…"curve" ? I am a big fan of this approach to learning mathematics, just forge ahead and when (if) things fall apart then go back and fix up the foundations. To this end I recommend a couple of books. "The Knot Book" by Adams is a very interesting exploration in topology (without requiring all the years of study at university before you are allowed to learn exactly what a topology is). And in another direction, group…
…theory (TQFT). I don't know the physics, but I'm under the impression you can interpret it as having something to do with quantum states of anyonic particles. For books, you might look at Adams "The Knot Book" or Prasolov "Intuitive Topology" to get a substantial taste of knots and low-dimensional topology.
……可以从几本开始：费曼的《Feynman's Lectures on Computing》。Scott Aaronson 的《Quantum Computing Since Democritus》（虽然预设读者具备一些量子计算背景知识）。我觉得 Colin Adams 的《The Knot Book》（关于拓扑学中的纽结理论）也很适合。
…can start with some. Feynman's Lectures on Computing. Scott Aaronson's Quantum Computing Since Democritus (though it assumes some background knowledge of quantum computing). I think Colin Adam's "The Knot Book" (on knot theory in topology) as well.
…pre-calculus background. We used an early draft of a textbook (not sure of the title or if it’s even been released - our teacher got access because she knew the author) and a lovely knots textbook called “The Knot Book.” I think we gained a really good intuitive understanding of homeomorphism, neighborhoods, and homology groups. Knowing about these topics has been super useful in my studies and career. On the other…
……“曲线”？我非常推崇这种学数学的方法，只管一往无前地学，什么时候（如果）崩了，再倒回去打牢基础。为此我推荐几本书。Adams 写的《The Knot Book》是拓扑学领域一次非常有趣的探索（不需要你在大学熬上几年才被允许了解究竟什么是拓扑）。而在另一个方向上，群……
…"curve" ? I am a big fan of this approach to learning mathematics, just forge ahead and when (if) things fall apart then go back and fix up the foundations. To this end I recommend a couple of books. "The Knot Book" by Adams is a very interesting exploration in topology (without requiring all the years of study at university before you are allowed to learn exactly what a topology is). And in another direction, group…
想要温和浅显的入门，Colin Adams 的《The Knot Book》非常通俗易懂（而且是一步步建立起多项式不变量的概念）。
For a gentile introduction, Colin Adams's "The Knot Book" is very accessible (and builds up the notion of polynomial invariants step by step).
……理论（TQFT）。我不懂物理，但我的印象中你可以把它解释为与任意子（anyonic particles）的量子态有关。至于书籍，你可以看看 Adams 的《The Knot Book》或者 Prasolov 的《Intuitive Topology》，能实打实地领略纽结理论和低维拓扑的风貌。
…theory (TQFT). I don't know the physics, but I'm under the impression you can interpret it as having something to do with quantum states of anyonic particles. For books, you might look at Adams "The Knot Book" or Prasolov "Intuitive Topology" to get a substantial taste of knots and low-dimensional topology.
……可以从几本开始：费曼的《Feynman's Lectures on Computing》。Scott Aaronson 的《Quantum Computing Since Democritus》（虽然预设读者具备一些量子计算背景知识）。我觉得 Colin Adams 的《The Knot Book》（关于拓扑学中的纽结理论）也很适合。
…can start with some. Feynman's Lectures on Computing. Scott Aaronson's Quantum Computing Since Democritus (though it assumes some background knowledge of quantum computing). I think Colin Adam's "The Knot Book" (on knot theory in topology) as well.
……微积分预备（pre-calculus）背景。我们当时用了一本教材的早期草稿（不确定书名，甚至不知道它到底出版了没有——我们老师因为认识作者才拿到的），还有一本很棒的纽结理论教材，叫《The Knot Book》。我觉得我们对同胚（homeomorphism）、邻域（neighborhoods）和同调群（homology groups）建立了非常好的直观理解。掌握这些内容在我的学业和职业生涯中都极为有用。另一方面……
…pre-calculus background. We used an early draft of a textbook (not sure of the title or if it’s even been released - our teacher got access because she knew the author) and a lovely knots textbook called “The Knot Book.” I think we gained a really good intuitive understanding of homeomorphism, neighborhoods, and homology groups. Knowing about these topics has been super useful in my studies and career. On the other…
我是在读完 Colin Adams 的《The Knot Book》之后受到启发做了这个。如果点击底部的“Rolfsen Table”，就能看到完整的画廊。
I was inspired to make this after reading "The Knot Book" by Colin Adams. If you click "Rolfsen Table" at the bottom, you'll see the entire gallery.