The Science of Programming

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1. steppiApr 2024
   Check out The Science of Programming Matrix Computations by Robert A. van de Geijn and Enrique S. Quintana-Ort. Chapter 5 walks through how to write an optimized GEMM. It involves clever use of block multiplication, choosing block sizes for optimal cache behavior for specific chips. Modern compilers just aren't able to do such things now. I've spent a little time debugging things in scipy.linalg by swapping out OpenBLAS with reference BLAS and have found the slowdown from using reference BLAS is typically at least an order of magnitude.

   [0] https://www.cs.utexas.edu/users/rvdg/tmp/TSoPMC.pdf

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2. jonsenMar 2022
   If interested in a comprehensive treatment of this kind of imperative program design: The Science of Programming by David Gries.
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3. noriudayJul 2020
   1) "The Science of Programming", by David Gries, is an excellent book dealing with mathematical proof based approach to programming.

   2) "The Book of Numbers", by John H. Conway and Richard Guy is a beautiful book which discusses about figurative numbers amoung several other beautiful topics.

   3) "Stories About Maxima and Minima", V. M. Tikhomirov has some beautiful anecdotes and interesting applications of calculus.

   4) "Contemporary Abstract Algebra", by Joseph Gallian is an algebra textbook that goes beyond just teaching material. It has quotations, biographies, puzzles and interesting applications of algebra.

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4. streetcat1Feb 2020
   You might also want to check out

   David Gries, the science of programming:

   https://www.springer.com/gp/book/9780387964805

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5. todd8Aug 2017
   My daughter's first class in programming used this book. She really liked the class and still has a fondness for Scheme, although her subsequent programming classes have used Java.

   I took a look at the online second edition (and I happen to have a hard copy of the first edition in my library). I like the book and believe that it is one of the best books I've seen for teaching a beginner to program. The subjects covered are non-trivial, but the book gets the students there in a well paced presentation. The book emphasizes the importance of breaking down problems into well defined parts, defining the interfaces, and implementing each part as a function that satisfies the desired contract.

   If you are an experienced programmer, I believe that your time would be better spent on a book that is less oriented around teaching the basic steps that you already know. Books that I can recommend to experienced programmers interested in advanced subjects in programming:

   1) Structure and Interpretation of Computer Programs, 2ed., by Harold Abelson, Gerald Jay Sussman, Julie Sussman. This book will teach you how to program in Scheme, and you will learn much more than just the syntax. I would consider this to be a very demanding book for a complete beginner. Available online: https://mitpress.mit.edu/sicp/full-text/book/book.html

   2) The Science of Programming (1981), by David Gries. This book and the smaller, but equally difficult monograph The Discipline of Programming (1976), by Dijkstra are great books but too hard and mathematical for many readers. They focus on verifying the correctness of programs and introduce a formalism that shows how the logical effects of each program statement can be combined to prove that the program satisfies its specification. There are practical limitations not addressed by these early expositions on program correctness, but the techniques covered can be applied by hand and I've often used them on especially troubling passages of code that I wanted to make sure were correct. If you are up for it these books will introduce new ways of thinking about your code. I'd advise taking a peek at the books before buying to make sure it will be worth the investment; it definitely was for me.

   3) Learn You a Haskell for Great Good!, by Miran Lipovaca. Like learning Scheme, learning Haskell will teach you about a new way of thinking about programming. This is a nice introduction to the language. Even though I'm still trying to learn Haskell, this book was my favorite of all my books on Haskell (I've got all of the ones written in English). Learn Haskell to understand where researchers are exploring the possible futures of programming. This book is also available online: http://learnyouahaskell.com

   4) Algorithms + Data Structures = Programs (1976), by Niklaus Wirth. This book is far easier on the reader than the ones I've listed above; I've included this book because it is just a fun read for any programmer. It's old and uses Pascal, but it still a great book on programming that introduces a number of algorithms and data structures. It's available used for reasonable prices: https://www.amazon.com/Algorithms-Structures-Prentice-Hall-A.... For a more advanced introduction to data structures I suggest MIT's Open Courseware videos taught by Professor Erik Demaine, https://ocw.mit.edu/courses/electrical-engineering-and-compu...

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6. contravariantDec 2016
   The book 'The science of programming' of David Gries is also a nice introduction to writing programs using mathematical logic and reasoning. The book is inspired by the techniques of Dijkstra and Hoare, and written in a way that's easy to follow.
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