Learning Data Science

Lecture 4
Data Science Workflow and NumPy

Functions

f

Inputs

Outputs

def c_to_f(celsius):
    return (celsius * 9/5) + 32

for temp in [0, 20, 100]:
    print(temp, "°C =", c_to_f(temp), "°F")

Typehints

  • Help other users (and your future self) know the inputs and outputs
def scream(word: str, times: int) -> str:
    saying = word * times
    return saying.upper() + "!"

def scale_numbers(numbers: list[int], factor: int | float) -> list[float]:
    result = []
    for n in numbers:
        result.append(n * factor)
    return result

Docstrings

  • Another way to help future you
  • And especially others, if you are collaborating
def scream(word: str, times: int) -> str:
    """
    Repeat a word several times and return it in uppercase with an exclamation mark.

    Parameters
    ----------
    word : str
        The word to repeat.
    times : int
        How many times to repeat the word.

    Returns
    -------
    str
        The repeated word in uppercase, followed by an exclamation mark.

    Examples
    --------
    >>> scream("ha", 3)
    'HAHAHA!'
    """
    
    saying = word * times
    return saying.upper() + "!"

There are many ways to format docstrings

This one is called the numpy style

Exceptions

  • Python's way of telling us something is wrong
  • They stop your program!
def circle_area(radius: float) -> float:
  
    if radius < 0:
        raise ValueError("Radius cannot be negative.")

    return 3.1415 * radius ** 2
import time

time.sleep(5)

# or you can import just one function
from time import sleep

sleep(5)

# nickname a module/function
import time as t

t.sleep(5)

Python Builtin Functions and Modules

class Character:
    """A character in our video game."""
    
    def __init__(self, name: str, base_health: int):
        # ...
        self.name = name
        self.base_health = base_health
        self.items: list[str] = []
        
    def pickup_item(self, item: str):
        """
        Add an item to the character's inventory.
        
        Parameters
        ----------
            item : str
                The item to pick up
        """
        self.items.append(item)
Character
  • name
  • health
  • items
  • pickup_item()
warrior = Character(name="Hodor", health=100)

print(warrior.items)

warrior.pickup_item("sword")

print(warrior.items)

Objects

"nouns"

"verbs"

Debugging

  • Debugging helps you efficiently find where errors or strange behaviors arise in your code

Debugging in VS Code

Lecture 4

  1. Recap
  2. Project Scaffolding with uv
  3. Python Notebooks
  4. Linear Algebra in a Nutshell
  5. NumPy Fundamentals

Project Scaffolding

  • Where do you start when beginning a new project?
  • How do you install external packages?
  • All can be easily done with uv

Let's work through it together!

Project Scaffolding

1. Create a new folder 'ds-lecture-4' in your projects directory. This will be the root of today's work.

2. Open this folder with VS Code

3. Run the command:

uv init -p 3.13

By the end you should see these files

4. Run the command: 

    - this will create the virtual environment

5. If the following popup appears, always say yes!

    - if it doesn't appear, use the command palette 

Project Scaffolding

uv sync

Everything here is review from Lecture 2 :)

6. Use the command palette to select "Publish to GitHub"

    - you can choose if you want your code to be public or        private

 

Adding a new project to your GitHub

Your repository is available now at github.com/username/ds-lecture-4 ✨

7. Let's install the 'tqdm' package to our environment

  • It allows you to create loading bars
  • Not built into Python, so we have to add it!

Adding external packages

uv add tqdm
tqdm got added to pyproject.toml !

8. Try using tqdm in a small script to test that it worked

Adding external packages

from tqdm import tqdm

for i in tqdm(range(30000000)):
    pass

9. Sync our changes to GitHub

    - Now we can use the VS Code UI to save time ✨

Adding external packages

  • Open the Version Control tab
  • Click the + button to add all files
    • Note: you could also select individual files or even individual lines of code
  • Type a commit message (e.g. "First commit") and click Commit
  • Push the changes to GitHub:

And that's how you start a project and install packages with uv! 

