Questions related to the teaching and learning of mathematics.

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17 views

Research scopes in Computational Geometry

I have taken a short a course on Computational Geometry and at present I want to do some research works of my own. Can anybody tell me about the research scopes on it? I mean, what are the active ...
0
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0answers
41 views

Prerequisites of Vector Calculus for Freshman

I'm doing BSc as Physics major, i had studied Calculus and Vectors in 12th grade. For now i want to study Mathematical physics myself, i had decided to follow Arfken but it starts from the topics ...
5
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1answer
77 views

What math have I missed as an Engineeering graduate? [on hold]

To explain, I have a Master's in Engineering from a well known university. We did a wide variety of mathematical topics, vector calc, perturbation methods, numerical methods, linear algebra, discrete ...
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2answers
121 views

Advice on helping a talented highschool student [on hold]

I've watched an interview of the famous mathematician Pierre Deligne. In it he says that the family had given him 'Set theory' by Bourbaki, which is known for its difficulty, and I happen to know a ...
4
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1answer
70 views

How would Johann Bernoulli have tutored Euler?

Early in Euler's life (when he was still a child/teenager), the Euler family friend Johann Bernoulli would tutor Euler in mathematics. Do we know how Johann Bernoulli would have tutored the young ...
4
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0answers
48 views

Where to post a Calculus review guide?

I created a PDF document (using LaTeX) in which I wrote relevant review materials and Calculus problems for Calculus 1, 2, and 3. Is there an appropriate forum where I could try to post this to ...
0
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1answer
12 views

Able to adjust a Function/Formula with Weighted Variables to correct for changes in a variable?

I apologize for the somewhat cryptic title as I don't quite know how to word it. I have a somewhat abstract question that may have a simple answer. But I am wracking my mind all over this! So ...
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2answers
17 views

Markup and Margins

My question is if I can have 80% margins with 180% markup of operating costs? For instance if I have an operating cost of 300 dollars and I mark it up by 180% I would charge the customer 540 dollars. ...
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0answers
31 views

International scholarship for maths [closed]

Do you mathematicians know if there is a scholarship (or something similar) for maths awarded at international level regardless of the country and/or university from which you come?
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3answers
46 views

“Full”-Simplification of arbitrary mathematical expressions

I've come across many (classroom) problems, like Roy did, whereby the solution to a problem, $$−3(7−2x)^2−5(1+x)^2$$ is the result of simplifying that expression as much as is possible, i.e. ...
8
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1answer
168 views

How much math is there? [closed]

Among other things I teach high school-level math, and one question that often comes up is: "How long would I have to study math in order to know all of it?" I usually tell them that it's like ...
0
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0answers
51 views

Is it necessary to know all the details in proofs of theorems you study in PDE's?

I've been studying PDE from the book by L.Evans for some time now. I came across some statements in the proofs which I couldn't justify. But to complete the exercises I didn't need to know all these ...
2
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0answers
75 views

On which occasions will the intelligent layperson fail to recognize a mathematics problem?

Suppose an intelligent lay person is ignorant of mathematics and believes all the crap taught in classrooms to the effect that mathematics consists of believing dogmas, obeying instructions, and ...
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0answers
36 views

Which Universities in US should I apply to study for a Masters in Statistics?

I've decided that I want to join a masters programme that prepares graduates for industry work as opposed for a phd. At the same time, I also want to really understand the theory behind the ...
5
votes
2answers
135 views

Misunderstanding the Theorem of Bayes

Saw this problem in an article on bbc.com (6 July 2014, "Do doctors understand test results?," by William Kremer BBC World Service; link below, slightly modified): A 50-year-old woman, with no prior ...
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4answers
54 views

Is it correct to write gcd(a,b) if a<b?

