Questions tagged [soft-question]

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.

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1
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0answers
17 views

Looking for connections between fields

warning: open ended question. I want to learn more about how topics in mathematics (especially group theory, graph theory, algebraic structures) connects different ideas that we use for systems ...
2
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0answers
29 views

Intuitive definition of the Euclidean group without reference to metric

Usually, Euclidean space is introduced by giving a three-dimensional vector space ($\mathbb{R}^3$ for simplicity) and the metric $$d_E\big((x_1,x_2,x_3),(y_1,y_2,y_3)\big)=\sqrt{(x_1-y_1)^2+(x_2-y_2)^...
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2answers
42 views

What is the appropriate title of a false statement/proposition?

What is the appropriate term to use for titling a mathematical statement which will be proven false? Note that I'm focusing on the context of labeling and organizing results within a paper or similiar,...
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5answers
61 views

Why flip and multiply works for division? [duplicate]

We learn instrumentally. This simple question occurred to me today. Consider following examples. $$\frac{10}{2}=10 \times \frac{1}{2}=5$$ $$\frac{5}{3}\div \frac{2}{7}=\frac{5}{3}\times \frac{7}{2}...
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0answers
55 views

What is mathematics studying nowadays [on hold]

In studying the history of mathematics, I see that mathematicians tends to, trough times to times, walk in a certain direction, chasing a certain question that is of great importance for that age. ...
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1answer
61 views

Is a (short and) beautiful proof for symmetric inequality must exist always?

There are several and almost similar inequalities in MSE that some of them can be proved in long page. some of these questions listed below: For $abc=1$ prove that $\sum\limits_{cyc}\frac{a}{a^{11}+1}...
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1answer
45 views

Do you need commutative algebra for Milne's Algebraic Number Theory course? [on hold]

I have completed Artin's Algebra. I was wondering if you need anything else or can I go ahead with Milne's course. I'm not providing a link since his lecture notes are very well known...
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0answers
33 views

List: interesting OEIS sequences

What are your favorite sequences? What are the sequences you think have the coolest/most interesting graphs? Context: I recently watched these videos [1], [2] featuring Neil Sloane, the founder of ...
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12answers
2k views

Unsolved Problems due to Lack of Computational Power

I was recently reading up about computational power and its uses in maths particularly to find counterexamples to conjectures. I was wondering are there any current mathematical problems which we are ...
5
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1answer
61 views

How to find (research) literature?

I noticed that if one wants to get into a new branch of mathematics it is really hard to find good literature to start with. Of course, if one googles the name of the subject one will find a 1000 ...
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0answers
71 views

Does this shape have a name and have people studied it?

It looks like the shape has $8$ triangles and I think it is a simplex. Does this shape go by a name? If you smoothed out the corners a bit could you do differential geometry and topology on this ...
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0answers
32 views

Mathematical applications of counting [on hold]

What are some non-trivial mathematical applications of counting outside of discrete mathematics? Are there any deep mathematical theorems where counting of certain objects is of primary concern in for ...
1
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2answers
51 views

Is the multivariable calculus in Apostol's 2nd Volume enough for Spivak's Differential Geometry Series?

The question is basically in the title. Will I need something more along the lines of Munkres' Analysis on Manifolds or Spivak's earlier Calculus on Manifolds, or will Apostol suffice?
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3answers
33 views

suggestions on first courses in game theory

I am looking for introductory texts in Game Theory. It will my first time studying this, and I prefer the non-economics kind (which I always find in the internet). If there is a biological slant to it,...
0
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0answers
30 views

Rules of Analytic Continuation

Context This summer, I have been reading Tom Apostol's "Introduction to Analytic Number Theory." I have yet to take a formal analysis class, but have been able to follow along until the very end. ...
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2answers
58 views

Why many people confused about the result of this algebraic operation $8:2(2+2)$ however it's seems easy and clear? [on hold]

I have accrossed these days in this Video discussed the result of this Algebraic operation $8:2(2+2)$ such that it mixed people in differents interactive website and social web like facebook about ...
1
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1answer
60 views

How much measure theory needed for advanced functional analysis? [on hold]

I have done a basic course in Functional Analysis following Kreyszig, and will start another one on more advanced topics that uses Rudin's Functional Analysis text. However, I have never studied ...
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2answers
90 views

Where can I download a full list of all primes below $10^{15}$?

