$$ \newcommand{\cis}{\operatorname{cis}} \newcommand{\norm}[1]{\left\|#1\right\|} \newcommand{\paren}[1]{\left(#1\right)} \newcommand{\sq}[1]{\left[#1\right]} \newcommand{\abs}[1]{\left\lvert#1\right\rvert} \newcommand{\set}[1]{\left\{#1\right\}} \newcommand{\ang}[1]{\left\langle#1\right\rangle} \newcommand{\floor}[1]{\left\lfloor#1\right\rfloor} \newcommand{\ceil}[1]{\left\lceil#1\right\rceil} \newcommand{\C}{\mathbb{C}} \newcommand{\D}{\mathbb{D}} \newcommand{\R}{\mathbb{R}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\N}{\mathbb{N}} \newcommand{\F}{\mathbb{F}} \newcommand{\T}{\mathbb{T}} \renewcommand{\S}{\mathbb{S}} \newcommand{\intr}{{\large\circ}} \newcommand{\limni}[1][n]{\lim_{#1\to\infty}} \renewcommand{\Re}{\operatorname{Re}} \renewcommand{\Im}{\operatorname{Im}} \newcommand{\cA}{\mathcal{A}} \newcommand{\cB}{\mathcal{B}} \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\cE}{\mathcal{E}} \newcommand{\cF}{\mathcal{F}} \newcommand{\cG}{\mathcal{G}} \newcommand{\cH}{\mathcal{H}} \newcommand{\cI}{\mathcal{I}} \newcommand{\cJ}{\mathcal{J}} \newcommand{\cK}{\mathcal{K}} \newcommand{\cL}{\mathcal{L}} \newcommand{\cM}{\mathcal{M}} \newcommand{\cN}{\mathcal{N}} \newcommand{\cO}{\mathcal{O}} \newcommand{\cP}{\mathcal{P}} \newcommand{\cQ}{\mathcal{Q}} \newcommand{\cR}{\mathcal{R}} \newcommand{\cS}{\mathcal{S}} \newcommand{\cT}{\mathcal{T}} \newcommand{\cU}{\mathcal{U}} \newcommand{\cV}{\mathcal{V}} \newcommand{\cW}{\mathcal{W}} \newcommand{\cX}{\mathcal{X}} \newcommand{\cY}{\mathcal{Y}} \newcommand{\cZ}{\mathcal{Z}} \newcommand{\bA}{\mathbb{A}} \newcommand{\bB}{\mathbb{B}} \newcommand{\bC}{\mathbb{C}} \newcommand{\bD}{\mathbb{D}} \newcommand{\bE}{\mathbb{E}} \newcommand{\bF}{\mathbb{F}} \newcommand{\bG}{\mathbb{G}} \newcommand{\bH}{\mathbb{H}} \newcommand{\bI}{\mathbb{I}} \newcommand{\bJ}{\mathbb{J}} \newcommand{\bK}{\mathbb{K}} \newcommand{\bL}{\mathbb{L}} \newcommand{\bM}{\mathbb{M}} \newcommand{\bN}{\mathbb{N}} \newcommand{\bO}{\mathbb{O}} \newcommand{\bP}{\mathbb{P}} \newcommand{\bQ}{\mathbb{Q}} \newcommand{\bR}{\mathbb{R}} \newcommand{\bS}{\mathbb{S}} \newcommand{\bT}{\mathbb{T}} \newcommand{\bU}{\mathbb{U}} \newcommand{\bV}{\mathbb{V}} \newcommand{\bW}{\mathbb{W}} \newcommand{\bX}{\mathbb{X}} \newcommand{\bY}{\mathbb{Y}} \newcommand{\bZ}{\mathbb{Z}} $$

Useful links

Office hours (Evans 851)

  • Mondays 13:30-14:30
  • Thursdays 13:00-15:00

Email

GSI:

Nima Moini (Evans 1010)
  • Mondays 8:00-12:00
  • Tuesdays 9:00-12:00
  • Wednesdays 9:00-11:00

Exams

Math 104 - Introduction to Analysis

Course Schedule

Below is an approximate schedule of topics to be covered in the course. Topics may have been covered before or after the dates listed, but it is mostly accurate.

Week ofTopicsRudin sections
Aug 26Ordered sets, fields1.1-1.3
Sep 2$\R$, the Archimedean Property, density of $\Q$, existence of roots1.4
Sep 9Metric spaces, open and closed sets, compact sets2.2, 2.3
Sep 16Compact sets, compact subsets of $\R^n$2.3
Sep 23Compact sets, sequences, convergence2.3, 3.1
Sep 30Properties of limits; review; midterm 13.1
Oct 7Subsequences; lack of electricity3.2
Oct 14Cauchy sequences, completions, limits of functions3.3, *, 4.1
Oct 21Limits of functions, continuous functions4.1-4.3
Oct 28Uniform continuity, connected sets; lack of electricity4.3, 4.4
Nov 4Limits and infinity, directional limits, derivatives; midterm 24.5, 4.7, 5.1
Nov 11Derivatives, local extrema, mean value theorem5.1, 5.2
Nov 18Riemann sums, integrals, the Fundamental Theorem of Calculus6.1-6.3
Nov 25Sequences of functions; Thanksgiving7.1, 7.2
Dec 2Uniform convergence, the Stone-Weierstrass Theorem7.3, 7.4, 7.7
Dec 9RRR Week
Dec 16Exam Week

Last updated: February 24, 2025.