Questions related to the teaching and learning of mathematics.

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14
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13answers
2k views

How to explain the perpendicularity of two lines to a High School student?

Today I was teaching my friend from High School about linear functions. One of the exercises we had to do was finding equations of perpendicular and parallel lines. Explaining parallel equations was ...
11
votes
7answers
2k views

What should the high school math curriculum consist of?

"Life is open book." With the advent of widely accessible, inexpensive (or even free) computational tools and Computer Algebra Systems (TI-89, Wolfram|Alpha, etc.), much of what traditionally ...
7
votes
4answers
389 views

Extracurricular ideas for UK GCSE level maths student

My daughter is 15 years old and enjoys her maths classes (perhaps only because her maths homework takes her the least amount of time). Until now I have managed to introduce her to subject matter ...
10
votes
6answers
227 views

When the approximation $\pi\simeq 3.14$ is NOT sufficent

It's common at schools to use $3.14$ as an appropriate approximation of $\pi$. However, here it's stated that for some purposes, $\pi$ should be approximated to $32$ decimal places. I need an example ...
7
votes
4answers
2k views

How do you rebuild your Math skills after college?

I minored in Math in college (B.S. Software Engineering), and went through advanced Calc, Differential Equations, etc. But about 6 months after I graduated I had lost all my formulas. Now, about 5 ...
5
votes
4answers
288 views

What sequence should I study these topics in?

I will shortly list a series of topics that amount to what is essentially the first two years of an undergraduate degree. I'd like to know what is considered best order in which to study these ...
4
votes
3answers
16k views

Largest prime factor of 600851475143 [duplicate]

I'm trying to use a program to find the largest prime factor of 600851475143. This is for Project Euler here: http://projecteuler.net/problem=3 I first attempted this with the code that goes through ...
4
votes
3answers
545 views

Need good material on multifractal analysis

I'm searching for some good reading material on multifractal analysis. Preferably something accessible that doesn't put the stress too much on mathematical proofs but rather on applications. As long ...
23
votes
1answer
495 views

How much math education was typical in the 18th & 19th century?

Was it unusual for people in those days to learn Calculus? Could a grad student take a course in differential equations or multi-variable Calculus, or did they have to learn from journals? I am always ...
18
votes
5answers
661 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 ...
11
votes
3answers
480 views

Elementary Geometry Nomenclature: why so bad?

A long-ish wall of text, and I apologize. Some background: when I was a first-year university student, my chemistry professor was lecturing and was trying to find the word to describe a shape. A ...
10
votes
1answer
552 views

Undergrad Student Trying to Figure Out What to Study

this is my first time on stack exchange and I am seeking advice for my future studies. Some background first; I am a undergraduate student pursuing a degree in mathematics and I hope to pursue ...
9
votes
1answer
247 views

General question: What one can do to help students one is grading?

Due to unknown reason I was assigned as a grader this semester for a certain proof writing class in my universtiy. The class size is 65 and students took it usually comes from a computer science ...
5
votes
3answers
138 views

Is there a simple geometrical description of $e$? [duplicate]

Of course I am not looking for a definition through $\int_1^e{1\over x} \, \mathrm{d}x=1$ or that slope of $a^x$ at $x=0$ is $1$ when $a=e$. I am looking for something understandable by a kid who has ...
5
votes
3answers
768 views

Good way to learn Ramsey Theory

What are some good books on Ramsey theory? I have Van Lints book on Combinatorics: is this enough preparation to start reading about Ramsey theory? I want a book that includes important results and ...
4
votes
2answers
357 views

Study program for algebra for an math-phobic person

I have a female friend (Mid 20's) who wants to get an associates degree, who has an absolute phobia of math, and algebra in particular. I'm trying to find a good program that can help her to study ...
2
votes
2answers
242 views

Real numbers as decimals

I'm looking for a book that develops the theory of real numbers in a rigorous way in terms of their decimal expansions. The exposition should be concrete and preferably aimed at mathematically ...
1
vote
1answer
232 views

Mathematical disciplines [closed]

Once I spoked to a mathematician about mathematics and he asked me what was my favourite area in Maths. My answer was "Chaos Theory" and he said this is not a discipline in Mathematics. What is a ...
1
vote
1answer
2k views

Would it be fine to use Serge Lang's two Calculus books as textbooks for freshman as Maths major?

