17 Free Books to learn about Programming, Mathematics & Physics

17 Free Books for transversal learning

How the books were selected

Their Free nature was one of the main criteria of selection. Each of these book will be accessible without need of payment. Either on the Author's website via webpages or downloads.

These books are meant to help you to develop transversal interest for Programming, Mathematics & Physics. To do so, I'll indicate synergies between book topics in the descriptions. One of the main themes here will be "Randomness & Information Openness". Regarding this theme the notions of Applied Statistics/Probabilities, Information Distribution/Dispersion and Entropy will be essential.

My main recommendation when it comes to reading many books is to find 1 Main Topic and to look for this topic in each book. This will allow you to discover or generate synergies between topics. This way, you could get interested by Thermodynamics regarding its application to Information Theory. And then, by extension to Statistical applications in Thermodynamics regarding the notions of distribution & dispersion.

The Main List

1. Automate the Boring Stuff with Python
2. JavaScript Learning Patterns
3. Practical Cryptography for Developers
4. Python Programming for Economics and Finance
5. Data Science at the Command Line
6. Game Programming Patterns
7. Deep Learning
8. A gentle introduction to the art of mathematics
9. The Book of Proof
10. Discrete Mathematics : An Open Introduction
11. Mathematics for Machine Learning
12. Elementary Differential Equations
13. A First Course in Electrical and Computer Engineering
14. Linux Appliance Design
15. Introduction to Signal Processing
16. Entropy and Information Theory
17. Geometry with an introduction to cosmic Topology

Books described & classified by Topic

Programming

Python - Automate the Boring Stuff with Python by Al Sweigart

• A Project based book to learn Python features by helping you facilitate daily tasks.

JavaScript Design patterns - Learning Patterns by Lydia Hallie & Addy Osmani (anciently Learning JavaScript Design Patterns)

• You can combine it with a JavaScript Web development book.

Python for Cryptography & Security - Practical Cryptography for Developers by Svetlin Nakov

• Cryptography is a transversal topic which can help you get interested to multiple parts of Programming, Mathematics & Physics.
• Can be supplemented with Open Workbook of Cryptology (with Source code) & Demystifying Internet of Things Security.

Python for Finance - Python Programming for Economics and Finance by Thomas Sargent & John Stachurski

• An Introduction to Statistical modeling for Finance & Economics.
• This Book is part of the series Quantitative Economics with Python.

Python for Data Science - Data Science at the Command Line by Jeroen Janssens

• Learn to obtain and manipulate data through the websites, APIs, databases, and files.
• The peculiarity of this book is its direct approach.

Game Programming - Game Programming Patterns by Robert Nystrom

• Learn Design patterns through game programming and code more clearly.

Deep Learning - Deep Learning by Ian Goodfellow, Yoshua Bengio & Aaron Courville

• Still one of the best introductions to Machine/Deep Learning.
• Learn about Neural Networks & their applications.

Mathematics

Mathematical Introduction - A gentle introduction to the art of mathematics by Joe Fields

• Alternative link to PDF
• For most mathematics books, you can do the exercises on paper, or on a computer using Sage.
• If you want to learn about Sage, the main system used in Mathematical Computation : Computational Mathematics with SageMath.

Proofs - The Book of Proof by Richard Hammack

• One of the best Proof Books.
• To read alongside How to Prove it by Daniel Velleman & Proof by Jay Cummings. Both of these books will be reviewed later.

Discrete Mathematics - Discrete Mathematics : An Open Introduction by Oscar Levin

• I recommend reading this one online as it is often updated. As for most books in this list, you can also find a PDF version.
• If you want to know more on Logic try A Friendly Introduction to Mathematical Logic by Christopher Leary & Lars Kristiansen.

Statistics & Probabilities - Mathematics for Machine Learning by Marc Peter

• Advanced book containing applications of Analytical Geometry & Vector Machines to Machine Learning.
• Can be supplemented with Probability for Data Science by Stanley Chan & An Introduction to Statistical Learning.
• To complete your Statistics & Probability education it could be useful to learn Combinatorics.
• If you want to learn Combinatorics you can try Foundations of Combinatorics with Applications by Edward Bender & Gill Williamson.

• Link to additional exercises for Marc Peter's book.

Differential Equations - Elementary Differential Equations and Solutions by William Trench

• Once you finished this book you can search for applications of these principles.
• Ideally, try to find Probabilistic applications of Differential Equations.

Physics

Electricity - A First Course in Electrical and Computer Engineering by Louis Scharf

• Also consider Fundamentals of Electrical Engineering by Don Johnson.

Electronics - Linux Appliance Design by Smith, Hardin, Phillips and Pierce

• Also consider Electronics Tutorials.

Information Processing - Introduction to Signal Processing by Sophocles Orfanidis

• Also consider Algorithms for Audio Watermarking and Steganography by Nedeljko Cvejic

Thermodynamics - Entropy and Information Theory by Robert M. Gray

• An introduction on Thermodynamics applied to Informatics.

Topology - Geometry with an introduction to cosmic topology by Michael Hitchman

• A global book on geometry with a transition to Topology.
• To use with supplemental books on Topology applied to finance, cryptography or differential equations.

Recommendation for reading each book in 1 week

If you have 30 to 60 minutes a day for reading you can finish the part of each book which interests you the most.

By doing so, you familiarize yourself with the book & are more likely to finish it.

Here's a way to do it simply :

1. Find your main topic of Interest
2. Find the simplest application possible
3. Build a Prototype - For mathematics, write a Template for Proofs & Demonstrations

If you have an additional 10 minutes for reading, review the book's plan twice. Being able to write the plan from memory will make you feel very familiar with the book.

The more attached you get to a book, the more likely you are to use it as a reference manual.

Another idea to consider is to make a Map of each book. I'll do it in the summary of each book listed here. Those summaries will be published in upcoming year.