The Big Naughty List

Mathematics is a vast and fascinating field, and having access to high-quality resources can make learning and problem-solving more effective. This article compiles a curated list of online platforms, repositories, and tools for students, educators, and enthusiasts studying mathematics at any level. From proof compendiums to interactive problem-solving platforms, these resources offer valuable support for deepening your mathematical understanding.

Maths general resources

For those exploring or wanting to unveil the awesome world of Maths, these resources provide valuable learning materials:

• How to Find reliable and useful information.
• Guide to Prompt Engineering & Curated List of AI Chatbots & Search Engines
• Awesome AI Tools: A curated list of top AI tools for various applications, from chatbots to automation.

• Awesome Math: A curated GitHub repository of high-quality mathematics resources, including textbooks, courses, and tools for all levels.
• Wolfram|Alpha: A computational knowledge engine for solving equations, graphing functions, and exploring mathematical concepts with step-by-step solutions.
• ProofWiki: An online compendium of mathematical proofs, covering topics from algebra to topology. It’s a collaborative wiki where users can contribute rigorously verified proofs, making it ideal for students and researchers seeking clear, formal explanations.
• Mathematics Stack Exchange: A question-and-answer platform for math enthusiasts at all levels, from high school to advanced research. Users can ask questions, share solutions, and learn from detailed discussions by a global community of mathematicians, students, and enthusiasts.
• Project Euler: A collection of challenging mathematical and computational problems designed to be solved with programming. Each problem includes a solution explanation, perfect for honing problem-solving and coding skills.
• OpenStax: A repository of free, peer-reviewed mathematics textbooks and resources, covering topics like calculus, algebra, and statistics. An alternative is Wuolah.
• Internet Archive: A digital library offering free access to mathematics textbooks, historical documents, and research papers. It’s a treasure trove for finding out-of-print or open-access math resources.
• Online Matplotlib Compiler: While not a compiler itself, Matplotlib’s documentation and tools like Replit or Google Colab allow users to write and visualize mathematical plots using Python’s Matplotlib library.
• Cheatography: A platform hosting cheat sheets for mathematical concepts, formulas, and techniques, useful for quick reference during study sessions.
• Mathematics LibreTexts: A comprehensive, open-source collection of math textbooks and resources, covering introductory to advanced topics, created by educators for accessibility.
• Khan Academy: A free learning platform with interactive lessons, videos, and exercises on topics from arithmetic to calculus, ideal for beginners and intermediate learners.
• InfoCoBuild (FreeEducation, Mathematics) is a place where you can enjoy watching documentary films and open lectures from educational institutions or reading the latest news.
• Evan Dummit’s Course Notes Page: A collection of detailed course notes on algebra, number theory, calculus, and more, provided by Evan Dummit for advanced students.
• Brilliant.org: An interactive platform offering guided problems and explanations in math and science, designed to build intuition and problem-solving skills.
• MIT OpenCourseWare: Free course materials from MIT, including lecture notes, assignments, and exams for undergraduate and graduate-level mathematics courses.

Using Mathematics Stack Exchange Effectively: To get the most out of Mathematics Stack Exchange, provide clear context for your questions, show your work, and use the site’s tagging system (e.g., calculus, algebra) to attract relevant experts. Check the How to Ask page for best practices.

LaTeX, Ascii, and Emoji

• The Evolution of Digital Characters: From ASCII to Unicode and Emojis.
• Mastering Markdown & LaTeX — A Comprehensive Editing Guide
• How to edit Markdown and LaTeX
• EmojiDB, Emojipedia.

Operating system, apps, tools, and AI

• Set up Windows, Set up Windows 2, and Essential Software.
• The best Maths software to learn and grow.
• A Curated List of AI, Audio, and Web Utility Tools.
• A Guide to AI Image and Video Creation Tool
• Productivity and Note-Taking Apps.
• Awesome Useful Websites.
• AI-Powered Tools and Local Models: The Gemini CLI (Command Line Interface) is an open-source AI agent developed by Google. Copilot: Microsoft’s AI assistant and companion to inform, entertain, write, code, task automation, inspire, and more. Ollama is a lightweight, privacy-focused platform that lets you run large language models (LLMs) locally on your own machine —no cloud dependency or costly monthly subscriptions required. It’s designed to make working with models like Llama 3, DeepSeek, Gemma, and others as simple as running a command in your terminal.

