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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1answer
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How big a text file will be for a wordlist composed of 10 HEX characters given certain conditions?

While discussing with another friend the insecurity with some wifi systems against dictionary attacks we couldn't reach a common ground on how big a WPA wordlist dictionary would be for the most ...
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8answers
2k views

How do authors make their problems/exercises for their math books? [closed]

I want to be a math professor one day, but I'm wondering how to make my own original problems to give them to my students. I think that it is a responsibility of the professor to create original and ...
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1answer
63 views

What book offers strategies and heuristics for theorem proving in the same spirit as Polya's How to Solve It?

Polya's How to Solve It is all about heuristics and strategies for problem solving, but it's mainly written for problems which require students to find values, not to prove theorems. While Polya's ...
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1answer
89 views

What are some good mathematical journals? [closed]

I would like to study mathematics when I'm older, but I want to read some of the current literature to learn what mathematics is truly about, maybe direct my studies into some particular field. What ...
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3answers
281 views

How do mathematicians invented and introduced $\pi$ term in the case of circle?

This is basic question. Since childhood I am mugging the mathematical formulae areas of square, rectangle and circle etc. Now,it is possible for me to understand formula of area of square I.e. ...
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2answers
229 views

What's interesting in latus rectum?

I'm a maths teacher in Italian secondary school and I've been spending some time trying to construct "meaningful" problems about conic sections. I particularly like problems which focus on practical ...
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1answer
180 views

Calculate the fourth proportional of the given numbers (Grade 7)

My son has this: Calculate the fourth proportional of the given numbers: 1/9, 1/6, 1/3 Similarly, another question: Calculate the fourth proportional of the given numbers: 9.1; 6.5; 2.8 It should ...
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2answers
647 views

I need to integrate, but I don't know where to start. I'm a bit (a lot) rusty.

Please help me solve the following integral. I'm not sure where to start in fact, I haven't done math for 7 years and now I have to jump back in the integrals. I'm not sure if I have to integrate by ...
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0answers
39 views

Math wheel from 1917 question [duplicate]

http://www.washingtonpost.com/news/morning-mix/wp/2015/06/06/eerie-chalkboard-drawings-frozen-in-time-for-100-years-discovered-in-oklahoma-school/ I hope this came out like it was on the webpage. It ...
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1answer
9k views

Strange old multiplication table found in Oklahoma school

Today I read an article about chalk boards from 1917 discovered in an Oklahoma school. One of the chalkboards included the following curious image: (Oklahoma City Public Schools) The article ...
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0answers
82 views

How to explain the topic of Fourier transform interactively? [closed]

This is a soft question . In the walk-in for the lectureship, I have decided to give demo lecture on the topic of Fourier transform. The principal of the institution ask me to take lecture ...
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2answers
867 views

High school algebra textbooks for gifted students

Cross-posted to Math Educators Stack Exchange. (link) I am looking for high school algebra/mathematics textbooks targeted at talented students, as preparation for fully rigorous calculus à la Spivak. ...
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1answer
39 views

Prove lines being parallel within a traiangle

Here is the problem: The only condition given is $DF//BC$, is it possible to prove that $GH//BC$? Please verify it. Any help will be appreciated.
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1answer
75 views

Undergraduate in Biomedical Engineering wants to pursue a Graduate Math degree.

I have a bachelor's degree in biomedical engineering, but I am looking to go to graduate school for mathematics; I know that the switch would not be easy (obviously an undergrad in math would've been ...
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1answer
29 views

Extract sum of coefficients in a binomial expression

I have two questions: (1) Given $(1-x+x^2)^{3n}=c_0 + c_1 x + \dots +c_{6n} x^{6n}$, find $c_0+c_1+ \dots +c_n$. I manage to find $c_0+c_1+ \dots +c_{6n}$ by putting $x=1$ but I do not know how to ...
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4answers
141 views

I call them squares. They called them arrays. What do they mean?

