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1answer
33 views

Recommendations for tutorials specifically devoted to real integration using contour integral techniques.

Complex analysis, and in particular contour integrals and the residue theory have proved a very powerful tool in computing a large class of real function integrals which would be quite troublesome to ...
4
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3answers
53 views

Vectors sometimes used in math just as arrays/lists of numbers, sometimes as concept of “change”

As a freshman in a small town college. Ive been getting mixed signals to what vectors (and matrices/tensors) are. Sometimes I get the feeling they are used just as containers/arrays for multiple ...
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1answer
41 views

Complex Roots of Unity?

I just had a question about complex roots of unity. It's not a computation thing; I know how to find them and I know what they mean. In my class last semester, my professor mentioned that they are ...
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0answers
17 views

What is the point of solving a system of linear equations using back-substitution (as opposed to reduced echelon form)

In lecture the other day, my professor offhandedly mentioned the existence of a process called back-substitution a way in which a computer program would solve a system of linear equations rather ...
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1answer
86 views

Pure mathematics research [closed]

What can a first year mathematics undergraduate, who wants to pursue research in pure mathematics, learn in 67 days that will help him in the future?
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2answers
33 views

Why are Optional Stochastic Processes Important?

I understand to some degree why adapted processes, progressive processes, and predictable processes are important. EDIT: I am referring only to the continuous time case, NOT discrete time. But why do ...
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4answers
563 views

Why do they call it base 10?

Now, I know intuitively why it's called base 10: because there's 10 numbers. But see here's the thing, if we're working with numbers 0-9 (and of course we are), we use up our numerical artillery at 9....
2
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0answers
16 views

Describe the position of $w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}$ w.r.t. $B_R(0)$ and $B_r(z_0)$

I am working with two circles $B_R(0)$ and $B_r(z_0)$ and want to describe the position of the point given by $$w_0=\frac{(|z_0|+r)+R}{2}\cdot\frac{z_0}{|z_0|}.$$ First I would like to know whether my ...
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2answers
39 views

What is Convex about Locally Convex Spaces?

This might be a silly question, but what motivates the name "locally convex" for locally convex spaces? The definition in terms of semi-norms seems to have nothing to do with convexity or with the ...
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1answer
65 views

Review of Differential and Integral Calculus in 60 hours

Hopefully this question isn't too narrow. It is similar yet distinct from this: Calculus Review On The Web and this: What are some good resources to review basic university calculus, years later? I ...
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1answer
34 views

The definition of random sequence

Suppose that I ask you to tell me four integers between $0$ and $10$ randomly. You tell your numbers, for example $\{3,7,2, 5\}$. However I don't trust you about your numbers being random, hence I ...
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2answers
36 views

What is the difference between Mapping and Morphism

I wonder if there's differences between Mapping and Morphism. Although the terms are used in different context i.e. mapping for set theory and morphism for category theory, from my understanding they ...
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3answers
185 views

Learning differential calculus through infinitesimals

In class, we've studied differential calculus and integral calculus through limits. We reconstructed the concepts from scratch beginning by the definition of limits, licit operations, derivatives and ...
2
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1answer
52 views

What is the difference between an adapted process and a predictable process?

As the footnote on page 1 of this document mentions, even most experts in the field of stochastic processes don't seem to know rigorously what the difference is. However, since I don't have any idea ...
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0answers
19 views

Continuous indicator-like functions

Let $\Omega$ be a compact subset of $\mathbb{R}^n$. Let $g:x\in\mathbb{R}^n\to\mathbb{R}$ be a continuously differentiable function such that $$ \begin{cases} g(x)>0 & x\in\text{int}\Omega,\\ ...
3
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1answer
58 views

Alternate Definition of Infinite Series Summation?

Question I was wondering if one could define the sum of conditional convergence without using the notion of before or after (time)? My Understanding We define the following partial sum: $$ S_n = ...
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1answer
62 views

Is there a list of recommended problems to do in each chapter of Spivak's Calculus anywhere?

