Questions related to the teaching and learning of mathematics.

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17
votes
5answers
514 views

Proving a certain map on the closed unit disc must be the identity

Bounty expired. Will gladly re-create one if a satisfactory answer is posted in the future. Prove: Let $f$ be a continuous function on the closed unit disc with two properties: 1. $f$ is the ...
4
votes
0answers
426 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
31
votes
22answers
7k views

Poems related to mathematics [closed]

I am supposed to be presenting a poem in my undergraduate math class, that relates to mathematics. The point of the presentation is to show the beauty of math , and the fun of it ,and also it will ...
6
votes
0answers
130 views

What is the best way to go about learning math?

I know this is a very subjective question, but after struggling on my own for a while I figured I might as well ask it. I did all the normal math classes in college (LinAlg, MultiVariable Calc, ...
10
votes
4answers
258 views

Is studying mathematics chronologically a good idea or not and why?

In high school nowadays most mathematics you learn is fairly 'old'. You have your geometry, all of which (taught in high school) was known to the Greeks more than 2 thousand years ago. You have ...
1
vote
0answers
80 views

How would you explain the pdf of the normal distribution to high school students (11th/12th graders)

I will be teaching the normal distribution in January and I need to know how to effectively explain the concepts that does not in any way confuse students or make them feel that the material is ...
14
votes
4answers
493 views

Reflections on math education

Why is there such a big difference in math education between The Americas and (Europe and Asia) ? except for a few privileged who have the opportunity to access to math much earlier than the ordinary ...
2
votes
1answer
61 views

Simple question about power

Please solve this question and describe it. $$a^2+b^2+ab=b-a-1\Longrightarrow a^{1001}+b^{1001}=?$$ By Newton formula.
4
votes
2answers
197 views

What is a good example to show high school students why a proof for induction is a reasonable kind of proof?

I teach average-level high school students who have not had much beyond Algebra 1. I want to show them why induction makes sense. I want the sort of problem where it is intuitive that a statement is ...
2
votes
3answers
75 views

$\sin^2$ notation and uses of the alternative.

So I was taking my calculus class and I was shocked by the following: Apparently its a convention for $\sin^2(\alpha)=(\sin(\alpha))^2$ As opposed to what I thought made more sense which was ...
0
votes
1answer
41 views

Equation For Multiples

So this is probably a super easy question for Math Stack Exchangers. Anyways I can determine the multiples of 3 up to 10 doing this. multiples of 3 up to 10 ...
0
votes
2answers
92 views

How to calculate profit share for this example [closed]

How can we calculate a profit share for Rs. 100,000 that remained in an account for 5 days only. See this question illustration below I was confused about which tags were more appropriate for ...
5
votes
1answer
165 views

Explain/illustrate Goedel's theorems and possible implications to non-mathematicians

I am asked to give a talk about (a) mathematical practice, (b) axiomatization, (c) Gödel's theorems and (d) possible antimechanist arguments based on the incompleteness theorems (as mentioned in P ...
1
vote
1answer
146 views

What major to choose, out of three possible math majors?

I need help with trying to figure out which major I should try to graduate with. Currently, I am a senior undergraduate student with an actuarial science major. I have three actuarial exams finished, ...
1
vote
1answer
156 views

Explain mathematical practice and axiomatization to non-mathematicians

I am asked to give a talk about (a) mathematical practice, (b) axiomatization, (c) Gödel's theorems and (d) possible antimechanist arguments based on the incompleteness theorems (as mentioned in P ...
2
votes
0answers
112 views

What is meant by “mathematical maturity”?

I have often heard people talk of "mathematical maturity", sometimes in the sense of the maturity required to understand an area of mathematics or in the approach to a problem or proof. However, it's ...
6
votes
4answers
194 views

Formality and mathematics

Why is it important to be formal in mathematics? Is formality beneficial for students? Or is it just to scare students away from mathematics?
4
votes
0answers
136 views

Math or CS PhD areas to look at. [closed]

I am looking into getting back to school to get a PhD in Mathematics or Computer Science (I hold MA in Math). I am wondering what new areas of research in Math and CS are promising in a sense that ...
3
votes
3answers
251 views

How do you validate that two math expressions are equal?

