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| --- | ||
| title: "CS177-lecture-20220202" | ||
| # date: 2022-02-02T09:23:12-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["data exploration"] | ||
| --- | ||
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| ## Exploratory analysis cont. | ||
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| ### Representing data cont. | ||
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| ### Analyzing data | ||
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| ## Mining introduction | ||
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| ### Tasks | ||
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| - anomaly detection is relatively new | ||
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| ### Classification | ||
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| --- | ||
| title: "CS177-lecture-20220203" | ||
| # date: 2022-02-03T15:59:28-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["data exploration"] | ||
| --- | ||
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| ## Data exploration cont. | ||
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| ### Classification cont. | ||
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| ### Regression | ||
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| ### Clustering | ||
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| ### Association | ||
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| ### Deviation / anomaly / change detection | ||
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| ### Challenges | ||
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| - the concept of neural networks has been around for a long time, however only because of recent computational power has it become widely used | ||
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| ## What is data? | ||
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| --- | ||
| title: "CS191-lecture-20220202" | ||
| # date: 2022-02-02T17:27:32-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["agile"] | ||
| --- | ||
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| ## Agile development | ||
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| ### SCRUM | ||
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| ### git | ||
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| --- | ||
| title: "MATH102-lecture-20220201" | ||
| # date: 2022-02-01T08:56:23-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["divisibility"] | ||
| --- | ||
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| ## Divisibility cont. | ||
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| There are many ways to represent 24, but there is only 1 way to represent it as a product of primes. | ||
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| <blockquote class="book-hint warning"> | ||
| <em>Theorem.</em> | ||
| Whenever we add a number to itself, the sum will be even. | ||
| </blockquote> | ||
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| <blockquote class="book-hint"> | ||
| <em>Proof.</em> | ||
| Let first number be {{<k>}} k {{</k>}}, let the second number be {{<k>}} k {{</k>}}. | ||
| So if | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| k + k = 2k | ||
| \end{aligned} | ||
| {{</k>}} | ||
| and {{<k>}} 2 | 2k {{</k>}} | ||
| <p align="right"> | ||
| {{<k>}} \square {{</k>}} | ||
| </p> | ||
| </blockquote> | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| Prove that if {{<k>}} 10 | a {{</k>}} and {{<k>}} 10 | b {{</k>}}, then {{<k>}} 10 | ma \pm nb {{</k>}}, where {{<k>}} a, b, m, n \in \mathbb{Z} {{</k>}}. | ||
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| <blockquote class="book-hint"> | ||
| <em>Proof.</em> | ||
| {{<k>}} 10 | a {{</k>}} so {{<k>}} a = 10k_1 {{</k>}}, | ||
| {{<k>}} 10 | b {{</k>}} so {{<k>}} b = 10k_2 {{</k>}}, where {{<k>}} k_1, k_2 {{</k>}} are unknown {{<k>}} \in \mathbb{Z} {{</k>}}. | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| ma \pm nb &= m (10k_1) \pm n (10 k_2) \\ | ||
| &= 10(m k_1 \pm n k_2) | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| Note that {{<k>}} (m k_1 \pm n k_2) \in \mathbb{Z} {{</k>}}. | ||
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| <p align="right"> | ||
| {{<k>}} \square {{</k>}} | ||
| </p> | ||
| </blockquote> | ||
| </div> | ||
| </details> | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| {{<k>}} 7 \not | a {{</k>}} and {{<k>}} 7 \not | b {{</k>}}. | ||
| {{<k>}} a + b {{</k>}} may or may not be divisible by 7. | ||
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| For example: {{<k>}} 7 \not | 13 {{</k>}}, {{<k>}} 7 \not | 15 {{</k>}}, but {{<k>}} 7 | (13 + 15) {{</k>}}. | ||
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| For example: {{<k>}} 7 \not | 15 {{</k>}}, {{<k>}} 7 \not | 16 {{</k>}}, and {{<k>}} 7 \not | (15 + 16) {{</k>}}. | ||
| </div> | ||
| </details> | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| If {{<k>}} 7 | a {{</k>}} and {{<k>}} 7 \not | b {{</k>}}, then it is certainly the case | ||
| that {{<k>}} 7 \not | a + b {{</k>}}. | ||
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| <blockquote class="book-hint"> | ||
