Image about connection of different parts of Mathematics

In summary, the conversation revolved around a graphic that illustrates the connections between different fields of mathematics, starting from basic concepts and leading up to QFT and GR. The graphic is simple, with yellow boxes representing different theories and possibly using rectangles and circles. The person asking for the graphic is looking for help in finding it, mentioning that it may be in the book "Mathematical Physics" by Robert Geroch or on arxiv.
  • #1
beta3
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0
Hi guys!


Today I remembered that I used to have a fantastic image (like a flow chart) about different parts of mathematics and how they are connected. In the final stage (at the top), they were connected to QFT and GR.
It's down->top, at the lower end were basic mathematics (sets, boolian algebra, etc.), going up came more complicated theories (groups, fields, linear algebra, analysis, vector algebra, manifolds, etc.), at the top were QFT and GR.

Interesting about that graphic was that it showed how different fields of mathematics are connected, like adding a operation to a set and you get a group. Or combining Linear Algebra and Analysis and you get Vector Algebra.

The graphic is rather simple, the boxes with the different theories were yellow and rectangles (and circles?)

Does anyone happen to know what I mean?

If yes, could you please post it here.
I've been looking for it for hours, but can't find it and i cannot recall where I saw it the first time.


Thanks
 
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  • #2
I remember there's one of these in the book "Mathematical Physics" by Robert Geroch.
 
  • #3
  • #4
morphism said:
Are you talking about this: http://www.math-atlas.org/?

No, not this one. It was more general.


ad) Robert Geroch's "Mathematical Physics"
No, I don't think so. But I have never seen his book (and it isn't available in my library), so i don't know for sure.

It might have been somewhere on arxiv... but I couldn't find it or wouldn't know how to search more effectively
 

1. How are different branches of mathematics connected?

Different branches of mathematics are connected through the use of common concepts, principles, and techniques. For example, algebra, geometry, and calculus all use the concept of variables and equations to solve problems.

2. What is the importance of understanding the connection between different parts of mathematics?

Understanding the connection between different parts of mathematics allows for a deeper understanding of the subject as a whole. It also allows for the application of concepts from one branch to another, making problem-solving more efficient and effective.

3. How does the study of one branch of mathematics help in understanding another branch?

The study of one branch of mathematics can help in understanding another branch by providing a foundation of fundamental concepts and techniques. For example, understanding basic algebra is essential in tackling more advanced concepts in calculus.

4. Can you give an example of how two seemingly different branches of mathematics are connected?

Yes, chaos theory and fractal geometry may seem like two very different branches of mathematics, but they are actually closely connected. Chaos theory uses complex equations to study the behavior of dynamical systems, while fractal geometry is used to describe the irregular and self-similar patterns found in chaotic systems.

5. How does the connection between different parts of mathematics impact real-world applications?

The connection between different parts of mathematics is crucial in real-world applications. For example, engineers use principles from calculus, geometry, and statistics to design structures, while economists use mathematical models and equations to make predictions and analyze data. Without understanding the connection between different branches, these applications would not be possible.

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