Quartz sync: Oct 3, 2024, 6:35 PM

CarterT27 · Oct 4, 2024 · df35cee · df35cee
1 parent cccd9f4
commit df35cee
Show file tree

Hide file tree

Showing 3 changed files with 206 additions and 0 deletions.
diff --git a/content/Class Notes/DSC 80 Lecture 3.md b/content/Class Notes/DSC 80 Lecture 3.md
@@ -0,0 +1,126 @@
+---
+tags:
+- "Type/Note"
+- "Topic/Data_Science"
+- "Class/DSC_80"
+date:
+- 2024-10-03
+---
+
+# Aggregating
+
+## Adding and Modifying Columns
+
+Adding a new column to a dataframe using `assign`
+```python
+dogs = pd.read_csv(Path('data') / 'dogs43.csv', index_col='breed')
+dogs.assign(cost_per_year=dogs['lifetime_cost'] / dogs['longevity'])
+```
+
+Chain methods together instead of writing long, hard-to-read lines
+- Need to wrap expression in parentheses to add newlines before every method call
+
+```python
+(dogs
+ .assign(cost_per_year=dogs['lifetime_cost'] / dogs['longevity'])
+ .sort_values('cost_per_year')
+ .iloc[:5]
+)
+```
+
+Assign with special column names (spaces, special characters)
+```python
+dogs.assign(**{'cost per year 💵': dogs['lifetime_cost'] / dogs['longevity']})
+```
+
+`df.copy()` copies a dataframe in place
+
+`df[] = ` assigns column in place
+
+`df.assign()` assigns a column to a new dataframe
+
+Avoid `inplace=True` - plans to remove in future releases of pandas, not good practice
+
+`df[column].to_numpy()` returns the numpy array of a column
+
+`dogs.max(axis=1)` won't work because you are trying to take the max of a mix of datatypes
+
+## Data Granularity and the `groupby` method
+
+Fine granularity: small details  
+Coarse: bigger picture  
+
+You should opt for **finer granularity** for more detail if you have the resources to do so
+
+How to go from fine to coarse granularity: **Aggregating**
+
+> [!definition] Aggregation
+> Aggregating is the act of combining many values into a single value
+
+`penguins.groupby('species')['body_mass_g'].mean()`
+
+"Split-apply-combine" Paradigm
+
+[https://dsc80.com/resources/lectures/lec03/imgs/image_0.png]()
+
+```python
+(penguins
+ .assign(is_dream = penguins['island'] == 'Dream')
+ .groupby('species')
+ ['is_dream']
+ .mean()
+)
+```
+
+```python
+%%pt
+penguins_small.groupby('species')
+```
+
+Allows us to visualize groupby_objects
+
+Aggregation Methods
+- `count()`
+- `sum()`
+- `mean()`
+- `max()`
+- `last()`
+- `first()`
+
+```python
+(penguins
+ .sort_values('body_mass_g')
+ .groupby('sex')
+ .last()
+)
+```
+
+Generally, you should select column(s) directly after groupby
+
+## Beyond default aggregation methods
+
+```python
+(penguins
+ .groupby('species')
+ ['body_mass_g']
+ .aggregate(['count', 'mean'])
+)
+```
+
+```python
+(penguins
+ .groupby('species')
+ .aggregate({'bill_length_mm': 'max', 'island': 'unique'})
+)
+```
+
+```python
+def iqr(s):
+    return np.percntile(s, 75) - np.percentile(s, 25)
+
+(penguins
+ .groupby('species')
+ ['body_mass_g']
+ .agg(iqr) # agg is short for .aggregate
+)
+```
