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.

learn more… | top users | synonyms (3)

14
votes
10answers
3k views

Are there 3 trig functions or are there 6 trig functions?

In my algebra class we are being taught that there are only the 3 basic trig functions (cosine, sine, and tangent). But my friend who is 2 math grade levels ahead of me is saying that there is 6 trig ...
14
votes
5answers
1k views

How can I convince my math teacher?

Ok, so I got an answer wrong on my exam because my teacher says that the function $f(x)=\frac{(x+2)x}{x+2}=x$ but I insist that it isn't defined for x=-2. If it was then $\frac{x}{x}=1$ for all reals ...
14
votes
8answers
3k views

What math should a programmer know?

I am an application programmer focussing on Line Of Business (LOB) applications. I am from non-mathematics and non-CS background. What mathematics should I learn which help me improve my programming ...
14
votes
5answers
2k views

Is $ 5 $ nearer to $ 0 $ or $ 10 $?

My 6-year-old’s homework was “to find the nearest $ 10 $.” For example, $$ 42 \to 40 \quad \text{and} \quad 28 \to 30. $$ For $ 55 $, she answered “$ 50 $” and was marked wrong. How is this wrong? ...
14
votes
5answers
1k views

Is the skill to learn new math by reading textbook alone (no lectures) required when one becomes a PhD student?

I've taken a few math classes in college. I'm wondering as one graduates college and applies to become a PhD student in math, is he/she going to be required to learn math related materials alone ...
14
votes
7answers
2k views

Teaching abstract maths concepts to young children.

I am interested in opinions and, if possible, references for published research, about the pros and cons of teaching abstract maths concepts to young children. My younger brother (five years old) ...
14
votes
6answers
2k views

Self studying math, how can I learn the most?

I am currently studying Pre-Calculus on my own. I have a few texts I am working with but feel like I could learning a lot more than I am. When people typically ask these kind of questions the common ...
14
votes
5answers
664 views

Inspiring a new generation

Tomorrow is a very special day for both my students and I: we will be starting a calculus course. I'm looking for some nice quotes to read to them to convey just what a complete game changer calculus ...
14
votes
4answers
1k views

Guidelines for learning about Ramanujan's work?

It is well known that one of the first books Ramanujan studied was "Synopsis of Pure and Applied Mathematics" and that it shaped the way Ramanujan thought and wrote about mathematics. Being interested ...
14
votes
7answers
2k views

Defining the derivative without limits

These days, the standard way to present differential calculus is by introducing the Cauchy-Weierstrass definition of the limit. One then defines the derivative as a limit, proves results like the ...
14
votes
4answers
7k views

Self-Paced Graduate Math Courses for Independent Study

Does anyone know of any graduate math courses that are self-paced, for independent study? I am a high school math teacher at a charter school in Texas. While I am quite happy with where I am right ...
14
votes
3answers
8k views

Best software to take math notes?

I have read some old discussions about this topic and would like to get some up-to-date advice, if possible. How can I take math notes, write formulas and draw graphs on my pc (win 7), the easiest ...
14
votes
3answers
181 views

Applications of functions of the form $f(x)^{g(x)}$

Early on in my calculus education, I learned how to take the derivative of $x^x$ by re-writing it in the form $e^{x\ln x}$. More generally, this technique is helpful in finding the derivative of ...
14
votes
2answers
923 views

Importance of Exercises in Mathematics for Self-Studying

I am a high school student wanting to major in Mathematics in the future. I started to like Mathematics recently, starting a year ago and I watched some interesting math videos on YouTube for fun (ex: ...
14
votes
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 ...
14
votes
1answer
470 views

Developing research experience in mathematics

I am not sure whether this is the right forum for this question, so it might be migrated somewhere else; but, it is, I think, certainly germane to the wider idea of pursuing interesting questions and ...
14
votes
1answer
569 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 ...
14
votes
1answer
333 views

Anecdote about mathematicians leaping to tops of problems and then building a staircase down?

I've run across this cute little story before, and now for the life of me I can't find it anywhere. It goes something like: Two people are looking out onto a mathematical landscape, and there are ...
13
votes
13answers
4k views

How to explain the formula for the sum of a geometric series without calculus?

How to explain to a middle-school student the notion of a geometric series without any calculus (i.e. limits)? For example I want to convince my student that $$1 + \frac{1}{4} + \frac{1}{4^2} + \...
13
votes
6answers
5k 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 ...
13
votes
9answers
874 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 ...
13
votes
4answers
1k views

Infinite Series: Fibonacci/ $2^n$

I presented the following problem to some of my students recently (from Senior Mathematical Challenge- edited by Gardiner) In the Fibonacci sequence $1, 1, 2, 3, 5, 8, 13, 21, 34, 55,\ldots$ each ...
13
votes
2answers
3k views

Is there a way of intuitively grasping the magnitude of Graham's number?

I have heard it stated before that Graham's number is so vast that it is completely beyond comprehension. It is way larger than the number of atoms in the universe, so cannot be related to real ...
13
votes
7answers
7k views

Why we need to know how to solve a quadratic?

