Questions related to the teaching and learning of mathematics.

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1
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3answers
91 views

Education problem - what to do ? Very intriguing problem [on hold]

I really love maths, I see some people complaining of being afraid of maths, or finding it difficult to have motivation to do maths and I can't understand them. Since I'm blinded by my love of maths; ...
17
votes
8answers
736 views

Exciting games and material to motivate children to math

We are a group of people trying to motivate children, especially living in the countryside, to science and math. We have different activities with children such as doing scientific experiments and ...
14
votes
4answers
1k 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 ...
6
votes
0answers
73 views

Examples of useful, insightful, and interesting hand-waving

I am really amused by the answers to this question on "Most harmful heuristic" posed on MathOverflow, from which I've benefited a lot. However, it seems to me that some hand-waving may be really ...
8
votes
5answers
147 views

Sources for mathematics outside the mathematics world

In this question I would like to ask you about material showing the uses (or occurrences) of mathematics in the everyday world. The aim is to encourage with it a group of young undergraduate ...
1
vote
0answers
15 views

Ability to View Answers in LaTex [migrated]

Is there an option or can one be implemented so that new users like myself can view the "source code" of others answers. Obviously there are many tutorials in which we can find the correct commands, ...
0
votes
0answers
23 views

advice for self studying [on hold]

I took up to ap calc bc, ap chem, and ap physics b until my sophomore year in highschool after that I quite school and came back to Korea and got a job I'm hoping to one day go to college here and ...
14
votes
6answers
3k views

No radical in the denominator — why?

Why do all school algebra texts define simplest form for expressions with radicals to not allow a radical in the denominator. For the classic example, $1/\sqrt{3}$ needs to be "simplified" to ...
15
votes
0answers
337 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
56
votes
4answers
1k 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 ...
2
votes
1answer
130 views

Why is the axiom of choice not taught from the start to mathematics undergraduates?

I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous ...
2
votes
5answers
121 views

Is there a proof that $\int \frac {dx}{x}=\ln |x|+c$?

Is there a proof that $$\int \frac {dx}{x}= \ln|x|+c$$ for $x\neq 0$ I would be interest for any replies or any comment.
7
votes
1answer
96 views

So bad at maths sometimes I feel depressed about it

I taught myself how to count before I even learnt how to talk or read. Playing with numbers was all I did when I was young. I didn't have anyone to foster that type of passion that I believe I still ...
2
votes
2answers
38 views

Printer toner coverage

I have a printer that I used for $2$ years. First year I printed $9630$ pages, with $17\%$ ink coverage per page. Ink coverage is the percent of the page that is not white. Second year I printed ...
0
votes
0answers
32 views

Algebra Questions-Academic

ı must solve this ı only know question 2)s' b) option is Euler's prime-generating polynomial.But ı dont know to show that,too.please help :(
1
vote
0answers
21 views

Calculate year for a provided yield

\$146.25 will yeild \$46.25 at 7.5% per annum. How to get the number of years? Answer is 6 but how do you get it? What is the formula?
3
votes
2answers
48 views

Condition of the mean value theorem

The usual formulation of the mean value theorem in a real analysis course is something like this: Let $f\colon [a,b] \to \mathbb{R}$ be continous on $[a,b]$ and differentiable on $]a,b[$. Then there ...
2
votes
3answers
1k views

Maths brain teaser. Fifty minutes ago it was four times as many minutes past three o'clock

Fifty minutes ago it was four times as many minutes past three o'clock. How many minutes is it to six o'clock..? I have got the solution online but have doubts in it : ...
0
votes
1answer
55 views

Question about independent study in differential geometry for an undergraduate.

I am a senior undergraduate math and physics student applying to graduate school in math for this upcoming fall. I have had classes in: Abstract Algebra (Rings, Fields, and Groups), Point-Set ...
7
votes
0answers
95 views

How to listen math lectures?

Many times, the lectures goes beyond the head and not easy to follow, (at least with me),mainly in the workshop/conferences, though the audience are eager to learn something from it. Also, most of ...
1
vote
1answer
84 views

What's the value of tau?

I've seen $\tau$ on a title of a YouTube video and I need help knowing what the value is. I'm serious. I've never heard of the value. So, what is it? Also, is it rational or irrational (this part ...
11
votes
3answers
233 views

Textbooks, lecture notes, and articles from arXiv for undergraduate students

I have found some interesting textbooks and articles on arXiv, such as the following one, that are accessible to an undergraduate student: Course of linear algebra and multidimensional geometry, ...
2
votes
1answer
441 views

Linear algebra and Multivariable calculus prerequisites for Stochastic Calculus

Which topics are considered "graduate-level" for the following subjects: Linear algebra Multivariable calculus On Internet, it is said that you need "graduate level" Linear algebra and ...
11
votes
6answers
3k views

Advice for Self-Study

I am a senior in high school who has taught myself through Calculus BC and I got a 5 on the exam. However, I have taken all the math I can at my school. I have also taught myself multi-variable ...
0
votes
1answer
456 views

Line Drawing Using Bresenham Algorithm

Indicate which raster locations would be chosen by Bersenham’s algorithm when scan converting a line from screen co-ordinates (1,1) to (8,5). First the straight values (initial values) must be found ...
0
votes
1answer
33 views

How do I remove decimals from cent amounts?

