William Stein "Doing Mathematics with CoCalc", Howard University 2023 скачать в хорошем качестве

William Stein "Doing Mathematics with CoCalc", Howard University 2023

What You'll Learn: Understand the origins and evolution of CoCalc, including its mathematical, teaching, and collaborative features. Learn how to use CoCalc for real-time editing, running code in SageMath and Jupyter notebooks, effective course management, and collaborative LaTeX editing. Explore integration with diverse programming languages and see how CoCalc facilitates workflows for mathematics education, research, and group projects. Discover More: CoCalc Documentation: https://doc.cocalc.com/index.html CoCalc Website: https://cocalc.com/ CoCalc Store: https://cocalc.com/store Stay Connected: Facebook:   / cocalconline   Twitter: https://x.com/cocalc_com LinkedIn:   / sagemath-inc.   Transcription: Hello everyone, my name is William Stein. Today, I'll be discussing "Doing Mathematics with CoCalc" at Howard University in 2023. CoCalc is a web-based software project I started, motivated by many years of teaching and mathematical research. It integrates Jupyter notebooks, SageMath worksheets, a collaborative LaTeX editor, a Linux terminal, slides, and supports real-time collaboration—allowing multiple users to edit documents or notebooks together, similar to Google Docs. A unique aspect of CoCalc is its integrated course management system. This system enables instructors to assign homework, communicate with students, view work in real time, and provide feedback directly within the platform. There are also features like peer grading and automated grading. For presentations, you can use CoCalc’s slide mode, which lets you run code (e.g., Sage) directly in your slides. For example, you can compute and plot in a slide cell: ```sage Compute and plot an example in a slide cell x = var('x') plot(sin(x), (x, 0, 2*pi)) ``` You can also interactively explore mathematics, such as generating random prime numbers or factoring a number: ```sage Generate a random 200-bit prime number random_prime(2^200) ``` CoCalc's history comes from earlier work with online calculators, tools for number theory, and experiences with licensing restrictions that motivated the creation of open-source alternatives like SageMath. CoCalc evolved by integrating these tools and supporting collaborative, browser-based mathematical computing—addressing software installation and compatibility challenges faced by students. Jupyter notebooks within CoCalc support various kernels including SageMath, Python, R, Julia, Octave, and even C++. This allows running code and annotating results in a rich, interactive environment. Here's an example of finding a matrix kernel using SageMath: ```sage Find the kernel of a matrix over the rationals A = matrix(QQ, [[1, 2], [3, 6]]) A.right_kernel() ``` CoCalc also enables collaborative editing. You can open the same document in several browser windows and see changes propagate in real time, with an integrated chat for communication. The "Time Travel" feature allows tracking changes over the life of any document: Drag a slider to watch how a notebook evolved step by step. See which user made each change and precisely what changed. For LaTeX documents, CoCalc’s editor provides live preview, connection to the file browser, code folding, and support for SageTeX and PythonTeX. You can run Sage code directly within your LaTeX document using the `%sage` magic, and the results are embedded automatically. ```latex %sage factor(2025) ``` CoCalc integrates diverse computation, collaboration, and authoring tools into a single platform—supporting both educational and research workflows. Please like, subscribe, and follow for more tutorials. Thank you for watching! Suggested Hashtags: #CoCalc #Mathematics #SageMath #Jupyter #OnlineCollaboration #LaTeX #STEM