For questions related to the teaching and learning of mathematics. Note that Mathematics Educators StackExchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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33
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8answers
7k views

How can I learn to “read maths” at a University level?

When I look at math, it's like my mind goes fuzzy. The only way to describe it is in terms of what I can relate it to. You know how when you read, you see the letters and words, but your brain picks ...
20
votes
5answers
2k views

How to debug math?

May seem strange as I'm good in programming, but I just started diving into math. ATM I'm learning combinatorics at Khan Academy, and here's an example of a question that I struggled with (that's not ...
-1
votes
2answers
46 views

What are the books that I should study for college? [on hold]

Baccalaureate exam approached Real Analysis (limits, differentiation and integration), Abstract Algebra, Functional Algebra, Linear Algebra, Combinatorics, Complex numbers, Vector Geometry, Analytical ...
-2
votes
0answers
77 views

Lack of continuity between undergraduate mathematics and “real” mathematics [on hold]

First, let me begin with some background. My mathematical knowledge is largely a product of self-study and though some are sure to be skeptical for that reason, I do consider myself at least competent ...
0
votes
1answer
29 views

Course or book - Math Foundations in CS

I want to improve my math skills, now I'm trying to find good route for this purpose. I'm using Khan Academy, and recently found "CS103 - Mathematical Foundations of Computing" course which looks good ...
12
votes
7answers
3k views

Should I do all the exercises in a textbook?

The problem sets that you usually get in a university course is a small fraction of the exercises in your textbook. Which raises a question: do you need to solve all the exercises from your textbook? ...
28
votes
1answer
3k views

GRE past papers

As it is required for most students who wish to do a Ph.D in maths in the US to sit the GRE subject specific mathematics exam, I hope this question will be of interest to the mathematical community ...
0
votes
0answers
18 views

How to find the longest diagonal if you fold a piece of rectangular paper in half?

An 8-inch by 12-inch paper napkin is folded in half three times with each fold resulting in a smaller rectangle. What is the longest possible diagonal for the final rectangle? Express your answers in ...
40
votes
11answers
2k 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 ...
0
votes
4answers
46 views

BEDMAS where the order of Addition before Subtraction matters?

Here is a recent "tricky problem" that is making the rounds on FB: BEDMAS is explained here in a video, with this being the upshot: Everyone understands that ...
2
votes
1answer
648 views

The NES mathematics accreditation test

I have to take the NES mathematics test to get accreditation 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 ...
-2
votes
1answer
132 views

How values of the constants are derived mathematically? [closed]

As said by Jan regarding constant value $\pi$ ,Imagine you have a circle and you are able to measure its circumference "c". Then, you can also find out what its diameter "d" is. When you divide ...
1
vote
1answer
23 views

generalization of the Pythagorean theorem

In school, students learn that in a triangle ABC, ACB is a right angle if and only if AB^2=AC^2+BC^2. This deep relation between geometry and numbers is actually only a partial result as one can say ...
1
vote
3answers
157 views

Where could I learn basic math terminology?

I am an english learner and I would like to learn the etymology of Mathematics. I would like to know the most common phrases in Algebra, and Geometry as well. I want to know at a level of UK's A+. ...
27
votes
6answers
840 views

Open source lecture notes and textbooks

This question is inspired by the popular "Best Sets of Lecture Notes and Articles". Indeed, I would like to collect a "big-list" of open source (that is, with $\LaTeX$ code available) high-quality ...
13
votes
9answers
858 views

Elevator pitch for a (sub)field of maths?

When I first saw the title of this question, I forgot for a moment I was on meta, and thought it was asking about quick, catchy, attractive, informative one-or-two-liner summaries of various fields of ...
1
vote
1answer
44 views

Where to start with mathematics for a person who failed mathematics in high school? [closed]

For someone that failed maths in high school, where would be the best place to start and with what kind of books. First things first: For one who is only interested in algebra and calculus at the ...
0
votes
1answer
38 views

Rename Real and Complex [closed]

Let's imagine that the definitions of Real numbers and Complex numbers were discovered today. What would be the most suitable names for those new number systems?
1
vote
1answer
30 views

What means to publish views/ideas are used, instead of blogs, among mathematicians today?

My question is motivated by the feeling that some mathematics blogs publish less and less over time. Are there other communication means which are used now instead with a similar role, or is it ...
17
votes
4answers
5k views

Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
0
votes
1answer
40 views

Good introductory book in geometric probability

I recently came across the proof of the Buffon theorem and I was fascinated by geometric probability. Could someone indicate me a good introductory book? Maybe with many exercises?
697
votes
53answers
417k 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 ...
3
votes
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.
89
votes
5answers
4k views

“Advice to young mathematicians”

I have been suggested to read the Advice to a Young Mathematician section of the Princeton Companion to Mathematics, the short paper Ten Lessons I wish I had been Taught by Gian-Carlo Rota, and the ...
0
votes
1answer
43 views

Is the Science and Knowledge Publishing Corporation a spam journal publisher? [closed]

I submitted my paper entitled " A new result for divisibility among sum power divisor from 3 month ago to this journal ,I have received in this day this message : Title: A new results for ...
22
votes
9answers
16k views

Online Math Degree Programs

Are there any real online mathematics (applied math, statistics, ...) degree programs out there? I'm full-time employed, thus not having the flexibility of attending an on campus program. I also ...
1
vote
1answer
13 views

