Machine Learning

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Foundations of Applied Mathematics is a free series of four textbooks created for the applied and computational mathematics program at Brigham Young University. 📚

The series includes four volumes:
*   Mathematical Analysis
*   Algorithms, Approximation, and Optimization
*   Uncertainty and Data
*   Dynamics and Control

The series is suitable for upper-level undergraduate and introductory graduate students. It also includes Python lab exercises and practical assignments, connecting mathematical theory with numerical computation, algorithms, data analysis, and scientific applications. 🐍

I particularly appreciate that these are not just theoretical textbooks. The accompanying Python materials help to illustrate how these concepts are applied to real-world computational problems. 💻

https://foundations-of-applied-mathematics.github.io

#Mathematics #Python #Education #DataScience #Algorithms #Learning

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Reading Materials

📖 Prompt Engineering Guide
📖 Awesome Generative AI (Curated Resource List)
📖 Generative AI: A Beginner's Guide
📖 Understanding Generative AI Capabilities
📖Stanford HAI: 2025 AI Index Report

Here's a Python tool for accurately extracting text from PDFs and images into Markdown and JSON. 📄✨

It supports tables, formulas, multiple OCR engines (Marker, Surya-OCR, Tesseract) and has built-in personal data removal. 🔒🤖

https://github.com/CatchTheTornado/pdf-extract-api

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📚 Mathematics without fluff: Three free books for those who want a solid foundation

Three free mathematics books by Allen Hatcher 🧮

If you're looking for a solid foundation in topology, K-theory, and number theory, Allen Hatcher has an excellent free collection. 🎓

1. Algebraic Topology 📐
A classic textbook on algebraic topology. The book was published by Cambridge University Press, but the online version is available for free under an agreement with the publisher. The website offers the complete PDF, chapters individually, corrections, and additional exercises.
🔗 https://pi.math.cornell.edu/~hatcher/AT/AT.pdf

Additionally: Spectral Sequences - a separate, expanded chapter for this book.
🔗 https://pi.math.cornell.edu/~hatcher/AT/ATch5.pdf

2. Vector Bundles & K-Theory 🧶
A concise book about vector bundles, topological K-theory, and characteristic classes. Currently, approximately 120 pages are available online, covering the basics of vector bundles, a portion of K-theory, Bott periodicity, characteristic classes, and the stable J-homomorphism.
🔗 https://pi.math.cornell.edu/~hatcher/VBKT/VB.pdf

3. Topology of Numbers 🔢
An unusual introduction to number theory through geometry and pictures. It focuses heavily on quadratic forms, Farey diagrams, continued fractions, Pell's equation, quadratic reciprocity, and Conway's topograph. A PDF of approximately 350 pages is available for free.
🔗 https://pi.math.cornell.edu/~hatcher/TN/TNbook.pdf

#Mathematics #Topology #FreeBooks #Learning #STEM #Education

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sequence of four inputs, carrying every hidden state forward yourself. 🔄

1. Given

Four inputs X1 to X4, recurrent weights and biases for hidden layers a, b, c, and an output layer y. 📊

2. Initialize

Let us set the hidden states a0, b0, c0 to zeros. Nothing has been read yet. 🛑

3. First hidden layer (a)

We build the transformation matrix by laying the input weights, the state weights and the biases side by side. We stack X1, the previous state a0, and an extra 1 underneath. Multiply the two, and a1 = [0, 1]. 🧮

4. Second hidden layer (b)

Let us do it again, one layer up. Now a1 is the input, and b0 is the previous state. Multiply: b1 = [1, -1]. ⬆️

5. Third hidden layer (c)

Once more. b1 is the input, c0 is the previous state, and c1 = [1, 1]. 🔁

6. Output layer (y)

Let us read the answer off the top of the stack. Weights and biases against [c1; 1], and Y1 = [3, 0, 3]. 📝

7. Carry the states forward

We copy a1, b1, c1 across. This is the whole trick of a recurrent network: the states are the only thing the next input gets to see. 🚀

8. Process X2

Repeat steps 3 to 6 for the second input: three hidden layers, then the output. Y2 = [5, 0, 4]. 🔢

9. Carry the states forward

Let us copy a2, b2, c2 across, exactly as before. 🔄

10. Process X3

Same four moves, third input. Y3 = [13, -1, 9]. 🧩

11. Carry the states forward

We copy a3, b3, c3 across, one last time. ⏭️

12. Process X4

Repeat once more. Y4 = [15, 7, 2]. ✅

You have just run a Deep RNN over a whole sequence by hand. ✍️

The outputs:
Y1: [3, 0, 3]
Y2: [5, 0, 4]
Y3: [13, -1, 9]
Y4: [15, 7, 2]

The takeaway: the hidden states are the memory, and they are the only memory there is. Everything the network learns from X1 has to fit in those little two-cell columns and get handed forward, one step at a time. 🧠

#RNN #DeepLearning #AI #MachineLearning #NeuralNetworks #Tech

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Maths, CS & AI Compendium: A free textbook for aspiring AI/ML engineers

🚀 A large open-source compendium on mathematics, computer science, and AI has gone viral on GitHub. The project already has around 6.3K stars.

📚 The author positions it as a "non-traditional textbook" for practitioners: less dry notation, more intuition, connections between topics, and real-world context.

📖 It contains 20 chapters:
* Vectors, matrices, calculus
* Statistics and probability
* Machine learning and deep learning
* NLP, computer vision, audio/speech
* Multimodal learning and autonomous systems
* GNN, OS, algorithms
* Production engineering, GPU/SIMD
* AI inference, ML systems design, and applied AI

🤖 There is also a MCP server so that Claude Code, Cursor, VS Code, and other AI assistants can use the compendium as a local knowledge base.

💡 This is a great resource for those who want to not just "learn ML," but to build a solid foundation: mathematics → CS → ML systems → modern AI.

🔗 GitHub: https://github.com/HenryNdubuaku/maths-cs-ai-compendium

#AI #MachineLearning #ComputerScience #Maths #OpenSource #DevCommunity

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🔖 A large collection of lectures on Machine Learning and Deep Learning 🧠

We found a repository that brings together high-quality materials on several areas of artificial intelligence. 🤖

Excellent material for both learning and reviewing key topics. 📚

⛓️ Link to GitHub
https://github.com/kmario23/deep-learning-drizzle

#MachineLearning #DeepLearning #AI #Tech #Coding #Learning

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