So I was in C++, and we had third graders come today to play our programs. Whilst the others just drilled them with problems, my game was subtract a square. It was fun watching them discover that ...
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5answers
4k views

Difference between Pure and Applied Mathematics?

So, I have been looking into college courses to see what I want my major to be, and I noticed that M.I.T offers two specified types of Mathematics. Pure and Applied. What is the major differences in ...
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1answer
84 views

Learning math by analyzing/proving theorems?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
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1answer
136 views

Is it useful to learn math by proving a formula/theorem?

Hello I want to learn mathematics. In order to do this I want to get familiar with formulas/theorems by taking one and just analyze it and try to manipulate it to understand it better. I wanted to ...
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1answer
54 views

I need some help understanding proofs for an upside-down cycloid being the tautochrone curve. Could someone show me or point me to a simple proof?

The tautochrone curve has fascinated me since I first heard about it and I want to share it with my Calculus class as an end of the year project. I think something similar to this (Demonstrating that ...
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0answers
37 views

How should the topic of frequency domain be taught?

This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics, Digital Signal and image Processing. Some of concepts which are very ...
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1answer
99 views

Severe problems with math undestanding

Recently (although still in high school) I've been at university, more precisely at information science engineering as apprenticeship. I want to become an operating system programmer but I severely ...
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0answers
23 views

Maths Economics Question

The demand for rail travel is $Q^d = 600 - 2P$ where quantity is thousands of train journeys per quarter and $P$ is in £ per journey. How much would the consumer surplus change if rising cost of ...
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14answers
11k views

Identification of a quadrilateral as a trapezoid, rectangle, or square

Yesterday I was tutoring a student, and the following question arose (number 76): My student believed the answer to be J: square. I reasoned with her that the information given only allows us to ...
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1answer
31 views

Explanation of $\textrm{argmax}_j{z_jt}$ and how to implement it

I'm struggling with one equation within a subtour elimination constraint. $$\sum_{i \in S} \sum_{j \in S, j<i} y^t_{ij} \le \sum_{i \in S} z_{it} -z_{kt} \quad S \subseteq M \quad t \in T \quad ...
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1answer
271 views

Difference between maths in physics degree and maths in a maths degree

I asked this question on the Physics site, but it got closed, so I'll try here. Basically, I was wondering what are the main differences between the maths you learn in a mathematics degree and the ...
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1answer
61 views

On the definition of sphere in analytic geometry…

Last year, when I was teaching mathematics (analytic geometry) for one of my clever freands, I arrived to the definition of sphere. I said Fix $r>0$, An sphere is the set of all triples ...
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2answers
137 views

Condition for Rectangle and Square to have the same area

Prove that if a rectangle and a square has the same area if and only if the length of the square is the geometric mean of the side length of the rectangle. I'm not sure how to start this problem. ...
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0answers
141 views

Prerequisites to Learning Real Analysis

I am a freshman, rising sophomore that is interested in learning Real Analysis, since it is required for many higher mathematics subjects. I have currently Calculus I, II, and Linear Algebra. Is ...
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0answers
86 views

Physical analogies of a math concepts [closed]

In a post Terence Tao explained a very nice way to think about convolution and noted that "one should try to use physical intuition to model mathematical concepts whenever one can". I found this very ...
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1answer
21 views

Finding amount of Days it will take for a Dam to empty

So say I have a dam, with a max capacity of 3,538,000 acres FT of water. It's currently storing 1,796,250 acre FT of water. Water is flowing IN at a rate of 1,050 cubic-FT per second, and out flowing ...
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3answers
58 views

What happens with a sign?

