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1
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0answers
28 views

Do mathematicians visualise what 4D would look like when they are working with abstract 4D concepts?

I was wondering if mathematicians do truly have a sense of visualising what the fourth dimension would look like in general, such as the fourth dimension as found in hypercubes. I know that we, as 3D ...
0
votes
3answers
91 views

Is this a valid logical problem or is it a joke? [on hold]

Given the sequence: 2, 3, 10, 12, 13 ... what is the next number? The answer is 20, because it begins with letter "T". Can this be considered a valid logical problem?
9
votes
4answers
191 views

Elementary problems that would've been hard for past mathematicians, but are easy to solve today?

I'm looking for problems that due to modern developments in mathematics would nowadays be reduced to a rote computation or at least an exercise in a textbook, but that past mathematicians (even famous ...
0
votes
2answers
58 views

What are the prerequisites required if I have to do induction to prove a certain theorem

I have always been fascinated by induction. The idea of induction is itself such a great analogy. But sometimes induction makes me feel that it is very messy. My professor keeps on saying that you ...
14
votes
5answers
205 views

Continuing math on my own? [on hold]

I am in 6th grade and neither of my parents are mathematicians. I feel that at school though my teacher is great, the stuff I am studying (Pre Algebra) is just a little too elementary. I often find ...
2
votes
1answer
46 views

What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?

I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or ...
0
votes
0answers
56 views

What are some applications of anabelian geometry outside of mathematics? [on hold]

I want to learn about some applications of anabelian geometry outside of mathematics. Practical things from any area are welcomed.
8
votes
3answers
970 views

I thought the | symbol meant “divides by”, but in set theory, does it mean something different?

I thought the | symbol meant "divides by", but in set theory it seems that it means "such that." However, I thought we wrote "such that" as ...
-1
votes
0answers
32 views

What does the derivative of acceleration represents?

The derivative of a distance function, represents instantaneous velocity. The derivative of the velocity function, represents instantaneous acceleration. What does the derivative of the acceleration ...
3
votes
0answers
23 views

Informal interpretation of meager sets

I've been wondering if there is a nice informal interpretation of meager sets akin to the respective interpretations I give below to other notions of "small" sets. The general setup to tease out ...
1
vote
0answers
16 views

Heuristic: Daniell integral vs. Lebesgue integral

What are the advantages of the Daniel Integral over the Lebesgue integral and visa-versa? Heuristically speaking, I was wondering why this axiomatic operator is less popular besides the fact that it ...
1
vote
1answer
112 views

Famous Problems the Experts Could not Solve [on hold]

After Yitang Zhang stunned the mathematics world by establishing the first finite bound on gaps between prime numbers, it got me thinking about the following question: $\underline{\text{Question}}:$ ...
2
votes
1answer
53 views

Themes in Mathematics [on hold]

My professors have alerted me to some themes throughout the subject. One that I've found useful is "abstraction and generalization": when studying rings, for instance, I initially saw nothing but a ...
1
vote
0answers
20 views

Can boosting be thought of as a genetic algorithm? [migrated]

Can boosting be classified as a genetic algorithm or as an instance of simulated annealing? Or, is it a completely different paradigm? Essentially, I'm trying to rectify discrete optimization ...
2
votes
2answers
21 views

Algorithmic procedure to establish the possibility of finding a proof of a conjencture

I was always puzzled by these conjectures which can be stated quite simply, yet finding a proper proof is a monumental task even for the most brilliant mathematicians . Consider the following ...
6
votes
0answers
82 views
+100

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
0
votes
1answer
57 views

What are the minimal mathematical prerequisites for starting to study Artificial Intelligence? [on hold]

This question is really broad as there are many aspects to the AI research. However, I just need a bare minimum of prerequisites that will allow me to approach any sub-field of the AI (coupled with ...
1
vote
0answers
29 views

Enough for Grad School? [migrated]

I just finished my 3rd year in a combined pure/applied math program at a Canadian university. I have been leaning towards pure math, but I'm not sure if I'll have done enough to go to grad school for ...
10
votes
4answers
174 views

Is there fundamental goal of mathematics? [on hold]

I did not ask this question before scaring of down-voting but could not stop the curiosity and cannot find the answer by searching the web. In physics we are looking for say smallest mass or particle, ...
2
votes
2answers
44 views

How do I get good grades in an exam?

