📚 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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