Reddit reviews The Knot Book

Last two problems in The Knot Book:

> 10.10 Figure out how to represent a four-sphere in six-space. "Draw" an unknotted four-sphere in six-space.

> 10.11 Draw a knotted four-sphere in six-space.

Though maybe that's not as challenging as it sounds (you know, drawing objects with four spatial dimensions on two-dimensional paper, twisted in six dimensions). I haven't read that far yet.

The book Ideals, Varieties and Algorithms by Cox, Litle and O'Shea is a very good undergraduate level algebraic geometry book. It has the benefit of teaching you the commutative algebra you need along the way instead of assuming you know it.

I'm not really aware of any algebraic topology books I'd consider undergraduate, but most of them are accessible to first year grad students anyway, which isn't too far away from senior undergrad. Some of my favorite sources for that are Munkres' book and Fulton's Book.

For knot theory, I haven't really studied it myself, but I've heard that The Knot Book is quite good and quite accessible.

>I didn’t mean to offend anyone.

None taken; I just meant that math is huge, and none of it is inherently boring, but I understand that it can seem that way if you're not used to thinking about it.

It looks like there are already some good suggestions regarding how math relates to other subjects, so let me propose something purely mathematical: knot theory. It may not seem like "math", depending on what you've been exposed to, but this is what might make it a great topic for you. Here's the kind of thing a knot theorist thinks about:

Take a piece of string, tie a knot in it, and then take the two ends and tape them together. There are many ways of doing this. Here's something you might get; and here's another possibility. But maybe secretly, those are actually the same, in the sense that you can get from one to the other by just adding twists or moving bits of the string around. How can you tell if they're different or not? This is what knot theory focuses on.

If this interests you, here's a really great book written for laypeople about knot theory. It has lots and lots of pictures that you can learn a tremendous amount from just by staring for a while. It will probably be a challenge to read through, and a lot of it might go over your head, but that's fine; that's what reading math is like for everyone. There's also a large chance that reading this will feel nothing like math at all, and in this sense there's no need to be afraid.

Read The Knot Book by Colin Adams.

I am in a knot theory class and we are using "The Knot Book" by Colin Adams. I think the book is very readable and informative and doesn't really expect much any prior knowledge.

I've heard good things about Adam's book The Knot Book if knot theory is your thing.

One thing that you run into in math is a distinct lack of books and articles that explore ideas without proving them. They certainly exist, but are not the norm. We also suffer from a wealth of very poorly written books.

Survey articles and introductory tracks aimed at introducing young mathematicians to advanced topics do exist in some volume and they tend to be better written and in a more conversational tone. They want to familiarize you with a body of work that proving all in one place would be a monumental task so they just don't do it. If I were you I'd look in that direction, but you wont learn very much about the nuts and bolts of what's going on.

https://www.amazon.com/Knot-Book-Colin-Adams/dp/0821836781

Knot Theory

It's simple and accessible great for casual learning.
If you've already had much topology, you'll want a more in-depth book after you finish this one. This book is accessible to undergrad and even high school learners. But it's a great jumping off point even if you're more mathematically sophisticated.