I study hard throughout the year and I am able to solve most problems in the text assigned to us and I am frequently the only one who can solve the hardest problems in the assignments or the problem ...
1
vote
3answers
48 views

Definition of a compact operator

Operator compactness is characterized by maps the send the unit ball to relatively compact sets. Does anyone have a good justification for why we call this property compactness? The best ...
4
votes
0answers
65 views
+50

Overview of nonlinear analysis, ODE and PDE, dynamical systems, and mathematical physics and their relationships

(Apologies in advance for my naive question.) The fields of (i) nonlinear analysis, (ii) ODE and PDE, (iii) dynamical systems, and (iv) mathematical physics are very huge, fertile, and, in ...
-2
votes
0answers
34 views

resource on integral operators

Can you please suggest for me a good resource on integral operators.These are the specific topics that I am looking for: Bounded linear operators in hilbert space. Compact operators Spectral theory ...
1
vote
0answers
22 views

Preparation for research in statistical inference for stochastic processes [on hold]

I am interested in building capacity to do research (and ultimately building a career) in statistical inference for continuous time stochastic processes. I am seeking advice on how best to go about ...
5
votes
1answer
58 views

How to get the most out of attending a conference talk or a research presentation?

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
2
votes
1answer
48 views

Background required to understand the mathematical definition of knots and their transformations

What are the concepts of math required as a prerequisite to understand Knot Theory? I'd like to be able to make a humble beginning by being able to mathematically define knots and the non-rigid ...
2
votes
1answer
24 views

Is there a way to extend operations as integration for summation?

I've read a few times that integration is a sort of extension of summation so my point is: is there any sensated way to extend other operations in the same way ? If this extension exists what branch ...
2
votes
1answer
124 views

Which mathematical topics should an applied math major know to be employable in industry? [closed]

Question I'm a junior majoring in applied math computation at UCLA, and I was wondering what exactly constitutes a viable mathematics education? That is, what kinds of mathematical topics should an ...
0
votes
0answers
25 views

Beyond the Basics:Complex Analysis Topics/textbooks Suggestions

I am currently taking a semester long Graduate course in Complex Analysis. We have covered Basics of Complex Analysis,Automorphisms of Disc and Upper Half Plane,Riemann Mapping Theorem,Weierstrass and ...
0
votes
1answer
48 views

Prime Numbers Primer [closed]

This may not the appropriate site—but I thought Academia SE would be less appropriate. I'd like to begin working towards the ability to discover something novel about prime numbers. That is, I want ...
-3
votes
0answers
55 views

How learning strategy might be used for remarkable mathematicians [closed]

Concerning learning processes in mathematics, how probably the remarkable mathematicians learn when they were students, or characteristics in common ? Though by trying certain advice from ...
0
votes
0answers
20 views

Finding Holand-Bell formulas

Could anyone help me please to find out Holand-Bell formulas and their true author preferably (not Holand and Bell:) ) These formulas refer to finite element methods, I guess
12
votes
6answers
252 views

What are some examples of generalizations to higher dimensions which do not hold? [duplicate]

My professor said (hesitantly) $\textit{If it works in 1-D, it is likely that it also works in N-D}$ Hesitantly because, she remarked, it is not true for everything (which is expected). After some ...
-1
votes
0answers
26 views

An intrdoduction to electronics for mathematicians (having some physic background). [closed]

I asked the same question in the electrical engineering site and it got closed. Can anyone recommend a source for learning basic analog electronics (preferably with a view towards signal processing) ...
1
vote
0answers
38 views

Preparing to start bachelor in Mathematics [closed]

In a couple of months I'll go to university to start my bachelor in Mathematics. Since the level of math in my high school is really low, I want to prepare myself as good as possible. The courses ...
3
votes
1answer
48 views

Why is a cartesian morphism called cartesian?