I've recently been self-studying Spivak's Calculus, and since I don't have the time to do every problem from every chapter at a and finish at reasonable rate, I've looked for a course syllabus or ...
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0answers
144 views

Isothermal coordinates

Is there an application or interest in studying the isothermal surfaces where the metric is $ds^2=E*(du^2+dv^2)$ and where $E>0$ is an harmonic function? I know that this metric is a special kind ...
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1answer
68 views

Examples of the use of $(p \vee q) \wedge (\neg p \vee r) \Rightarrow (q \vee r)$ in “real” mathematics?

Here, a proof is requested for the following tautology: $$(p \vee q) \wedge (\neg p \vee r) \Rightarrow (q \vee r)$$ Its pretty easy to prove; nonetheless, I don't find the formula at all intuitive, ...
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1answer
36 views

Eulers identity history

When Euler discovered/invented $e^{ix} = \cos(x)+i\sin(x)$. Did he doubt his calculations for a length of time? Was it Readily accepted by the mathematical community quickly or did they object at ...
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1answer
16 views

Is there a Relationship Between Multi-Valued Logic and n-Satisfiability?

Is binary (Boolean) logic related at all to the two-satisfiability problem? And is ternary logic related in some way to the three-satisfiability problem? Would it follow then that if one were to ...
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0answers
34 views

Why does (h,k) generally represent the center of a circle?

Why are h and k generally used to denote the coordinates of the center of a circle? After a bit of research, we found that h may represent "horizontal shift" or "horizontal translation", but we're ...
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0answers
68 views

Bringing Up Weak Derivatives on Calc I Quiz

Ok so I realize that I was being a bit of a smart ass but we had a quiz in my honors Calc I class the other day and one of the questions was: "Is the following function $f:[-2,2] \to [0,1]$ ...
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2answers
95 views

Is Wikipedia a reputable source for Mathematics? [closed]

I am currently in High School, possibly interested in pursuing a career in Mathematics or the Philosophy/Logic behind Mathematics. I don't have a lot of money for books or videos about Higher ...
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2answers
75 views

Dissertation on Integrals

I'm considering doing a dissertation on Integrals: Riemann, Henstock-Kurzweil, Lebesgue and more I'm wondering if I can do it. This is usually a masters level dissertation (while I'm an undergraduate ...
2
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0answers
37 views

Lagrangian densities, Lie Groups and Lie Algebras

I'm quite new to Physics and I was having a look for the first time to the Standard model. I'm not sure if the mechanism that I'm describing is directly from Weyl or from others but what I found quite ...
2
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0answers
69 views

Is Leibnizian calculus embeddable in first order logic?

We just published an article making what we feel is a plausible case in favor of an affirmative answer in Foundations of Science, see preprint here. The basic argument is that while such a requirement ...
2
votes
1answer
51 views

Have humans ever used the Log Scale convention in the past rather than the Linear one?

There are many examples where our senses are based off of log scales such as volume of a noise, ability to guess (i.e.) plus or minus a power of 10 with Fermi, and even when we measure pain on 1 to 10 ...
2
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1answer
74 views

What is the difference between Math and Maths? [closed]

Probably considered an off topic question, but I have only heard math referred to as maths with a plural "s" recently. Why is it maths now? What is wrong with math? Is this just a regional ...
14
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2answers
143 views

Egg vs. chicken: trig functions, exponential, real and complex

This is something I was shaky about when I took calculus, real analysis, and then complex analysis. Specifically, is the following chain of definitions circular in any way? Define the set $\mathbb{N}...
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0answers
32 views

Examples of Beal's conjecture for higher powers

Does anybody know of any examples of Beal's conjecture for higher powers? I found this web page that has probably the most examples I've come across so far. However, I'd like to find some examples, ...
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0answers
53 views

Why is the area of a rectangle given as $l\times h$? [duplicate]

While this may seem like a simple question, I have found it very difficult to answer. My question is "Why is the area of a rectangle given as $l\times h$?" We define area as the "size of a two ...
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7answers
2k views

Do the axioms of set theory actually define the notion of a set?

In Henning Makholm's answer to the question, When does the set enter set theory?, he states: In axiomatic set theory, the axioms themselves are the definition of the notion of a set: A set is ...
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0answers
49 views

Can Stochastic Integration be Further Generalized?

