# soft-question's questions - English 1answer

8.146 soft-question questions.

### 1 Is it necessary for an undergraduate math major to understand all the proofs of major theorems in order to ace their exams? [closed]

1 answers, 56 views soft-question education
One of my acquaintance who is a math major undergraduate once told me that most students at his level focus on problem solving and ignored understanding proofs of major theorems, for example ...

### 2 mathematics of version control systems

1 answers, 46 views reference-request soft-question
Has anyone written a paper on the mathematics of version control systems? The background for this question: Many people are now studying the mathematics of computer systems. However, one aspect of ...

### -1 List of elementary operations on sets and ways to generate new sets

0 answers, 29 views elementary-set-theory soft-question
I am trying to make a list of basic operations or relations on sets, such as: Union Intersection Complement Inclusion as well as ways of building new sets: Subset Cartesian product Power set ...

### 6 In the formula $\frac{(x+y)^n}{x}=\sum_{k=0}^n\binom{n}{k}(x-ak)^{k-1}(y+ak)^{n-k}$, what is $a$? What is this formula named?

1 answers, 97 views soft-question binomial-coefficients
I would like to know more about this formula (via the Worldwide Center of Mathematics website): $$\frac{(x+y)^n}{x}=\sum_{k=0}^n\binom{n}{k}(x-ak)^{k-1}(y+ak)^{n-k}$$ What is $a$? Does the formula ...

### 7 What does it mean when we say a mathematical object exists?

I learned recently that there are mathematical objects that can be proven to exist, but also that can be proven to be impossible to "construct". For example see this answer on MSE: Does the existence ...

### Modules in preadditive categories?

I have been studying preadditive categories similar to specific types of rings. See for instance here. The clearer answer I have found is in this article. The result shown is that the category of ...

### 3 Why does the symbol for implication vary from class to class, university to university?

1 answers, 87 views soft-question notation
Some (neccesary) background and motivation for my question: In some of my undergraduate math classes, specifically my proofs course, I have been required to use the $\Rightarrow$ symbol to denote any ...

### 107 Irrationality of $e$

I have a question about the irrationality of $e$: In proving the irrationality of $e$, one can prove the irrationality of $e^{-1}$ by using the series e^x = 1+x+\frac{x^2}{2!} + \cdots + \frac{x^...

### -1 What essential topics should a prospective pure maths PhD student have studied? [closed]

What topics should absolutely every applicant have studied. I believe on overview of essential topics would include Linear Algebra Topology Real and Complex Analysis Geometry Algebra I am hoping to ...

### 152 Counterintuitive examples in probability

I want to teach a short course in probability and I'm looking for some counterintuitive examples for it. Results that seems to be obviously false but they true or vice versa... I already found some ...

### 2 Some strange set notations used in mathematical texts.

0 answers, 46 views soft-question notation
In some kind of old mathematical text, writers use notations like following. I guess at the left side it is written as "G". My question is where can I find a list that contains that kind of ...

### 5 Zeros of Polynomials in Arbitrary Rings

The book I'm reading introduces polynomials over a field and proves the statement that a polynomial of degree $n$ has at most $n$ zeros. They do this by using division algorithm and induction. Then ...