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