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Polar System with Short Answers, How $U(0, \theta)=\pi$ will be calculated?

I read some notes on Laplace. I ran into a short answer question as follows. We have a Laplace equation in Polar Systems: $\frac{1}{r}\frac{\partial}{\partial r}(r\frac{\partial u}{\partial ...
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0answers
13 views

Good introductory book in geometric probability

I recently came across the proof of the Buffon theorem and I was fascinated by geometric probability. Could someone indicate me a good introductory book? Maybe with many exercises?
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1answer
97 views

Is it to the students' advantage to learn the language of infinitesimals?

A colleague of mine asked an interesting question reproduced below with his permission. It is reasonable to ask whether it is to the students' advantage to learn the language of infinitesimals - ...
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0answers
10 views

Dynamic systems formula

One simple questions that i dont seem to find a answer for, is there a general equation for dynamic systems and/or is there a way to describe dynamic systems in equations? Thank you!
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0answers
35 views

Methods for solving for partial fraction coefficients.

When I present partial fraction decomposition, there are typically two approaches to solve for the coefficients of the fractions: Clear the fractions, multiply out the products, and equate ...
24
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19answers
466 views

What are some surprising appearances of $e$?

I recently came across the following beautiful and seemingly out-of-the-blue appearance of $e$: $E[\xi]=e$, where $\xi$ is a random variable that is defined as follows. It's the minimum number of ...
2
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2answers
28 views

How to express $\log_5 2$ in terms of a and b (Refer to qn)

In my textbook, I came across this interesting question which I am currently struggling to solve: If $\log_6 2 = a$ and $\log_5 3 = b$, express $\log_5 2$ in terms of a and b The solution given is ...
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1answer
19 views

convert Hex value to two's Complement

for example, let's say: 0xE5 assume the system is 8 -bit in decimal it's = 229 and in Binary it's = 1110 0101 the Two's Complement rules said: sign-bit, which's the most left, indicates a negative ...
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0answers
26 views

Game Theory Projects for Undergrads

I am looking for some project ideas for beginning math students in the topic of game theory. I am not very knowledgeable in the topic so it would be great if I could get an good introductory source to ...
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2answers
80 views

recommend math books [on hold]

So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number ...
1
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1answer
27 views

Why are surds put on the numerator in the final answer when it is a fraction. [duplicate]

I have learnt that a fraction with a surd in its most simplest form should have the surd in the numerator and not the denominator? Why is it convention not to leave the surd on the denominator? Is it ...
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0answers
42 views

mathematician who changed the world [closed]

I’m interested to know about mathematician and mathematical problems that changed the world. For example enigma machine + code braking, if you know amazing stories like this please comment them below
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1answer
116 views

Why do we teach Calculus in High School instead of, say, programming? [closed]

I was wondering "Why do we teach Calculus in High School instead of programming?" 'Calculus' only goes up to about partial derivatives, then its called different things like real analysis and other ...
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0answers
61 views

Why are math textbooks that are considered good books so hard to read? Why do authors make their books difficult to read? [closed]

I've noticed that many books that are difficult to read are considered some of the best. Why does hard to read indicate that it is rigorous? For example: Rudin, Apostol, Lang, Hungerford, Ahlfors, ...
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0answers
12 views

consider the coordinates of the bounding area inclusive the range coordinates

I am stuck with a very trivial issue here. I have following coordinates: (xMin,yMin) = (-500,-500) (xMax,yMax) = (764,-26) and the step size is 79. I need to consider all the coordinates inclusive ...
2
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0answers
29 views

E versus e when using scientific notation

When I was calculating pressures in different units, I decided to use Google out of laziness. First I tried: 1.013e-10 mbar and received a result of: ...
2
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2answers
47 views

Mathematical usage of “$\dots$” during enumeration, is it ok to be imprecise?

I am guilty of writing things like the following in proofs: so by lemma 1.2 we have that for $k<n$ all of the integers $k,k+1,k+2,k+3,\dots ,n$ are pompous. I really like how this looks, the ...
2
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1answer
45 views

Theorem 2.27 (a) in Baby Rudin: Is his proof complete enough?