I would like to do some computing on a large list of primes. Unfortunately my computer is not strong enough to quickly generate such a list, so I'm looking to download a file that already contains ...
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0answers
7 views

Matrix generator / representation matrix for equal spacing along a chirp function?

This question is similar to several sets of previous questions dating back to when I joined the site 1, 2, 3. This time it regards a sine function of quadratic frequency. a.k.a. a "chirp signal". I ...
3
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2answers
130 views

Besides seminars, what other social outings are there for mathematical hermits?

I'm assuming I can attend a seminar without a fee. I already checked into auditing courses. I used to think that was free, but apparently you have to pay full tuition costs to do that nowadays. I ...
4
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0answers
71 views

Soft Question: Textbook for first graduate course in Functional Analysis

I will be studying Functional Analysis for the first time, at the first-year grad school level. My relevant background is $1$ basic course in Topology and $1$ basic course in Measure Theory. I was ...
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3answers
45 views

Is $2\int\frac{d^2x}{dt^2}*\frac{dx}{dt}dt=(\frac{dx}{dt})^2 $ true??

I was watching a video online about motion under inverse square law here and the producer mentioned that, $$2\int\frac{d^2x}{dt^2}*\frac{dx}{dt}dt=\left(\frac{dx}{dt}\right)^2 $$ i donot understand ...
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0answers
50 views

Is it normal to find half of textbook's exercises extremely challenging? [closed]

I'm taking a measure-theoretic probability course next semester and after looking at the exercises in the first section, I have only been able to solve about half of them. My question is: should ...
25
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9answers
2k views

Is Calculus necessary for computer science student? [closed]

I'm a freshman in university and I'm studying Computer science and engineering. This will be my second year of studying. We don't have Calculus as a mandatory class but I can take it from elective ...
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0answers
18 views

Pinhole camera model and Linearization of system of equations derived from model.

Let us assume I have a camera that photographs according to a pinhole camera model: Rays are measured projected on a regularly sampled plane linearly stretching out from the lens. $$\begin{bmatrix}...
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0answers
76 views

Is it officially proven that the Collatz sequences can't go to infinity?

Has the mathematician Jeffrey Lagarias proved that in his work the Collatz sequences cannot go to infinity (divergent trajectory), that only cyclicity can exist? I don't have enough mathematics to ...
1
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0answers
36 views

Prerequisites for the complex analysis part of Rudin RCA

What are the prerequisites for the complex analysis part of Rudin Real and Complex analysis book? Is it possible to start studying the complex analysis part with the knowledge acquired from the first ...
2
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1answer
41 views

Book recommendations for highschool algebra for concepts and hard problems

I am looking for a book recommendations for learning algebra for high school. Can you suggest me some good books which have the proper theory and can very well be used to self teach yourself and be ...
5
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1answer
54 views

On completing the square and symmetry

The quadratic form $f(x,y)=x^2+xy+y^2$ appears quite often on the site here. It is provably positive definite by completing the square: $$f(x,y)=\left(x+\frac y2\right)^2+\frac {3y^2}{4}$$ and this ...
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2answers
37 views

Visualzing a nontrivial element of $\pi(\mathbb{R}P^2)$

Visualzing a nontrivial element of $\pi(\mathbb{R}P^2)$. I'd like to visualize a nontrivial element of $\pi(\mathbb{R}P^2)$ whilst thinking of $\mathbb{R}P^2$ as $S^2$ with antipodal points being ...
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0answers
48 views

Does Coxeter's “Geometry Revisited” help with developing skills for Olympiad geometry? [closed]

I'm interested in learning elementary Olympiad geometry. I've heard a lot of good things about Geometry Revisited by HSM Coxeter. But could someone tell whether it is good for developing skills in ...
0
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1answer
50 views

Advice for solving “hard” elementary geometry problems (no complex trig or heavy coordinate-based calculations) [closed]

How do I learn to solve hard elementary geometry problems (the ones don't involve complex trig or heavy coordinate based calculation)? Those problems are difficult, not because I don't know the ...
1
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0answers
54 views

Are there huge differences between textbooks?

