For questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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5
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2answers
92 views

Looking for a specific female maths writer

This is going to be an annoying question, but I have to ask it as it is annoying me. I once read a book on infinity that was written by an American female maths writer. She was very easy to read and a ...
1
vote
2answers
79 views

Standard Deviation of Population from Sample.

I guess I am a little confused. I am doing t test statistics in my class. I think I know but I would love some insight. I am trying to get the estimated standard deviation for the population. These ...
1
vote
1answer
46 views

Matrices of the form $A^p=(a_{ij}^p)$

I am wondering if there is a name for these kind of matrices and if they are interesting or not? Do they even exist? Let $A$ be a $n\times n$ matrix with elements $a_{ij}$. $A= (a_{ij})_{i,j\in\{1, ...
5
votes
1answer
192 views

What's the trick to re-focusing on your math studies?

If you check my history on MSE, you'll see that I was very active about 1/2 a year ago. Right now I'm working and socializing a lot, which is important, but I also have spare time to devote to my ...
3
votes
0answers
34 views

Classroom enhancement resources for linear algebra

My university offers small grants (in the \$100 - \$300 range) for classroom enhancement resources. In the past, I've applied for and received a grant to purchase a Zometools kit used for ...
1
vote
2answers
63 views

What does $e^b$ means?

What does it mean $a^b$ where $a$ and $b$ are real numbers not integers, not rationnals (I do not know the name of this set). Real numbers means $\mathbb{R}$ but $1\in \mathbb{R}$ So, what does it ...
4
votes
1answer
250 views

Where to begin my Math journey

I apologize if this is not the correct forum for this, but I felt it appropriate. I want to start getting into more mathematics and learning all I can to step up my programming career. I know plenty ...
3
votes
5answers
457 views

What area of Abstract Algebra do you find most interesting? [closed]

For my Abstract Algebra class, we will be doing small presentations (2 class periods) covering some topic in Abstract Algebra. Thus far, I have studied groups, rings, fields, modules, tensor ...
11
votes
1answer
261 views

why is that most of the books in mathematics don't include answers?

I am currently going through the " Topics in Algebra" By I. N. Herstein. The problems are pretty good. But there are no answers on the back. Same is the case with "Mathematical Analysis" by Rudin. I ...
0
votes
2answers
45 views

Power calculation for simplification?

I have this simple question I saw here: ±(2 - 2^(-23)) × 2^128 = ±6.8 × 10^38 How did they get to ...
0
votes
1answer
242 views

Parabola problem. How far from the vertex is the focus?

A spotlight has a parabolic cross section that is 8 ft wide at the opening and 2.5 ft deep at the vertex. How far from the vertex is the focus? I'm getting 8/5 ft. Is this correct? Appreciated!
5
votes
2answers
150 views

Why the $\log$ is so special?

When I first learn about the logarithm function $\log$ or $\ln$. My professor said that $\log x$ is a function that when we derive we get the inverse function $1/x$. This $\log$ becomes very popular ...
6
votes
1answer
622 views

Is an undergraduate in engineering sufficient preparation for a masters in mathematics?

I'm a high school student who is considering doing an undergraduate in engineering. However my the long term plan is to pursue math at a higher level. I want to do engineering at undergrad because I ...
1
vote
1answer
202 views

Max value - Mantissa calculation clarification?

I've been reading this article about floating point representation floating point representation is : Where mantissa is : All understood. But they also say : How did they get to ...
94
votes
20answers
19k views

Visually deceptive “proofs” which are mathematically wrong [closed]

Related: Visually stunning math concepts which are easy to explain Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
0
votes
1answer
2k views

Upper and Lower Bounds for Confidence Intervals on a one tail hypothesis test.

CI(99) = xbar ± Zcv( σ / √ n -1 ) My question is if the test is a one tail hypothesis test, do I still do two separate equations + and -. Here is the formula filled in (if it is the correct ...
7
votes
2answers
342 views

Closed, orientable surface whose genus is very hard to find intuitively

I'm introducing the Classification Theorem on closed and orientable surfaces in a talk on (intuitive) topology, and to motivate it I'd like an example of an embedding of a surface in $\mathbb{R}^3$ ...
0
votes
1answer
15 views

Why am I getting 84.25 instead of 97.68 for my Confidence Interval?

