Collaborative Calculation and Data Science

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Algebra to solve logic puzzles
Convert boolean polynomials to probability

This notebook details some computations in the extremal Reissner-Nordström spacetime. 

Math 208 Interactive Notebooks © 2024 by Soham Bhosale, Sara Billey, Herman Chau, Zihan Chen, Isaac Hartin Pasco, Jennifer Huang, Snigdha Mahankali, Clare Minerath, and Anna Willis is licensed under CC BY-ND 4.0

The computer randomly selects a number between 1 and 100. The player has a limited <a href="https://buckshotroulette.com/baseball-bros-io">Baseball Bros Io</a> number of attempts (e.g., 7) to guess the number. After each guess, the game provides feedback whether the guess is too low, too high, or correct. If the player guesses correctly within the limit, they win. Otherwise, they lose and the number is revealed.

A red box appears randomly on the screen. You have 30 seconds to click it as many <a href="https://buildnow-gg.io">build now gg</a> times as possible. Each click gives you 1 point. After time runs out, the game stops and shows your score.

Exploding sheep, destructible maps, and zero microtransactions—this indie chaos-fest is turning heads for all the right reasons.

Lecture slides for UCLA LS 30B, Spring 2020

Supplementary code for the paper "Stochastic effects on plankton dynamics: insights from a realistic 0-dimensional marine biogeochemical model" by G. Occhipinti et al. 2024

Type rock, paper, or scissors when prompted. The computer will randomly pick one, too, and <a href="https://agargame.io">agario</a> the result will be shown. Simple and fun!

The player enters a number between 1 and 10. The program checks <a href="https://pokerogue.io/">Pokerogue</a> if it's correct and shows the result.  

This project demonstrates a basic data analysis workflow using Python. It loads a CSV dataset, cleans missing data, performs exploratory <a href="https://block-blast.io">Block Blast</a> analysis, and visualizes key insights such as age distribution and feature correlations.

This CoCalc project contains a simple Python script with a hidden bug for debugging practice. The function calculate_average() is meant to compute the <a href="https://retrobowl.college">Retro Bowl College</a> average of a list of numbers but triggers an IndexError due to an off-by-one mistake in a for loop. It's a great hands-on example for beginners to learn how to read error messages and fix common logical errors in code.

Calculating Stapledon's h*-representations of S_n for hypersimplices

### YouTube Tutorial: https://youtu.be/P92boGjCnPA

What You'll Learn:
Discover how to create a log-log plot using SageMath within a Jupyter notebook on the CoCalc platform. Learn to visualize functions with both standard and logarithmic scales.

Transcription:

Hello everyone, my name is Blaec Bejarano. Today, I'll show you how to create a log-log plot using SageMath in a Jupyter notebook within the CoCalc platform.

The log-log plot displays both the x and y axes on logarithmic scales, which can help visualize certain characteristics of the function.

### YouTube Tutorial: https://youtu.be/t7x3iUJDJyc

Transcription:
Hello everyone, my name is Blaec Bejarano. Today, I'll demonstrate how to plot the gradient of a function alongside its contour plot using SageMath in a Jupyter notebook on CoCalc. This example is inspired by Gregory Bard's textbook "Sage for Undergraduates" and attributed to Augustin O'Keefe.

1. Define the multivariate function $f(x,y) = \cos(x) - 2\sin(y)$. 

The gradient of this function can be written in angle bracket notation as:
   
$$\nabla f(x,y) = \left\langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right\rangle = \left\langle -\sin(x), -2\cos(y) \right\rangle$$

2. In the Jupyter notebook, define the function and compute its gradient:
   f(x,y)=cos(x)-2*sin(y)
   gradient = derivative(f)
3. Create the vector field plot of the gradient:
   plot1 = plot_vector_field(gradient, (x, -5, 5), (y, -5, 5))
4. Create the contour plot of the function:
   plot2 = contour_plot(f, (x, -5, 5), (y, -5, 5), fill=True) 
5. Display both plots together:
   show(plot1 + plot2)

This tutorial showcases CoCalc's ability to perform mathematical computations and visualizations seamlessly within a collaborative environment. Please like, subscribe, and follow for more content. See you next time. Thanks again!

#SageMath #Jupyter #Gradient #ContourPlot #CoCalc

### YouTube Tutorial: https://youtu.be/TRbWjocJ2ZI

What You'll Learn:
How to create visually appealing plots with grid lines using SageMath in a Jupyter notebook on the CoCalc platform. Learn to specify functions, define domains, and customize your plots with a few simple lines of code.

Transcription:

Hello everyone, my name is Blaec Bejarano. Today, I'll show you how to create plots with grid lines using SageMath in a Jupyter notebook on the CoCalc platform.

1. Log in to your account at cocalc.com and open your desired project. 

2. Create a new Jupyter notebook by clicking on the "+New" button and selecting "Jupyter Notebook". Name your notebook and choose the SageMath kernel.

3. In a code cell, use the `plot()` function to define your desired function. In this example, we'll plot $x^5$:

   - Specify the function you want to plot, e.g., `x^5`.
   - Define the domain using tuple notation `(x, start, end)`, e.g., `(x, 1, 16)`.
   - Add the `gridlines` parameter and set it to `'minor'` to display grid lines on the plot.

4. Click the run button or press Shift+Enter to execute the code cell and view your plot with grid lines.

CoCalc at AISTATS & ICLR: Connect with us at two leading machine learning conferences! Discover how CoCalc empowers AI and deep learning researchers with collaborative tools, scalable GPUs, and a unified environment for Python, TensorFlow, PyTorch, and more.

SIAM Optimization 2023 Insights: CoCalc shares highlights from the SIAM OP23 conference in Seattle, including real-world applications of optimization at Amazon, smarter algorithms, and unifying theories. See how CoCalc supports this cutting-edge work.

Browse publicly shared documents on CoCalc

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