Wharton - 2019/01/17