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--- math104-s21:s:divi [2021/05/08 03:38]
67.188.175.218 [Jan 26]
+++ math104-s21:s:divi [2026/02/21 14:41] (current)
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-**Divi Schmidt**
+====== 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.
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-Notes: {{ :math104:s:divi:jan19.pdf |}}
+Notes: {{ math104-s21:s:divi:jan19.pdf |}}
 ====== Jan 21 ======
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-Notes: {{ :math104:s:divi:jan21.pdf |}}
+Notes: {{ math104-s21:s:divi:jan21.pdf |}}
 ====== Jan 26 ======
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-Notes: {{ :math104:s:divi:jan26.pdf |}}
+Notes: {{ math104-s21:s:divi:jan26.pdf |}}
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 ====== 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 ======
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 ====== April 6 ======
-Notes: {{ :math104:s:divi:april6.pdf |}}
+Notes: {{ math104-s21:s:divi:april6.pdf |}}
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+====== Questions ======
+  - What are the differences between max and limsup?
+  -

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