diff --git a/content/Class Notes/MATH 109 Discussion 1.md b/content/Class Notes/MATH 109 Discussion 1.md
@@ -0,0 +1,71 @@
+---
+tags:
+- "Type/Note"
+- "Topic/Mathematics"
+- "Class/MATH_109"
+date:
+- 2024-10-03
+---
+
+# Necessary and Sufficient Conditions, Axiomatic Properties of the Real Numbers
+
+> [!proposition] 2.3.1: + and - for real numbers
+> $a,b\in \mathbb{R}$
+> 1. Commutativity: $a+b=b+a, a\cdot b = b\cdot a$
+> 2. Associativity: $(a+b)+c=a+(b+c), (a\cdot b)\cdot c = a\cdot (b\cdot c)$
+> 3. Distributivity: $a\cdot(b+c) = c\cdot b + a\cdot c, (a+b)\cdot c = a\cdot c + b \cdot c$
+> 4. Zero Identity: $0\in \mathbb{R}, a+0=a\forall a \in \mathbb{R}$
+> 5. Unity: $1\in \mathbb{R}, a\cdot 1 = a \forall a \in \mathbb{R}$
+> 6. Subtractivity: $\forall a, \text{the equation } a+x=0\text{ has a unique solution, called }-a$ ($b-a$ is defined as $b+(-a)$)
+> 7. Division: $\forall a \neq 0,\text{ the equation }a \cdot x = 1 \text{ has a unique solution }\frac{1}{a}$ ($\forall b$, $\frac{b}{a}$ is defined as $b\cdot\left(\frac{1}{a}\right)$)
+> 
+> In one word, 1-7 collectively say $\mathbb{R}$ is a **field**.
+
+> [!question] Which of the following conditions are necessary for the positive integer $n$ to be divisible by 6 (proofs are not necessary)?
+> 1. 3 divides $n$
+> 2. 9 divides $n$
+> 3. 12 divides $n$
+> 4. $n=12$
+> 5. 6 divides $n^2$
+> 6. 2 divides $n$ and 3 divides $n$
+> 7. 2 divides $n$ or 3 divides $n$
+
+> [!answer]-
+> Necessary is the same as saying $n$ is divisible by 6 $\implies$ a condition
+> 1, 5, 6, 7
+> Strong condition (6) implies weak condition (7)
+> 
+> Sufficient is the same as saying condition $\implies$ $n$ is divisible by 6
+> 1. 3 divides $n$ - necessary
+> 2. 9 divides $n$ - neither
+> 3. 12 divides $n$ - sufficient
+> 4. $n=12$ - sufficient
+> 5. 6 divides $n^2$ - necessary, sufficient
+> 6. 2 divides $n$ and 3 divides $n$ - necessary, sufficient
+> 7. 2 divides $n$ or 3 divides $n$ - necessary
+
+> [!question] Use the properties of addition and multiplication of real numbers given in Properties 2.3.1 to deduce that, for all real numbers $a$ and $b$,
+> 1. $a\times 0 = 0 = 0 \times a$
+> 2. $(-a)b=-ab=a(-b)$
+> 3. $(-a)(-b)=ab$
+
+> [!answer]
+> **Problem 1.** $a\times 0 = 0 = 0\times a$
+> 
+> $a\times (1+0) = a\times 1= a$
+> $a\times (1+0) = a\times 1 + a\times 0= a + a\times 0$
+> Subtracting $a$ from both sides:
+> $a\times 0 = 0$
+> Commutative: $0\times a = a \times 0 = 0$
+> 
+> **Problem 2.** $(-a)b=-ab=a(-b)$
+> 
+> $(a+(-a))\times b = 0 \times b = 0$
+> $=a\times b + (-a) \times b$
+> Subtracting $a\times b$: $(-a)\times b = -ab$
+> Commutative: $b\times(-a) = -ba$
+> 
+> **Problem 3.** $(-a)(-b)=ab$
+> 
+> $(-a)(-b) = -(a\cdot(-b)) = -(-(ab))$
+> $-(-ab)$ and $ab$ both solve the equation $x+(-ab)=0$ so $-(-ab)=ab$
diff --git a/content/Daily Notes/2024-10-03.md b/content/Daily Notes/2024-10-03.md
@@ -0,0 +1,9 @@
+---
+tags:
+- "Daily_Note"
+---
+
+- [[DSC 80 Lecture 3]]
+- [[CSE 158 Lecture 3]]
+- [[DSC 40B Lecture 3]]
+- [[MATH 109 Discussion 1]]