While creating an algorithm to compute the greatest common divisor of two numbers I saw that — on various websites/books — when you have "gcd(a,b)" a is superior to b ; is it an obligation or am I ...
2
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0answers
60 views

Science Fair project ideas? [closed]

It the summer for me right now, and I'm approaching my junior year. I'm attending a very rigorous high school in Florida in the Math, Science and Engineering program. The program requires that I ...
0
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2answers
42 views

Mathematical field theory Application in real world and other branches of Mathematics

I need to write work about applications of Mathematical field theory in real world and in other branches of Mathematics. Can someone guide me to an appropriate book, resource? Thanks, Denis.
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0answers
17 views

Imaginary roots and Real values when using Newton-Raphson Values

I am studying Newton-Raphson Method but I am facing questions in my head. How do I know if I have an imaginary number or imaginary numbers? and What to do when I have them when using Newton Raphson ...
1
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0answers
45 views

Soft question — I need books and exercise books that will be working on my fundamental skills.

I need help, urgently. I acquired a book called: Mathematics, Its Content, Method and Meaning. Now the problems is the book doesn't provide me with any exercises. I was searching for a book that would ...
0
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3answers
34 views

A lab worker needs $5$ litres of $20\%$ alcohol solution.

A lab worker needs $5$ litres of $20\%$ alcohol solution. A $10\%$ solution is mixed with a $60\%$ solution. How many litres of the $60\%$ solution will be required?
0
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0answers
38 views

Number theory problems relating to Fermats theorem [duplicate]

For all odd primes $p$ show $\left ( \frac{2}{p} \right )= \left ( (-1)^\tfrac{\left ( p^2-1 \right )}{8} \right )$. I have proven that if $q = 2Q + 1$ is prime then $q\mid 2^Q -1$ when $q=8k \pm ...
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2answers
43 views

Find point in 3D plane

I have four points in a 3D space, example: $$(0,0,1),\ (1,0,1),\ (1,0,2)\ \mbox{and}\ (0,0,2).$$ Then I have a 2D position on that square plane: $$x = 0.5,\ y = 0.5.$$ I need to find out the 3D ...
0
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1answer
82 views

The fourth pillar of mathematics? (analysis, algebra, geometry and …) [closed]

Many universities claim that there are three general areas in mathematics: analysis, which deals with continuous aspects of mathematics; algebra, which deals with discrete aspects; and geometry. If ...
0
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1answer
39 views

What are the topics taught in Pennsylvania for the Algebra 1 course?

I am entering 8th grade and I recently took a placement test. I am hoping to get into the 11th grade mathematics course (Algebra 2), but I am not sure whether or not I will qualify. The school that I ...
7
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3answers
731 views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
0
votes
2answers
74 views

What is the meaning of calculating sine of a number?

When we calculate sine/cos/tan etc. of a number what exactly are we doing in terms of elementary mathematical concept, please try to explain in an intuitive and theoretical manner and as much as ...
0
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2answers
239 views

Why it is always circle to represent a Set?

When we draw a Venn diagram, we use circle to represent a Set. We can use any closed plane figure but most of the time it is a circle. Why? are there any specialty about that?
3
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2answers
343 views

What's after undergrad? Advice needed.

I'm currently a rising senior at a small, yet well ranked liberal arts college studying Pure Mathematics. I've taken multiple high level mathematics courses and plan on doing a few more independent ...
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1answer
33 views

SAT word problem

Set S consists of all positive multiples of 5 that are less than 100, and set T consists of all positive multiples of 10 that are less than 100. The median of the numbers in set T is how much greater ...
2
votes
1answer
55 views

Rigorous Book on Topology of Surfaces and Simplicial Complexes

In the undergraduate course I am on the topology course covered the basics of point set topogly very well and everything was done, but then moved on to simplicial complexes and surfaces which was very ...
7
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0answers
603 views

Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
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1answer
30 views

how to check the variables which underwent the maximum change in a time course data?

I have time series data of many variables (these data for these variables are coming from a high-throughput experimental studies) The time series looks like $x \to x_1, x_2, x_3..$ which is the value ...
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2answers
61 views

$f(x)=\log x\Leftrightarrow f^{-1}(x)=e^x$. Why $e=2.73\cdots$?

$$f(x)=\log x\Leftrightarrow f^{-1}(x)=e^x.$$ Ok, $\log x$ is defined as the function $f(\cdot)$ such that: $f'(x)=\dfrac{1}{x}$. How to get, from this, the inverse of it $f^{-1}(x)$? And why ...
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3answers
23 views

What is the difference between the derivative of a sine function between the degrees and radian values?

