Differences

This shows you the differences between two versions of the page.

--- math104-s21:s:divi [2021/05/09 04:12]
pzhou
+++ math104-s21:s:divi [2026/02/21 14:41] (current)
@@ Line 10: / Line 10: @@
-Notes: {{ :math104:s:divi:jan19.pdf |}}
+Notes: {{ math104-s21:s:divi:jan19.pdf |}}
 ====== Jan 21 ======
@@ Line 16: / Line 16: @@
-Notes: {{ :math104:s:divi:jan21.pdf |}}
+Notes: {{ math104-s21:s:divi:jan21.pdf |}}
 ====== Jan 26 ======
@@ Line 25: / Line 25: @@
-Notes: {{ :math104:s:divi:jan26.pdf |}}
+Notes: {{ math104-s21:s:divi:jan26.pdf |}}
@@ Line 32: / Line 32: @@
 ====== Jan 28 ======
+This one takes a bit.
+In the first part of this lecture, we go over how to do proofs using the definition of a limit. This takes a little bit to get used to when first learning, but soon becomes fairly straightforward and a lot of the concepts learned here can be applied to questions throughout the course.
+In the second part of the lecture, we introduce the idea of monotone sequences, which are very handy as they guarantee convergence and other useful properties. Then, we introduce the idea of limsup and liminf, concepts which seem very foreign at first but give a good introduction to thinking about sequence behavior at infinity. These become very important concepts throughout the course and its important to understand the nuances of these concepts (ex: the difference between limsup and max).
+Notes: {{ math104-s21:s:divi:jan_28.pdf |}}
 ====== Feb 2 ======
+Cauchy Sequences
+This lecture we focus on understanding one proof, or rather, 4 proofs as there are three properties which guarantee each other. A cauchy sequence, a convergent sequence, and limsup = liminf. There are quite a few nuances to these proofs, but we do notice some similar themes from the limit proofs in the previous lecture and those from the homework. Rewatching this lecture, these proofs are much easier to understand as I have a much stronger grasp of what these three properties mean.
-====== Feb 4 ======
-====== Feb 9 ======
+Notes: {{ math104-s21:s:divi:feb2.pdf |}}
+====== Feb 4 and Feb 9 ======
+Subsequences
+Just as we can guarantee properties of monotone sequences, once we introduce the idea of a subsequence, we can use these to guarantee new properties.
+Notes: {{ math104-s21:s:divi:feb4.pdf |}}
 ====== Feb 11 ======
+Notes:
 ====== Feb 16 ======
+Notes: {{ math104-s21:s:divi:feb16.pdf |}}
 ====== Feb 18 ======
+Notes:
 ====== Feb 23 ======
+Notes: {{ math104-s21:s:divi:feb23.pdf |}}
 ====== Feb 25 ======
+Notes:
 ====== Mar 2 ======
+Notes: {{ math104-s21:s:divi:mar2.pdf |}}
 ====== Mar 4 ======
 ====== Mar 9 ======
@@ Line 64: / Line 94: @@
 ====== April 6 ======
-Notes: {{ :math104:s:divi:april6.pdf |}}
+Notes: {{ math104-s21:s:divi:april6.pdf |}}
@@ Line 88: / Line 118: @@
+====== Questions ======
+  - What are the differences between max and limsup?
+  -

Lecture Notes

User Tools

Site Tools

Differences

Page Tools