数学课堂笔记50页 (数学笔记200字以上)

晓查 乾明 发自 凹非寺

量子位 报道 | 公众号 QbitAI

又出现一位“神仙”本科生！

数学课上，全程键盘手打1700页笔记。

速度紧追老师板书，公式、图形一个不落。

效果？请看下图：

不仅排版媲美教科书，而且还能够批注，检索关键词……

笔记被他Po到网上之后，便引来大量围观。

不到一天，相关推文就已经有2000多赞，Hacker News论坛上盖了200多楼。

甚至有网友评论称：“你就是我们需要的英雄！”

他是怎么做到的呢？秘密*器武**就是：LaTeX+Vim！

这位来自欧洲的小哥非常强烈安利Vim文本编辑器，他说：

用LaTeX写数学公式，我选Vim编辑器。它强大、通用、可扩展性很强。只要是基于文本的任务我都用它，写代码、编辑LaTeX、写markdown都是。

虽然入门阶段的学习曲线超级陡峭，但只要掌握了基本的操作方式，就会欲罢不能。

下面就让我们看一下他完成这一壮举的具体流程，文中提到的工具*载下**地址，我们都附在了最后。

快速上手教程

我们先看看小哥的工作环境配置。

他用Vim编辑LaTeX的场景，就像下面这样：

左边是Vim，右边是pdf阅读器Zathura，它也有类似Vim的快捷键。

小哥用的操作系统是Ubuntu，使用bspwm作为窗口管理器。在Vim中，使用的LaTex插件是vimtex，它有语法高亮显示、目录视图、同步对象等功能。

然后，使用vim-plug做如下配置：

Plug 'lervag/vimtex'
let g:tex_flavor='latex'
let g:vimtex_view_method='zathura'
let g:vimtex_quickfix_mode=0
set conceallevel=1
let g:tex_conceal='abdmg'

最后两行控制的是“隐藏”功能。开启了这个功能，除了你光标所在的那一行之外，文本里夹杂的LaTeX代码就都会隐藏或者替换成其他符号。

比如说在下面动图里，隐藏了[，]，$之后，没有了它们的干扰，整个文档就更易读。这个功能还会用∩替代\bigcap，∈替代\in等等。

设置完成，接下来就到了整个教程的精华所在：

用LaTeX记笔记，怎么才能像老师写板书一样快？

这就是片段（snippets）发挥作用地方了。

片段

片段是什么？

片段是一小段可复用的文本，由其他文本触发。

例如，输入sign，再按下Tab键，这个单词就会自动扩展为一段签名：

片段也可以是动态的：输入today并按下Tab键，它就会变成当前的日期。

而输入box按Tab，就会出现一个框，还会随着输入文字自动变大。

片段，甚至可以嵌套在另一个片段里用：

怎么创建片段？使用UltiSnips

管理片段的插件UltiSnips，小哥是这样配置的：

关于sign片段的代码如下：

snippet sign "Signature"
Yours sincerely,
Gilles Castel
endsnippet

对于动态的片段，你可以将代码放在``之间， 在片段扩展的时候，就会运行。下面的例子，就是用 bash 格式化当前日期：date+%f。

snippet today "Date"
`date +%F`
endsnippet

你也可以在!p ...代码块里使用Python，比如上面box片段的代码就是这样的：

snippet box "Box"
`!p snip.rv = '┌' + '─' * (len(t[1]) + 2) + '┐'`
│ $1 │
`!p snip.rv = '└' + '─' * (len(t[1]) + 2) + '┘'`
$0
endsnippet

