For questions whose answers can't be objectively evaluated as correct or incorrect, but which are still relevant to this site. Please be specific about what you are after.

learn more… | top users | synonyms

1
vote
1answer
39 views

The fastest Gröbner basis algorithm available?

for my undergraduate thesis I'm (pseudo) replicating algebraic attack on certain cryptosystem using gröbner basis approach. The heart of original attack was F5/2 algorithm (since the cryptosystem is ...
1
vote
0answers
41 views

Ideas for approaching set theory when you've already studied higher abstractions?

I've come to acknowledge (or so I think). That many of the concepts e.g. in real analysis (like, say, continuity), actually don't (in modern times) boil down just real analysis. But rather, e.g. set ...
0
votes
0answers
3 views

Convergence in constraint propagation

Introduction To the best of my knowledge, constraint propagation can be thought of (in a very heuristic sense) as a class of algorithms that solve a sort of generalized Sudoku problem. Some initial ...
4
votes
3answers
539 views

Independent math learning

I'm an undergraduate math and econ major and I'm planning on graduating relatively soon and I am very limited to the number of math classes I have left (very sad about this fact). So far I have ...
3
votes
1answer
26 views

Why is Logistic Distribution called logistic?

What is logistic about Logistic Distribution, in a common sense way? What is the lexical rationale of the name, not just pure math definition?
9
votes
6answers
10k views

Math Textbooks for High School

I'm a high school student who is trying to figure out a complete course of self study for each year of high school. Is there a way to self learn grades of math without devoting too much time? For ...
1
vote
0answers
23 views

Where does the name of the hypergeometric distribution come from?

I understand what it does and how to get there, but why is it called hypergeometric? All the other distributions I know of have rather self-explanatory names like "binomial" or "exponential", or are ...
1
vote
1answer
24 views

Suggest books on Combinatorial Graph Theory

I am going to start self-studying Combinatorial Graph Theory. Kindly suggest books or study materials available online. I have been told that it is basically application of linear algebra , mainly ...
0
votes
0answers
9 views

Books for large deviations and maximum entropy principle?

What are some good introductory resources for learning more about the theory of large deviations and the maximum entropy principle?
9
votes
4answers
785 views

What is linearity? [duplicate]

Once someone asked me the question "What is linearity?" in a proficiency exam. I went hot and cold all over. Although, I heard and even used the term linearity many many times, I had not really ...
1
vote
1answer
33 views

“Guesstimation” problems within pure mathematics

Wikipedia defines a “guesstimate” as “an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by guesswork or conjecture.” Guesstimation problems ...
1
vote
1answer
52 views

Launching a Plaintext Attack against Affine Cipher

Update 2 Being new to the world of Stack Exchange I did not realize that there exists a site solely devoted to cryptography. In light of this, I hope someone could help me migrate this question to ...
1
vote
3answers
45 views

Recommend book Taylor expansions

I've taken up self-study of math and i start using the book called : Mathematical Analysis I Authors: Canuto, Claudio, Tabacco, Anita I would like to start from zero to understand taylor ...
1
vote
2answers
30 views

Implication as defined in mathematical logic [duplicate]

If we can take the truth of an implication to mean the validity of reasoning, then that would mean that all reasoning that begins with false premises is valid reasoning. Are there no counterexamples ...
0
votes
0answers
13 views

“Canonical” choice of parity check matrix from generator matrix

Let $\mathcal{C}$ be a binary linear code of length $n$ and dimension $k$, given as the left-image of an $k \times n$ generator matrix $G$: $$ \mathcal{C} = \{ i G : i \in \mathbf F_2^k \} \subset ...
1
vote
3answers
66 views

Is there a difference between $S_n$ and $V_n$

$$S_n=10+10+10+...$$ $$V_n=22-12+42-32+62-52+...$$ Do they represent the same series ?
1
vote
2answers
58 views

Summation up to $n$ terms : $\sum r\cdot (r+1)^2$

Summation up to $n$ terms : $$\sum_{r=1}^{n} r\cdot (r+1)^2$$ My attempt : $$\sum_{r=1}^{n} r\cdot (r+1)^2=\sum_{r=1}^{n} r^3+2\sum_{r=1}^{n} r^2+\sum_{r=1}^{n} r$$ $$\sum_{r=1}^{n} r\cdot ...
42
votes
14answers
8k views

Can math be subjective?

