#9 in Applied mathematics books
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Reddit mentions of Introduction to Graph Theory (Dover Books on Mathematics)
Sentiment score: 11
Reddit mentions: 16
We found 16 Reddit mentions of Introduction to Graph Theory (Dover Books on Mathematics). Here are the top ones.
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Specs:
Height | 8.5 Inches |
Length | 5.5 Inches |
Number of items | 1 |
Release date | February 1994 |
Weight | 0.51 Pounds |
Width | 0.5 Inches |
You are in a very special position right now where many interesing fields of mathematics are suddenly accessible to you. There are many directions you could head. If your experience is limited to calculus, some of these may look very strange indeed, and perhaps that is enticing. That was certainly the case for me.
Here are a few subject areas in which you may be interested. I'll link you to Dover books on the topics, which are always cheap and generally good.
Basically, don't limit yourself to the track you see before you. Explore and enjoy.
In the case of this paper, it's referring to dimensions in a mathematical sense, not a physical "space-like" or "time-like" sense. In that regard, the more abstract mathematical notion of "dimension" is used all the time to describe things on a computational level that most people wouldn't associate with their idea of "dimension". For example, a picture on the computer can be thought of as a single point in some extremely high dimensional space (Im talking on the scale of millions of dimensions).
Personally, I'd find a more interesting occult correlation between the neural network structure shapes being directed/undirect simplices. If anyone is curious about learning about some of the mathematics behind those sorts of structures (called graphs) I'd recommend Introduction to Graph Theory by Dover books on the subject. It's a great introduction and has a great preface on the subject of mathematics.
Here is the book I always recommend for people who want an introduction to graph theory:
It's super cheap (only $3.99 on Amazon) and I think it's really a good introduction to the subject. It doesn't go as far in depth as more advanced books, but Kuratowski's theorem is covered in Chapter 3.
He really should be starting with the Trudeau, much better bed side reading.
They may not be the best books for complete self-learning, but I have a whole bookshelf of the small introductory topic books published by Dover- books like An Introduction to Graph Theory, Number Theory, An Introduction to Information Theory, etc. The book are very cheap, usually $4-$14. The books are written in various ways, for instance the Number Theory book is highly proof and problem based if I remember correctly... whereas the Information Theory book is more of a straightforward natural-language summary of work by Claude Shannon et al. I still find them all great value and great to blast through in a weekend to brush up to a new topic. I'd pair each one with a real learning text with problem sets etc, and read the Dover book first quickly which introduces the reader to any unfamiliar terminology that may be needed before jumping into other step by step learning texts.
You could start by going through here and seeing if anything catches your eye but if your still in high school I suppose you might not know what to look for. When I was in high school (currently an undergraduate in math) this book was one that really made me first consider the idea of trying to become a mathematician: R. Trudeau's Introduction to Graph Theory. It is a pretty short read but gives a very nice introduction to graph theory and what pure mathematics is all about.
Yea John Green certainly isn't for everyone, particularly outside of the YA target audience. I wouldn't say it's his strongest book either, but it might be useful to check out.
In terms of mathematical directions you could go, graph theory is actually a pretty solid field to work in. It's basics are easy to grasp, the open problems are easy to understand and explain, and there are many obscure open ones that are easily within reach of a talented high schooler. In fact a lot of combinatorics is like that as well. I would recommend the book Introduction to Graph theory by Trudeau (which was originally titled Dot's and Lines). It's a great introduction to mathematical proof while leading the reader to the forefront of graph theory.
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
Introduction to Topology
Coding the Matrix: Linear Algebra through Applications to Computer Science
A Book of Abstract Algebra
An Introduction to Information Theory
To pedal off of this, graph theory is pretty much everywhere and it's really straightforward to learn. This is a really good intro book and it's really cheap.
Read this: https://www.amazon.com/Algebra-Israel-M-Gelfand/dp/0817636773 and you're more than set for algebraic manipulation.
And if you're looking to get super fancy, then some of that: https://www.amazon.com/Method-Coordinates-Dover-Books-Mathematics/dp/0486425657/
And some of this for graphing practice: https://www.amazon.com/Functions-Graphs-Dover-Books-Mathematics/dp/0486425649/
And if you're looking to be a sage, these: https://www.amazon.com/Kiselevs-Geometry-Book-I-Planimetry/dp/0977985202/ + https://www.amazon.com/Kiselevs-Geometry-Book-II-Stereometry/dp/0977985210/
If you're uncomfortable with mental manipulation of geometric objects, then, before anything else, have a crack at this: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709/
Since last we spoke, I have mostly been reading:
Today I purchased:
What are you majoring in?
What you're describing could just be a personality issue that's unrelated to maths, that maths is just be an example of. That being said, I find the way people are taught maths to be a form of abuse. It's like the way someone who was molested as a child might have weird issues with sex, so do most people have issues with maths who have had to go through maths in high school.
Just so that you know, what you think maths is, is actually almost not at all what maths really is. I would recommend, after you finish your exams and have nothing better to do, read this book about graph theory. It's $4 + shipping from amazon, or you may have it in the library wherever you're studying. It's kind of pointless, but there are a few nice bits about the philosophy of maths.
If anyone is interested in learning more about graph theory, this is a great (and brief) book that requires very little mathematical background. I highly recommend it.
>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:
-Set Theory
-Topology (Better than Munkres)
-Graph Theory
-Abstract 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.
Not a book, but you might like this: https://dev.to/vaidehijoshi/a-gentle-introduction-to-graph-theory
As for a book, try this: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709
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