Lecture 4

  1. Recap
  2. Project Scaffolding with uv
  3. Python Notebooks
  4. Linear Algebra in a Nutshell
  5. NumPy Fundamentals

Python Notebooks

Ways to interact with Python code

REPL

✅ Interactive
❌ Sharable
❌ Version Control friendly
❌ Reproducible
❌ Mix code, text, plots

Scripts

❌ Interactive

✅ Sharable

✅ Version Control friendly

✅ Reproducible
❌ Mix code, text, plots

Notebooks

✅ Interactive

✅ Sharable

⚠️ Version Control friendly

⚠️ Reproducible

✅ Mix code, text, plots

Python Notebooks

Python Notebooks

  • Interactive files where you can
    • Run Python code
    • Create images and plots
    • Take notes with Markdown
  • All inside one file!

⚠️ Reproducing results

⚠️ Tracking changes with Git

⚠️ Scalability

⚠️ Performance

  

✅ Playing with data

✅ Taking nodes

✅ Making plots

✅ Interactive 

✅ Good for demos

Notebooks in VS Code

Do it!

  1. Open VS Code to a new project folder
  2. Add the package ipykernel to your project with uv
  3. Find and install the Jupyter extension
  4. Create a new file called "test.ipynb"
  5. Create a Markdown cell and make a header
  6. Create a code cell and add a Hello World

3.

6.

5.

ipynb = Interactive Python Notebook

Notebooks in VS Code

When you first try to run a cell with code, it will ask you to select your interpreter again.

 

Remember to use the one located at

.venv

Notebooks in VS Code

Add a code cell
Add a markdown cell
Run all notebook cells sequentially
Run this cell only
Delete this cell
Switch this cell between python/markdown
Restart the notebook (all imports and variables lost)

Lecture 4

  1. Recap
  2. Project Scaffolding with uv
  3. Python Notebooks
  4. Linear Algebra in a Nutshell
  5. NumPy Fundamentals

Linear Algebra

The math of vectors and matrices

How to combine and transform them

What is a vector?

A vector is a list of numbers.

That's it ✨

Many concepts and physical quantities can be expressed in terms of vectors

What is a vector?

A vector is a list of numbers.

That's it ✨

Coordinates

Data

Equations

4x^2 + 2x + 1 = 0 
[4, 2, 1]
[x, y]
[4, 7, 8, 2]

What is a vector?

Vectors don't live in isolation:
there is usually some underlying information

Coordinates

Data

Equations

[x, y]
[4, 7, 8, 2]
4x^2 + 2x + 1 = 0 
[4, 2, 1]

Spatial coordinates and origin is assumed [0, 0]

Units are luminosity and data is captured every 1s 

Numbers represent coefficients of a polynomial

Vector Math at a Glance

addition / subtration
\mathbf{a} \pm \mathbf{b} = [a_1 \pm b_1,\ a_2 \pm b_2,\ ...]
vector multiplication
c\mathbf{a} = [ca_1,\ ca_2,\ ...]
\mathbf{a} \odot \mathbf{b} = [a_1 b_1,\ a_2 b_2,\ ...]
dot product
\mathbf{a} \cdot \mathbf{b} = \sum_i a_i b_i = a_1 b_1\ + a_2 b_2\ + ...
magnitude / norm
·
·
||\mathbf{a}|| = \sqrt{\mathbf{a} \cdot \mathbf{a}} = \sqrt{\sum_i a_i^2}
√

Challenge #1

Challenge #1

\mathbf a=[1,\,2], \mathbf b=[3,\,-1]

Pen and paper exercises

find:

\mathbf a \cdot \mathbf b = \, ?
|| \mathbf b || = \, ?

What is a Matrix?

Multiple vectors stacked together?

This can represent higher-order information

Coordinates ➡️ many points at once

What is a Matrix?

\begin{bmatrix} x_1 & x_2 & x_3 & ... & x_n \\ y_1 & y_2 & y_3 & ... & y_n \\ \end{bmatrix}

pair of coordinates

Matrix as a transformation

What is a Matrix?

\begin{bmatrix} 2 & 0 \\ 0 & 3 \\ \end{bmatrix} = \begin{bmatrix} 2x \\ 3y \\ \end{bmatrix}
\begin{bmatrix} x \\ y \\ \end{bmatrix}
\begin{bmatrix} 2 & 0 \\ 0 & 3 \\ \end{bmatrix}

Matrix as data with attributes

What is a Matrix?

