What is the logical interdependence of mathematics?

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In summary, for understanding the map of mathematics, you will need a strong foundation in linear algebra and calculus. These are important for other branches, especially differential equations. To understand topology, mathematical maturity is necessary, along with some knowledge of propositional calculus. For partial differential equations, real analysis, complex analysis, and measure theoretic functional analysis are essential. Some helpful resources for these topics include the book "Topology" by Alexandrov, the Mathematical Atlas by Dave Rusin, and books by V. Arnol'd, such as "Lectures on Partial Differential Equations" and "Ordinary Differential Equations."
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Anti Hydrogen
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I mean what is the map of mathematics? for example, what do i need to know for understanding topology? or what do i need know for understanding partial differential equations?
thanks in advance
 
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  • #2
Anti Hydrogen said:
Summary: I mean what is the map of mathematics? for example, what do i need to know for understanding topology? or what do i need know for understanding partial differential equations?

thanks in advance
Here is your map
32264483720_c51bdde679_b.jpg


but I doubt that this is of much help. However, your question is so broad that it is impossible to answer in such a generality, except that mathematics usually starts with linear algebra and calculus. These are important for anything else, esp. for differential equations.
 
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fresh_42 said:
Here is your map
View attachment 249703

but I doubt that this is of much help. However, your question is so broad that it is impossible to answer in such a generality, except that mathematics usually starts with linear algebra and calculus. These are important for anything else, esp. for differential equations.
i have already seen that map but thanks anyway
 
  • #4
You need nothing for topology, except mathematical maturity (i.e. knowing how to write proofs and being comfortable working with sets).

For partial differential equations (from a pure mathematician's point of view), you certainly need real analysis and further down the road some complex analysis and measure theoretic functional analysis.
 
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Some understanding of propositional calculus is helpful, especially of the opertation ##\Rightarrow##, which confuses the hell out of countless first year students.

Then there's nothing much to it. Take relevant definitions and try to reproduce proofs. Start with simple ideas such as introductory linear algebra or naive set theory. Topology can wait.

Don't try to fly too high too early. Get comfortable with walking, first.
 
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  • #8
fresh_42 said:
Here is your map
View attachment 249703

but I doubt that this is of much help. However, your question is so broad that it is impossible to answer in such a generality, except that mathematics usually starts with linear algebra and calculus. These are important for anything else, esp. for differential equations.
I think graffiti is against PF rules ;).
 
  • #9
I suggest books by V. Arnol'd, such as Lectures on partial differential equations, where he says prerequisites for at least his book on PDE, are linear algebra, analysis, and ordinary differentil equations; which leads to my recommending his book on Ordinary differential equations.
 

FAQ: What is the logical interdependence of mathematics?

1. What is the definition of logical interdependence in mathematics?

Logical interdependence in mathematics refers to the relationship between different mathematical concepts and how they rely on each other to form a logical system. It is the idea that one mathematical concept or statement can be derived from another, and that all mathematical ideas are interconnected.

2. How does logical interdependence apply to real-world situations?

In the real world, logical interdependence in mathematics allows us to make accurate predictions and solve complex problems. For example, in physics, the laws of motion (which are mathematically interdependent) can be used to predict the trajectory of a projectile.

3. Can you give an example of logical interdependence in mathematics?

One example of logical interdependence in mathematics is the relationship between addition and multiplication. The concept of multiplication can be derived from repeated addition, and addition is necessary for solving multiplication problems.

4. How does understanding logical interdependence help in learning mathematics?

Understanding logical interdependence in mathematics can help in learning by providing a deeper understanding of how different concepts are connected and how they build upon each other. This can make it easier to learn and apply new mathematical ideas.

5. Are there any drawbacks to logical interdependence in mathematics?

One potential drawback of logical interdependence in mathematics is that it can make it difficult to understand a concept without first understanding the concepts it relies on. This can create a barrier for some learners and may require a more comprehensive approach to teaching and learning mathematics.

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