Anisha/calc #107

k-anisha · 2025-05-29T03:47:48Z

📝 Summary

Adding rates of change notebook for Calculus in ML

📋 Checklist

I have included package dependencies in the notebook file using --sandbox
If adding a course, include a README.md
Keep language direct and simple.

Copilot

Pull Request Overview

This PR adds a new Marimo notebook covering rates of change in calculus for machine learning and provides a README for the Calculus module.

Introduces RatesOfChange.py, a Marimo notebook demonstrating derivatives, gradient descent, kinematics, and an economics example
Adds README.md with course description and instructions for running notebooks

Reviewed Changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 4 comments.

File	Description
calculus_for_ML/RatesOfChange.py	New Marimo notebook on rates of change concepts
calculus_for_ML/README.md	README for the Calculus for ML course, with setup and contribution info

Comments suppressed due to low confidence (2)

calculus_for_ML/RatesOfChange.py:1

[nitpick] Module filename uses CamelCase; per PEP8 it may be clearer to rename the file to lowercase 'rates_of_change.py'.

import marimo

calculus_for_ML/RatesOfChange.py:39

Consider adding unit tests for this f(x) function (and deriv_f) to verify correctness of outputs.

def f(x):

Copilot · 2025-05-30T07:30:11Z

calculus_for_ML/RatesOfChange.py

+
+@app.cell
+def _(np, plt):
+    # First, let's start by definiting a simple function. 


Typo in comment: 'definiting' should be 'defining'.

Suggested change

# First, let's start by definiting a simple function.

# First, let's start by defining a simple function.

Copilot · 2025-05-30T07:30:12Z

calculus_for_ML/RatesOfChange.py

+    def f(x):
+        return x ** 2
+
+    # Now, we can plot the function.abs


Remove the stray '.abs' in the comment, e.g. 'plot the function.'

Suggested change

# Now, we can plot the function.abs

# Now, we can plot the function.

Copilot · 2025-05-30T07:30:12Z

calculus_for_ML/RatesOfChange.py

+def _(mo):
+    mo.md(
+        r"""
+        We can use another example in economics. In economics, there is a term known as 'Price Sensitivity,' wjich essentially measures the rate of change in the quantity demanded or supplied of a good. The price elasticity is given by the formula:


Typo in preceding line: 'wjich' should be 'which'.

Suggested change

We can use another example in economics. In economics, there is a term known as 'Price Sensitivity,' wjich essentially measures the rate of change in the quantity demanded or supplied of a good. The price elasticity is given by the formula:

We can use another example in economics. In economics, there is a term known as 'Price Sensitivity,' which essentially measures the rate of change in the quantity demanded or supplied of a good. The price elasticity is given by the formula:

Copilot · 2025-05-30T07:30:12Z

calculus_for_ML/RatesOfChange.py

+@app.cell
+def _():
+    return
+
+
+@app.cell
+def _():
+    return
+
+


[nitpick] This empty cell appears unused; consider removing redundant stub cells at the end of the notebook.

Suggested change

@app.cell

def _():

return

@app.cell

def _():

return

Haleshot · 2025-05-30T08:21:29Z

Relevant issue #58

Haleshot

The math content throughout the notebook is solid - the derivatives, the GD implementation & physics relationships you've laid out are accurate. The economics example at the end also makes good sense and ties things together nicely.

For styling, you could polish this up with some markdown formatting. Using backticks around function names like f(x) and f'(x) would make them stand out better.

Overall, I really like how you build things step-by-step (the flow). Would recommend improving the above PR description to be more descriptive and capture the contents of the notebook accurately (refer to previous PRs).

Also, a nice summary at the end of the notebook going over the contents of the notebook (what was covered, etc.). would be nice. Usage of appropriate markdown extensions &/or admonitions would also make it stand out better.

Haleshot · 2025-05-30T08:35:35Z

calculus_for_ML/RatesOfChange.py

+@app.cell
+def _(mo):
+    mo.md(
+        r"""
+        In this notebook, we'll learn about rates of change in Machine Learning. 
+


I'd start the notebook with the title being mentioned (h1 tag) followed by the author's name. Something like

# Rates of Change in Machine Learning *By [YourName](https://github.com/k-anisha)* In this notebook, we'll learn about...

Haleshot · 2025-05-30T08:36:09Z

calculus_for_ML/RatesOfChange.py

+@app.cell
+def _():
+    import marimo as mo
+    import numpy as np
+    import matplotlib.pyplot as plt
+    from sympy import symbols
+    from sympy import diff
+    return diff, mo, np, plt, symbols


I'd move this cell to the bottom (better to directly start with the notebook topic - also consistent and followed in most notebooks in the learn repo).