Data=\begin{bmatrix} \text{lum}_1 & \text{freq}_1 & \text{snr}_1\\ \text{lum}_2 & \text{freq}_2 & \text{snr}_2\\ \text{lum}_3 & \text{freq}_3 & \text{snr}_3\\ \text{lum}_4 & \text{freq}_4 & \text{snr}_4 \end{bmatrix}

Each row in the matrix is a one data point

Parameters of multiple functions

What is a Matrix?

\begin{aligned} y_1 &= 2x_1 + 3x_2 + 1 \\ y_2 &= -x_1 + 4x_2 - 2 \\ y_3 &= 0.5x_1 - x_2 + 0 \end{aligned}

Parameters of multiple functions

What is a Matrix?

\begin{aligned} y_1 &= 2x_1 + 3x_2 + 1 \\ y_2 &= -x_1 + 4x_2 - 2 \\ y_3 &= 0.5x_1 - x_2 + 0 \end{aligned}
\mathbf{y} = \mathbf{A} \mathbf{x} + \mathbf{b}
\mathbf{y} = \begin{bmatrix} 2 & 3 \\ -1 & 4 \\ 0.5 & -1 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} + \begin{bmatrix} 1 \\ -2 \\ 0 \end{bmatrix}
\mathbf{A}
\mathbf{x}
\mathbf{b}
+

What is a Tensor?

Multiple matrices stacked together.

A higher-order matrix.

What is a Tensor?

Rank 0
Tensor
Rank 1
Tensors
Rank 2
Tensor
Rank 3
Tensors
Everything is a tensor

Color images are tensors!

Graphics from: St. Lawrence U CS140 and Montesinos-López et al (2022)

Image width (4px)
Image height (4px)
Image "depth"
(3 color channels)

Metrix Math at a Glance

matrix x vector
\mathbf{A} \mathbf{x} = \mathbf{Y}
matrix multiplication
\text{cell}\ c_{ij} = \sum_{k=1}^n a_{ik} b_{kj}

C

\mathbf{AB} = \mathbf{C}

Metrix Math at a Glance

transpose
\mathbf{A} \rightarrow \mathbf{A^T}
*flips matrix along main diagonal*
\mathbf{A} = \mathbf{(A^T)^T}
it's inversable

Now let's put it all together:

jupyter + linear algebra

✨

Lecture 4

  1. Recap
  2. Project Scaffolding with uv
  3. Python Notebooks
  4. Linear Algebra in a Nutshell
  5. NumPy Fundamentals

NumPy

💻 The rest of today's lecture will be spent learning NumPy.

Open up a new notebook which you can use for note-taking and completing challenges

Please install NumPy with

uv add numpy

What is NumPy?

NumPy is array library that powers all of scientific Python

Fancy lists

NumPy Superpowers:

⚡️ Vectorization

⚡️ Broadcasting

⚡️ Fassssst

We'll come to these later

🔗 source for visualizations

Lists need loops

my_list = [1,2,3,4,5]

print(my_list ** 2)
# raises an Error!
import numpy as np

my_array = np.array([1,2,3,4,5])

print(my_array**2)
my_list = [1,2,3,4,5]

squared = []
for i in my_list:
	squared.append(i**2)
    
# OR
squared = [i**2 for i in my_list]

print(squared)

Solution using lists

Solution using numpy

Vectorization

import numpy as np

my_array = np.array([1,2,3,4,5])

print(my_array**2)
# array([ 1,  4,  9, 16, 25])

This is called vectorization ✨

Operations on vectorized objects are:

  • faster
  • no loops involved
  • easier for the user
print(my_array + 5)
# array([ 6,  7,  8,  9, 10])
other = np.array([6,7,8,9,10])
print(my_array + other)

# array([ 7,  9, 11, 13, 15])

What is NumPy?