Five years ago I was tutoring orphans in a local hospital. One of them asked me the following question when I tried to ask him to solve a quadratic: Why do I need how to solve a quadratic? I am ...
13
votes
4answers
1k views

Best way of introducing determinants in a linear algebra course

What is the best way of introducing determinants in a linear algebra course? I want to give real life examples of where the determinant is applied. It should have a real impact.
13
votes
3answers
2k views

Very elementary proof of that Euler's totient function is multiplicative

Well, I know two or three proofs of this fact $$\gcd(m,n)=1\implies \varphi(mn)=\varphi(m)\varphi(n)$$ where $\varphi$ is the totient function. My problem is this: I'd like to explain this to some ...
13
votes
3answers
467 views

Being mathematically critical: how should a student approach statements that appear to be obvious?

Very occasionally, I will read or hear a theorem, and think: isn't that obvious? Not in a contemptuous "I can immediately see how to prove this" way, but rather in a "I would have thought this was ...
13
votes
2answers
579 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 ...
13
votes
3answers
1k views

I want to learn math!

Let me introduce myself. My name is Filip and I am going to 10th grade now. My school deals with electrotechnics and computers (programming, hardware etc.) I was always good at math but not quite ...
13
votes
1answer
1k views

What is the expected mathematical repertoire of a Ph.D. program applicant?

I am an undergraduate (currently a sophomore) studying to prepare for applying to a Ph.D. program in mathematics. I have thus far structured my course selection upon the advice of a friend I met ...
13
votes
2answers
469 views

Is ripping off exercises plagiarism? [closed]

Just a quick question. I teach some undergraduate mathematics. I like to produce notes that contain exercises. Sometimes I make my own exercises, sometimes I take exercises from various sources and ...
13
votes
3answers
631 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, ...
12
votes
9answers
810 views

Proof that doctors could relate to [closed]

I am supposed to present a mathematical proof to a lecture hall full of doctors in order to show them how mathematicians think. I'm having trouble picking a proof that will be easily followed by ...
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? ...
12
votes
11answers
3k views

Good examples for mathemathical problems/statements that are easely solvable/provable in one theory and hard to solve/prove in another

Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria: Given two (or more) mathematical points of view ...
12
votes
7answers
14k views

practical uses of matrix multiplication

The use of matrix multiplication is usually given with graphics initially (scalings, translations, rotations, etc). Then there are more in-depth examples such as counting the number of walks between ...
12
votes
4answers
5k views

Is “locally linear” an appropriate description of a differentiable function?

In this answer on meta, Pete L. Clark said: I think the question concerns the idea that a differentiable curve becomes more and more like a straight line segment the closer one zooms in on its ...
12
votes
5answers
272 views

Issues with text problems

When I tutor, I often see people who kind of know the stuff they cover in school at the moment and succeed at straight problems like: Find the derivative of $f(x) = \frac 12 x^2$ But when it ...
12
votes
7answers
3k 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 ...
12
votes
5answers
1k views

Mathematicians who overcame academic failure to achieve success [closed]

Does anyone have any story of mathematicians who overcame "academic failure" or setbacks to achieve success later as a result of their perseverance? This is a soft question, that hopefully can inspire ...
12
votes
5answers
724 views

Can the order of learning be changed?

I have been advised by many people to learn from scratch. So I decided to learn it. But I have the following questions in my mind. Can we skip "the Trinity" and learn something else directly? ("the ...
12
votes
10answers
1k views

Sources of problems for teaching/tutoring young mathematicians

I am tutoring several talented students, middle school level and early high school level, in mathematics. I am always looking for new sources from which to draw questions. Can anyone recommend books, ...
12
votes
4answers
419 views

A Book of Neat Theorems for Laymen

I'm looking for reading assignment ideas for my students. I'd like them to read up on results in mathematics in layman's terms. For example, the Monty Hall problem, or Borsuk Ulam as the "Ham ...
12
votes
2answers
808 views

Interesting but elementary properties of the Mandelbrot Set

I suppose everyone is familiar with the Mandelbrot set. I'm teaching a course right now in which I am trying to convey the beauty of some mathematical ideas to first year students. They basically know ...
12
votes
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 ...
12
votes
6answers
299 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 ...
12
votes
4answers
349 views

Communicating mathematics

As a TA, my ratings have been fairly mediocre. There's nothing to suggest I'm a problem, but I have room to improve. What's more disturbing to me is that I even struggle to communicate math with ...
12
votes
3answers
606 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 ...
12
votes
5answers
288 views

Is $1 : 7 = 1 / 8$ or is it $1/7$?

In a certain (non-mathematical) Stack Exchange, when I wrote $n : m = n / m$ where $n$ and $m$ are positive integers, one of the moderators said "No! $n : m$ is usually the notation for "$n$ parts in $...
12
votes
4answers
3k views

What is an intermediate definition for a tangent to a curve?

Most students come to calculus with an intuitive sense of what a tangent line should be for a curve. It is easy enough to give a definition of a tangent to a circle that is both elementary and ...