Proof Theorems: Learn How to Make Proofs | Beginner's Guide

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In summary, the conversation revolves around the topic of learning to make proofs for various theorems. The speaker is seeking a systematic way to make proofs and wondering where to start and what statements to base the proofs on. They also ask for a website or book to learn different proof techniques. The response mentions that there is no general list of theorems that engineers need to know how to prove, and using Google can be helpful in finding famous proofs. It is also mentioned that engineers do not necessarily need to know how to prove theorems, but rather apply them.
  • #1
nebbione
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Hi everyone! I'm a new user of this forum!
I was interested in learning to make proofs of the various theorems.
Is there a schematical way to make the proofs ?
Where should i start ? And what are the statement for my proofs that are absolutely true so that i can base my proof on ?
Is there a website or a book i can use to learn the various ways to proof something ?
 
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  • #2
Are there any particular theorems you had in mind - this is a big subject.
There are no general, systematic, methods though. Some theorems have taken generations to prove (eg. Fermat's Last theorem.)

Proofs are built from statements that are assumed true (maybe they were proved earlier).
The rules of arithmetic would be an example.

Probably a good start would be a course on linear algebra.
 
  • #3
thank you! but which are the theorems that i have to know the proof as an engineer ?
 
  • #4
nebbione said:
thank you! but which are the theorems that i have to know the proof as an engineer ?

There is no magic list.

And you aren't giving us enough information to answer you questions.
 
  • #5
Sorry i mean demonstration of famous theorems or most known so that i can learn how to proof
 
  • #7
thank you very much ! i know about google sorry for a too general question!
 
  • #8
nebbione said:
thank you! but which are the theorems that i have to know the proof as an engineer ?
I accord with the usual physicist snobbiness I will point out that Engineers do not need to prove theorems - they only need to apply them. :D
 
  • #9
Post 6 and 8... awesome.
 

What is a proof theorem?

A proof theorem is a mathematical statement or argument that is used to prove the truth or validity of a mathematical or logical statement. It involves using logical reasoning and existing mathematical concepts to support or demonstrate the truth of a statement.

Why is it important to learn how to make proofs?

Learning how to make proofs is important because it helps develop critical thinking and logical reasoning skills. It also allows for a deeper understanding of mathematical concepts and the ability to solve more complex problems.

What are the key elements of a proof theorem?

The key elements of a proof theorem include a statement to be proven, assumptions or given information, logical reasoning steps, and a conclusion that follows from the previous steps.

What are some common strategies for making proofs?

Some common strategies for making proofs include using direct proof, proof by contradiction, proof by contrapositive, and mathematical induction. It is also important to clearly define all terms and assumptions, and to use clear and concise logical reasoning steps.

Are there any tips for beginners learning how to make proofs?

Yes, some tips for beginners include practicing regularly, starting with simple proofs and gradually progressing to more complex ones, seeking help or guidance when needed, and breaking down the proof into smaller steps to make it more manageable.

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