Wolfram Computation Meets Knowledge

Wolfram Summer School


Silas Grossberndt

Science and Technology

Class of 2019


Silas Grossberndt is a patent examiner for Artifical Intelligence applications at the United States Patent and Trademark Office. Silas received a bachelor’s in math and physics from Columbia University in the city of New York in February of 2018, and, in January to April of that year, he worked at CERN as a researcher, investigating the effect of ionizing radiation on next-gen trackers for ATLAS and helping to improve performance of ROOT version 7. Further, Silas has been involved with the search for the Higgs boson in the Z-gamma channel, the search for heavy vector triplets in the Higgs-Z/W channels and the construction of the milli-qan dark fermion detector for CMS. Silas has also performed research into the structure of the X(3872) tetra-quark and the higher twist corrections to large Nc structure functions of Deep Inelastic Scattering procedures. Silas is currently applying to PhD programs in particle and nuclear physics.

Computational Essay: The Music of the (Point-Like) Spheres

Project: Math Autograder for Variety of Student Levels


Today, with the rise of online courseware and self-learning, more and more students are being tested and graded by completely automated systems. This, unfortunately, has its drawbacks, as the questions are often multiple choice, allowing the student to rely on guessing, or require the entering of exact input, penalizing students for correct answers that are written in non-identical but equivalent forms. One wants to create a system that can verify if the student has submitted an answer that is correct, not only checking for the answer but instead checking equivalent forms. Each equivalence class must have an associated level and derive its definition from those that may be garnered using mathematics taught by that point.

Summary of Results

In this project I have:

  1. Prepared and trained a Markov classifier that can read a mathematics question in algebra I, algebra II or calculus and establish which of the three it is with 93% accuracy.
  2. Built and tested an engine containing all the necessary parts of a mathematics autograder on these subjects.
  3. Integrated these two together into a single application that provides a robust and scalable backend system to be implemented in a GUI.

Future Work

Further work could encompass the addition of further levels of question, the use of graphical data as a selected answer or the inclusion of a retraining function in the neural net to improve classification accuracy, as well as the integration of the data into two GUIs. One has the student submit an answer to a randomly selected question from a database that has been built using Wolfram Problem Generator. The student may select one of the three levels, receive a question, submit an answer and check that it is correct. After the correct answer has been submitted, the system automatically pulls a new question from the list in the selected type. The second allows for the teacher to create a quiz and store it as a new database, which will then be fed to the first exemplar.