Is the idea of stochastic integration to accept convergence towards the stochastic integrals in probability instead of almost surely (pathwise)? I.e. to accept a weaker form of convergence for the ...
3
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1answer
35 views

Recommend of English video about math

My mother tongue is not English, but sometime there are some math reports or conference using English .Because my English is poor, I can't understand it well and can't suitably describe my question. ...
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2answers
2k views

Why are Boolean Algebras called “Algebras”?

Boolean algebras aren't algebras (to the best of my understanding). So why are they called algebras? Wouldn't it make more sense to call them a "Boolean system" or a "Boology" or something else like ...
6
votes
1answer
175 views

Why can't we order Complex Numbers? [duplicate]

I know this may very well be a silly question. I always hear that Complex numbers cannot be ordered. But there's something I'm missing... Why can't we just compare two complex numbers $z_1,z_2$ as ...
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0answers
33 views

Advanced Trig/Periodic Functions Books?

Before this question is removed for being a duplicate, let me specify what I'm looking for. The book should have a treatment of the foundations of periodic/trigonometric functions. Students are often ...
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2answers
61 views

What is the purpose of approximating solutions to equations?

Many times one wants to approximate solutions to equations, particularly when the equation in question has no closed form. For example: $x^5 - x + 1 = 0$. The approximate solution to this, which one ...
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2answers
173 views

Is it Possible to Construct all Proofs in Complex Analysis using Brownian Motion?

(First, I am very aware of the fact that Brownian motion is actually probably more difficult to understand than at least basic complex analysis, so the pedagogical merits of such an approach would be ...
2
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0answers
52 views

'Math teaching in india is robotic,make it creative'-Manjul bhargava. Then how to make it creative? [closed]

Manjul Bhargava once said "Math teaching in India is robotic,make it creative."My question is then what is the true way to study math?I am postgraduate student from India.In our institute normally ...
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2answers
36 views

A generalization of working problem.

Question: If X finishes for 4 hours a project and Y for 6 hours a project than how long it takes if they work together in same project? These questions for two people are pretty simple, just product ...
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0answers
20 views

Dimensionality of a function

When people refer to the "$x$-dimensional" case of a function or relation, how is the dimensionality determined? For example, let's say I have the functions $f(x,t)$ and $g(x, t)$. I could refer to ...
6
votes
4answers
495 views

What should “The Fundamental Theorem of Linear Algebra” assert? [closed]

Unlike some other basic fields of mathematics, linear algebra does not seem to have a universally agreed-upon fundamental theorem. This I imagine might be because the subject usually admits a lot of ...
0
votes
1answer
22 views

Representation of indeterminate forms?

I am learning about l'Hospitals rule (side note - interesting history behind it in that it should really be called Bernoulli's rule) and indeterminate forms such as $\frac{0}{0}$ , $\frac{\infty}{\...
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2answers
93 views

How do you understand calculus ideas? [closed]

I have dyscalculia, so I'm wondering how most people process math ideas. I can only solve problems by memorizing what to do after being shown step-by-step how to solve similar problems. None of the ...
0
votes
1answer
60 views

Soft Question: Do most mathematicians agree that the function is “the most important concept in all of mathematics”?

Spivak (Calculus, 3e, p. 39) writes: Undoubtedly the most important concept in all of mathematics is that of a function---in almost every branch of modern mathematics functions turn out to be ...
3
votes
1answer
129 views

Is there some kind of deep relationship between substitution and recursion?

Define $\mathbb{N}$ as the initial object in the following category: Objects. Sets $X$ equipped with a function $S : X \rightarrow X$ and an element $0:X$. Morphisms. Functions that preserves ...
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1answer
32 views

What is the Difference Between a Version and a Modification of a Stochastic Process?

Under what circumstances would one say that: The stochastic process $X$ is a version of the stochastic process $Y$? Background: See here for a related but slightly different question on ...
6
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3answers
571 views

What does “the average continuous function is nowhere monotonic” mean?

I plan on asking my professor what he meant by "average continuous function," but as it is possible that this is a concept as vague as the statement, I was hoping to get some interesting answers/...