This course was aimed at lower division students looking to gain experience writing formal proofs, to ease their transition into their more advanced mathematical coursework.

Description

At the time that I taught this course, MUSA 74 covered roughly the following:

• Basic set theory (sets and their operations, functions, and relations)
• Basic propositional logic (formulae, quantifiers, equivalences)
• Induction (weak and strong induction on the naturals, the well-ordering principle)
• Cardinality (countability and uncountability, diagonalization)
• Basic real analysis (constructions of the real numbers, sequences, continuity)
• Basic group theory (symmetries, subgroups and quotient groups, homomorphisms)

A particular emphasis was placed on teaching students how to reason mathematically, and how to express their arguments as well-written proofs. A convenient side-effect of teaching a small class consisting of mostly freshmen and transfers was also that it offered an easy gateway into the math community at Berkeley for new students.

Background

I took MUSA 74 during my first semester at UC Berkeley in Fall 2019, and first became involved in MUSA when I later assisted in teaching the course during Spring 2020. I officially joined the course staff the following year. In addition to giving lectures, I also rewrote a handful of chapters of the course notes. The experience was a really good way to get to know my peers, and I was fortunate to met many of the people who would later become both mentors and mentees of mine through taking, assisting with, and finally teaching the class.

Legacy

MUSA 74 had been taught at Berkeley for years before me. Initially it was officially listed in the math department under the name Math 74, hence the somewhat arbitrary course code when later offered as a DeCal under MUSA’s banner. Since my tenure as one of its instructors, the course has again been adopted by the math department as an official course taught in Fall semesters; during the Spring it is still taught by MUSA as a DeCal.

Syllabus

The course syllabus can be found here.