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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2answers
236 views

Recommendation for learning math [duplicate]

I'm in the 11th grade. At the bachelor exam, my main focus will be on mathematics and informatics. I'm a hard working man, but due to the school norms, I can consider myself idiot at math. Why? ...
1
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4answers
3k views

How to explain why a parabola opens up or down

I am being ask to explain in 2 ways why is it that y=ax^2+bx+c parabola opens up if a is positive and why is it that y=ax^2+bx+c opens down when a is negative. One of the explanations has to be ...
4
votes
3answers
222 views

What is the best way to solve this high school exercise?

Can you share with me how would you best solve this exersise to a high school student? Show that $f(x)=x^2-6x+2$ , $x\in(-\infty,3]$ is $1-1$ and find its inverse.
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votes
1answer
121 views

How to document undergrad math knowledge?

If you did a degree which is low on math (read economics, psychology), but want to proceed to a more mathematically loaded master, how would you document your knowledge? Are there standarized ...
3
votes
0answers
156 views

Why to Use the Same Sign for Minus and Negative?

Using the same symbol for two different concepts may cause confusion. So if one decides to do so, they should justify this choice by showing its advantages over other choices. What about the minus ...
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3answers
131 views

How to show $\Bbb R$ is Archimedean?

Suppose $X$ is a real number such that $X > 0$. We want to show there exists and $n \in \mathbb{N}$ such that $X \geq \frac{1}{n} $. MY attempt: If $X < \frac{1}{n} \; \; \; \forall n $ then $X ...
6
votes
1answer
234 views

Is the computer changing the way we teach and learn math in schools?

Back in school, what I got taught during school was labeled 'math', but it was actually 'rote arithmetics.' This seems to also be the case of many other people. Some came to hate it and never came ...
0
votes
1answer
288 views

What are the big ideas needed to develop conceptual understanding of fractions?

In order to be able to perform arithmetic on fractions, students need to understand what fractions are and how they operate. Just teaching rules (e.g. "to add fractions you must have common ...
2
votes
3answers
166 views

Derivative in interesting way

I am supposed to give a 15-20 minutes math lecture, where I am expecting around 20-30 people. The lecture is about derivative. Since this would be my first "class", I would appreciate any suggestions ...
3
votes
1answer
610 views

What is the use of Euler Totient or Phi Function?

What is most motivating way of introducing this function? Does it in itself have any real life applications that have an impact. I can only think of a^phi(n)=1 (mod n) which is powerful result but ...
1
vote
1answer
125 views

which one? permutation or combination?

Let say we have a bookshelf that can fit 6 books, we want 4 computer science books and 2 physics books but computer books should be together and physics books also should be together, we have 8 ...
36
votes
13answers
3k views

How To Present Algebraic Topology To Non-Mathematicians?

I am writing my master thesis in algebraic topology (fundamental groups) and as a system in my school students must write about one page about their theses explaining for non mathematicians the ...
3
votes
2answers
1k views

Are universities teaching math too fast? [closed]

I love math and I feel happy to learn it. But in universities, I think there's too much to learn. For example, in my university, there are mathematical analysis(I,II,III), linear algebra(I,II), ODE, ...
2
votes
3answers
70 views

Why do I see i and k as the indices of summation?

I'm working on linear algebra and just wanted to clear up an uncertainty regarding whether there is a difference in the use of i and k as the dummy variables for the index of summation? $\sum\limits_{...
2
votes
2answers
3k views

Number of Lines Passing Through a Given Point in the Plane

How can one prove that infinite number of lines pass through a given point in plane, using Euclid's axioms (or Hilbert's, if necessary)?
0
votes
1answer
49 views

On the largest and smallest values of $ {D_{\mathbf{u}} f}(x,y) $, assuming that $ ∇f(x,y) ≠ 0 $.

I appreciate your time. If anyone can explain this problem, I would be most grateful. I need to understand this for a test, but I was not given any explanation. Assume that $ ∇f(x,y) ≠ 0 $. Show ...
4
votes
5answers
298 views

Why $\sqrt {-1}\cdot \sqrt{-1}=-1$ rather than $\sqrt {-1}\cdot \sqrt{-1}=1$. Pre-definition reason!