Often times in math, ever since Kindergarten and before, math has been defined by the fact that there are only one answer for problems. For example: $1+1=2$ and $\frac{d}{dx}x^2=2x$. What I am showing ...
1
vote
2answers
61 views

“The order of a differential equation is the highest derivative in the equation”. What's wrong with this statement?

I am asked the following "The order of a differential equation is the highest derivative in the equation". What's wrong with this statement? I've checked my text and several other sources, and ...
0
votes
1answer
50 views

Unique prime factorization [duplicate]

We all know that $$15=3 \times 5$$ And $$15 =(-3) \times(-5)$$ Since $3 \neq -3$ and $5 \neq -5$ , we have two different prime factorizations ! Is this wrong ? If this is wrong , then there are ...
0
votes
0answers
43 views

What's the name of this problem? Interesting minimisation of a length.

There is a problem which has to do with minimising the length of a (possibly disjoint) barrier in a region of space (often a 2D circle) such that no straight line can pass through the particular ...
1
vote
2answers
41 views

Roots of $f(x)+g(x)$

Question : Let $p,q,r,s \in \mathbb R$ such that $pr=2(q+s)$. Show that either $f(x)=x^2+px+q=0$ or $g(x)=x^2+rx+s=0$ has real roots . My method : To the contrary suppose that both $f(x)$ and ...
4
votes
1answer
25 views

Study of algebraic structures analogous to the ring of smooth functions and module of vector fields

$\newcommand{\Ga}{\Gamma}$ Let $M$ be a smooth manifold. $\Ga(TM)$ is a module over the ring of smooth (real) functions (which is also an algebra, and denoted by $C^{\infty}(M)$). Also, each $X \in ...
1
vote
1answer
62 views

The four colour theorem

I have been reading about the four colour theorem and the fact that it is proved using a computer. My question is whether it is likely that we will ever achieve a proof without the use of a computer? ...
654
votes
48answers
408k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
2
votes
1answer
94 views

How important is the choice of books in studying Analysis?

I am in a fix. I have done a graduate course in Pure Mathematics.I love to study abstract algebra.I want to do postgraduate in Mathematics especially in Abstract Algebra . In order to enter a ...
27
votes
6answers
3k views

Tell me problems that can trick you

I am looking for problems that can easily lead the solver down the wrong path. For example take a circle and pick $N$, where $N>1$, points along its circumference and draw all the straight lines ...
18
votes
5answers
854 views

Categorical introduction to Algebra and Topology

At the moment I am reading books on Algebra and on Category theory. More exactly, I started working through the book Algebra by Serge Lang. I have read the chapters on groups and rings, but then my ...
1
vote
1answer
102 views

Grothendieck's “Relative” Point of View

I have often read that Grothendieck's insight was to put emphasis on studying the morphisms between schemes as opposed to just the schemes by themselves. What do we gain from this point of view? Why ...
1
vote
2answers
176 views

Should I be worried that I can't prove these theorems on my own yet?

I'm a mathematics major, and when I'm studying Real Analysis, Numerical Analysis, etc, when I look at theorems like the Intermediate Value theorem, Mean Value theorem, etc, the results seem obvious ...
7
votes
2answers
284 views

Finding the first digit of $2^{74207281}-1$ (new biggest prime record)

I heard that the record for finding the largest prime number was broken a few days ago with the following Mersenne prime $$2^{74207281}-1$$ also called $M_{74207281}$. Now my question is: it is ...
0
votes
1answer
39 views

$\{x|x$ is a positive integer definable in one line of type $\}$

$\{x|x$ is a positive integer definable in one line of type $\}$ I found this example in Enderton's book of set theory ! What does it mean ? I have no idea about "definable" and "in one line of ...
19
votes
3answers
5k views

Real life examples of commutative but non-associative operations

I've been trying to find ways to explain to people why associativity is important. Subtraction is a good example of something that isn't associative, but it is not commutative. So the best I could ...
1
vote
1answer
74 views

Multivariable optimization for time to build a ship in a game, and maybe some possible application in “everyday” life

I precise first that english is not my monther tongue and I may will not be as clear as I would like, just ask me question if you need, thank you. I am playing a game (Galaxy Empire) for a while, ...
21
votes
3answers
3k views

Research Experience for Undergraduates: Summer Programs (that accept non-American applicants)

There are many summer research programs in the United States, targeted at good motivated undergraduate students majoring in mathematics. The main aspects that characterize such programs are: (a) a ...
27
votes
2answers
2k views

When writing proofs, is logical notation a crutch?

