Questions related to the teaching and learning of mathematics.

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0
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1answer
10 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 ...
1
vote
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. ...
0
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0answers
29 views

International scholarship for maths [on hold]

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?
1
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3answers
42 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. ...
6
votes
0answers
103 views

Will Mathematical discoveries slow down? [on hold]

With more and more Mathematics being discovered through time is it not the case that to make new discoveries, old theorems would have to be learned? Therefore would this not mean that there is a point ...
8
votes
1answer
157 views

How much math is there? [on hold]

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
49 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
votes
0answers
71 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 ...
1
vote
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
130 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 ...
0
votes
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
57 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.
0
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0answers
16 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
vote
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
votes
3answers
33 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 ...
0
votes
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
votes
1answer
79 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
votes
1answer
38 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
votes
3answers
727 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
votes
2answers
236 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
votes
2answers
340 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 ...
0
votes
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
votes
0answers
600 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 ...
1
vote
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 ...
1
vote
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 ...
-1
votes
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
votes
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
votes
6answers
179 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
65 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 ...
0
votes
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 ...
1
vote
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 ...
0
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0answers
37 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} ...
-2
votes
3answers
212 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
97 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
votes
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 ...
1
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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
88 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
votes
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
414 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 ...
3
votes
0answers
105 views

Which is the best transitional mathematics book for self-teaching among the ones listed?

What is Mathematics, An Elementary Approach to Ideas and Methods - Courant Robbins Stewart How to Solve It, A New Aspect of Mathematical Solving - Polya Introductory Mathematics, Algebra and Analysis ...
3
votes
3answers
112 views

Explaining to kids that $2^n$ can quickly yield high values

I have to explain to kids that $2^n$ can yield high values. Not with math and numbers but with a story rather. There was a story about a pharaoh and wheat..
4
votes
5answers
406 views

How to defend Mathematics from “ignorant” people? [closed]

Some of my friends are blaming me to stop talking about and studying Math. But I love Math so much and I do Math almost everyday. The problem is that some of my friends told me "go and get a life". I ...
0
votes
1answer
100 views

Going to math grad school with low GPA [closed]

I am a pure mathematics major and I want to do Ph.D in math, however I want to change to Applied math. I have a low 3.2 < GPA < 3.3 though. I have taken most of Pure math requirements, and ...
1
vote
0answers
37 views

What are some good statistics resources?

A year ago, I took a statistics course at my university. The course was based on Rice's "Mathematical Statistics and Data Analysis". Apart from the fact that I did not find the book terribly good, I ...