这些 Python 代码块将被变量 snip.rv 的值替换。在这些代码块中，你可以访问代码段的当前状态，例如t[1]包含第一个制表位，fn是当前文件名等等。

LaTex片段

使用片段编写LaTeX，要比纯手工编写快得多。特别有些非常复杂的片段能帮你大大节约时间，有效防止抓狂。

下面是一些非常有用且容易上手的片段：

环境

想插入一个环境，只需要在一行的开头输入beg。然后键入环境的名称，这个名称在\end{}命令中也是一样。按下Tab键，就能够将光标放置在新创建的环境中。

这个片段的代码如下：

snippet beg "begin{} / end{}" bA
\begin{$1}
 $0
\end{$1}
endsnippet

其中，b表示这个片段只会在代码行的开头展开，A代表自动展开，也就是说不用按Tab键了。制表位(Tab stop)——也就是你可以通过按Tab 和Shift+Tab跳转到的位置——用$1、 $2、......来表示，最后一个用$0。

行内和数学显示

在记数学笔记的过程中，最常用的两个片段是mk和dm。

它们负责启动数学模式。第一个片段用于“行内数学”，第二个用于“显示数学”。

代码行内的数学片段是“智能的”：它知道什么时候在$符号后面直接输入一个单词，它会自动加个空格。但如果输入一个非单词的字符，它就不会添加空格了，比如在““$p$-value”情况下，是这样的：

这个片段的代码如下：

snippet mk "Math" wA
${1}

1700页数学笔记火了！全程敲代码，硬核小哥教你上手LaTeX+Vim-*今条头日**





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!p
if t[2] and t[2][0] not in [',', '.', '?', '-', ' ']:
 snip.rv = ' '
else:
 snip.rv = ''
`$2
endsnippet

第一行末尾的w，意味着这个片段会在单词边界处扩展，例如，hellomk不会扩展，但是hello mk会。

用于显示数学的片段更简单，也更加方便；有了它，你可能再也不会忘记用句号结束方程了。

代码：

snippet dm "Math" wA
\[
$1
.\] $0
endsnippet

小写和上标

另一个很有用的片段就是下标。能够把a1改为a1，把a_12改为a{12}。

这个片段的触发器是使用正则表达式。有两种情况会扩展片段。一是你键入一个字符，后面跟着一个数字，比如[A-Za-z]\d；另一种是，一个字符后面有并跟着两个数字，比如[A-Za-z]\d\d。

当你使用括号将正则表达式的一部分装在一个组中时，例如(\d\d)，你可以在 Python中通过match.group (i)来使用它们扩展片段。

至于上标，可以使用td，它就会变成^{}。然而，对于平方、立方和其他一些常见的片段，可以使用专门的代码片段，如 sr、cb等等。

效果图：

代码：

snippet sr "^2" iA
^2
endsnippet
snippet cb "^3" iA
^3
endsnippet
snippet compl "complement" iA
^{c}
endsnippet
snippet td "superscript" iA
^{$1}$0
endsnippet

分数

分数是一个用起来最方便的一个片段，扩展的形式如下：

/ / → frac {}{}
3 / → frac {3}{}
4 pi ^ 2 / → frac {4 pi ^ 2}{}
(1 + 2 + 3) / → frac {1 + 2 + 3}{}
(1 + (2 + 3) /)→(1 + frac {2 + 3}{})
(1 + (2 + 3)) / → frac {1 + (2 + 3)}{

第一个片段的代码很简单：

snippet // "Fraction" iA
\\frac{$1}{$2}$0
endsnippet

第二个和第三个示例，可以使用正则表达式来匹配3/、4ac/、6pi^2/、a2/等表达式。

snippet '((\d+)|(\d*)(\\)?([A-Za-z]+)((\^|_)(\{\d+\}|\d))*)/' "Fraction" wrA
\\frac{`!p snip.rv = match.group(1)`}{$1}$0
endsnippet

