…all fluff with not much substance. I found http://jeffe.cs.illinois.edu/teaching/algorithms/ pretty good for an overview over Algorithms. If you like something in a similar vein to TAOCP, the book 'Combinatorial Optimization' by Alexander Schrijver fits the bill. It teaches you everything you ever wanted to know and then some on the mathematics behind problems in P. Just like TAOCP it is also a detailed overview over known…
……数学，所以我不太相信自己能判断一段数学对门外汉来说有多难。我觉得引用的那个证明读起来很容易。关于你的补充：你可以看看 Alexander Schrijver 的《Combinatorial Optimization: Polyhedra and Efficiency》。它风格上有趣的地方在于，作者能让每一行都需要持续思考，而大多数书里总有特别难和特别简单的部分。
…mathematics, so I do not trust myself to judge how hard a piece of mathematics is for outsiders. I find the proof cited is easy to read. About your addendum: You could have a look at Alexander Schrijver's "Combinatorial Optimization: Polyhedra and Efficiency". The interesting thing about its style is, that the author manages to make all lines require constant thought, while in most books there are really hard and really easy parts.
我有一个聪明的同事也喜欢 Skiena 的《Algorithm Design Manual》。不过我觉得那本书太花架子了。但我喜欢 Alexander Schrijver 的《Combinatorial Optimization: Polyhedra and Efficiency》这样的书。（不是入门书，但关于 P 和 NP 你想知道的它都有。）
I have a smart co-worker who also likes Skiena's Algorithm Design Manual. I found that book to fluffy, though. But then I enjoy books like "Combinatorial Optimization - Polyhedra and Efficiency" by Alexander Schrijver. (Not a beginner's book, but it has anything you ever wanted to know about P and NP.)
免责声明：我完全不知道完整的学习路径。但这里有些你可能会感兴趣的建议。如果你想在复杂性上猛下功夫，可以试试 Alexander Schrijver 的《Combinatorial Optimization: Polyhedra and Efficiency》。但它基本上相当于复杂性领域的 Knuth《Art of Computer Programming》（就严谨程度和方法广度而言）。我有那三……
Disclaimer: I have no clue of a complete learning path. But here are some suggestions you might find interesting. If you want to go heavy on complexity, you could try 'Combinatorial Optimization: Polyhedra and Efficiency' by Alexander Schrijver. But it's basically the equivalent of Knuth's Art of Computer Programming for complexity (in terms of rigour and breadth of approach). I have the three…
…non-linear mathematical optimization is most more typical for many machine learning applications. Many pratical applications in scheduling, logistics, planning etc used linear (integer) programming and combinatorial optimization. The following are some points towards that body of literature. Alexander Schrijver [1] has lecture notes on Combinatorial Optimization on his website [2]. He also has an affordable 1800 page three volume…
……全是花架子，没什么实质内容。我觉得 http://jeffe.cs.illinois.edu/teaching/algorithms/ 作为算法概览相当不错。如果你喜欢类似 TAOCP 那种风格，Alexander Schrijver 的《Combinatorial Optimization》正合口味。它会教你关于 P 类问题背后数学的一切你想知道的东西，甚至更多。和 TAOCP 一样，它也是对已知……的详细综述。
…all fluff with not much substance. I found http://jeffe.cs.illinois.edu/teaching/algorithms/ pretty good for an overview over Algorithms. If you like something in a similar vein to TAOCP, the book 'Combinatorial Optimization' by Alexander Schrijver fits the bill. It teaches you everything you ever wanted to know and then some on the mathematics behind problems in P. Just like TAOCP it is also a detailed overview over known…
……数学，所以我不太相信自己能判断一段数学对门外汉来说有多难。我觉得引用的那个证明读起来很容易。关于你的补充：你可以看看 Alexander Schrijver 的《Combinatorial Optimization: Polyhedra and Efficiency》。它风格上有趣的地方在于，作者能让每一行都需要持续思考，而大多数书里总有特别难和特别简单的部分。
…mathematics, so I do not trust myself to judge how hard a piece of mathematics is for outsiders. I find the proof cited is easy to read. About your addendum: You could have a look at Alexander Schrijver's "Combinatorial Optimization: Polyhedra and Efficiency". The interesting thing about its style is, that the author manages to make all lines require constant thought, while in most books there are really hard and really easy parts.
我有一个聪明的同事也喜欢 Skiena 的《Algorithm Design Manual》。不过我觉得那本书太花架子了。但我喜欢 Alexander Schrijver 的《Combinatorial Optimization: Polyhedra and Efficiency》这样的书。（不是入门书，但关于 P 和 NP 你想知道的它都有。）
I have a smart co-worker who also likes Skiena's Algorithm Design Manual. I found that book to fluffy, though. But then I enjoy books like "Combinatorial Optimization - Polyhedra and Efficiency" by Alexander Schrijver. (Not a beginner's book, but it has anything you ever wanted to know about P and NP.)
免责声明：我完全不知道完整的学习路径。但这里有些你可能会感兴趣的建议。如果你想在复杂性上猛下功夫，可以试试 Alexander Schrijver 的《Combinatorial Optimization: Polyhedra and Efficiency》。但它基本上相当于复杂性领域的 Knuth《Art of Computer Programming》（就严谨程度和方法广度而言）。我有那三……
Disclaimer: I have no clue of a complete learning path. But here are some suggestions you might find interesting. If you want to go heavy on complexity, you could try 'Combinatorial Optimization: Polyhedra and Efficiency' by Alexander Schrijver. But it's basically the equivalent of Knuth's Art of Computer Programming for complexity (in terms of rigour and breadth of approach). I have the three…
……非线性数学优化在许多机器学习应用中更为常见。排程、物流、规划等领域的许多实际应用使用的是线性（整数）规划和组合优化（combinatorial optimization）。以下是针对这块文献的一些指引。Alexander Schrijver [1] 在他的个人网站上放了组合优化的讲义 [2]。他还写过一套价格亲民、厚达 1800 页的三卷本……
…non-linear mathematical optimization is most more typical for many machine learning applications. Many pratical applications in scheduling, logistics, planning etc used linear (integer) programming and combinatorial optimization. The following are some points towards that body of literature. Alexander Schrijver [1] has lecture notes on Combinatorial Optimization on his website [2]. He also has an affordable 1800 page three volume…