
The boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. In this book the authors introduce the reader to the fundamental concepts of computational complexity and give in-depth explorations of the major interfaces between computer science and physics.
It's a classic ... and available now at the everyday low price of $0 on LibGen.
It is really an underrated book and hands-down is the most enjoyable technical book that I have ever read.
1."Uncle Petros & Goldback's Conjecture" & "Logicomix" (both by Apostolos Doxiadis),
2."Chaos" by James Gleick,
3. "The Man Who Loved Only Numbers" by Paul Hoffman
4. "A Mathematician's Apology" by G.H. Hardy
5. "The Indian Clerk" (fiction) by David Leavitt (about GH Hardy & Ramanujan)
6. "Genius at Play" by Siobhan Roberts (about John Conway). Normally I stay away from pop-math books with the words "The mind of..." or "Genius" in the title but this is a delightful book.
Some "actual" math books: 1. Nonlinear Dynamics & Chaos (Strogatz)
2. the Way of Analysis (Strichartz) -- note, this one is controversial as to its quality as a math book but I really like the presentation style
3. The Nature of Computation (Moore & Mertens)
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There's a bunch of methods that come out of casting an optimization or search problem into a thermal system with an artificial energy and corresponding conjugate (artificial) temperature.
Most people are familiar with (Gibbs-ish) Monte Carlo methods, for example. Then there's simulated annealing, tempering, parallel tempering, etc. Simulated annealing is universal optimizer with remarkable richness coming from the "energy landscape" perspective. Recent work by Riccardo zecchina has studied neural nets from this perspective, and the whole (largely) Italian gang of glassy landscape people have done really cool stuff with it including fundamental CS stuff like K-SAT.
Lots of optimization algos use tricks that exploit analogies to thermal systems, given a sufficiently clever "Hamiltonion".
I'm not up to date with the latest and greatest in NN training stuff, but I know a few of the preferred optimization algorithms used some form of gradient descent often with some artificial "momentum". Can't remember what it was called, maybe Adam or something? I know Michael Jordan at Berkeley does a lot cool stuff with along these lines.
Very rambly message I see now, so I'll stop and just give some references/recs and maybe polish up later.
A few recommendations--
Nature of computation - Cris Moore I think
Information and physics(?) - Mezard and montanari
Computational beauty of nature -Flack(?)
Newish book from SFI from a conference I was at a few years ago may interest you, The Energetics of Computing in Life and Machines https://www.amazon.com/dp/1947864076/ref=cm_sw_r_apan_i_JQXY...
And most emphatically, Information, inference, and learning - Mackay
Approximately in that order below:
Too many stat mech books, but honestly favorite is this old one. If you want a real challenge try to read to the OG Gibbs. Thermodynamics and an Introduction to Thermostatistics
Lectures On Phase Transitions And The Renormalization Group
Probability Theory: The Logic of Science
Information Theory, Inference and Learning Algorithms
Information, Physics, and Computation
Elements of Information Theory
Pattern Recognition and Machine Learning
The Nature of Computation
Principles of Cyber-Physical Systems
Introduction to Embedded Systems, Second Edition: A Cyber-Physical Systems Approach
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
An Invitation to Applied Category Theory: Seven Sketches in Compositionality
BTW, feel free to ask for recommendations in physics, especially stat mech, simulation/computation, condensed matter theory
[0]: https://www.amazon.com/Nature-Computation-Cristopher-Moore-d...