| <em>Proof.</em> | ||
| {{<k>}} 7 | a {{</k>}} so {{<k>}} \frac{a}{7} {{</k>}} is a whole number. | ||
| {{<k>}} 7 \not | b {{</k>}} so {{<k>}} \frac{b}{7} {{</k>}} is not a whole number. | ||
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| So {{<k>}} \frac{a}{7} + \frac{b}{7} {{</k>}} is not whole. | ||
| Therefore, {{<k>}} \frac{a + b}{7} {{</k>}} is not a whole number. | ||
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| So, by statement 5: {{<k>}} 7 \not | a + b {{</k>}}. | ||
| <p align="right"> | ||
| {{<k>}} \square {{</k>}} | ||
| </p> | ||
| </blockquote> | ||
| </div> | ||
| </details> | ||
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| ### Nmemonics for divisibility | ||
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| So, based on the examples above: | ||
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| 1. IS + IS = IS | ||
| 2. IS + IS NOT = IS NOT | ||
| 3. IS NOT + IS NOT = IS or IS NOT | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| 7^3 \cdot 19^{24} \not = 5^2 \cdot 11^{30} | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| By the fundamental theory of arithmetic, each number only has 1 pf, therefore these number cannot equal each other. | ||
| </div> | ||
| </details> | ||
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| Can {{<k>}} 2^6 | 2^5{{</k>}}? | ||
| No, because {{<k>}} \frac{2^5}{2^6} = \frac{1}{2} {{</k>}}, which is not a whole number. | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| Prove that {{<k>}} 5^3 {{</k>}} cannot divide {{<k>}} 3^2 \cdot 5^2 \cdot 11^3 {{</k>}}. | ||
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| <blockquote class="book-hint"> | ||
| <em>Proof.</em> | ||
| Numbers that are divisible by {{<k>}} 5^3 {{</k>}} are of the form {{<k>}} 5^3k {{</k>}}. | ||
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| There are two cases: | ||
| 1. {{<k>}} k {{</k>}} contains a power of 5, therefore the power of {{<k>}} 5^3k {{</k>}} will be greater than 3. | ||
| 2. {{<k>}} k {{</k>}} does not contain a power of 5, therefore the power of {{<k>}} 5^3k {{</k>}} is 3. | ||
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| Both of these scenarios have too many 5s to go into numbers with a {{<k>}} 5^2 {{</k>}} in their prime factorization. | ||
| <p align="right"> | ||
| {{<k>}} \square {{</k>}} | ||
| </p> | ||
| </blockquote> | ||
| </div> | ||
| </details> | ||
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| ### Amount of divisors | ||
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| If {{<k>}} N = 2^{11} \cdot 3 \cdot 19^{20} {{</k>}}. | ||
| We can multiply the exponents (+ 1) together to get the total amount of divisors: {{<k>}} (11 + 1) (1 + 1) (20 + 1) = 25 {{</k>}}. | ||
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| - the multiplication principle | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,51 @@ | ||
| --- | ||
| title: "MATH102-lecture-20220203" | ||
| # date: 2022-02-03T08:52:46-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["divisibility"] | ||
| --- | ||
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| ## Divisibility cont. | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| Find a number with the amount of divisors of {{<k>}} N {{</k>}} to be {{<k>}} 4 \cdot 6 \cdot 3 {{</k>}}. | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| N = 7^3 \cdot 11^5 \cdot 41^2 | ||
| \end{aligned} | ||
| {{</k>}} | ||
| </div> | ||
| </details> | ||
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| <blockquote class="book-hint warning"> | ||
| <em>Theorem.</em> | ||
| Consider the 4 digit number {{<k>}} n = \overline{abcd} {{</k>}}. | ||
| {{<k>}} n {{</k>}} is divisible by 9 if the sum of its digits {{<k>}} a + b + c + d {{</k>}} is divisible by 9. | ||
| </blockquote> | ||
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| <blockquote class="book-hint"> | ||
| <em>Proof.</em> | ||
| {{<k display>}} | ||
| \begin{aligned} | ||
| \overline{abcd} &= 1000a + 100b + 10c + d | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| <p align="right"> | ||
| {{<k>}} \square {{</k>}} | ||
| </p> | ||
| </blockquote> | ||
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| <blockquote class="book-hint info"> | ||
| Note: {{<k>}} \overline{abcd} {{</k>}} means a 4 digit number. | ||
| </blockquote> | ||
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| --- | ||
| title: "RPTA125-lecture-20220201" | ||
| # date: 2022-02-01T17:59:38-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["leisure"] | ||
| --- | ||
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| ## Overview of Leisure | ||
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| To endure rather than to enjoy means: trying to make a living, just to get by. | ||
| I plan on being able to balance work life with leisure to not burn out. | ||
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| ### What is leisure? | ||
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| ### Leisure as a state of mind | ||
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| ### Leisure is political | ||
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