Find the value of the Infinite product in terms of k which is a positive integer

$$\prod_{n=k+1}^{+\infty}\left(1-\frac{k^2}{n^2}\right)$$ The only help we have been able to find is that of Euler, anything would be amazing!
2
votes
1answer
92 views

How to succeed in upper-level math [closed]

This question will essentially be more of a how-to plea or general help request. I'm currently studying math and I'm at the point where I've transitioned into upper-division classes, most if not all ...
1
vote
2answers
86 views

a healthy perspective on “knowing everything” [closed]

This is a question about attitude, but related to math studies. I have trouble with two things: 1. making "normal" progress in my learning and 2. having the satisfaction that I understand what is ...
1
vote
2answers
90 views

Integral as “Area Under the Curve”

I'm a high school math teacher teaching an introductory calculus course, and I'm having a problem teaching one particular student about the physical definition of an integral. The intuition is that ...
5
votes
2answers
52 views

Where is a good source for serious math (wall-size) posters?

Where is a good source for math wall posters that give glimpses of serious and beautiful mathematics? I'm a faculty member looking to find some wall posters (e.g. 2 ft x 3 ft) to hang in a handful of ...
2
votes
1answer
82 views

What's the mathematical symbol to say “It doesn't depend on …”?

If I want to say x doesn't exist I would use the symbol $\nexists$ If I want to say x is a member of... I would use $\in$ But what's the symbol to say y doesn't depend on x? I know I could write ...
-3
votes
1answer
38 views

Formula Derivation

What is the formula that can be derived using the values and formulas below to get the value of K43? Here's what I have, so far, but no luck in getting the correct formula: 0 = 925191 - 119355 - ...
4
votes
2answers
655 views

What's the most effective ways of teaching kids - times tables?

I'd like to help a $6$ year old who already has a pretty good grasp of $2$, $5$, and $10$ times tables.
5
votes
3answers
9k views

What is the most effective way of teaching mathematics to my 7 year old kid?

I want to help my kid excel in Math. I can see she has some trouble with additions,subtraction, multiplication and division. Will it help if I let her memorize the multiplication table? or use ...
2
votes
1answer
26 views

An error on the BBC maths revision website?

The multi-choice question, for revision for 12 year olds, is here: A company exchanges foreign currency. They offer $\$1.5$ for each pound. On top of this, they charge a fee of $£4.50$. Which ...
1
vote
0answers
37 views

how to solve y^2<x^2 y^2>x^2

Can someone help me with the steps how to solve those inequistins? y^2<x^2 My wrong solution: y^2<x^2 /sqr y<x or y<-x or -y<x or -y<-x ...
2
votes
2answers
335 views

Dynamic Geometry Software for Straight-edge and Compass Constructions

Geogebra is a very good dynamic geometry software. It has so many default tools, e.g. parallel line, angle bisector, tangent to the circle, inscribed and circumscribed circles, etc. But I want the ...
616
votes
160answers
38k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)

I'm a children's book writer and illustrator, and I want to to create a book for young readers that exposes the beauty of mathematics. I recently read Paul Lockhart's essay "The Mathematician's ...
1
vote
1answer
54 views

Should I remember the proof of mathematical theorems(every step)?

The problem is, that when I am reading the proof of mathematical theorem(in my case - it is calculus), U understand the idea and every step of proof. But i can't prove the theorem individualy even if ...
0
votes
0answers
55 views

Confused about 'staircases'

Hi I'm currently reading a paper, which contains an experiment I was to re-create - is there any chance someone can explain the staircase to me? I've had a quick Google - and I haven't really got ...
0
votes
2answers
35 views

Converting from decimal to any number base.

I know that this can a silly question. But I can not find the answer. When converting number bases (from decimal to any other number bases), we divide the decimal number by that base, and write down ...
11
votes
1answer
94 views

Math for blind people…

What happens if some blind person want to study math? Is there some "braille alphabet" for mathematical symbols? Are there math books, at least for undergraduate students, written for blind people?
11
votes
1answer
245 views

why is that most of the books in mathematics don't include answers?

I am currently going through the " Topics in Algebra" By I. N. Herstein. The problems are pretty good. But there are no answers on the back. Same is the case with "Mathematical Analysis" by Rudin. I ...
0
votes
1answer
25 views

Statement and Proposed Negations

I know this may seem like a really unintellectual question however I was wondering what statements and proposed negations are. My teacher didn't really go over this and I can't seem to find it in my ...
0
votes
0answers
23 views

Algorithmic differentiation graph

I have very basic question about reverse mode algorithm calculation. It is well-known that we calculate derivatives according to chain rule, using sub expressions. I was trying to find kind of proof, ...
6
votes
1answer
82 views

Visual questions for 6th graders

I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed ...
1
vote
1answer
112 views

Hypothesis Test Questions

I am currently teaching an introductory level statistics course and I had two quick questions on hypothesis tests. Just to be clear, I have a fairly good background in probability and analysis, but I ...
2
votes
1answer
81 views

Why is Gaussian elimination still being taught when there are more efficient methods? [closed]

Why is Gaussian elimination still being taught when there are more efficient methods? By efficient methods I mean less time and effort consuming ways to solve a system of linear equations. I have ...
2
votes
3answers
46 views

How to solve for $\theta$ in $130\cos(\theta) - 122\sin(\theta)=10$?

The original question was solve for $\theta$ in $65\cos(2\theta)-56\sin(2\theta)-55=0$. I reduced it to $\cos(\theta)((130\cos(\theta)-122\sin(\theta))-10=0$, therefore we have a $\theta=0$ but I ...