2020/07
This book introduces the mathematics behind computer programming.
The book can be downloaded in both English (EN) and Chinese (中文).
- 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.
To build the book in PDF format from the sources, you need the following software pre-installed.
- TeXLive, The book is built with XeLaTeX, a Unicode friendly 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 provide a gui based installer, in Mac OS X, there's a MacTeX.
If the host system fonts are available, e.g. under VM. they could be imported as the following example:
$ sudo mkdir /usr/share/fonts/host-system
$ sudo cp /Host-System/Fonts/{FontName, fontname}* /usr/share/fonts/host-system/
$ fc-cacheYou 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 install the MSYS for it. 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 unplugged-en.pdf and unplugged-zh-cn.pdf. If you only need the Chinese version for example, you can run make cn instead.
--
LIU Xinyu
``Cogito ergo sum''