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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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 ...
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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
5k 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 ...
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1answer
56 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 ...
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1answer
1k 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 ...
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4answers
528 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, ...
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4answers
343 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. ...
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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 ...
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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
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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 ...
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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 ...
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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 ...
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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;...
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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....
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2answers
542 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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2answers
852 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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4answers
5k 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 ...
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0answers
424 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....
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4answers
700 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?
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1answer
311 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
154 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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7answers
11k 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.
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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
97 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 ...
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1answer
998 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 ...
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2answers
970 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" ...
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1answer
117 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 ...
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1answer
598 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 ...
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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 ...
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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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5answers
478 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 ...
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1answer
158 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 ...
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1answer
427 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 ...
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6answers
444 views

“$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing

I am supposed to teach undergraduate students who do not major in mathematics and I would like to give them a short introduction to mathematical reasoning and to the concept of proof. I am looking for ...
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0answers
148 views

Variation on the Sobolev space $H^1_0$

Let $\Omega\subset\mathbb{R}^n$ be a bounded open set, let $$ C^1_0(\overline\Omega) = \{u\in C^1(\Omega)\cap C(\overline\Omega):u|_{\partial\Omega}=0\}, $$ and let $C^1_c(\Omega)$ be the space of ...
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1answer
452 views

Where can I find the 1960s New Math syllabus?

I've been looking everywhere for even a short summary of the content of the 1960s New Mathematics Math education reform in the US but I cannot ;-; Does anyone know?
0
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1answer
185 views

Lattice Squares; Basic Interesting Facts and Problems

I'm going to write an article in an educational magazine for middle school students, about the game Square It. The purpose of the game is to make lattice squares: I want to introduce the game, and ...
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3answers
3k views

how to explain prime numbers to children

My little cousin (12year) asked me about how emails are encrypted and I want to answers her in such a way she understands it. This is diffuct, but I am happy with teaching the definition of a prime ...
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3answers
1k views

A round table probability question

Hi guys I am writing my P exam for the second time and I remembered two question that confused me when writing the exam. I asked my prof. but it confused him as well. For simplicity I will ask one ...
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2answers
174 views

Finding the variance of x,y by discrete distribution

I am writing my P exam for actuaries. I have the solution manual but I ran into this question, which confused me. I understood the solution but it did differently in how I wouldve tackled the problem. ...
93
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23answers
8k views

Why is there no “remainder” in multiplication

With division, you can have a remainder (such as $5/2=2$ remainder $1$). Now my six year old son has asked me "Why is there no remainder with multiplication"? The obvious answer is "because it wouldn'...
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2answers
2k views

What is the distance between the line and plane if it is parallel?

So far, I've gotten that the line is parallel to the plane $x = 2 + t$, $y = -3 + 2t$, $z = 1 + 4t$ With the vector of that being $U$ is $(1,2,4)$ and the plane $2y-z = 1$ with the vector $V$ being $(...
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2answers
179 views

Can abstract nonsense be helpful here?

Here a question for those among you, who teach Homotopics/Algebraic Topology at university. I encountered some questions that were in my view quite easier to solve in category hTop instead of Top (...
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6answers
1k views

Am I just bad at math? [closed]

I currently pursuing a degree in computer science. When I started back 4 years ago, I took a test to see how I would place into certain subjects. My math scores were absolutely horrible. I started ...
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1answer
278 views

teaching inverse functions using ideas of codomain and onto functions

I am looking for some resources (books, Web sites, etc.) for teaching calculus students about inverse functions, using the ideas of codomain and onto functions (as well as one-to-one functions, of ...
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1answer
68 views

Proofs as games?

A long time ago (but I can't remember when), I was introduced to the (pedagogical) concept of writing a proof as giving a winning strategy for a game. Basically, given a statement $\forall x\exists y ...
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11answers
3k views

Puzzles or short exercises illustrating mathematical problem solving to freshman students

At high school, the solution method to almost all mathematical exercises is to apply some technique or algorithm you have learned before. At the university, the situation is fundamentally different. ...
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5answers
188 views

Motivation for Studying Combinatorics (Middle School Version!)

I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real ...