Transition to mathematical proofs, often shortened to Ma 0, is an online course designed to help incoming freshmen adjust to Caltech's rigorous math core curriculum.  The goal is to teach students how to express the mathematical ideas in their proofs eloquently but succinctly through detailed feedback on submissions. The course consists of eight "toy" modules in topics from real analysis, logic, complex analysis, and algebra. Each week students are provided with lecture notes for each of the modules along with a homework assignment catered to the module. Throughout, students are encouraged to reach out to TA's with any questions during weekly office hours and discuss among themselves on the forums. The content of the modules was mainly used as a medium for the proof writing, but it sometimes inspired curiosities from students, which I was more than happy to entertain. Below is a list with a link to the homework assignments and the intended solutions for each module. 

1.  

2.  

Logic

Set Theory

Functions

Real Sets

Complex Numbers

Induction

Peano Axioms

1. ​

​