2023/10
This book introduces the mathematics behind computer programming.
The book can be downloaded in English (EN). The 1st edition in Chinese (中文) was published in 2023 (中文样章).
- Preface
- Chapter 1, Natural numbers. Peano Axiom, list and folding;
- Chapter 2, Recursion. Euclidean algorithm, Lambda calculus, and Y-combinator;
- Chapter 3, Symmetry. Group, Ring, and Field. Galois Theory;
- Chapter 4, Category theory and type system;
- Chapter 5, Deforest. Build-fold fusion law, optimization, and algorithm deduction;
- Chapter 6, Infinity. Set theory, Infinity and stream;
- Chapter 7, Logic paradox, Gödel's incompleteness theorems, and Turing halting problem.
- Answers to the exercise.
You need TeXLive to build the book in PDF format. We use LuaLaTeX, an extended version of TeX.
In Debian/Ubuntu like Linux environment, do NOT install the TeXLive through apt-get. Go to TeXLive official site to download the setup script.
$ wget http://mirror.ctan.org/systems/texlive/tlnet/install-tl.zip
$ unzip install-tl.zip
$ cd install-tl
$ sudo ./install-tl -gui text -repository http://mirror.ctan.org/systems/texlive/tlnetIn Windows, TeXLive provides a gui based installer, in Mac OS X, there's a MacTeX.
The default build supports Linux, Mac OS X, and Windows. You can install additional font (like Noto CJK) typesetting (see prelude.sty).
6B1F
Some system fonts, e.g. STKaiti, were moved to /System/Library/AssetsV2/com_apple_MobileAsset_Font7 in Mac OS X from 2022, you need add the path to the local TeXLive configuration:
sudo tlmgr conf texmf OSFONTDIR /System/Library/AssetsV2/com_apple_MobileAsset_Font7You need the GNU make tool, in Debian/Ubuntu like Linux, it can be installed through the apt-get command:
$ sudo apt-get install build-essentialIn Windows, you can use WSL or install MSYS. In Mac OS X, please install the developer tool from this command line:
$ xcode-select --installenter the folder contains the book TeX manuscript, run
$ makeThis will generate the pdf files (Run make en to only build the English version; run make force-en to force build the book).
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LIU Xinyu