Why am I getting 84.25. I am doing 97.96*(6/sqrt[50-1]) = 97.96*(6/7) I am obviously not doing this correctly please help. It has been sometime since I have done any math.
12
votes
7answers
3k views

Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
2
votes
1answer
53 views

Looking for mathematics teaching article

Some time in the last month, I read a great article somewhere on the web that discussed the sorry state of secondary school math education in the U.S. One of the examples in that article was a ...
1
vote
1answer
79 views

Can I use order of operations (BIDMAS) on any question?

Does BIDMAS only apply to simple calculations, or can you use them in algebra etc?
0
votes
1answer
26 views

return a number between 3 to 5 by get a number between 1 until 10000! [closed]

I want to have a math math formulas to do this operation: A:get a number between 1 to 10000 B:reteun a number between 3.00 until 5 for example 3.89 for greater number return greater number too! ...
5
votes
2answers
526 views

I'm stuck with rounding decimals and have been for years

I'm in year 10 and have a B grade - yet still manage to mess it up when I face a question regarding decimals. For example: Round 8.647 to one decimal place. Would this be 8.7 or 8.6 as I have never ...
0
votes
1answer
346 views

A Ferris Wheel Word Problem (Trigonometry)

Please help, will give me an idea how to do more of these. A Ferris Wheel called Colossus has a diameter of 158 feet. Using the figure as a model, find the distance traveled by someone starting at ...
3
votes
2answers
7k views

Linear Homogeneous Recurrence Relations and Inhomogenous Recurrence Relations

I'm having some difficulty understanding 'Linear Homogeneous Recurrence Relations' and 'Inhomogeneous Recurrence Relations', the notes that we've been given in our discrete mathematics class seem to ...
707
votes
53answers
418k views

Visually stunning math concepts which are easy to explain

Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain, but are ...
2
votes
1answer
387 views

Revenue Function - Silly Definition

I'm teaching the section 4.7 on optimization in Stewart Calculus. It has a subsection on "Applications to Business and Economics." There the author defines the price function $p(x)$ to be the price ...
10
votes
4answers
1k views

Why would you expand a square wave in a Fourier series?

The periodic square wave $$ f(x) = \cases{ 1 \text{ if } 0 \le x \le \pi \\ 0 \text { if } -\pi \le x < 0} $$ seems easy enough to work with. Why transform it into a series of sines and cosines? ...
4
votes
4answers
2k views

Linear combinations of sine and cosine

If you take a linear combination of the cosine and sine function, then the result is again a sinusoid, but with a new amplitude and phase shift. $$a \cos(\theta) + b \sin(\theta) = A \cos(\theta + ...
2
votes
0answers
119 views

Pen-and-paper educational games

I'm teaching maths at the 8-16 year level, one-on-one tuition. What are some good pen-and-paper maths games I can play with these kids? Googling "math games" just gets me a load of interactive ...
0
votes
1answer
35 views

What are the variables by which I can differentiate the different fields of math?

Ironically, I'm on a mathematics-based forum using the terms "variables" and "differentiate" in entirely non-mathematical ways, but what I mean by this question is as follows: I'm self-studying and ...
3
votes
2answers
94 views

Help finishing proof via induction for a summation

So I have to prove the following equation using induction for n >= 2: $$ \sum\limits_{i=1}^n 4/5^i < 1 $$ However the question asks me to prove something stronger such as this: $$ ...
4
votes
3answers
892 views

Solve the equation $(x-3)(x+9)(x+5)(x-7)=385$

I have one question please...I solved it in this way..so I am not sure..that is it right or not? and If I solved it in the wrong way..so would like to know about the correct way and method to solve ...
0
votes
1answer
64 views

$S=\{0,1,2,3\}$. Show that $(S,+)$ is a Semi group where $+$ defines addition Modulo 4

I have search out my whole maths book for it..but didn't got this question in my book and I need to learn it for my exam..So if you people can please solve this for me? $S=\{0,1,2,3\}$. Show that ...
3
votes
1answer
201 views

Bessel function integral

How to solve the integral for $J_1{(2x\sin{\frac{\theta}{2}})}$ at $[0,\pi]$? If solving by Matlab, please provide me the source. Thank you!
4
votes
3answers
1k views

Is it possible to learn abstract algebra no precalculus or calculus?