NumPy is array library that powers all of scientific Python

Fancy lists

Fancy linear algebra

You can put arrays in arrays to create/manipulate vectors, matrices, and tensors

You can put arrays in arrays to create/manipulate vectors, matrices, and tensors

Later we'll see how it makes sense to manipulate data as vectors and matrices

This will be super important for the ML section next week as well!

Challenge #1

Challenge #1

import numpy as np

my_array = np.array([1, 2, 3, 4, 5])
other    = np.array([6, 7, 8, 9, 10])
  • Find a way to do element-wise multiplication of the two lists without numpy
  • Then try again using numpy arrays
  • Which is easier?
my_list    = [1, 2, 3, 4, 5]
other_list = [6, 7, 8, 9, 10]

With normal lists

With numpy arrays

# expected result
[ 6 14 24 36 50 ]

Next up: 1D arrays (aka Vectors)

Array Attributes

Easily get the type or shape of an array

my_array = np.array([1,2,3,4,5])
print(my_array.dtype)   # int64
print(my_array.shape)   # (5)

my_array = np.array([1,2,3,4,5], dtype=float)
print(my_array.dtype)   # float64

Array Creation Patterns

print(np.ones(6))

# [1 1 1 1 1 1]

Array Creation Patterns

You can also create arrays that are the same size as an already-existing one

my_array = np.array([1,2,3,4,5])
print(np.ones_like(my_array))

# [1 1 1 1 1]

Initializing With Sequences

Random Arrays

my_array = [6, 89, 384]

rng = np.random.default_rng()
rng.choice(my_array)
# 89
 
# can pass probabilities
rng.choice(my_array, p=[0.1, 0.1, 0.8])
# 384 (probably ;)

Challenge #2

Challenge #2

Create a function that uses numpy to generate n random numbers
between -1 and +1

# expected result
print(my_rand(n=3))
# [-0.348, 0.894, -0.028]

Reproducible Randomness

  • Sometimes (ie testing purposes), you want the same answer from an RNG
  • You can pass a seed 
rng = np.random.default_rng()
print(f"Seed: {rng.bit_generator.seed_seq.entropy}")
print(rng.random(5))

Seed: 121739455997546233386808762441738277564
[0.7538113  0.33547651 0.08440574 0.97809579 0.06358138]

rng2 = np.random.default_rng()
print(f"Seed: {rng2.bit_generator.seed_seq.entropy}")
print(rng2.random(5))

Seed: 187878457149970364692539552433862812938
[0.24586211 0.91028715 0.23901012 0.56294228 0.25043037]

No seed provided

Reproducible Randomness

  • Sometimes (ie testing purposes), you want the same answer from an RNG
  • You can pass a seed 
rng = np.random.default_rng(42)  # <--- seed is 42
print(f"Seed: {rng.bit_generator.seed_seq.entropy}")
print(rng.random(5))

Seed: 42
[0.77395605 0.43887844 0.85859792 0.69736803 0.09417735]

rng2 = np.random.default_rng(42)
print(f"Seed: {rng2.bit_generator.seed_seq.entropy}")
print(rng2.random(5))

Seed: 42
[0.77395605 0.43887844 0.85859792 0.69736803 0.09417735]

Seed provided: 42

Vector Indexing

Not too different from lists

Main difference: editing a slice of an array, changes the original!

a = np.arange(1, 6)
# [1 2 3 4 5]

a[2:4] = 0
print(a)
# [1 2 0 0 5]

Boolean Indexing

Logical operations on arrays

# boolean indexing
a = np.array([1, 2, 3, 4, 5, 4, 3, 2, 1])
print(a > 3)

# [False False False  True  True False False False False]

a[a > 3] = 0
print(a)

# [1 2 3 0 0 0 3 2 1]

Vector Math

  • We already touched on this a bit

Element-wise operations between two arrays

Vector Math

  • We already touched on this a bit

Element-wise operations between one array and one number (scalar)

This is called broadcasting ✨

In these cases, the scalar gets 'promoted' to an array behind the scenes

Vector Math

Most functions from the built-in `math` module also are in numpy and work on arrays!

