Combinatorics/graph theory or number theory books

In summary, the conversation is about recommendations for books on combinatorics and number theory. The speaker suggests "A Walk Through Combinatorics" by Bona for an overview of combinatorics and also mentions "Schaum's Outline to Combinatorics" and "Number Theory" by Burton as good options. They also mention using these books for Math Olympiad preparation.
  • #1
modnarandom
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I'm going to be at an REU for discrete math and combinatorics over the summer. Do you have suggestions for combinatorics books to look at? An introduction to graph theory would especially help (I'm taking an algorithms class but I doubt that it would go into much depth regarding graph theory)? I think the book "A Walk Through Combinatorics" (Bona) is quite good for a general overview of combinatorics, but I'm also wondering about what other things I could look at. Also, any suggestions for a number theory book for someone already familiar with elementary number theory and some background in algebra?
 
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These are the best books I read during Math Olympiad Preparations, Surely It will help you.
Schaum's Outline to Combinatorics.

Number Theory by Burton.
 

1. What is the difference between combinatorics, graph theory, and number theory?

Combinatorics is the branch of mathematics that deals with counting and arranging objects. Graph theory deals with the study of graphs, which are structures made up of vertices and edges. Number theory is the branch of mathematics that studies properties of numbers and their relationships. While all three fields are closely related and use similar techniques, they have distinct focuses and applications.

2. What are some real-world applications of combinatorics, graph theory, and number theory?

Combinatorics has applications in computer science, cryptography, and physics. Graph theory is used in computer networking, transportation systems, and social networks. Number theory has applications in cryptography, coding theory, and computer science.

3. What are some recommended books for learning about combinatorics, graph theory, and number theory?

For combinatorics, "A Walk through Combinatorics" by Miklos Bona and "Combinatorics: Topics, Techniques, Algorithms" by Peter J. Cameron are popular choices. For graph theory, "Introduction to Graph Theory" by Douglas B. West and "Graph Theory" by Reinhard Diestel are highly recommended. For number theory, "Elementary Number Theory" by Kenneth H. Rosen and "A Course in Number Theory and Cryptography" by Neal Koblitz are well-regarded texts.

4. Is it necessary to have a strong background in mathematics to understand these topics?

While a strong foundation in mathematics can certainly be helpful, it is not always necessary to understand these topics. Many introductory books on combinatorics, graph theory, and number theory assume only a basic knowledge of algebra and geometry. However, as the subjects become more advanced, a deeper understanding of mathematical concepts and techniques will be required.

5. How can I apply the concepts learned from these books to my own research or projects?

The concepts learned from these books can be applied to a wide range of research or projects. For example, combinatorics can be used to analyze and optimize algorithms in computer science, while graph theory can be used to model and study various network systems. Number theory is also a crucial component in many modern day technologies, such as cryptography and coding. By gaining a strong understanding of these topics, you can apply them to your own research or projects in a variety of fields.

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