Let's say you have a few expressions like the following: $$\begin{array}((x+17)^2 \\ x^2 + 34x + 289 \end{array} \\ 288 + \frac{x^2}{2} + \frac{x^2}{2} + 34x + 1 \\ [...] $$ You get the idea: ...
0
votes
0answers
38 views

Convention on the order of scalar multiplication (Multiplier vs multiplicand)

Is there a convention on the order of scalar multiplication? I know there were questions before mine, but I would like to know if such distinction is culturally dependent. This came from a news in ...
2
votes
0answers
45 views

Resources for Teaching High School Statistics

I am a student teacher looking for resources to teach high school Probability & Statistics (untracked). The second semester will be inferential statistics and will include these following topics: ...
6
votes
0answers
96 views

Educational software for graduate mathematics

Our university uses computer software to help automate and expedite the learning process for basic math classes (college algebra, trigonometry, precalculus, etc.). Software such as this provides ...
4
votes
1answer
86 views

Planning a mockup maths class for high school related to river reactivation

I have to plan a mockup maths lesson where the "main topic" should be river reactivation. The given suggestion is to focus on computing cross-sectional areas of rivers using basic geometry and for ...
2
votes
1answer
89 views

Describing the impossibility of trisecting the angle to high school students.

Does anyone have an idea on whether it would be possible to present the proof of the impossibility of trisecting the angle (or doubling the cube, for example) in order to demonstrate the power of ...
0
votes
3answers
178 views

Practical context for a quadratic equation with negative discriminant.

I'm looking for practical questions that lead to quadratic equations with negative discriminant. The pupils involved are 16 years old and technically educated. Abstract mathematic questions are ...
3
votes
0answers
83 views

To what extent a recommendation letter about teaching will influence the application to math Ph.D program?

I'm currently in a math graduate program in the US and am applying for a Ph.D program in other universities (also in US). The problem of mine is I cannot find enough recommenders. My thought right now ...
2
votes
0answers
193 views

Math gre subject test scores and results?

I took the math gre scores back in October and did terribly (52%) even though I was scoring in the 70-80% on practice exams. I am interested in applying to Stanford's ICME and Berkeley's Stats ...
8
votes
1answer
177 views

Learning Mathematics in a Second Language

My first language is English, and since all of my formal education has been undertaken in the USA, I have learned mathematics entirely in the English language. However, I have spent a fair amount of ...
4
votes
1answer
223 views

Explaining math solution to a 9-year-old

I have a problem called "The Prison Problem" that I need to explain to my 9-year-old cousin. I would think that he has just started learning about divisors and perfect squares, and as such, I have a ...
1
vote
0answers
33 views

Question pertain to graduate programme in astronomy from mathematical background

I am currently an undergraduate student in mathematics, and wanted to pursue a career in astronomy area. What graduate programme should i take? is applied mathematics sufficient? I am currently ...
8
votes
4answers
328 views

What's the deal with integration?

So at uni we learned tricks and techniques for integration until cows came home. But to what end? Any/All definite integrals can be evaluated using numerical methods. Most integrals in application can ...
3
votes
1answer
202 views

Basic Fourier Series Question

Let $f$ be a $2π$ periodic function where $$f(x) = \frac{π - x}2$$ over $[0, π]$. It is known that the Fourier series of $f$ is $$\sum_{n=1}^{\infty}\frac{\sin nx}n$$ At which points in $[-π, π]$ ...
2
votes
1answer
96 views

Pre Algebra Text book or online

I have a kid who just started middle school. I would like to introduce them to pre algebra. I would like her to know the fundamental concepts. Just like "What is mathematics" book, if there is a book ...
1
vote
3answers
28 views

significant figure representation?

