# Tagged Questions

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

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### 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 ...
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 ...
233 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!
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 ...
597 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 ...
198 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 ...
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 ...
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 ...
339 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 $\mathbb{R}^3$ ...
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### 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.
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? ...
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### 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 ...
78 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?
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! ...
513 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 ...
341 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 ...
6k 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 ...
417k 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 ...
381 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 ...
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? ...
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### 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 ...
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 ...
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!
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 ...
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 ...
596 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 ...
143 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. ...
516 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 ...
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 ...
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 ...
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. ...
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 ...
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 $$\lim_{x \to 0} \frac{10^x - 2^x - 5^x + 1}{x \cdot \tan x}.$$
136 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? ...
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 ...
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 ...
79 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 ...
904 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 ...
7k views

### Should an undergrad accept that some things don't make sense, or study the foundation of mathematics to resolve this?

I'm a second year math student. And I've the following problem. When I prepare myself for an exam, I can distinguish two phases. First I'm mainly interested in whatever is necessary to pass the ...
61 views

### Is there a name to refers to anything that is a point, line, plane, etc?

I'm teaching my juniors in high school some beginning linear algebra, but I find there is some vocabulary I am missing. I want to say that points, lines, and planes are all related, but is there a ...
318 views

### I want to pursue Computer Science as a major but I don't know if i should…HELP!? [closed]

I'm currently a second semester sophomore who's currently pursuing a Global Affairs major and minoring in Japanese Studies. I plan on going to law school after college and I'm interested in ...
69 views

### Pre requisites of linear algebra

I want to learn abstract linear algebra. Do I require the knowledge of discrete mathematics before I start? I have the impression that abstract maths and their proofs can be understood easily by the ...
731 views

### When should I start learning Set Theory?

I started to learn a few disciplines on my own over the break after my first year in college and one of them was Real Analysis. In the process I came across many issues in Analysis texts concerning ...
138 views

### Elementary “bugs” in computer algebra systems?

There's a discussion of bugs in CAS's here, but these are technical errors of interest mainly to the professional mathematician. I am more interested in simple errors which might arise in the use of ...