It is for years that I teach complex numbers following a historical route. I start with the famous problem of Cardano: Find two numbers whose sum is equal to 10 and whose product is equal to $...
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1answer
6k views

How to build a mathematical formula

We can see mathematical formulas, graphs in thesis paper. Together those are used to prove some theorem. Graphs are generated based on some test using those formula. My question is how those formulas ...
1
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1answer
58 views

Survey/encyclopaedia/website of mathematical theorems connected

Is there, or is someone creating a survey/encyclopaedia/website of mathematical theorems which connects theorems together with their assumptions (axioms, other theorems, hypotheses etc.)? I'm thinking ...
17
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1answer
2k views

Research in differential geometry

I am an 3rd year undergrad interested in mathematics and theoretical physics. I have been reading some classical differential geometry books and I want to pursue this subject further. I have three ...
6
votes
4answers
531 views

How should I grade my students?

Anyone who is interested in my experience as a grader in the past can check this thread. This semester I was assigned a grader for a certain class, which runs two sections. There are two professors, ...
6
votes
4answers
360 views

When does something become a “mathematical object”?

A mathematical object is an abstract object arising in philosophy of mathematics and mathematics. Abstract object: Abstract and concrete are classifications that denote whether a term describes ...
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2answers
2k views

Is 9/1 an improper fraction?

My son took a test in school. The teacher told them that they did not need to simplify improper fractions in their answers. On one question, for example, the answer of 28/3 was marked as correct. ...
0
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1answer
83 views

Linear Transformation Brief Question

$T:P_{3}\rightarrow P_{3}$ defined by $T(p(t))=tp'(t)+p(0)$ is a linear transformation. Determine whether $T$ is invertible. If yes, find $T^{-1}(q(t))$, where $q(t)$ is a polynomial of degree at ...
3
votes
3answers
100 views

why check all primes under the root of an interger?

I am in high school and I need to factorize numbers. My teacher told me to check all numbers which are smaller than the root of the number I want to factorize. This seems to work just fine, but I do ...
3
votes
1answer
190 views

How does math education vary from school to school?

Is there a significant difference in the material taught across universities in the United States? For example, if I get a bachelor's degree in mathematics (or something related such as physics or ...
43
votes
11answers
3k views

Refuting the Anti-Cantor Cranks

I occasionally have the opportunity to argue with anti-Cantor cranks, people who for some reason or the other attack the validity of Cantor's diagonalization proof of the uncountability of the real ...
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2answers
2k views

How to do math and help people

I am currently an junior math and statistics student at the University of Florida. For my whole life I have really enjoyed math and really do find a calling in mathematics. Math classes are the only ...
0
votes
1answer
40 views

why there is a need of one prime number while using affine cipher

I am creating an encryption application. when I use values of a & b as 2 & 3 respectively. My message get encrypted successfully, but while decrypting it does not work. Is there any formula ...
2
votes
2answers
2k views

Interesting Topics to Give a Seminar On?

So recently I've been attending seminars for the graduate students (and VAP's) at my local university, and after yesterday's seminar, the professor asked if I would like to give a seminar next quarter;...
2
votes
2answers
99 views

What are some good games for teaching maths to children?

I am due to teach maths to a ten-year-old. I'd like to try out some games such as Nim and Conway's Soldiers. I've found this list on Wikipedia but Googling for more just gives me a load of Flash games....
7
votes
2answers
552 views

Resource for low level maths explained in high level perspectives

I would really never ask a question about resources, noting that it is a soft-question, unless I thought it was very difficult to find elsewhere, and I have looked. Furthermore, I believe that this ...
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votes
2answers
855 views

Factoring Quadratics: Asterisk Method

I'm teaching my students about factoring quadratics. We've done GCF, difference of two squares, squared binomials, and grouping. One of my colleagues then found this asterisk method on line. It's ...
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votes
4answers
6k views

converting a number from base 10 to base 8

I'm really confused and I can't get the concept. How is 14 in base 8 = 16? And how does 8 in base 8 = 10? In case of 14 isn't 1 * 8 + 4 * 1 = 12? Shouldn't any number in base 8 be lower than a ...
9
votes
0answers
434 views

Is there an elementary introduction to higher order functions?