How do I change "23.96" CENTS into something that makes sense? Can I just say \$ $0.2396$? It's important that I keep the value behind the decimal I just don't know how.
4
votes
1answer
92 views

How to get university level Mathematics education on my own?

As far as Mathematics go, I have a highschool level education. I wonder how I could learn more about Mathematics to be on the level of those who had Mathematics level education at a university. Is ...
0
votes
2answers
73 views

What have been “taught” without being proved? [closed]

I would like to make a list investigating the following:- Can you recall (if any):- What topic(s)/formula(s) were being ‘taught’ and told to be true/memorized and subsequently applied without being ...
8
votes
1answer
415 views

Is it possible to learn mathematics right from the source instead of reading textbooks. By studying the masters and not their pupils

I was wondering if mathematics learning process require the use of textbooks. When I was a high school student, I read as a preparation for university, Legendre book on Elements of geometry and ...
2
votes
1answer
302 views

The NES mathematics accredidation test

I have to take the NES mathematics test to get accredidation 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 ...
0
votes
2answers
72 views

Area+Pythagoras Theorem

In the figure below show that Area A + Area B = Area C. What is the answer to this question?
0
votes
3answers
65 views

Is there an elementary “proof” that the first degree equation has only one solution?

I was asked from a student why the first degree equation has only one solution (if it has a solution) Let's consider the equation $2x+5-3x=-4x+14$ for example. How can I explain to a 13 year old ...
0
votes
1answer
77 views

How can I convince students a certain polynomial equation is symmetric?

How can I convince students that $p(x)=0$ is a symmetric equation if they ask me, where $p(x)$ is polynomial of degree $n$ with reals coefficients. For example : $A(x)=2x^4-9x^3+8x^2-9x+2=0 $ is ...
2
votes
1answer
50 views

Characteristic of a Ring not making sense.

The characteristic of a ring with unity is defined to be the least positive integer $n$ such that $1$ plus itself $n$ times $=0$. How does this make sense? $1$ plus itself $n$ times $=n1=n=0$, but ...
1
vote
7answers
3k 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.
8
votes
1answer
515 views

Where does the “Visual Multiplication” technique originate from?

There is a geometric technique to perform multiplication of numbers. But as the internet goes, it is hard to figure out who deserves the credit. What I've heard is A mayan technique From Vedic ...
6
votes
2answers
45 views

How to improve concentration when beginning to work on a math problem that seems boring?

I am a college student and my current situation is that I have an extremely hard time getting myself to start doing math. I feel like math is 'boring,' but ONLY until I start actually doing it. Once I ...
0
votes
0answers
71 views

Complexity of graph radius algorithm

I am a bit new so I hope I don`t break any rules. I have an algorithm: Given H = (V, E) a graph. If v ∈ V and r ∈ N, we will note with SH(v, r) the sphere of radius r with the center in v: SH(v, r) ...
0
votes
0answers
31 views

Where can I get detailed and comprehensive notes of a functional analysis course taught using the book by Erwine Kryszeg?

Where on the Internet can I find detailed and comprehensive lecture notes of an elementary functional analysis course taught using the book Introductory Functional Analysis with Applications by Erwine ...
3
votes
1answer
79 views

Studying for analysis- advice

I find that studying for analysis is unlike other math classes that I've taken. I dedicate a lot of time to studying for it, but it seems like no matter how much time I put into it I am not getting ...
5
votes
1answer
56 views

Is a thorough study of algorithms useful for a mathematician?

In my university, there is a core course called "basics computer science for mathematicians". The topics covered range from algorithms, to the bases of programming, to theory of computability. The ...
6
votes
6answers
4k views

Steps to Re-Learn Mathematic the right way

I was always branded weak mathematics back at school though i loved it. The reason was that I was not having many basics in maths. Due to this problem I stopped learning Maths after my 10th grade. But ...
1
vote
1answer
22 views

math classes to take for path

I have taken: Calc 1, 2, & 3, Introduction to Discrete Math, and Introduction to Statistics. The maths I learn I wish to be most applicable to programming (any kind of programming, game, physics, ...
0
votes
0answers
29 views

Dividing from right to left

Suppose a number is given 6401024, I want to divide it by 1024. But I want to do it from right to left. so in a computer memory storage, Here Let us assume its an array, we hold the remainder of the ...
17
votes
6answers
358 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 ...
2
votes
14answers
577 views

Interesting piece of math for high school students? [closed]

I'm giving an hour long lecture to high school math students with a fairly high aptitude in math. I want to present something a little advanced for them (undergrad level) that they have to struggle ...
43
votes
8answers
6k views

When to learn category theory?

I'm a undergraduate who wishes to learn category theory but I only have basic knowledge of linear algebra and set theory, I've also had a short course on number theory which used some basic concepts ...
2
votes
0answers
51 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
3
votes
1answer
80 views

Advice for Math Majors -What to do if you come into college with a lot of college credit? [closed]

In high school I was a good maths student and took AP Calculus BC my freshman year and got a 5 and then took Multivariable Calculus, Linear Algebra, Differential Equations, Introduction to ...
4
votes
2answers
87 views

where to start if you lack basics? [closed]

I've joined this forum for few weeks now and it amazes me that so many people are good at math. For me, I'm more of a history person rather than math person, so I hated math since I was young, not ...