Haleshot · 2025-05-30T08:40:08Z

calculus_for_ML/RatesOfChange.py

+    def f(x):
+        return x ** 2
+
+    # Now, we can plot the function.abs
+
+    x = np.linspace(-10, 10, 500)
+    y = f(x)
+
+    plt.plot(x, y, label=r'$f(x) = x^2$')
+    plt.title('Graph of f(x) = x^2')


Instead of a static plot, consider adding sliders to explore different functions:

# Could use mo.ui.slider to let users change the coefficient coeff = mo.ui.slider(1, 5, value=1, label="Coefficient") def f(x): return coeff.value * x**2

This would let users see how changing the coefficient affects the parabola (+ also adds to the interactivity of the notebook).

Haleshot · 2025-05-30T08:41:12Z

calculus_for_ML/RatesOfChange.py

+    mo.md(r"""Now, let's get into gradient descent. Below is an example on a quadratic function.""")
+    return
+
+
+@app.cell
+def _(deriv_f, f, np, plt):
+    # Our parameters below
+
+    learning_rate = 0.1
+    initial = 8
+    iterations = 20
+
+    current = initial
+    history = [current]
+
+    for i in range(iterations):


The learning rate, initial point, & iterations are hardcoded. Consider making these interactive:

learning_rate = mo.ui.slider(0.01, 0.5, value=0.1, step=0.01, label="Learning Rate") initial = mo.ui.slider(-10, 10, value=8, label="Starting Point") iterations = mo.ui.slider(5, 50, value=20, label="Iterations")

Users could experiment with different values and see how it affects convergence.

Haleshot · 2025-05-30T08:49:24Z

calculus_for_ML/RatesOfChange.py

+
+@app.cell
+def _(np, plt):
+    # First, let's start by definiting a simple function. 


Btw, I'd recommend checking out our plotting tutorial: https://links.marimo.app/tutorial-plotting
Has a good example where various functions are visualized iteratively.

Haleshot · 2025-05-30T09:01:07Z

calculus_for_ML/RatesOfChange.py

+    return diff, mo, np, plt, symbols
+
+
+@app.cell


Suggested change

@app.cell

@app.cell(hide_code=True)

Would recommend doing this (hiding markdown cell blocks) throughout the notebook

Haleshot · 2025-05-30T09:04:37Z

calculus_for_ML/RatesOfChange.py

+        In simple terms, the rate of change measures how one quantity changes as we adjust its inputs or parameters. The rate of change can represent how a model's output changes as we adjust the input or parameters. 
+
+        In calculus, the rate of change of a function is given by calculating the derivative at a certain point. So, if f(x) is a function, then f'(x) is the rate of change. 
+
+        In the context of Machine Learning, rates of change are especially useful when working with optimization problems - for example, minimizing a loss function, or using gradient descent to try and find optimal parameters and minimize error.
+
+        Let's get into rates of change!
+        """
+    )
+    return


One thing that would help connect this to the issue description - consider adding a section before you get into derivatives directly, that shows the difference between:

Average rate of change: (f(b) - f(a)) / (b - a) (slope between two points)

Instantaneous rate of change: f'(x) (slope at exactly one point)

You could use your f(x) = x^2 function (or the plotting notebook) to show a line (secant?) b/w two points, then demonstrate how as the points get closer, it approaches the tangent line.

Something like picking points at x=2 & x=4, then x=2 & x=3, then x=2 & x=2.1, showing how the slopes approach the derivative value at x=2.

Haleshot · 2025-06-25T11:53:53Z

Hey @k-anisha; just wanted to follow-up if you had a chance to revisit this PR and the review comments posted above.

k-anisha added 5 commits May 12, 2025 15:43

numpy files

0f96445

Merge branch 'marimo-team:main' into main

1dce711

update

a166d1c

Rates of Change

84a4fc3

adding files

f27a7ff

Haleshot requested a review from Copilot May 30, 2025 07:28

Copilot AI reviewed May 30, 2025

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	# First, let's start by definiting a simple function.
	# First, let's start by defining a simple function.

	# Now, we can plot the function.abs
	# Now, we can plot the function.

	We can use another example in economics. In economics, there is a term known as 'Price Sensitivity,' wjich essentially measures the rate of change in the quantity demanded or supplied of a good. The price elasticity is given by the formula:
	We can use another example in economics. In economics, there is a term known as 'Price Sensitivity,' which essentially measures the rate of change in the quantity demanded or supplied of a good. The price elasticity is given by the formula:

Anisha/calc #107

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k-anisha commented May 29, 2025

📝 Summary

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Pull Request Overview

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