I am teaching a pre-calculus course (using the textbook by Michael Sullivan if it helps), and I realized that higher order functions seem to show up in with some frequency in pre-calculus and calculus....
3
votes
4answers
708 views

How to explain Fractional and Negative Exponents

My classmates doesn't understand Fractional and Negative exponents, since I was the top of my class, so they all came to me... Is there any way to explain it clearly to them?
5
votes
1answer
321 views

Polynomials in nature

What polynomials occur in "nature"? I am interested in polynomials of degree three and higher. I am aware of Stefan Boltzmann Law and Chemical Equilibrium Examples.
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1answer
156 views

I'm a CS PhD student. I want to re-study some of college mathematics

I'm a PhD student in CS and I have a fair amount of background in mathematics. But it's been many years since I studied Mathematics in college. I would like to refresh and in many cases, understand ...
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votes
7answers
12k views

Explain why perpendicular lines have negative reciprocal slopes

I am not sure how to explain this. I just know they have negative reciprocals because one one line will have a positive slope while the other negative.
0
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2answers
34 views

on visualising arithmetic with roots ansd radicals

Is there a visual way to simplify $4\sqrt{12}+4\sqrt{27}$? I know the answer is $20\sqrt{3}$, but I want to geometrically explain it to a 14 year old. Is there also a way to geometricaly interpret ...
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2answers
98 views

An Integral With an Odd Function That Isn't Contrived

When ever I teach calculus, single or multivariable, there is always the point in the text when the author covers odd functions and then gives an example of an integral to evaluates to $0$ because the ...
4
votes
1answer
1k views

What is the use of the Chinese Remainder Theorem

What is the most tangible way to introduce the Chinese Remainder Theorem? What are the practical and really interesting examples of this theorem. I am looking for examples which have a real impact on ...
11
votes
2answers
975 views

What's an induction problem that will be hard to answer with “backwards reasoning?”

I'm currently the teaching assistant for a course that serves as an introduction to rigorous proofs, and I've noticed some of my students have a tendency to try and use a sort of "backwards reasoning" ...
2
votes
1answer
118 views

Visual proof ot the distributive property in $\mathbb{Z}$

Is there a intuitive/visual (not formal) "proof" that the distributive property holds in $\mathbb{Z}$? For the natural numbers $\mathbb{N}$ I know something like this: There are two ways to get ...
8
votes
1answer
604 views

Best applications-oriented introductory calculus textbooks?

Note: I've edited this question on October 9th, after establishing a bounty on it. What are the best introductory calculus textbooks that explain why calculus is important in a broad intellectual ...
3
votes
2answers
158 views

Trying to teach supremum and infimum.

I'm helping out my former calculus teacher as a volunteer calculus advisor, and I have under my supervision 5 students. They've already had an exam and... well, they failed. I read their exams and I ...
28
votes
6answers
2k views

Cool mathematics I can show to calculus students.

I am a TA for theoretical linear algebra and calculus course this semester. This is an advanced course for strong freshmen. Every discussion section I am trying to show my students (give them as a ...
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votes
5answers
479 views

How to explain infinty to a $3^{rd}$ grader?

In my country in $3^{rd}$ grade in math kids learn the four basic arithmetic operation (addition, subtraction, multiplication and divison) up to $10 000$. My sister this year goes to $3^{rd}$ grade ...
2
votes
1answer
160 views

What does one need to teach Mathematics in American schools with a BSc Mathematics degree?

I'm graduating with a math degree next year (BSc Maths - more theoretical than applied) from an African university, and am going to the US next year to visit a friend for a few months. However, I'd ...
4
votes
1answer
429 views

Workshop on Pascal's Triangle for Middle School Students

We're going to hold a three-hour math workshop for some middle school students. It'll about the Pascal's triangle. Well, we can ask the students to find patterns in the triangle, or try to prove some ...