Tagged Questions

4
votes
0answers
58 views

Good examples of proofs in mathematics exemplary of creative reasoning [closed]

Just what the title says. I'm not looking for any proofs that require specialized knowledge past the very fundamentals of real analysis. I'm looking for proofs for important results (don't have to be ...
23
votes
2answers
451 views

English words in written mathematics

I recently marked over $100$ assignments for a multivariable calculus course. One question which a lot of people did poorly was proving a given set was open. Aside from issues relating to rigour and ...
2
votes
1answer
94 views

Providing a sketch for a proof before proceeding through the actual proof. [closed]

Question is pretty straightforward. My mathematics is sloppy, and I recognize my inaptitude in that my proofs are more or less too intuitive. My diagnosis dictates the fact that I attack a problem ...
30
votes
7answers
2k views

How does a non-mathematician go about publishing a proof in a way that ensures it to be up to the mathematical community's standards?

I'm a computer science student who is a maths hobbyist. I'm convinced that I've proven a major conjecture. The problem lies in that I've never published anything before and am not a mathematician by ...
5
votes
3answers
192 views

In a proof that is reliant on proven theorems, does one assume the reader's familiarity with said theorems, or explicitly include their logic?

In composing a proof that is reliant on proven theorems, does one simply assume the reader's familiarity with said theorems, or does one explicitly include their logic in the new logic?
3
votes
0answers
48 views

What do you do to facilitate proof clarity? [closed]

I tend to write proofs in the style of a paragraph or essay, using words (if-then) for the "logic" and reserving symbols (e.g. $\in, \subseteq$ etc.) for the "mathematics." (On the other hand, within ...
7
votes
4answers
281 views

Should one imagine diagrams/figures when working?

I'm working through Baby Rudin and find it exceedingly difficult to understand what's happening without drawing a small figure. For instance when proving properties of compactness, I would often draw ...
5
votes
6answers
379 views

How to make sure a proof is correct

If you come up with a proof of a mathematical proposition, how do you verify the proof is correct? Put it another way, how do you avoid a wrong proof? I guess there is no definitive answer to this. ...
1
vote
1answer
185 views

Two weird proofs about continuity in normed vector spaces

I am reading a pair of "proofs" that a friend sent to me. I really don't understand some passages, so I hope someone could help me. The questions are the following First Question. The result to be ...
0
votes
1answer
106 views

Combinatorical Proof Rigor [closed]

Many people feel that a combinatorical proof of a particular algebraic identity is not as rigorous as an analytic one. However, I'm not quite sure why people feel this way. So, I am curious as to what ...
12
votes
4answers
430 views

Advice for writing good mathematics?

It's been a (far-fetched, possibly) goal of mine to some day write a math Textbook. I've been thinking about writing this question for a while, but reading an exceedingly mediocre text on Mathematical ...
0
votes
0answers
94 views

What is the convention for using results of theorems left as exercise in the text?

I'm working on an exam, and have a solid proof for one of the problems, but it's reliant on a number of theorems left exercises in the textbook which were not assigned as coursework. What, if any ...
2
votes
1answer
156 views

Found a simpler proof, now how do I know if it's original?

I've found a simpler proof for some identity/theorem, hypothetically speaking, of course ;) How do I know if it hasn't been done before? For important results it's fairly easy to find. By the way, I ...
2
votes
2answers
183 views

Introduction to proofs with a fair amount of hand-holding?

Lately I've gotten a friend of mine interested in mathematics. He has no college-level education to speak of, but is well employed as a software engineer. So I feel he's competent to learn this stuff ...
1
vote
2answers
154 views

How formal or informal should math texts (written for different purposes) be?

When writing math articles (or just math text), do you write down mathematical expression in a formal way or describe it in words, e. g. "Let $X$ be a normed vector space. Then $X$ is called a ...
6
votes
1answer
171 views

I feel the need to prove every result for myself

I am, at best, a novice mathematician. I started teaching myself the subject while writing my thesis in computer science. I find that I have a strong urge to prove every relationship or formula that I ...
14
votes
5answers
1k views

What are some common proof strategies in mathematics?

I want to start out by saying that I am new at proof based mathematics. I am used to seeing patterns and using them to solve similar problems. However, I have found this is not a very good way to ...
21
votes
4answers
699 views

Are there any common practices in mathematics to guard against mistakes?

It occurred to me that math is somewhat like programming (or vice-versa, if you prefer) because, in both, it is easy to make mistakes or overlook them, and the smallest error or misguided assumption ...
4
votes
6answers
716 views

Looking for Proofs Of Basic Properties Of Real Numbers

I have just begun my study of complex numbers and I learned where imaginary numbers came from and their importance. However there's one thing that I need to clarify and that is the properties of real ...
63
votes
7answers
2k views

Why do people use “it is easy to prove”?

Math is not generally what I am doing, but I have to read some literature and articles in dynamic systems and complexity theory. What I noticed is that authors tend to use (quite frequently) the ...
0
votes
2answers
100 views

how can I present an idea about the difference between two functions clearly?

I have a presentation in which I want to point out a difference between two functions. Instead of putting the two functions on a slide and pointing to the differences, I want to do something simple. ...
16
votes
6answers
702 views

Difficulty in Mathematical Writing

Lots of people (including myself) face lot of problems in tackling Mathematical Problems, which appear as if we can solve it, but then writing out a solution becomes difficult. Let us consider some ...