Vector Math

Linear algebra 😱

Vector Math

Stats! 😱

Challenge #3

Challenge #3

  • Using numpy arrays, calculate the sin^2 of every integer degree in [0, 360] deg
  • Then find the mean and standard deviation of this array
  • No for loops allowed!

Vectors / 1D arrays review

x = np.array([1,2,3,4,5])
# OR
l = [1, 2, 3, 4, 5]
x = np.array(l)

Create an array

x = np.ones(5)
x = np.zeros(5)

Initialize an array

x = np.array([1,2,3,4,5])
y = np.ones_like(x)

Initialize from another array's shape

x = np.arange(6)
x = np.arange(1, 6, 2)
x = np.linspace(0, 1, 11)

Initialize a sequence

rng = np.random.default_rng()
# 5 ints between [0,100)
rng.integers(0, 100, 5)

# 10 ints between [0, 1)
rng.random(10)

# 6 samples from a gaussian
# mean=5, std=3
rng.normal(5, 3, 6)

Random number generator

x = np.arange(1, 6)
# [1, 2, 3, 4, 5]
x[1] # = 2
x[2:4] # = [3, 4]
# everything from index -2 and onwards
x[-2:] # = [4, 5]
# Every 2 indices (step=2)
x[::2] # = [1, 3, 5]
# specifically indicies 1, 3, 4
x[[1, 3, 4]] # = [2, 4, 5]

Indexing

x = np.array([1, 2])
y = np.array([3, 6])
x + y # = [4, 8]
x * y # = [3, 12]
x + 2 # = [3, 4]
np.sqrt(x) 
np.sin(x)

Vector operations

x.max()
x.sum()
x.mean()
# etc

Stats

Matrices, 2D Arrays

Matrices

In NumPy, matrices are arrays inside an array!

np.array([1, 2, 3])
x.shape  # (3)

1D Array / Vector

np.array([1, 2, 3])
x.shape  # (3)
np.array([1, 2, 3])
x.shape  # (3)

2D Array / Matrix

x = np.array([
    [1, 2, 3],
    [4, 5, 6]  
])
x.shape  # (2, 3)
("rows", "columns")

Matrix Initialization

Most logic from 1D cases can be expanded

Indexing syntax

[row, column]

: means 'all'

(3, 4)
First row,
every element

Every row,
second element

First row,
second col

Let's pretend this matrix represents student grades

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0

Indexing syntax

[row, column]

: means 'all'

Jay's Geometry Grade

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
(3, 4)
First row,
every element

Every row,
second element

First row,
second col

Indexing syntax

[row, column]

: means 'all'

All Jay's Grades

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
(3, 4)
First row,
every element

Every row,
second element

First row,
second col

Indexing syntax

[row, column]

: means 'all'

All Geometry Grades

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
(3, 4)
First row,
every element

Every row,
second element

First row,
second col

The Axis Argument

a.sum() =

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
= 28.5

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
a = 
grades = np.array([
    [1.3, 1.3, 3.7, 2.3],
    [4.0, 4.3, 2.0, 2.3],
    [1.3, 1.0, 2.0, 3.0]
])

a.sum(axis=0) =

Susie

Jay

Lara

= [6.6, 6.6, 7.7, 7.6]
Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
a.sum(axis=1) =

Susie

Jay

Lara

= [8.6, 12.6, 7.3]
Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0

The Axis Argument

Susie

Jay

Lara

Trig. Alg. Geom. Calc.
1.3 1.3 3.7 2.3
4.0 4.3 2.0 2.3
1.3 1.0 2.0 3.0 
a = 
grades = np.array([
    [1.3, 1.3, 3.7, 2.3],
    [4.0, 4.3, 2.0, 2.3],
    [1.3, 1.0, 2.0, 3.0]
])

Tabular data (i.e. row/column data) is naturally represented as a 2D matrix!

