Lecture Notes

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====== Danny Wu  ======
Hi! I'm a fourth year majoring in Economics and Data Science, and minoring in Statistics. I'm from the Bay Area and went to high school in Albany, the city right next to Berkeley. I enjoy cooking and eating food and recently got very interested in coffee making.

Beside Math 104, this semester I'm taking CS 189 (CDSS offering) and STAT 230A.  

==== Course Journal ====

=== Week 1 ===
  * Natural numbers, $\mathbb{N} = \{0, 1, 2, 3, ...\}$
  * Integers, $\mathbb{Z} = \{... -1, 0, 1, ...\}$
  * Rational Numbers, $\mathbb{Q} = \{\frac{m}{n} | m,n \in \mathbb{Z}, n \neq 0\}$
  * $\mathbb{Q}$ problematic because a bounded subset might not have a "most economical" upperbound in $\mathbb{Q}$
  * $\sqrt{2}$ is not a rational number because there exists no such $m, n \in \mathbb{Z}$ such that $\frac{m}{n} = \sqrt{2}$

=== Week 2 ===
{{ :math104-s22:s:dannywu:math104_homework1.pdf |Homework 1}}

=== Week 3 ===
{{ :math104-s22:s:dannywu:math104_homework2.pdf |Homework 2}}

=== Week 4 ===
{{ :math104-s22:s:dannywu:math104hw3.pdf |Homework 3}}

=== Week 5 ===
{{ :math104-s22:s:dannywu:math104_hw4.pdf |Homework 4}}

Questions: 
  - When we modify the rational numbers such that it appears like we are only accessing a certain part of them - why is it still able to get arbitrarily close to any real number? 
  - Since the rationals are infinite, when we consider all rational numbers of the form $n/3^k$ (from midterm s21), is it that there are infinite numbers in that form or are there infinite subsets of the rationals that you can create? More or less, is it like a infinite amount of fixed subsets, a finite amount of infinite subsets, or both? Kind of related to first question 
  - What are fast ways to see when to use root test, ratio test, and comparison test? 
  - How did they go from first line to second line in this proof (Ross Section 8 Example 6). {{:math104-s22:s:dannywu:wtf.jpg?400|}}
  - Lots of and rules use absolute values. For the most part I feel like I've been ignoring them and just treating the values as if there were no absolute values (such as the ratio test and root test). Why is this a bad habit and why should I pay more attention to the absolute values? 

=== Week 7 ===

{{ :math104-s22:s:dannywu:math104hw5.pdf |Homework 5}}
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