I'm a freshman in Maths major, but the recommanded textbook(Calculus:A Complete Course by Robert A. Adams) by Prof. of Calculus course is too much expensive, well, I found there're Serge Lang's two ...
1
vote
4answers
344 views

Which discussion board is good for homework questions?

I'm a CompSci university student and i want some help for my math questions. Therefore i am looking for a good discussion board for math homework questions. I don't know any (good), because I come ...
10
votes
5answers
2k views

Common misconceptions about math

YARFMO (Yet another reposting from Mathoverflow) ;-) The more you know about math the more you find conceptions previously thought correct to be false: 1.) math is not as exact as many believe - in ...
8
votes
4answers
355 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 ...
8
votes
4answers
800 views

How To Reach The “Next Level” of Mathematics

I am a junior-high pre-algebra student. I feel that my class is holding me back, so I wanted to learn "higher-level math". So what should I learn now? What do you believe is a "next step"?
5
votes
4answers
368 views

Would nonmath students be able to understand this?

For a course, I am required to do a presentation. The topic could either be something mundane, like a career strategy report, or something more interesting, such as a controversial topic, or an ...
3
votes
1answer
118 views

Prove that the exponential function is differentiable

Imagine that you are writing a book on the foundations of analysis. You have already proved that for each $a > 1$ there is a unique function $f_a(x) = a^x$ satisfying the following: $f_a$ is an ...
3
votes
2answers
107 views

Prove withoui calculus: the integral of 1/x is logarithmic

It was known in the 17th century that the function $$ t \mapsto \int_{1}^{t} \frac{dx}{x} $$ is logarithmic: a geometric sequence in the domain produces an arithmetic sequence in the codomain. This ...
3
votes
3answers
460 views

Is it possible to learn abstract algebra no precalculus or calculus?

See above. I am trying to re-teach myself mathematics in a different manner than is formally taught (i.e., set theory, number theory, mathematical logic, abstract algebra, discrete math and then ...
3
votes
2answers
209 views

What's the right moment to learn Set Theory?

I've seen a question in which the OP asked when is the right moment to learn Category Theory, it seems this moment comes a little after a course of algebra, and indeed some books on abstract algebra ...
2
votes
1answer
263 views

What textbook should I get to self-learn Calculus? [duplicate]

I did not have the option to take calculus during high school. I would like to pick up this subject during my free time. I am a software engineer. I would like to improve my understanding of maths. ...
2
votes
2answers
165 views

At what education level is this “simple” problem adequate?

Given the following problem: Alice, Bob and Carl stand on a straight line. Alice is one rod away from Bob. Dana stands one rod away from both Bob and Carl. Carl is as far from Alice as Alice ...
1
vote
4answers
190 views

Looking for a simple problem for math demonstration

I'm holding a 3-5 minute speech next week on mathematical problem solving, and how it makes me happy, to 15-20 non-mathematicians. As a part of it, I had thought about demonstrating two problems, but ...
0
votes
4answers
71 views

A vector should more be thought an identity of an entity in space rathar than magnitude + direction?

