Questions related to the teaching and learning of mathematics.

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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 ...
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0answers
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+200

What are some strong algebraic number theory PhD programs?

I am currently applying for PhD programs in the US. My main interests are number theory and algebra. More specifically, I am interested in algebraic number theory (number fields, Galois groups, ...
15
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2answers
4k views

Path to Basics in Algebraic Geometry from HS Algebra and Calculus?

In this question, Why study Algebraic Geometry?, Javier Álvarez, develops a succint but encompassing description of algebraic geometry and its spread across different areas of mathematics. Indeed, it ...
15
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5answers
1k views

Is high school contest math useful after high school?

I've been prepping for a lot of high school math competitions this year, and I was just wondering if all the math I learn would actually mean something in college. There is a chance that all of it ...
15
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6answers
3k views

No radical in the denominator — why? [duplicate]

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
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11answers
792 views

Maths at university [closed]

Next year I'm going to start university (maths, obviously), and would like to ask you (I suppose you're mathematicians or, at least, people who studied maths somehow) some advice: what did you learn ...
15
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4answers
855 views

Why study Hopf Algebras?

I'm looking for reasons that motivate the study of Hopf Algebra, like its applications in other branches of mathematics or maybe with physics. The first I've got is that they're interesting by ...
15
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7answers
424 views

Common inadequate definitions

I had the good fortune of assigning the following problem on the first day of my freshman honors calculus course: Is $a$ contained in the interval $[a,a)$? Explain. The majority of my students ...
15
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2answers
606 views

How to deal with exercises with no solutions given?

Probably most people will acknowledge the importance of doing exercises when reading a mathematical textbook. Here I am talking about a textbook of similar level as those ones listed in GTM. However, ...
15
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1answer
322 views

Do lay persons really believe that all of mathematics is known?

I once found a professor of medicine to be under the impression that everything in mathematics is already known. It's probably commonplace to hear that the masses labor under that misconception. In ...
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 ...
14
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6answers
4k views

Why teach linear algebra before abstract algebra?

Is there a reason why most undergraduate curriculums put linear algebra before abstract algebra? I'm asking this because personally it seems to be much easier to understand the architecture behind ...
14
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8answers
2k 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
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8answers
749 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 ...
14
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7answers
1k views

Films about math: a question about math education and motivation for learning math

I'm interested in movies about or related with mathematics or physics, I mean not documentaries which I also consider movies, but artistic or mainstream films about math. Now I have the following in ...
14
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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
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5answers
836 views

Do non-mathematical fields use the appropriate level of analytic/probabilistic rigor?

Talking to students in different areas and taking different classes in math, physics, electrical engineering I have been struck by the differing amounts of rigor in use. I know little about economics ...
14
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5answers
8k views

Which calculus text should I use for self-study?

I am 36 years old, and have forgotten a lot of math from high school, of which I only took up to Algebra 2. However I am teaching myself mathematics and am now, as an adult, completely fascinated ...
14
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5answers
522 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
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6answers
5k views

Best intuitive metaphors for math concepts (of any level)

Frequently, we introduce a new concept with a formal definition, then immediately say "Intuitively, what this means is..." What are the absolute best metaphors you've seen (for concepts of any level)? ...
14
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8answers
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Elementary Papers at ArXiv

Inspired by this question, at MO i am asking this question. Can anyone list some elementary articles at ArXiv which can be understood by High-School/Undergrad Students. I am asking this because, i ...
14
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3answers
5k 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
2answers
747 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
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1answer
319 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
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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
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11answers
7k views

Which 4 maths courses to take as an Economics PhD student?

I am doing a PhD in economics and I have the chance of taking one subject a semester in the maths department (I would like to do more, but "unfortunately" I have to work on my thesis). I want to have ...
13
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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) ...
13
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3answers
3k views

What makes a good mathematician?

A soft question but I believe important to help get maturity in maths. Not until I got admitted to a graduate applied math program that I started to learn math. Before that, I was a life science ...
13
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3answers
398 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
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5answers
950 views

Areas of math that can be “gamified”?

My old high school math teacher has started up a math club recently. It's become quite popular (to my pleasant surprise), and I've been looking for ways to contribute. To that end I've been looking to ...
13
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3answers
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 ...
13
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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
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1answer
816 views

Research in differential geometry

I am an 3rd year undergrad interested in mathematics and theoretical physics. I have been reading some classical differential geometry books and I want to pursue this subject further. I have three ...
13
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1answer
391 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 ...
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5answers
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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 ...
12
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6answers
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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 ...
12
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5answers
674 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
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6answers
249 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
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4answers
298 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
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3answers
506 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
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1answer
579 views

How do you remember theorems?

I am currently a Master's student in math. I do very well in my classes, understand the material, can do the proofs w/o having to read the text, etc, but as time passes, I find that I will forget ...
12
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5answers
220 views

Scholarly work on the beauty of math

When reading mathematical books written for a general audience, or even searching questions on this site, the adjective beautiful is often used to describe mathematics. My question is whether there ...
12
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4answers
4k 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 ...
12
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3answers
1k views

What should a math graduate know? [closed]

There are a lot of undergraduate courses out there and most of them agree on certain things, with regard to the subjects covered. Courses that include mathematics (engineering, physics, etc) are ...
12
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3answers
301 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, ...
12
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1answer
861 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 ...
12
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2answers
2k views

Learning Mathematics using only audio.

Are there any mathematics audio books or other audio sources for learning mathematics. I ask this because I make about 1 hour from my house to the school and staring at a screen on the car makes me ...
12
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2answers
731 views

Is Mathematics graduation important for a Computer Scientist?

I know this might be a personal problem, but I often find some friends in the same problem as me so I think this might be helpful to them after all. I am going to graduate in Computer Science in ...
12
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1answer
215 views

Studies on lack of mathematical education

I am looking for studies which compare students who did not receive mathematical education beyond basic mthematics and those that learned maths upto introductory calculus, with the assumption that ...
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11answers
2k 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 ...