Here's Theorem 2.27 (a) in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition: If $X$ is a metric space and $E \subset X$, then $\overline{E}$ is closed. Now here's ...
2
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0answers
56 views

What's the mathematical symbol to say “It doesn't depend on …”?

If I want to say x doesn't exist I would use the symbol $\nexists$ If I want to say x is a member of... I would use $\in$ But what's the symbol to say y doesn't depend on x? I know I could write ...
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3answers
54 views

Logic with numbers

Nick wrote each of the numbers from 1 to 9 in the cells of the 3x3 table below. Only 4 of the numbers can be seen in the figure. Nick noticed that for the number 5, the sum of the numbers in the ...
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5answers
79 views

How to prove $\sin3θ=3\sinθ-4\sin^3θ$

I was solving an A Level past paper (November 2014 P32) when I stumbled upon this question. It first asks us to expand $\sin(2θ+θ)$ which is easy using the identity $\sin(A+B)=\sin A\cos B+\cos A\sin ...
2
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1answer
91 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 ...
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0answers
23 views

What does meant “Uncounditional proof” and why should believe it that is a complet proof?

I have tried many times to understand what it does meant "Uncounditionally proof" but i don't succed , only I think that is the proof which produced from Insufficient conditions and and havn't enough ...
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0answers
66 views

Got some problem with math [closed]

First of all sorry, if this is the wrong place to post this, didn't found a better tag for it. So I used to be/am quite good in math, however recently I discovered a big weakness I have. Whenever I ...
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0answers
31 views

List of Interesting African Mathematics Blogs

Title says it all: looking for info on any Mathematics blogs that are either contributed to by bloggers on the African continent, or have an African continent focus (for example someone living outside ...
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1answer
30 views

Estimating Number of Scratch Tickets Remaining

So, in my statistics class we discussed the recent huge jackpot, but we decided to focus on something more "trackable"—scratch tickets. A part of the assignment is to figure out how many tickets are ...
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3answers
61 views

What is the probability that a person wins the game on the first roll?

I can't seem to find an answer for the title/question above and so I thought I'd ask. The aim of the game is to get a higher number than your competitor using only one dice. If two people (For ...
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3answers
54 views

Understanding (proportional to) through an example.

This question may be redundant and I apologize in advance but I am really having a hard time to digest the notion of proportional to in mathematics. Kindly, can someone simplify the idea of it and ...
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2answers
26 views

Can someone explain how I can triangulate using angles and one side of a Right-angled triangle?

I've been looking around, trying to find a simple way explaining why and how to calculate distance using the triangulation technique, but I'm still pretty confused, I've got some simple math notions, ...
2
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0answers
56 views

Increased Math Productivity on Mobile Devices [closed]

I have been answering questions on Math.SE for a (relatively) short time now, and I have found that answering questions on my Android phone is somewhat of a nightmare. I end up commenting much of the ...
1
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0answers
23 views

summer program for college freshman

I'm a college freshman and I'm studying mathematics. Do you know any summer programs that would be suitable for a European student? If you have any personal experience, can you tell me about it? ...
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0answers
23 views

Are there any online math games similar to CheckIO or CodeCombat?

There are several nice online programming games where you need to solve problems in one place to unlock other places on the map. Are you aware of similar games focussing on math problems? Or (even ...
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0answers
108 views

Freshman calculus - Stokes's theorem proof

Many calculus text books and courses do not introduce full proof of Stokes's theorem because of differential forms and topological concepts. There are only restrict proofs (for example, simple ...
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0answers
13 views

Input a matrix with integral element in matlab

I am working on stochastic fractional differential equation , like below $$ D^2y+D^{\frac{3}{2}}y+y=1+t ,\space y(0)=0 ,y(1)=2$$I use RBF's (radial basis function) to solve it .so $y \sim \lambda_1 ...
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1answer
58 views