I was wondering: Why does $1.30 \times 10^3$ have $3$ significant figures while $1300$ has $2$ significant figures (they are both the same number) Why is that distinction ? When should I use ...
16
votes
1answer
411 views

Learning Math Efficienctly and Succeeding in Grad School

I'm currently a second year Ph.D. student studying pure math. I've recently come to the conclusion that I must be studying wrong. Actually, more to the point, I must be thinking about mathematics ...
3
votes
3answers
398 views

Minimizing perimeter given rectangle's area for 10-years-olds

I was recently in touch with some person from Russia how is busy with books for Russian elementary schools, in particularly I learned that now they give elementary set theory for the 2nd grade ...
8
votes
2answers
192 views

Why do we want probabilities to be *countably* additive?

In probability theory, it is (as far as I am aware) universal to equate "probability" with a probabilistic measure in the sense of measure theory (possibly a particularly well behaved measure, but ...
1
vote
3answers
241 views

Roadway and book recommendations to math study.

I had some calculus, linear algebra and complex analysis courses back in college. But it is not comprehensive. And I felt that my college math was not taught in a logical sequence (maybe because my ...
1
vote
0answers
221 views

What are some good ideas in teaching combinations and permutations

I am a student teacher trying to brainstorm some effective lesson plans for combinations and permutations for a high school statistics course. My master teacher has decided that he will introduce ...
13
votes
0answers
1k views

What are some strong algebraic number theory PhD programs?

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
1
vote
0answers
71 views

Help in mathematical combinatorics.

Hi guys I am studying for my exam which is in a few hours and I ran into two past exam problems. Questions: 1) how many 7 letter sequence you can make with a,b,c such that there is at least one b ...
2
votes
0answers
96 views

About the raised negative sign in some basic textbooks

In a math document recently (a UK A level test paper from the EdExcel board), I noticed that the negative/minus sign was raised and aligned to the top of the number. I'm interested to know whether ...
1
vote
0answers
59 views

Who made now part of the problem?

Who came up with the meme of putting the current year as a four digit number into exercise problems? Is there a known first historical account?
2
votes
1answer
176 views

The NES mathematics accredidation test

I have to take the NES mathematics test to get accredidation as a High School teacher to become highly qualified to teach mathematics. I have a PhD in physics so I thought that I wouldn't have to ...
1
vote
1answer
98 views

Book about Tensor Product of Vector Spaces

This subject is very commun for any book about modules. However, some undergraduate majors have Linear Algebra course before the Abstract Algebra one (where we treat about modules) and it is not ...
0
votes
1answer
83 views

What is the rank of the differentiation operator on Pn? What is the kernel?

For this question I was thinking of saying Pn(x)=Ax^n+Ax^(n-1)+...+Ax^2+Ax^1+1 and finding the first derivative P'n(x)=n.Ax^(n-1)+(n-1)Ax^(n-2)+...+2Ax^1+A+0 so in matrix form would get a n by 1 ...
3
votes
0answers
61 views

understanding maths by translating it to real world? Any learn to formulate Initiatives? [closed]

I am CSE graduate, I was very much interested in physics. I had several theories during my higher secondary school like i thought of vacuum as a special medium than nothingness and like gravity is ...
0
votes
0answers
41 views

Online testing systems with extensive question banks?

Some months ago I asked a question about online testing systems here: Online homework/testing systems? I am still searching for the best system to use with my students. When I asked that earlier ...
42
votes
11answers
3k views

Are all mathematicians human calculators?

I asked my dad why he did not major in math he said "because he is not good at math". I think I like math, and I think I'm ok at it, but I'm not gifted or anything like that, I just like math. I think ...
1
vote
0answers
52 views

Evaluating elementary school math textbook

My daughter's elementary school is currently using Saxon curriculum, and I'd like to figure out what other sources, if any, should be age appropriate for elementary school children to enhance their ...