# Use of Ollama
user@pc:~$ ollama run llama2
user@pc:~$ A circle has a radius of 5. What is the area of the circle?
The area of a circle is calculated using the formula: Area = πr², where r is the radius. For a radius of 5:
Area = π × 5² = π × 25 ≈ 3.14159 × 25 ≈ 78.54

The area of the circle is approximately 78.54 square units.

• Web-based development environment: Jupyter Notebook and Jupyter Lab.

Video Lectures

1. Free Video Lectures, All Courses, Mathematics.
2. Andrew Misseldine.
3. ICTP Mathematics, Abstract Algebra - Lothar Göttsche
4. Oxford Mathematics, 1st Year Student Lectures.
5. MIT OpenCourseWare, MIT 18.01 Single Variable Calculus, Fall 2007.
6. Richard E. BORCHERDS.
7. A First Course in Calculus.

Calculus

1. Calculus Early Transcendentals
2. MTH 210 Calculus I (Professor Dean))
3. UTRGV Calculus
4. Study Guides, Calculus.
5. Paul’s Online Notes, QUICK NAV, Calculus I.
6. Math24, Calculus.
7. Calculus, 4ed. Michael Spivak.

Algebra

• Mathonline, and more specifically, Abstract Algebra.
• Abstract Algebra: Theory and Applications.
• Andrew Misseldine: College Algebra and Abstract Algebra.
• Michael Penn (Abstract Algebra), and MathMajor
• Lectures by Benedict Gross, Abstract Algebra
• LibreTexts Mathematics, Bookshelves, Abstract and Geometric Algebra, Abstract Algebra: Theory and Applications (Judson). Calculus and Calculus 3e (Apex).
• Course Notes - J.S. Milne Top. All of Milne’s books are really kind and very easy to read (math.stackexchange.com).
• Contemporary Abstract Algebra, Joseph, A. Gallian.
• A First Course in Abstract Algebra, John Fraleigh.
• Abstract Algebra, 3ed. David S. Dummit. Richard M. Foote.
• Topics in Algebra” by Herstein

Topology

• Marius Furter (Topology).
• Introduction to Topological Manifolds. John M. Lee. Available in Internet Archive.
• MAT327 at the University of Toronto Online Notes with Problems: MAT327 Course Note

Linear Algebra

• Andrew Misseldine, Linear Algebra Done Openly.
• Linear Algebra Done Right by Sheldon Axler & Videos: Sheldon Axler’s Playlist.
• GeoGebra 3D Calculator
• MyWhyU, Algebra.
• Linear Algebra Done Openly is an open source linear algebra textbook developed by Dr. Andrew Misseldine
• Online Python
• LibreTexts Mathematics, Bookshelves, Advanced Algebra.

College Algebra

• Andrew Misseldine, College Algebra.

Galois Theory

1. NPTEL-NOC IITM, Introduction to Galois Theory.
2. Algebra, Second Edition, by Michael Artin.
3. Galois theory (2ed, London, 1944) by Dr. Emil Artin. Lectures delivered at the University of Notre Dame.
4. Richard E. BORCHERDS, Galois Theory.
5. Notes by Tom Leinster
6. Evan Dummit’s Course Notes Page, Fields and Galois Theory, Fall 2020.

Complex Analysis

• Visual Complex Functions: an Introduction with Phase Portraits” by Elias Wegert
• Complex Analysis” by Serge Lang
• Mathematics - Complex Analysis, nptelhrd, @ii
• Complex Analysis by George Cain.
• Complex Analysis. A Visual and Interactive Introduction, by Juan Carlos Ponce Campuzano
• Complex Analysis, Free Video Lectures, Complex Analysis, Recommended Books and Lectures

Algebraic Topology

• Book: Algebraic Topology by Allen Hatcher
• Lectures by Pierre Albin

YouTube Channels

• Socratica.
• The Math Sorcerer.
• Kimberly Brehm.
• Numberphile.
• Eddie Woo.
• patrickJMT.
• blackpenredpen.
• math Antics.
• Stand-up Maths.
• Professor Leonard.
• 3Blue1Brown.
• blackpenredpen
• The Organic Chemistry Tutor.
• A Mathematical Room.
• Chau Tu.
• Others: Math with Professor V, Dr. Trezor Bazett, Houston Math Prep.

YouTube Math Visual

• Mathemaniac
• Aleph 0
• Infinity Learn Class 9&10.
• The Bright Side of Mathematics.