看了上边这些，你可能觉得正则表达式太难了。没关系，下面有一个解释得非常直观的图表：

在第四和第五种示例下，要换一种方法。使用UltiSnips的正则表达式引擎解决不了的，Python可以：

这里最后要分享的关于分数的片段，能根据你的选择，来生成一个分数。

你可以先选择一些文本，然后按Tab键，继续输入、然后再按Tab键。

代码中，使用${VISUAL}变量来表示所选的内容。

snippet / "Fraction" iA
\\frac{${VISUAL}}{$1}$0
endsnippet

Sympy和Mathematica

还有一个很酷但用得不多的片段，是使用Sympy来计算数学表达式。例如，输入sympy，然后按下Tab，可以扩展为sympy | sympy，输入sympy 1 + 1 sympy，按下Tab，可以扩展为2。

片段代码：

nippet sympy "sympy block " w
sympy $1 sympy$0
endsnippet
priority 10000
snippet 'sympy(.*)sympy' "evaluate sympy" wr
`!p
from sympy import *
x, y, z, t = symbols('x y z t')
k, m, n = symbols('k m n', integer=True)
f, g, h = symbols('f g h', cls=Function)
init_printing()
snip.rv = eval('latex(' + match.group(1).replace('\\', '') \
 .replace('^', '**') \
 .replace('{', '(') \
 .replace('}', ')') + ')')
`
endsnippet

用Mathematica，也可以做类似的事情：

片段代码：

priority 1000
snippet math "mathematica block" w
math $1 math$0
endsnippet
priority 10000
snippet 'math(.*)math' "evaluate mathematica" wr
`!p
import subprocess
code = 'ToString[' + match.group(1) + ', TeXForm]'
snip.rv = subprocess.check_output(['wolframscript', '-code', code])
`
endsnippet

后缀片段

除了上边这些之外，后缀片段也很值得分享。例如phat→hat{p}和zbar→overline{z}。还有类似的后缀向量，例如v,.→vec{v}和v.,→vec{v}。.和,的顺序没关系，所以可以同时按下它们两个。

这些片段真的可以节省时间，可以按照和老师写板书一样的顺序来记。

注意，bar和hat前缀也依然可以用，只要以较低的优先级添加它们就行。

这些片段的代码是：

priority 10
snippet "bar" "bar" riA
\overline{$1}$0
endsnippet
priority 100
snippet "([a-zA-Z])bar" "bar" riA
\overline{`!p snip.rv=match.group(1)`}
endsnippet

priority 10
snippet "hat" "hat" riA
\hat{$1}$0
endsnippet
priority 100
snippet "([a-zA-Z])hat" "hat" riA
\hat{`!p snip.rv=match.group(1)`}
endsnippet

snippet "(\\?\w+)(,\.|\.,)" "Vector postfix" riA
\vec{`!p snip.rv=match.group(1)`}
endsnippet 

其他片段

此外，小哥还有大约100个常用的片段（*载下**地址附于文末），大多数都很简单。比如，输入!>变成\mapsto，输入->变成\to等等。

fun变成f: \R \to \R :，!>变成\mapsto，->变成\to，cc变成\subset。

lim变成\lim{n \to \infty}，sum变成\sum{n = 1}^{\infty}，ooo变成\infty。

特定课程的片段

除了一些常用的片段，也可以针对特定的课程设定片段。例如，在量子力学这门课中，可以设定一些关于bra/ket符号的片段。

<a|→\bra{a} <ψ|→\bra{\psi}="" a="">→\ket{a}

|ψ>→\ket{\psi}

→\braket{a}{b}

代码：

snippet "\<(.*?)\|" "bra" riA
\bra{`!p snip.rv = match.group(1).replace('q', f'\psi').replace('f', f'\phi')`}
endsnippet
snippet "\|(.*?)\>" "ket" riA
\ket{`!p snip.rv = match.group(1).replace('q', f'\psi').replace('f', f'\phi')`}
endsnippet
snippet "(.*)\\bra{(.*?)}([^\|]*?)\>" "braket" riA
`!p snip.rv = match.group(1)`\braket{`!p snip.rv = match.group(2)`}{`!p snip.rv = match.group(3).replace('q', f'\psi').replace('f', f'\phi')`}
endsnippet

上下文

在编写这些片段时需要考虑的一件事是,“这些片段会与长与常用的文本冲突吗?”

