Is it possible to become fluent in proofs without prior experience?

  • Thread starter Winzer
  • Start date
In summary, I want to take a real analysis course, and eventaully an analysis course. I would really like to become fluent in the language of the calculus as well as proofs, almost to make as a second language. It can take years to master it but is rewarding. I am a physics major so it could be tough going from applied to pure, but I do not have much expierence in proofs. How can I resolve this?
  • #1
Winzer
598
0
I want to take a real analysis course, and eventaully an analysis course. I would really like to become fluent in the language of the calculus as well as proofs, almost to make as a second language. (I hear it can take years to master it but is rewarding). I am a physics major so it could be tough going from applied to pure.

However, I do not have much expierence in proofs. How can I resolve this?
Show I buy a book on logic? I have "how to prove it," by Daniel J Velleman. It is just hard getting motivated reading it as aposed to a Physics read.

A thing I notice when I look at a proof sometimes is that complicated notation/symbols are used to express simple ideas. There are tons of subtlies that must be taken into account.
This gets on my nerves but I can grip through it.
I hear it is hard getting started in proofs, but it gets easier, is this true?
Advice would be appreicated.

By the way I am done with all three semesters of Calc, and will be taking diff eq, and linear algebra.
 
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  • #2
i recommend a good calc book with proofs like spivak. since you know the calc, the proofs will be easier to follow.
 
  • #3
mathwonk said:
i recommend a good calc book with proofs like spivak. since you know the calc, the proofs will be easier to follow.

Mathwonk I have heard Spivak is excellent, how does it compare to Apostoll?

Also am I right about proofs starting out to be difficult? It might be harder since I am a phys major.
Being a respectable Professor in Mathematics, can you give me any general advice when it comes to proofs?
Thank you
 
  • #4
Winzer said:
Mathwonk I have heard Spivak is excellent, how does it compare to Apostoll?

Also am I right about proofs starting out to be difficult? It might be harder since I am a phys major.
Being a respectable Professor in Mathematics, can you give me any general advice when it comes to proofs?
Thank you

Similar to that question; how does the Howard Anton book compare to the Spivak book? I bought an old, thick, Calculus book by Anton but have never seen the Spivak book.
 
  • #5
You could try a number theory book for learning proof by induction, bu that will only get you so far in Analysis. A good Calculus book is really the way to go. Get very familiar with Epsilon and Delta, as well as terms like increasing, strictly increasing, monotone, convergence, divergence, continuity, uniform continuity. Maybe review sequences and series a bit if you have had them before.
if you ever find yourself writing "given Epsilon < 0," then you need to go back and start over with your Calculus 1 proofs
 
  • #6
I was looking at these tow books:
Mathematical Analysis- by T. Apostol
Mathematical Analysis- Zador

Both look really good.
 
  • #7
Similar to that question; how does the Howard Anton book compare to the Spivak book?

Not favorably.
 
  • #8
i would recommend a transition to advanced mathematics by gary chartrand.
 
  • #9
I just started reading Spivak's book, it's hard and I've already taken Calculus 1 and 2.

Thinking vs. Computing, it's a big change ... uh. I can't wait for school to start up again, then I can bug my Professors :-]
 

FAQ: Is it possible to become fluent in proofs without prior experience?

What is the purpose of preparing for analysis/proofs?

The purpose of preparing for analysis/proofs is to organize and structure your thoughts and ideas before conducting the actual analysis or proof. It helps to ensure that your arguments are logical, supported by evidence, and well-reasoned.

How do you prepare for analysis/proofs?

To prepare for analysis/proofs, start by clearly defining the problem and identifying the key concepts and variables involved. Then, gather and review relevant information and data, and create an outline or framework for your analysis or proof. It can also be helpful to brainstorm and test different hypotheses or approaches.

What are some common mistakes to avoid when preparing for analysis/proofs?

Some common mistakes to avoid when preparing for analysis/proofs include not fully understanding the problem or question, not considering alternative perspectives or counterarguments, and not providing enough evidence or support for your arguments. It is also important to be aware of biases or assumptions that may affect your analysis or proof.

How do you know when you are adequately prepared for analysis/proofs?

You can know when you are adequately prepared for analysis/proofs when you have a clear understanding of the problem or question, a well-organized and structured approach, and sufficient evidence or support to back up your arguments. It can also be helpful to have someone else review your preparation and provide feedback or suggestions.

Are there any tools or resources that can help with preparing for analysis/proofs?

Yes, there are several tools and resources that can help with preparing for analysis/proofs. These include brainstorming techniques, concept mapping software, and online databases for gathering information and data. It can also be helpful to consult textbooks, research papers, and other relevant sources for guidance and examples.

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