Can I say that vector is more like a "unique identity" of an entity in space rather than calling it an entity with magnitude and direction ? For example a line. A vector $(10,10,0)$ is the identity ...
9
votes
5answers
207 views

The use for solving quadradic equations for high school students

I have a little brother who is in high school and he just learnt the quadratic formula for finding roots of second degree polynomials. He asked me what why we learn this and how this could apply to a ...
9
votes
4answers
1k views

Learning math: still paper and pen

Is it, from an educational perspective, still sound advice to recommend people to use paper/a notebook (of the traditional sort, not the device) and pen/pencil? I wonder if computers are a ...
8
votes
2answers
267 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 ...
7
votes
2answers
100 views

Information on crucial results concealed as exercises or neglected in a textbook

First, where can students find lists, information, or resources on the crucial results, inequalities, theorems, etc... which a textbook might not explictly feature or even bring up at all? Second, ...
6
votes
10answers
1k views

how to see the logarithm as the inverse function of the exponential?

I saw here in math.stackexchange some proofs of how the log and exp functions are related to each other, but I want to get an intuition for that. In layman terms, how would you explain the connection ...
6
votes
3answers
885 views

How to fill gaps in my math knowledge?

Just finishing highschool, even though I am doing "well" (in the context of the math course itself), I have significant holes in my actual math knowledge. As I think many people who explore math ...
5
votes
1answer
307 views

When should I start learning Set Theory?

I started to learn a few disciplines on my own over the break after my first year in college and one of them was Real Analysis. In the process I came across many issues in Analysis texts concerning ...
5
votes
1answer
728 views

Quickest way to understand Kruskal's Tree Theorem

I came across the Kruskal Tree Theorem the other day and thought it looked pretty interesting (especially the stronger finite form due to Friedman). I'm currently a first year mathematics ...
5
votes
1answer
405 views

Is it ever really Pi Time?

Walking with my son at 3:14pm the other day, I mentioned to him, "Hey, it's Pi Time". My son knows 35 digits of $\pi$ (don't ask), and knows that it's transcendental. He replied, "is it exactly ...
4
votes
2answers
121 views

Why learn abstract mathematics? What is the point? [closed]

I'm a mathematics college lecturer and have an mphil degree in the subject. But I often wonder why I'm learning this senior undergrad level mathematics---analysis, topology, functional analysis, ...
4
votes
1answer
312 views

Online classes/books in multivariable calculus?

So does anyone know of any good online courses in multivariable calculus? (Or in a possible alternative leap of curriculum, if said path has proven to be better/moar interesting.) I'm coming straight ...
4
votes
5answers
310 views

how to explain that Prob[heads, tails] = 2 * Prob[heads, heads] to a student?

I throw two coins (simultaneously). A student (very much a beginner in both math and probability theory) thought that the following 3 outcomes are equally likely: "two heads", "two tails", "a head and ...
3
votes
0answers
111 views

Do expressions like $(-1)^{2/3}$ show up naturally in pure or applied math?

Let $x$ denote an arbitrary real number. Then $x^n$ makes sense for arbitrary $n \in \mathbb{N},$ via the obvious recursive definition. We can extend this definition by asserting that if $x$ is ...
3
votes
1answer
242 views

Functions that generate “easy” matrices of full rank

While explaining how to invert matrices I once used this ill-fated example $A=\begin{pmatrix} 1&2&3\\4&5&6 \\7&8&9 \end{pmatrix}$ which can not be inverted ($\det(A)=0$). That ...
2
votes
1answer
143 views

Teaching the Concept of Infinity to Children.

I was recently out with the family and we left it up to the children where we ate lunch (11 and 9 years old). They couldn't agree and were going back and forth calling each other names. This ...
2
votes
3answers
100 views

Do users of RTL languages adopt an LTR standard for mathematics (in the same way they often do when using LTR words or phrases in RTL text)?

Non-mathematician here. There is a discussion on this forum titled "Is “applying similar operations from left to right” a convention or a rule that forces us to mark one answer wrong?" I found it ...
2
votes
3answers
65 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? ...
2
votes
0answers
70 views

Looking for online matlab-based differential equations course/text.

I am looking for an online ODE course that would be matlab/project-oriented. A full online text/course in the spirit of this linear algebra text is preferred. I know about the following CODEE and ...