See above. I am trying to re-teach myself mathematics in a different manner than is formally taught (i.e., set theory, number theory, mathematical logic, abstract algebra, discrete math and then ...
1
vote
0answers
34 views

Strange conundrum involving mean and variance of numbers.

Given $n$ numbers $a_1<a_2<...<a_n$ how would we find a $m$-element subset ($m \leq n$), with the smallest variance? If I knew what the optimal mean for the smallest variance is I could just ...
2
votes
3answers
617 views

Set Theory, Number Theory, and Logic before any other math

I am trying to teach myself set theory, number theory and logic before I engage in mathematics. I have been able to get through Calculus but I think that it was just by repeating different types of ...
3
votes
4answers
145 views

Chain Rule: Is the notation $\frac{dy}{du} \cdot \frac{du}{dx} = \frac{dy}{dx}$ accurate?

My question is if it is okay / mathematically rigorous to write the Chain Rule like that (the Leibniz way). I thought that $dx$, etc. do not follow the rules of algebra and cannot be treated as such. ...
6
votes
4answers
537 views

University-level books focusing on intuition?

I help some students with difficulties in Mathematics and Physics (especially math, physics, and engineering majors). While in high school they usually don't study, or are not interested, etc., in ...
20
votes
7answers
6k views

Why teach linear algebra before abstract algebra?

Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra? I'm asking this because personally it seems to be much easier to understand the architecture behind ...
2
votes
5answers
1k views

Applications of inflection points

Recently, I was teaching maxima, minima and inflection points to first year engineering students. I motived extrema by giving practical examples of optimization problems, but when a colleague asked me ...
0
votes
2answers
131 views

linear congruence questions

A: For the two systems of linear congruences, one system has integer solutions while the other does not. For the system with integer solutions, write down 2 of them whose difference is less than 192. ...
18
votes
11answers
1k views

Why limits work

I'm currently a first year student in electrical engineering and computer science. I know how to compute limits, derivatives, integrals with respect to one variable that is things from one variable ...
0
votes
1answer
66 views

Calculating $\lim\limits_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}$ [duplicate]

I am trying to solve this limit without using Taylor expansions to explain it to a secondary school student $$\lim_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}.$$
2
votes
2answers
137 views

$f(x)=\sin(43x)+\cos(2x)$ is periodic function?

$f(x)=\sin(43x)+\cos(2x)$ is periodic function. I got the period of $\sin(43x)$ is $\frac{2\pi/}{43}$ and period of $\cos(2x)$ is $\pi$. Then the period of $f(x)$ is $2\pi$. Am I right? Any comment? ...
2
votes
1answer
2k views

Real world applications of exponential function; continous case

I am looking for interesting applications in everyday life, technology or science of exponential functions of the type: $$ f\colon \mathbb{R} \to \mathbb{R}, \quad x \mapsto ab^x $$ for the case $a ...
1
vote
1answer
60 views

Generally speaking, how should one read notation?

I became a better reader when I stopped sub-vocalizing (hearing the words in my head). I still do that when I read math. I tried not to do that when I read an expression today. I felt less confident ...
0
votes
1answer
81 views

How to work out 3 dimensional vector angles

I've come across this question and cant for the life of me think how to work it out. I understand working out the angle between two vectors e.g. given, vector a(2i+3j-k) and vector b(8i-6j+2k) but am ...
2
votes
1answer
944 views

About the epsilon definition of a convergent sequence. Is this definition equivalent?

I read that it is appreciated to include the context and motivation of a question. I may have overdone this a little bit in this question. To summarize, my question is: Are the two blockquoted ...