https://courses.pzhou.org/ 2026-04-17T10:04:31+00:00 https://courses.pzhou.org/ https://courses.pzhou.org/lib/tpl/dokuwiki/images/favicon.ico text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:ahwang&rev=1771684873&do=diff Anya Hwang Personal Notes Collection of lecture notes focusing on theorems. Questions and answers to HWs, Midterms, Textbook text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:anon&rev=1771684873&do=diff Question List: text/html 2026-02-21T14:41:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:antonthan&rev=1771684872&do=diff Anton's Notebook Posting list of questions and practice final solution sketches here. Will add as time goes on. Practice Final Solution Sketches Problems from <https://ywfan-math.github.io/104s21_final_practice.pdf>. Solutions here vary in how detailed they are; they could be full solutions or only guiding steps. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:carsonl&rev=1771684873&do=diff Carson's Review Notes This page is for my notes and the course material as I understand it, although it may contain some errors as it remains a constant work in progress. There are also questions after the notes to help improve my understanding. Notes text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:darembardales&rev=1771684873&do=diff Welcome to Math104 Real Analysis Study Guide This page is edited by Darem Bardales Page Contents * Chapter 1:Introduction * Natural,Rational and Real Number Sets * Rational Zeros Theorem * The Completeness Axiom * Chapter 2:Sequences * Limits of Sequences * Limit Theorems for Sequences * Monotone Sequences and Cauchy Sequences * Subsequences * * Chapter 3:Continuity * Chapter 4:Sequences and Series of Functions * Chapter 5:Differentiation * Mean Value Theorems … text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:dingchengyang&rev=1771684873&do=diff I have kept most of my notes handwritten throughout the semester. Instead of taking tons of photos of my handwritten notes, I will pick some of the important concepts and theorems to put on this website so that I can review the final in a more efficient way. Feel free to comment on my website:) text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:divi&rev=1771684873&do=diff Divi Schmidt The following notes are organized by lecture date. The notes from lecture are handwritten on my iPad and vary in format depending on the content of the lecture. I include questions underneath the relevant lecture notes. Additionally, there is a short summary for each lecture that includes my thoughts on the content and discusses the content in perspective of the entire course. text/html 2026-02-21T14:41:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:edwardhe&rev=1771684872&do=diff Edward He's Notes and Questions Key theorems from Ross: * Midterm 1 * Midterm 2 Questions: 1. HW11 question 5 (bonus) It seems like this would effectively be the same as an integral, but instead of summing the areas of increasingly thin rectangles, you're summing the areas of increasingly small squares. Is there a reason that they're not equal? Here's my visual interpretation: text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:franceskim&rev=1771684873&do=diff Questions + Notes Lecture 1 1. Why is |sin(nx)| <= n|sin(nx)| ∀ n ∈ N, ∀ x ∈ R? A) If r = c/d ∈ Q is a rational number and r satisfies the equation c_n*x^2 + c_(n-1)*x^(n-1) + ... + c_0 = 0 w/ c_i ∈ Z, c_n ≠ 0, c_0 ≠ 0: d | c_n, c | c_0 (i.e. factors of constant/factors of leading coefficient is a solution to the equation) text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:genevievebrooks&rev=1771684873&do=diff 1. Review Ross Ch.1 Introduction - We defined the set of natural numbers and explored its successor property: if $n$ $\epsilon$ $\mathbb{N}$ then $n+1$ also in $\mathbb{N}$. - We defined Induction, a method which is used to prove an infinite number of successive propositions. Induction always begins by defining a base case. If some proposition holds for this base case then one may assume the proposition hold for all $n$ and then prove that it must then hold true for $n+1$. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:jodiejepson&rev=1771684873&do=diff Hello! Use the link to see my review notes and 50 questions and answers: <https://www.overleaf.com/read/pkyjwwtwwbtb> text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:johndufek&rev=1771684873&do=diff Review Limit Proofs of Sequences . A very helpful technique for proving the limit of some sequence where it is really hard to isolate n can be the following: Example: say you want to prove the limit of $\frac{4n^3 + 3n}{n^3 - 6} => \frac{3n+24}{n^3 - 6} = 4 $ . It would be hard to isolate $n$ to find such an $N > 0$. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:kaylenestocking&rev=1771684873&do=diff Kaylene tries analysis Course notes For my notes I followed the philosophy that you don't understand something unless you can explain it to others, and set out to describe my intuition for all the major concepts we covered intuitively. You can find them text/html 2026-02-21T14:41:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:kelvinlee&rev=1771684872&do=diff Kelvin Lee Personal Notes Here is the link to my personal course notes for this class. Notes (They might contain typos or logical errors.) They are created based on Ross's, Rudin's textbooks and Professor Zhou's lectures. Questions 1. What's the difference between continuity and uniform continuity ? text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:lylekahney&rev=1771684873&do=diff Questions: (In reverse order) 1)What is the function dα? 2)Why are you allowed to change the variable of integration? 3)Is α a function? 4)Is there a way to show integration is the reverse of differentiation? 