I'm near the end of Velleman's How to Prove It, self-studying and learning a lot about proofs. This book teaches you how to express ideas rigorously in logic notation, prove the theorem logically, and ...
6
votes
3answers
169 views

What are the disadvantages of non-standard analysis?

Most students are first taught standard analysis, and the might learn about NSA later on. However, what has kept NSA from becoming the standard? At least from what I've been told, it is much more ...
1
vote
2answers
67 views

Which of the Following Sets are compact (C.S.I.R 2015)

$\{ (x,y,z) \in \mathbb R^3 : x^2 + y^2 + z^2 = 1 \}$ in the Euclidean Topology $\{ (z_1,z_2,z_3) \in \mathbb C^3 : z_1^2 + z_2^2 + z_3^2 = 1 \}$ in the Euclidean Topology. $\prod_{n=1}^{\infty} A_n$ ...
46
votes
18answers
6k views

What's the goal of mathematics?

Are we just trying to prove every theorem or find theories which lead to a lot of creativity or what? I've already read G. H. Hardy Apology but I didn't get an answer from it.
1
vote
1answer
54 views

How to know if I can't solve an equation with “standard” methods?

I'm particularly fascinated by transcendental equations whose posses closed form solutions and when I pose some of them to my friends or teachers I heard a lot of "You can't solve this in closed form" ...
58
votes
13answers
2k views

Unconventional mathematics books

I've recently purchased Oliver Byrne's reproduction of Euclid's Elements. It's a beautiful tome, that's rather unique in its presentation of the material as it represents many of Euclid's proof as ...
98
votes
19answers
4k views

Past open problems with sudden and easy-to-understand solutions

What are some examples of mathematical facts that had once been open problems for a significant amount of time and thought hard or unsolvable by contemporary methods, but were then unexpectedly solved ...
0
votes
1answer
36 views

What can we say about a function $g$ if we know${f \over f + g} \to 1$?

This question came to me thinking about the prime counting function, $\pi (x)$. It is known that ${\pi(x) \over \text{li}(x)} \to 1$ but this does not imply $\pi(x) - \text{li}(x) \to 0$. I asked a ...
0
votes
1answer
17 views

$a_{A,B}=a_{A,E}+a_{E,B}$ - Relative acceleration

When two balls $A,B$ are moving under gravity , Find acceleration of $A$ relative to $B$ (That is $a_{A,B}$) a) Both $A$ and $B$ are moving down ! b) $A$ moves upwards and $B$ moves downwards (above ...
1
vote
2answers
101 views

Is there a well known nontrivial counterexample to this claim?

Suppose we have $A\subseteq\mathbb{N}$ with the property that if $B\subseteq\mathbb{N}$ and $B$ is finite, then $\exists a\in A\setminus\{ 1\}$, $\forall b\in B$, $\gcd(a,b)=1$. Are there any well ...
1
vote
1answer
217 views

Collatz conjecture and related problems - mathematical machinery

Collatz conjecture stands as an open problem. That leads me to believe that the conjecture cannot be resolved by elementary means. Which brings me to my question: What techniques/machinery from ...
4
votes
2answers
58 views

Defining vertical tangent lines

In looking at the definition of vertical tangent lines in some popular calculus texts, I noticed that there are a few different definitions for this term, including the following: A function $f$ ...
0
votes
0answers
41 views

Comprehensive Mathematics References/Textbooks (Like Bourbaki's Elements, or the Stacks Project)

Are there any comprehensive mathematics reference/textbooks that could be considered somewhat like a modern version of Bourbaki's Elements? "Comprehensive" here could refer to a single area of ...
0
votes
1answer
46 views

Can I take cryptography after doing pure Mathematics $?$ [closed]

This is not a mathematics problem . May be it's not appropriate to ask this here but I don't know anywhere else to go for advice . I have taken Pure Mathematics at the university and quite enjoying ...