I have something simple to ask, but it often confuses me. What happens with number-sign when it crosses over the equal sign or less-than and greater-than sign. I have an example. $$1-3x\geq0$$ ...
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2answers
55 views

Basic simultaneous equation with logarithms

Question Solve giving your answers as exact fractions, the simultaneous equations : $$8^y = 4^{2x + 3} \tag{1}$$ $$\log_2 y = \log_2x + 4 \tag{2}$$ I think that the RHS of eq 1 can be split up, ...
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0answers
129 views

Mathematical Thinking - How does it work? [closed]

Not only am I hoping you can answer my question, but perhaps refine my question itself. Unfortunately it is something I do not know how to ask, but I will give it my best attempt. Either I ask it, or ...
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1answer
143 views

Is it ill-advised to read books casually for entertainment? [closed]

I'm a student who has about a year (and a few months) to go before entering a university and I've been reading some math books recently. I'm on Chapter 6 on Rudin's PMA, Chapter 5 in Munkres' Analysis ...
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0answers
35 views

Scale Factor meaning

I need to do this fast because tomorrow I got math exam and suddenly my friend said that scale factor is tested (Basic ones)None of my friend understands...But my question is 1.If I were to get a ...
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0answers
43 views

Criterion for Improvement

I was recently asked the question "How do you know when you've become a better mathematician/better at mathematics?," and I realized that at that moment I did not have a valid answer, since I have ...
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1answer
184 views

Is it worth proving every theorem you learn?

Ever since I determined mathematics - mainly set theory and number theory - was my main passion, and I began learning mathematics formally outside of the curriculum posed within secondary schools I ...
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1answer
70 views

Differential equation concerning echolocation

I am in the process of trying to solve a differential equation using MATLAB. Given information is the following: $$ c(z) = 4800 - 20.2090 + \frac{17.3368z}{1000}+272.9057e^\frac{-0.7528z}{1000} $$ ...
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1answer
49 views

Algorithm for finding Complex Eigenvectors?

I'm wondering if there's a fairly easy algorithm by which one can, by hand, find eigenvectors corresponding to complex eigenvalues for small matrices. Of course, one can always row reduce, but it can ...
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4answers
886 views

The meaning of various equality symbols

I'm interested in knowing what is the meaning of the various equality symbols: $=,\sim, \cong,\approx,\equiv$. For example, the speed of a car $V$ in m/s: what would be the meaning of each of these ...
3
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1answer
244 views

What are the primary disadvantages of Dummit and Foote's abstract algebra text (3rd ed.)?

I have done a fair amount of research concerning which abstract algebra book to "settle down into"; that is, I wanted to pick an algebra text and really commit to it as my "primary text," more or ...
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1answer
70 views

Explaining intersections to a 6th grader

$A=\{1,2,3,4,5\}$ $B=\emptyset$ How to explain to a learner from 6th grade the result for $A \cap B$ ? For a 6th grade student, it could be difficult to understand why the result is $\emptyset$. ...
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2answers
267 views

Why study Lowest Common Multiple - LCM

What is the most motivating way to introduce LCM of two integers on a first elementary number theory course? I am looking for real life examples of LCM which have an impact. I want to be able to ...
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2answers
38 views

Help Finding the Equation of a Line with a Given a Point and a Slope

I have been receiving a lot of help today and I really appreciate it, I am nearing the end of my class and need help studying for my final. In my review I came across a problem that i am having ...
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3answers
72 views

Simplify the Complex Fraction

I am having trouble with the following complex fraction. I have simplified everything for the most part, but I am stuck on the last part and need to know what I have to do next. ...
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1answer
543 views

How to fill my mathematical gaps?

To do the story short, I became interested in mathematics in a serious way like two years ago, I'm currently in graduate school, but the problem is that my mathematical background is not as good as ...
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1answer
272 views

A question on the remainders of integer division

This is a question on the remainders of integer division from my student. Notations. Let $p$ be a positive odd prime integer. We write $r_{i,j}$ for the remainder of $i \times j \div p$. Now for an ...
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2answers
91 views

How to get the most out of attending a conference talk or a research presentation? [closed]

I'll say up front that I imagine there's a resource for this somewhere, but I was unable to find it. I've been attending conference talks and research presentations for about a year at my university, ...
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3answers
586 views

Best program for creating educational math animations?

I'm looking for recommendations on what program to use for creating mathematical animations. These animations will be used in creating educational videos for high school math -- Trigonometry first, ...