I am about to start my first year in college. I am not a class type student. I like going deep while studying myself and understanding the reasons, beauty behind these ideas. I have been looking for ...
5
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1answer
86 views

Is doing Olympiad problems in Undergrad,worth it?

I am about to enter in second year as a math major, due to some reasons I have never been into amc and imo like stuffs, but as I am gaining interest in math, it is the regret which is hurting me again ...
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2answers
52 views

Are two proofs better than one? [closed]

I have proved a simple conjecture two ways, for an essay I need to do for my highschool maths. How do I justify in my essay why I have included two proofs instead of one. Is there any good reason, to ...
2
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0answers
100 views

Necessary conditions for a PDE to be “interesting”

Motivated by this answer, which points out (emphasis added): In general, it is naive to ignore applications when studying or looking for motivations for theoretical objects in PDEs. Nearly all ...
1
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1answer
27 views

Trigonometry calculation doubt

While solving trigonometry in physics especially, I often encounter values or things like $\tan \theta = 0.524$, $\tan^{-1} \frac{-3.1}{-2.4}$ ande etc... The answer just puts the solution as $\tan^{-...
2
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0answers
27 views

Classification of all “Big O equivalence classes”

Given functions $f$, $g$, $f = \Theta(g)$ defines an equivalence relation. The equivalence classes of this relation are intensively used in computer science. See for example https://en.wikipedia.org/...
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0answers
50 views

Logic is applied to describe what actualy Logic is?

Logic turns up in the sylabus later, one usually starts with linear algebra and analysis where one assumes the underlying logic to be given. I think the reason is because the study of logic already ...
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0answers
28 views

What is the largest natural number for which a theorem on the natural numbers is known to “break down” for the first time? [duplicate]

Suppose we have a theorem $X$ that is true for each $n \in \mathbb{N}$. In any rigorous mathematical proof of $X$ we will generalise for all such $n$, So we will say something like: Let $n \in \...
3
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1answer
84 views

Propositional Logic and Redundancy

There are Philosophical problems with the Material conditional. The Dutch philosopher Emanuel Rutten has written an article about it, titled: Dissolving the Scandal of Propositional Logic? From that ...
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6answers
499 views
+50

Could *I* have come up with the definition of Compactness (and Connectedness)?

Ok, buckle up for a rather long question. I've spent a large portion of today learning about compactness, stemming mainly from this wikipedia article about point-set topology. The article mentions ...
1
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0answers
23 views

Seeking name on common descriptive statistical measure.

I recently took upon a job role where in part I have to make evaluations on how to price 2nd Hand Cars. There is a software (online based) that using a variety of very elementary descriptive ...
1
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2answers
93 views

Why do we want lots of $0$’s in a matrix?

I am working thru Axler’s “Linear Algebra Done Right.” I am okay with the math, but I’m losing sight of the forest. Like all books on linear algebra, there’s a lot of time and energy spent on ...
71
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9answers
8k views

Why should I “believe in” weak solutions to PDEs?

This is a sort of soft-question to which I can't find any satisfactory answer. At heart, I feel I have some need for a robust and well-motivated formalism in mathematics, and my work in geometry ...
8
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0answers
42 views

Exemples of applications of “groupoidification” to linear algebra

I just read Baez's very nice blog notes about groupoidification, and around the beginning, he states : "From all this, you should begin to vaguely see that starting from any sort of incidence ...
0
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0answers
36 views

Math required for Economics

I'm looking for some math topics to learn about, with the aim of being able to get into some mathematical economics readings. I can always pick up a "math for economics" book, but I want to learn the ...
6
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0answers
86 views

Elementary Differential Geometry before Manifolds?

Many courses called Differential Geometry (at least in Germany; at least as far as I know!) solely deal with manifolds and not classical/elementary Differential Geometry (curves, curvature, ...
6
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2answers
98 views

Advice on how to read a mathematical paper [closed]

I am a 2nd year graduate student in Number Theory. My advisor has sent me papers to read and I have trouble getting through even a paper. Be warned that my problems may be noobish and borderline ...
1
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0answers
26 views

Are Lebesgue integrals equivalent to Daniell integrals?

Please excuse me if this is a silly question. I graduated from university many years ago and am now trying to re-learn some mathematics. I don't know much advanced mathematics and I have difficulty to ...