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| Original file line number | Diff line number | Diff line change |
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| --- | ||
| title: "CS177-lecture-20220210" | ||
| # date: 2022-02-10T16:04:06-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["numpy", "pandas"] | ||
| --- | ||
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| ## NumPy | ||
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| We can use NumPy with | ||
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| ```py | ||
| import numpy as np | ||
| ``` | ||
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| We can create new arrays with | ||
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| ```py | ||
| a = np.array([1, 5, 7]) | ||
| ``` | ||
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| We can specify number of dimensions or data types: | ||
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| ```py | ||
| b = np.array([1, 2, 3], ndim=2) | ||
| c = np.array([1, 2, 3, 4], dtype=complex) | ||
| ``` | ||
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| We can see the shape of an array via | ||
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| ```py | ||
| print(a) | ||
| print(a.shape) | ||
| ``` | ||
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| You can set the shape of an array | ||
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| ```py | ||
| d = np.array([1, 2, 3], [4, 5, 6]) | ||
| d.shape = (3, 2) | ||
| ``` | ||
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| To create an array in a range | ||
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| ```py | ||
| a = np.arange(24) | ||
| ``` | ||
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| We can reshape this new array: | ||
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|  | ||
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| If we already have a Python list, we can create a NumPy array from it: | ||
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| ```py | ||
| x = [1, 2, 3] | ||
| a = np.asarray(x) | ||
| ``` | ||
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| ## Pandas | ||
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| - High performance data manipulation and data analysis | ||
| - `DataFrame` object, default and customized indexing | ||
| - High efficient merging and joining of data | ||
| - Columns from a data structure can be deleted or inserted | ||
| - Label based slicing, indexing of large datasets | ||
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| ### Structures | ||
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| - `Series`, 1D labeled homogenous array | ||
| - `DataFrame`, 2D labeled hetergenously typed columns | ||
| - `Panel`, 3D labeled, size mutable array | ||
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| ### Plotting | ||
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| --- | ||
| title: "CS177-lecture-20220215" | ||
| # date: 2022-02-15T15:51:31-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["data preprocessing"] | ||
| --- | ||
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| ## What is data? | ||
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| ### Attributes | ||
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| ### Difference between ratio and interval | ||
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| --- | ||
| title: "CS177-lecture-20220217" | ||
| # date: 2022-02-17T15:56:23-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["data preprocessing"] | ||
| --- | ||
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| ## Data preprocessing cont. | ||
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| ### Attributes cont. | ||
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| ### Types of data sets | ||
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| ### Data quality | ||
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| --- | ||
| title: "CS191-lecture-20220216" | ||
| # date: 2022-02-16T17:56:30-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: [] | ||
| --- | ||
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| ## Project showcase | ||
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| ## JIRA/Flying donut | ||
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| ## Assignments | ||
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| --- | ||
| title: "MATH102-lecture-20220208" | ||
| # date: 2022-02-08T08:57:44-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["divisibility"] | ||
| --- | ||
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| ## Returning to an old problem | ||
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| ## Quiz 1 sols | ||
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| ## 2Th review | ||
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| --- | ||
| title: "MATH102-lecture-20220210" | ||
| # date: 2022-02-10T08:58:35-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["divisbility", "least common multiple"] | ||
| --- | ||
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| ## 3T solutions | ||
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| ### Least common multiples | ||
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| Consider {{<k>}} a = 2^2 \cdot 5^4 \cdot 7 \cdot 41^{10} {{</k>}} and {{<k>}} b = 5^2 \cdot 19 \cdot 41 \cdot 47^2 {{</k>}}. | ||
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| If {{<k>}} M {{</k>}} is a common multiple of {{<k>}} a {{</k>}} and {{<k>}} b {{</k>}}, that means that {{<k>}} a | M {{</k>}} and also {{<k>}} b | M {{</k>}}. | ||
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| So what can we say about the pf of {{<k>}} M {{</k>}}? | ||
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| The closed form of {{<k>}} M {{</k>}}: | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| M &= 2^i \cdot 5^j \cdot 7^r \cdot 19^k \cdot 41^s \cdot 47^t \cdot u | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| where | ||
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| {{<k display>}} | ||
| \begin{aligned} | ||
| i &\geq 2 \\ | ||
| j &\geq 4 \\ | ||
| k &\geq 1 \\ | ||
| r &\geq 1 \\ | ||
| s &\geq 10 \\ | ||
| t &\geq 2 \\ | ||
| u &\in \mathbb{Z} | ||
| \end{aligned} | ||
| {{</k>}} | ||
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| So the shortcut is the union of primes with the higher power in each number. | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| {{<k>}} a = 2 \cdot 5^3 \cdot 19^4 {{</k>}} and {{<k>}} b = 2^4 \cdot 19 \cdot 41^7 {{</k>}} | ||
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| So our {{<k>}} \text{LCM} (a, b) = 2^4 \cdot 5^3 \cdot 19^4 \cdot 41^7 {{</k>}} | ||
| </div> | ||
| </details> | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| {{<k>}} a = 2 \cdot 5^3 {{</k>}} and {{<k>}} b = 2^2 \cdot 5^4 \cdot 11^9 {{</k>}} | ||
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| So our {{<k>}} \text{LCM} (a,b) = 2^2 \cdot 5^4 \cdot 11^9 {{</k>}} | ||
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| Notice that the least common multiple is {{<k>}} b {{</k>}} ({{<k>}} b {{</k>}} is a multiple of {{<k>}} a {{</k>}}). | ||
| </div> | ||
| </details> | ||
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| <details open> | ||
| <summary>Example</summary> | ||
| <div class="markdown-inner"> | ||
| {{<k>}} a = 2^2 \cdot 3^2 \cdot 7 {{</k>}}. | ||
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| Find {{<k>}} b {{</k>}} such that {{<k>}} \text{LCM} (a, b) = 2^2 \cdot 3^{15} \cdot 7 \cdot 19^3 {{</k>}} | ||
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| {{<k>}} b = 2^2 \cdot 3^{15} \cdot 7 \cdot 19^3 {{</k>}} | ||
| </div> | ||
| </details> | ||
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,32 @@ | ||
| --- | ||
| title: "MATH102-lecture-20220215" | ||
| # date: 2022-02-15T08:59:26-08:00 | ||
| draft: false | ||
| bookToc: true | ||
| tags: ["least common multiple"] | ||
| --- | ||
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| ## Quiz 2 solns | ||
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| ## 3Th solns | ||
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| ## Some word problems | ||
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| 1. Yes | ||
| 2. No | ||
| 3. {{<k>}} \text{gcd} (220,308) {{</k>}} | ||
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