5)What is a weight function? text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:martinzhai&rev=1771684873&do=diff Martin Zhai's Review Note Content Summary Week 1 Lecture 1 (Jan 19) - Covered Ross Section 1.1, 1.2, 1.3 * Natural Numbers($\natnums$) $\{ 1, 2, 3, ... \}$ * Integers($\Z$) $\{..., -2, -1, 0, 1, 2, ... \}$ (an example of Ring structure) * text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:morganmakhina&rev=1771684873&do=diff Morgan's Real Analysis Review Page Number systems: 1-5) What are real numbers, anyway? Why do we need them? How can we rigorously define (ie, construct) them? What are some properties of $\R$ that other number systems don't have? And, by the way: what are some properties of $\N$ that we use in real analysis (perhaps sometimes taking them for granted)? text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:noahlee&rev=1771684873&do=diff Here is a link to some of my notes: <https://docs.google.com/document/d/1sm9K-J2u9mpIUNK1ezpGjBUMvhuftW70pHSIm4tUMTE/edit?usp=sharing> text/html 2026-02-21T14:41:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:oscarxu&rev=1771684872&do=diff Oscar Xu's review notes A brief review of key concepts in Math 104. The notes are organized in the order of chapters with respect to Professor Peng Zhou's lectures. 1: Introduction $\mathbb{Z}$: integers, has subtraction and zero. $\mathbb{Z}$ is an example of text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:owenyeung&rev=1771684873&do=diff Owen Yeung's Page Notes: <https://www.overleaf.com/read/nxhtfsdzrzfr> Questions: <https://www.overleaf.com/read/pqsfqpnvqvps> text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:rohandsouza&rev=1771684873&do=diff Rohan D'Souza Notes Notes Questions Finalizing latex file. will upload soon (sorry) text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:ryanpurpura&rev=1771684873&do=diff Ryan Purpura's Final Notes Questions can be found at the very bottom. Number systems $\mathbb{N}$ is the set of natural numbers $\{1, 2, 3, \dots\}$. Key properties of $\mathbb{N}$ are that $1 \in \mathbb{N}$ and $n \in \mathbb{N} \implies n + 1 \in \mathbb{N}$. This natually leads to the idea of mathematical induction, which allows us to prove statements for all $\mathbb{N}$. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:rylanbeal&rev=1771684873&do=diff Questions: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:ryotainagaki&rev=1771684873&do=diff Ryota Inagaki's Math 104 Webpage Here you will find review material for this semester's final. Topics of the class/Review Site will be organized as follows: 1. Sets and sequences. (Ch 1- 10 in Ross) 2. Subsequences, Limsup, Liminf. (Ch 10 - 12 in Ross) text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:start&rev=1771684873&do=diff Student Area This is a wiki style. You are free to create your page here, keep your note. Please respect each other's contents. You can think of a username (e.g. JohnDoe), and put this in the address line https://courses.wikinana.org/math104/s/JohnDoe text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:thomasdahlke&rev=1771684873&do=diff Thomas Dahlke Notes are organized by topic collected together with both Ross and Rudin. Thomas Dahlke Links to resources and rages I have found helpful: Youtube Channels: Wrath of Math: Large Real Analysis Playlist that goes over many definitions and proof explanations. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:tingyingyan&rev=1771684873&do=diff Notes: text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:victoriatuck&rev=1771684873&do=diff Victoria's Page Course Notes Sequences Limsup and Liminf Metrics and Topology Series Continuity Convergence Mean Value Theorem Taylor Expansions Differentiation Integration Questions 1. Question: $(-\sqrt{2}, \sqrt{2}) \cap \mathbb{Q}$ = $[-\sqrt{2}, \sqrt{2}] \cap \mathbb{Q}$ is both closed and open on $\mathbb{Q}$. However, for a given space E, Rudin Theorem 2.27 states that if $X$ is a metric space and $E \subset X$ then $E = \bar{E}$ if and only if E is closed. [$\bar{E} = E \cu… text/html 2026-02-21T14:41:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:vpak&rev=1771684872&do=diff vpak Hi welcome to my note page Summary of Material 1. Numbers, Sets, and Sequences Rational Zeros Theorem. For polynomials of the form cnxn + ... + c0 = 0 , where each coefficient is an integer, then the only rational solutions have the form $\frac{c}{d}$ where c divides c text/html 2026-02-21T14:41:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:xingjiantao&rev=1771684872&do=diff Xingjian Tao's Notes and Question List Notes I made notes of some Chapters on LaTex. You can see the PDF here . The organization of definitions and theorems is mainly based on Rudin, though supplemented by Ross. Sometimes I tried to rewrite the contents in a more symbolic way, so there maybe minor mistakes. text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:xinyuzhang&rev=1771684873&do=diff Xinyu Zhang's notebook Summary of Notes Questions text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:yichendai&rev=1771684873&do=diff Final Review: Contents before Midterm 1: <https://docs.google.com/document/d/1z3ai44MExf0F6VBgL14UAJhWpxlibryAnz0o7VRCo0U/edit?usp=sharing> Contents before Midterm 2: <https://docs.google.com/document/d/1wUgms-5QziIUSLckgVF1j0usMIT1WDyIL8g4drvz2vs/edit?usp=sharing> Questions: Some of the questions are covered in the review notes text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:zheyuanhu&rev=1771684873&do=diff Questions: * From the lecture on April 15th * * I cannot think of why $x^2$ is an example of f(x) ≠ P_x0(x) * I tried fixing $x_0 = 0$, so $P_0(x) = ∑ c_n \cdot (x)^n$, where $\alpha = lim sup |c_n|^{1/n} = 1$, so $R=1$ * Then $f(0.5) = 0.25 = P_0(0.5) = 0 + 0 + 1 * 0.5 ^ 2 + 0 + text/html 2026-02-21T14:41:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://courses.pzhou.org/doku.php?id=math104-s21:s:zoezhang&rev=1771684873&do=diff Zoe's Math 104 Page Notes: Hello! Below is the link to my personal notes for this class. They are written based on Professor Zhou's lecture notes, and Ross's and Rudin's textbooks. There are also some personal notations of mine to facilitate the understanding of certain theorems/concepts.