Learning to learn STEM courses

Anonymous

Abstract: We curate a new dataset from MIT EECS (Course 6), Physics (Course 8), Economics (Course 14), Mathematics (Course 18), Harvard Statistics, and Columbia Computer Science course questions, transform them into programming tasks using OpenAI Codex, and solve them by executing programs. We curate, transform, and solve ten courses: (i) MIT EECS 6.003 Signal Processing, (ii) MIT EECS 6.036 Introduction to Machine Learning, (iii) MIT EECS 6.042 Mathematics for Computer Science, (iv) MIT Physics 8.282 Introduction to Astronomy, (v) MIT Economics 14.01 Principles of Microeconomics, (vi) MIT Mathematics 18.05 Introduction to Probability and Statistics, (vii) MIT Mathematics 18.06 Linear Algebra, (viii) MIT Mathematics 18.781 Theory of Numbers, (ix) Harvard Statistics STATS110 Probability, and (x) Columbia University COMS3251 Computational Linear Algebra. Our approach works surprisingly well since question solutions and programs share an underlying tree representation. We are able to use Codex to correctly solve all questions by specifying both question and programming contexts such as which mathematical rules to use or which programming packages to load. In addition to generating code which solves problems the resulting code generates plots which are useful for understanding the solutions. We interactively transform the original course questions until they are solved correctly and measure the similarity between the original and transformed questions. Finally, we automatically generate novel questions for each course, providing a way to rapidly synthesize new course content. Our approach is the first scalable solution towards automatically learning to learn all university STEM courses by machine.