Is the derivative of the sine function, where the angle is measured in degrees, the same as the derivative of the sine function, where the angle is measured in radians.? Please spare me the ...
0
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1answer
36 views

I want an intutive/theoretical understanding of the $\sin(\omega t +f)$

What is the meaning of $x(t)=x_0\cos(\omega t+f)$, where $x_0$ is the amplitude, $\omega$ the angular frequency, $t$ time and $f$ phase constant? I know how to solve the mathematical problems which ...
9
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6answers
180 views

When the approximation $\pi\simeq 3.14$ is NOT sufficent

It's common at schools to use $3.14$ as an appropriate approximation of $\pi$. However, here it's stated that for some purposes, $\pi$ should be approximated to $32$ decimal places. I need an example ...
6
votes
10answers
1k views

how to see the logarithm as the inverse function of the exponential?

I saw here in math.stackexchange some proofs of how the log and exp functions are related to each other, but I want to get an intuition for that. In layman terms, how would you explain the connection ...
2
votes
1answer
66 views

How do you use reference books?

Reference books at the research levels often does not include any problem or exercise. While you can't read these books like novels(you normally need to work on other sheet of paper), I'm just ...
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2answers
27 views

How do we emphasize that $\displaystyle x\mapsto\frac{1}{f(x)-y}$ “makes sense” if we know $y\notin\text{im }f$?

Please take a look at the following function $$x\mapsto\frac{1}{f(x)-y}$$ where $f$ is "some other function". Suppose we know $y\notin\text{im }f$, i.e. the expression in the denominator "makes ...
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4answers
374 views

Help for Mathematics High school

I'm looking for mathematics books, courses + exercises for high school level. My daughter was high school certificated but she has stopped her studies for 5 years. She would like to be involved in new ...
2
votes
1answer
82 views

How to get the domain of $x^x$?

The function $$f(x)=x^x.$$ is defined on $(0,\infty)$ because it is equal to $\exp\left(x\log\left(x\right)\right)$. But what happen when $x\leqslant0$? I tried for example $x=-1$, so ...
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0answers
41 views

Simple Math Problem on Interval

It's not clear for me. I see this wikipedia page for a difference of half interval on $\mathbb{R}$ and interval on $\mathbb{R}$? For example $$ \{ (-\infty \le x \le a) \, \left|\, a \in \mathbb{R} ...
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votes
3answers
213 views

Are there a mathematical theorieshelp us to prove $ i^2={-1}$? [closed]

We know that $ i²$=$-1$ made a great move to a new and wide ensemble group $\mathbb{C} $, but always we want to know how $i²$=$-1$ , students asked how we could prove it ? i: is the imaginary ...
4
votes
3answers
99 views

How is math used in computer graphics? [closed]

I'm doing a research paper on the mathematics of computer graphics and animation (3D) and I do not know where to start. What mathematical equations and concepts are used for computer graphics and ...
3
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0answers
91 views

In which field of science that we can prove $0! =1$ and what i can say to studentof high school if he asked about it's prove ?? [duplicate]

In mathematics there are some data , we have took them by convention and mathematics is not able to show us them proves , now want just to know if the "convention" term enough mathematics ...
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4answers
77 views

Euclidean Geometry in Physics

I've started tutoring my 13 year old niece in math. She learning geometry this year (it's a year-round school). Obviously, it'll just be basic Euclidean geometry -- though I might try to get to a ...
2
votes
1answer
89 views

Does math have to be learned linearly?

I am asking because often times one doesn't know where to start in math. "Just learn what you need" is very vague and unspecific ... for example, assume I'm a beginner at Algebra and was considering ...
14
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12answers
2k views

How to explain the perpendicularity of two lines to a High School student?

Today I was teaching my friend from High School about linear functions. One of the exercises we had to do was finding equations of perpendicular and parallel lines. Explaining parallel equations was ...
3
votes
1answer
416 views

Do only certain people exceed at math well? [closed]

It's obvious if you look around that math has always been one of the toughest subjects in all areas, from federal-traditional public schools to simply people learning it as an autodidact, hobby, or as ...