Scratch paper alternatives? [closed]

How do you practice complicated calculation when the problem is displayed on your computer screen? Do you always have pieces of paper on the side, or do you have a Wacom tablet connected to your ...
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0answers
33 views

New method to solve this fractional differential equation

this is my problem \begin{align} & D{{\text{ }}^{2}}\text{ }y\left( x \right)\text{ }+\text{ }D{{\text{ }}^{\frac{3}{2}}}\text{ }y\left( x \right)\text{ }+\text{ }y\left( x \right)\text{ ...
16
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2answers
83 views

why don't standard analysis texts relax the injectivity requirement of the multivariable change of variables theorem? [duplicate]

In standard multivariable analysis texts, the change of variables for multivariable integration in Euclidean space is almost always stated for a $C^1$ diffeomorphism $\phi$, giving the familiar ...
0
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1answer
48 views

Is there a place that lists graduate institutions and their specialties? [closed]

I'm currently a sophomore at a Canadian university, and due to some recent head butts in a few maths classes, I'm realizing I don't know what I want to do in grad school (or if I even want to go for ...
6
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1answer
99 views

New Elementary Function?

In the February 2000 issue of FOCUS magazine, a short article suggests that the Lambert W function could be introduced into curriculum as a new elementary function saying: "... a case can be made for ...
6
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4answers
207 views

How to explain “why study prime numbers” to 5th Graders?

I tend to teach 5th graders math ever so often just so they can be "friendly" with math in a playful manner, instead of being afraid. However, one question that I constantly struggle with is this: ...
3
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2answers
59 views

What is the Pedagogical Justification for Substitution?

My mom is re-learning calculus for the third time (She tutors High School students). And she asked me a question invovling limits: $$\lim_{x\rightarrow \infty} \frac{\ln 2x}{\ln 3x}$$ I led her ...
28
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7answers
3k views

Why does topology rarely come up outside of topology?

I am currently taking topology and it seems like a completely different branch of math than anything else I have encountered previously. I find it a little strange that things are not defined more ...
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17answers
2k views

What are some math books written in dialogue or story form, e.g., a teacher explaining to a student?

Good examples would be The Square Root of 2 by David Flannery or Math Girls by Hiroshi Yuki.
1
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1answer
22 views

Finding the probability of X_Bar with sample variance included?

The question I am asked is $P(\bar{X} > 3 + 0.4984S)$, where I am additionally provided $n = 25, \mu = 3.0, \sigma^2_\text{pop} = 3.0$. $\bar{X}$ is the sample mean and $S$ is the sample variance. ...
0
votes
1answer
108 views

Questions wrong or theorems useless because hypothesis impossible [closed]

Consider the following question: The area of a right triangle with integral sides is 5. What is twice its area? The answer is 10. But on closer inspection, there is no such right triangle. What can ...
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1answer
26 views

defining the (cw/ccw) in radians (pos/neg) [closed]

are there any negative radians? **deg° 0.0 32.9 /-32.9 **rad* 0.0 0.5742133 / -0.5742133 enter image description here
5
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1answer
159 views

Dividing numbers with dots?!

OK. This intrigues me. I recently came across this video. Which presumably tells you how to divide 133,342 with 121 only using hand drawn dots! Fair enough but I don't think this works for every ...
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0answers
28 views

Equation for circle tangent to differentiable functions.

This question addresses a problem from this question. Sketching a possible approach to attack it. If we have the differentiable function $t(x)$ which we want to create a sequence of circles as ...
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0answers
34 views

Is it possible to visit all points on a differentiable function by “rolling”?

I recall from a discussion thread some week ago we talked about different ways to pedagogically explain differentiability. So I came up with this idea that if there for each point there exists a ...
3
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3answers
111 views

What to teach first: Riemann sums or anti-derivative? [closed]

In some text books, I see that they teach Riemann sums first. In other texts, I see they teach anti-derivatives first. Is there any pedagogical preference? It seems to me that we should teach ...