What is Reddit's opinion of
Introduction to Graph Theory (Dover Books on Mathematics)?
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7 reviews of this product found across Reddit:
I'd recommend graph theory as a way to learn about real math (by which I assume you mean more abstract math that is less focused on computation and more on learning to develop conjectures, prove them rigorously). One advantage of graph theory is that the prerequisites for it are fairly simple, not like say analysis where a lot of it won't make sense if you don't have a good background in calculus. Another is that the material has a ton of practical applications (assuming you will care about these eventually) in Computer Science and Electrical Engineering.
There are many books out there on this subject, I like this cheap dover book.
I'm currently reading through this, and it's extremely accessible. The way Trudeau starts with the most basic set theoretic definition of a graph and gradually introduces and builds on additional properties of graphs is so natural and intuitive.
It's also available on Amazon for dirt cheap.
EDIT: It's worth mentioning that it's a older text, which hinders it in a few areas. For example, at the time it was written, the Four Color Conjecture was still an open problem. As such, the book focuses on the Five Color Theorem instead.
From the ground up, I dunno. But I looked through my amazon order history for the past 10 years and I can say that I personally enjoyed reading the following math books:
An Introduction to Graph Theory
Coding the Matrix: Linear Algebra through Applications to Computer Science
Oops! I'm sorry, for some reason I was under the impression you were still in college.
Here's a link to Tao's Analysis. This one's a solid textbook, so it's not leisure reading persay. It would be a good idea to brush up on calculus. I recommend this book. I'm not exactly sure how much calculus you're expected to know before you do real analysis (I'm not actually a math student, I was a physics student who never took real analysis).
Here's a link to that youtube video of Terence Tao's talk on gaps between primes.
I'll definitely read that book about Mochizuki! I knew there was that controversy about it like a year ago, but I never really kept up with it.
And here's a bunch of things that I thought were cool, hopefully you think some of these are cool too!
- You might like this book on graph theory. "A stimulating excursion into pure mathematics aimed at "the mathematically traumatized," but great fun for mathematical hobbyists and serious mathematicians as well."
Here are some youtube channels that I like.
- https://www.youtube.com/c/brightsideofmaths
- https://www.youtube.com/c/numberphile
- https://www.youtube.com/user/standupmaths. This guy also has a book called Humble Pi, which a collection of stories of when math goes wrong (or when people use math incorrectly).
- https://www.youtube.com/c/Mathologer
- https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A
- https://www.youtube.com/channel/UCIyDqfi_cbkp-RU20aBF-MQ
- https://www.youtube.com/user/singingbanana
- https://www.youtube.com/user/Vihart
I know this is removed, so I can recommend my tool which builds a graph of products that are often bought together at Amazon.
http://www.yasiv.com/#/Search?q=graph%20theory&category=Books&lang=US - this is a network of books related to graph theory. Finding the most connected product usually yields a good recommendation. In this case it recommends to take a deeper look at https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709
>I like how you came here to make a distinction without a difference
That you think these sets are equivalent is the problem with "STEM" in this country. I'm not blaming you, it's not your fault. For whatever reason, set theory is barely discussed. Even in multivariate calculus, the most you care about sets is with domain and range, just like in algebra. Here are a few topics that are mathematics, and not arithmetic:
-Topology (Better than Munkres)
-<strong>Abstract</strong> Algebra (Groups/Rings/Fields)
Basic quantifiers pop up first in set theory, which as far as I can tell is only recommended after integral calculus. Things like ∀, and ∃ have a particular meaning, and their orders and quantities are very specific.
If you would like to know more about the difference between mathematics and arithmetic (which is a subset), then start with set theory. You'll need that to do anything else. I can try to answer any other questions you may have.
Trudeau's Introduction to Graph Theory is fantastic and it's like $5. There's also Keller and Trotter from Georgia Tech, which is a fantastic free book.
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