Lecture Notes

Hi! I am a second year student intending to major in Math and Physics. I have taken Math 53, Math 55, and Physics 89 (like Math 54), but this is the first semester in which I am taking an upper division math class. I am currently taking Physics 5C, Physics 5CL, Math 104, Math 110, and Math 113.

My Homework 1 can be found here.

My Homework 2 can be found here.

My Homework 3 can be found here.

Jan 18th We learned about the structure of the course and talked about $\N, \Z$, and $\Q$.

My exercises for lecture 1 can be found here. Note: Here I did Ross 1.11 in place of Ross 1.12 by accident. Ross 1.12 can be found in Homework 1, alternatively.

Jan 20th Today we finished up with rational numbers by talking about the Rational Zeroes Theorem. We then discussed real numbers, the Archimedean Principle, and $\R$'s completeness. We then begun discussing sequences and convergence.

My exercises for lecture 2 can be found here.

Jan 25th We used the definition of a limit of a sequence to prove some properties about sequences and their limits.

My exercises for lecture 3 can be found here. I added Exercise 8.9 from Ross to the exercises from lecture since the results from Exercise 8.9 are used to solve 9.12 ©.

Jan 27th We discussed properties of monotone sequences and defined limsup and liminf in the context of sequences.

My exercises for lecture 4 can be found here.

Feb 1st We discussed the properties of Cauchy sequences and introduced the notion of subsequences and subsequential limits and some of their properties.