Questions related to the teaching and learning of mathematics.

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0
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1answer
153 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
495 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 ...
415
votes
45answers
284k 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 ...
0
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0answers
36 views

Finding an exam grade average

Someone else got a 68% on their first account and an 83% on their second account. At a minimum, what value do they need on the third account so that their overall bank dividenda (mean) is at least an ...
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4answers
699 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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0answers
58 views

Necessity of writing Math in a patent?

I don't know if its appropriate question here...but I anyway want to try... I have an algorithm in which I have a finite data in which each element is assumed as an element of a metric space with a ...
1
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0answers
36 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
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1answer
23 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
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2answers
60 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
380 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
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1answer
60 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
157 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!
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3answers
247 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 ...
0
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0answers
59 views

Comic that makes clear that it might be a good idea to prove something…

I want to make a teaching unit in a high school class about beautyfull elementary mathematical proofs. At the beginning I want to motivate that it is really essential to proof something (because ...
1
vote
0answers
26 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 ...
1
vote
3answers
106 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 ...
0
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0answers
100 views

Don't feel like I grasp the mathematics I'm supposed to understand

In high school, I used to spend my free time proving the formulas that we were asked to use. I'd prove loads of formulas in Calculus that we never even studied, just because I enjoyed getting to the ...
0
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0answers
29 views

Learning resources for Probability Distributions/Models

I've a good background in basic probability. I need to learn and get a good grip on the probability distributions and stochastic processes, counting processes, and other related topics. I am already ...
3
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5answers
119 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. ...
3
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3answers
172 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 ...
13
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6answers
2k 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 ...
0
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2answers
95 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. ...
16
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11answers
912 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
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1answer
58 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
116 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? ...
0
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0answers
18 views

Does Volterra’s example prompted development of a generalization of the Riemann integral?

Volterra's function is a real-valued function X defined on the real line R with the following curious combination of properties:(a)X is differentiable everywhere. (b)The derivative x ′ is bounded ...
2
votes
1answer
498 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 ...
0
votes
1answer
19 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
89 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 ...
62
votes
14answers
6k 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 ...
0
votes
1answer
184 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 ...
0
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1answer
45 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 ...
5
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1answer
183 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 ...
2
votes
1answer
75 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 ...
6
votes
1answer
218 views

Is making the math learning process deliberately more challenging an effective teaching strategy?

I've often come across a view on teaching/learning math to the effect that forcing students to struggle rather then "spoon-feeding them" (as they put it) makes for much more able students in the long ...
3
votes
2answers
360 views

best books for learning algebra

My name is Aniket and I have started 11th class recently. I have studied only my school textbooks(NCERT Books) and I am not happy with them. I want to learn Algebra,i.e, all the topics covered in ...
2
votes
2answers
84 views

Do users of RTL languages adopt an LTR standard for mathematics (in the same way they often do when using LTR words or phrases in RTL text)?

Non-mathematician here. There is a discussion on this forum titled "Is “applying similar operations from left to right” a convention or a rule that forces us to mark one answer wrong?" I found it ...
1
vote
1answer
390 views

How to use point estimation on an interval? Statistics question

I got part a and part b just fine, but I am confused on how to do part (c), (d), and (e). I don't really understand what the question is asking, nor do I understand how to do that sort of interval ...
2
votes
0answers
117 views

What are some cool projects that can be done in a high school math class?

I'm studying to be a secondary math teacher and will be starting student teaching next month (an algebra 2 class). It's difficult to find activities and projects that are actually informative and time ...
0
votes
2answers
94 views

Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
4
votes
2answers
233 views

Careers in Mathematics?

I am a college freshman, and I really like to have goals for my life, one of the big ones is my career of choice. Previously, I have always wanted to be a programmer, and I have written a lot of code. ...
0
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0answers
39 views

Events for high school students which can look good on a cv.

I'm a european high school student and I'll apply to university in July. Are there any interesting activities/events which can look good on the curriculum I'll submit with the application? Further ...
2
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0answers
66 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
0
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1answer
29 views

This is regarding a verbal math problem

A Shopkeeper buys sweets at 11 for a rupee. He bought an equal number of sweets at 10 for a rupee. he sold all the sweets at 8 for a rupee. find loss or gain % Please solve this for me. I am not able ...
0
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2answers
46 views

Fundamentals of Algebra - Cancelling Like Terms in Divison

When can, or can't, terms be cancelled. ie: $\frac{3x^2-1}{x^2}$ $x^2$ cannot be cancelled. Why not, and what are the rules?
1
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1answer
71 views

Looking for data science-oriented “Applied Maths for dummies” summer school

I'm a PhD candidate who critically lake of maths skills for his data science projects. I'm looking for a summer school that would enable me to take off in this aspects. This could be ...
1
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2answers
132 views

Re-learning Math and becoming more comfortable

As someone finishing up their BSc in Electrical Engineering, it is becoming very clear that I need to improve my mathematically abilities significantly if I want to pursue any more education. I ...
1
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1answer
30 views

function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
2
votes
2answers
84 views

Why doesn't this work? — The V.I. Arnold Primary School Problem (Two women started at sunrise…)

I've got a, perhaps silly, question. I understand the various solutions to this problem: Two women started at sunrise and each walked at a constant velocity. One went from A to B and the other ...
0
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1answer
80 views

Interpretation of First Isomorphism Theorem

I understand that the first isomorphism theorem basically says that any homomorphism f from group G to group G' induces an isomorphism from G/Ker(f) to the f(G). What I don't quite understand is the ...