例如，在英语中大约有72个单词包含sr，这意味着当输入disregard这个词时，sr会扩展到^2，出现一个di^2egard。

这个问题的解决方案是，为代码片段添加上下文。

通过使用 Vim 的语法突出显示，可以确定UltiSnips是否应该扩展片段，这取决于你使用的是数学还是文本。

global !p
texMathZones = ['texMathZone'+x for x in ['A', 'AS', 'B', 'BS', 'C',
'CS', 'D', 'DS', 'E', 'ES', 'F', 'FS', 'G', 'GS', 'H', 'HS', 'I', 'IS',
'J', 'JS', 'K', 'KS', 'L', 'LS', 'DS', 'V', 'W', 'X', 'Y', 'Z']]
texIgnoreMathZones = ['texMathText']
texMathZoneIds = vim.eval('map('+str(texMathZones)+", 'hlID(v:val)')")
texIgnoreMathZoneIds = vim.eval('map('+str(texIgnoreMathZones)+", 'hlID(v:val)')")
ignore = texIgnoreMathZoneIds[0]
def math():
 synstackids = vim.eval("synstack(line('.'), col('.') - (col('.')>=2 ? 1 : 0))")
 try:
 first = next(
 i for i in reversed(synstackids)
 if i in texIgnoreMathZoneIds or i in texMathZoneIds
 )
 return first != ignore
 except StopIteration:
 return False
endglobal

现在，你可以将context “math()”添加到只希望在数学上下文中展开的片段中。

context "math()"
snippet sr "^2" iA
^2
endsnippet

请注意,“数学上下文”是一个微妙的东西。 有时你可以使用\text{…}在数学环境中添加一些文本。在这种情况下，你不需要扩展片段。但是，在以下情况下: \[ \text{$...$} \]，它们可以扩展。 这就是为什么math上下文的代码有点复杂。下面的动图说明了这些微妙之处。

除了上述一些片段，你也可以根据自己的需要，来自己添加一些插件或者片段，来提高自己的效率。

用笔还是用电脑？

纯手打记下1700页数学笔记，awesome都不够形容了这位小哥了，堪称理工科学生中的“英雄”。

并非所有人都赞同小哥的做法，强大的高科技工具在传统面前常常会被质疑。

有部分网友认为手写比电脑打字印象深刻，而且要达到这位小哥的熟练程度，恐怕LaTeX和Vim得练习好几年。

既然用笔更方便，为什么还要用电脑来记笔记呢？原因很简单：字太丑！

如果记下来的内容连自己看的欲望都没有，怎么复习课堂笔记呢？至少用电脑记下来的排版工整，让人赏心悦目。

虽然国外网友争论不休，但在国内只要一个条件就可以彻底否决这个方法：不让带电脑进课堂。

对此，你怎么看？

工具传送门：

Linux和Mac系统自带Vim。

Windows用户安装Vim：

https://ftp.nluug.nl/pub/vim/pc/gvim81*ex.e**

Vim插件管理：

https://github.com/junegunn/vim-plug

Vim上的LaTeX插件：

https://github.com/lervag/vimtex

窗口平铺管理器：

https://github.com/baskerville/bspwm

管理Vim片段工具：

https://github.com/SirVer/ultisnips

如果你用不惯Vim，还有Emacs、Atom、VS Code、Sublime，它们都有LaTeX插件，总有一款文本编辑器适合你。

LaTeX常见数学符号输入方法：

https://en.wikibooks.org/wiki/LaTeX/Mathematics

想要熟悉更多的LaTeX使用方法，就需要系统地学习，平时多加练习也必不可少。

博文链接：

https://castel.dev/post/lecture-notes-1/