  • Row: each data sample
  • Column: each feature (i.e. attribute) in your data

Challenge #4

Challenge #4

Copy the data from the code block below

  1. What is the shape of the data (amounts matrix), and what does each axis represent?
  2. How many fruits were sold in total over this week?
  3. Which day sold the most fruits?
  4. Which fruit was the best seller?
fruits = np.array([
    "apples",
    "bananas",
    "cherries",
    "dates",
    "elderberries",
    "figs",
    "grapes",
    "huckleberries",
    "kiwis",
    "lemons",
    "mangos",
    "nectarines",
])

# amount sold per weekday
amounts = np.array([
    [10, 20, 30, 40, 50, 60, 70],
    [15, 25, 35, 45, 55, 65, 75],
    [20, 30, 40, 50, 60, 70, 80],
    [25, 35, 45, 55, 65, 75, 85],
    [30, 40, 50, 60, 70, 80, 90],
    [10, 24, 30, 36, 42, 48, 54],
    [10, 20, 30, 40, 50, 60, 70],
    [4, 8, 12, 16, 20, 24, 28],
    [1, 2, 3, 4, 5, 6, 7],
    [3, 5, 7, 9, 11, 13, 15],
    [1, 4, 7, 10, 13, 16, 19],
    [34, 12, 23, 12, 23, 12, 23],
])

Note: The week starts from Monday-Sunday

Matrix Math

All element-wise except :

  • @ is a special operator for matrix product

More Matrix Math

Normalization

Multiplying several columns

Row-wise normalization

Outer Product

This all must seem very overwhelming, like a lot to remember! 

 

But you don't have to memorize any of this.

 

You will get used to this notation as you use it, and can look things up as you go along 💫

Creating Matrices from Arrays

When you have a single, long array and you want to turn it into a matrix:

Use the reshape() method!
a.reshape(2,3)

Creating Matrices from Arrays

When you have a single, long array and you want to turn it into a matrix:

Go back with the flatten() method!
a.flatten()

Row and Column Vectors

You can use the @ operator to perform dot/outer products on 2 vectors

But how does numpy know if the vector is a row vector or a column vector?

We must encode the 1D vectors as 2D vectors

(3,1) @ (1,3) -> (3x3)
(1,3) @ (3,1) -> (1x1)

Row and Column Vectors

np.array([1, 2, 3, 4])
Normal 1D Vector (4,)
4 rows, 0 columns
np.array([[1, 2, 3, 4]])
Row 2D Vector (1, 4)
1 row, 4 columns
np.array([[1], [2], [3], [4]])
Column 2D Vector (4, 1)
4 rows, 1 column

Notice how this has double brackets, making it a 2D matrix with 1 row!

Row and Column Vectors

np.array([1, 2, 3, 4])
Normal 1D Vector (4,)
4 rows, 0 columns
np.array([[1, 2, 3, 4]])
Row 2D Vector (1, 4)
1 row, 4 columns
np.array([[1], [2], [3], [4]])
Column 2D Vector (4, 1)
4 rows, 1 column
x.T
x.T
x.reshape(1, -1)
x.flatten()
x.reshape(-1, 1)
x.flatten()

Challenge #5

Challenge #5

Let's play around with tensors:

  1. Initialize a size (2,3,4) tensor with random integers between 0-9
  2. Print the tensor and examine what it looks like
  3. Check its .shape attribute
  4. Transpose the matrix. Print it. What is the shape?
  5. Try to .flatten() the matrix. What does it look like now? What is the shape?
  6. Try to reshape the flattened version back to its original (2,3,4) tensor

One last (useful) thing!

Saving and loading numpy arrays

  • You can save a numpy array to a file
  • Great for backing up you work!
import numpy as np

a = np.arange(6).reshape(2,3)

np.save("my_array.npy", a)   # save to file
b = np.load("my_array.npy")  # load back

print(b)
print(f"They are equal: {np.all(a == b)}")

Surprise mini-challenge:

Why did I use np.all() in the above code

Lecture 4

  1. Recap
  2. Project Scaffolding with uv
  3. Python Notebooks
  4. Linear Algebra in a Nutshell
  5. NumPy Fundamentals

The End

Learning Data Science Lecture 4

By astrojarred

Private

Learning Data Science Lecture 4

More from astrojarred