I am reading about fibred categories. After reading the definition of "vertical" morphism, I can imagine why they are named like that. What about "cartesian" morphisms? What is cartesian about them? I ...
1
vote
1answer
61 views

Where can I learn to define mathematical terms?

For example, take the following: The radian measure of a central angle of a circle is defined as the ratio of the length of the arc the angle subtends, s, divided by the radius of the circle, ...
2
votes
1answer
70 views

How to understand cocategories

$\newcommand\CC{\mathsf{C}}$The notion of a category is well-known. There are multiple equivalent definitions; small categories can be seen as an internal category in $\mathsf{Set}$, that is a ...
13
votes
2answers
83 views

Knowing when to ask for help

I'm an undergrad with weekly problem sets due. Often if I begin the problem set early and think about it a bit each day, I can solve all of the problems. But other times it will quickly become ...
7
votes
1answer
76 views

Error function etymology: Why the name?

I've recently been introduced to the error function: $$\operatorname{erf}(z) =\frac{2}{\sqrt{\pi}}\int_0^z e^{-t^2}dt$$ Naturally, I wondered about the origin of its name: The error of... what? I'm ...
2
votes
1answer
83 views

When is $0^{0}=0$ useful?

Are there mathematical areas/situations in which defining $0^{0}$ as $0$ is useful/sensible and convention (in contrast to the "common" definition as $1$) ?
1
vote
0answers
60 views

Three theorems for the price of one? (like duality)

Why the notion of "duality" (when we get two theorems for the price of one) are ubiquitous in mathematics (order and lattice theory, category theory, group theory), but "triality" (three theorems for ...
0
votes
0answers
23 views

Suggestions for potential research areas in graduate school based on my preferences [closed]

I'm currently finish up my first year in graduate school (phd pure/applied math), and after I finish my quals I need to find a potential research topic. Ignoring the aspect that largely depends on my ...
2
votes
1answer
69 views

How to Do Well in a Math Course [closed]

I am not really sure if this question has been asked before, or if this question is considered off-topic. I am mostly a B and C student, even though I put a lot of time and effort into studying. I ...
0
votes
1answer
18 views

Why is it important to recognize CRT establishes an isomorphism between $Z/p\#Z$ and $Z/qZ$

As I understand it, it is well known that CRT can be used to show that $Z/p\#Z$ as a ring is isomorphic to the product of the finite fields $Z/qZ$ where $q$ ranges over the primes up to $p$. For ...
2
votes
3answers
97 views

Mistakes in simple math problems [closed]

I am generally good at maths, but sometimes, maybe because I underestimate easy problems, I do them quick and I make stupid mistakes like 8*9 = 73, not 72. But this also happens sometimes when I look ...
3
votes
2answers
50 views

What's the significance of the Church-Turing Thesis?

My understanding is that the thesis is essentially a definition of the term "computable" to mean something that is computable on a Turing Machine. Is this really all there is to it? If so, what makes ...
5
votes
3answers
75 views

What would be an effective way to learn group theory on my own?

I've read the basics of this branch and I found it extremely interesing, and I would really love to learn more about it. I want to study as much as I can on my own, as my course doesn't have group ...
0
votes
0answers
42 views

Some notes on $D_n, S_n$ and $A_n$

http://www.stat.uchicago.edu/~lekheng/courses/repth/sol2.pdf In these solutions it refers to See "Some notes on $D_n, S_n$ and $A_n$". Does anyone know where these notes can be found? They sound ...
5
votes
5answers
181 views

Proof writing: how to write a clear induction proof?

What is an effective way to write induction proofs? Essentially, are there any good examples or templates of induction proofs that may be helpful (for beginners, non-English-native students, etc.)? ...