Questions related to the teaching and learning of mathematics.

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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 ...
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3answers
202 views

Video Lessons in Complex Analysis

Does anybody have some link for good video lessons of a complete course in Complex Analysis? Grateful.
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2answers
197 views

Good Reference for Justifying (less well-known fields of) Math?

How do we as mathematicians justify the study of math to students? Or, indeed, how do we justify it to the general public? How do you justify your particular field? I'm particularly interested in ...
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2answers
521 views

How to assess a non-natively english speaking high-schooler's mathematical ability?

I'm a math PhD who has been asked to interview a high school student and determine what he/she is interested in and how strong the student is. Usually I would want them to talk as much as possible ...
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1answer
172 views

A graph of all of mathematics

In mathematics, one often makes (proves) statements on the basis of: Previously proven statements Axioms I like to think of these dependencies as a directed graph, with edges from the accepted ...
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1answer
143 views

How and what to teach on a first year elementary number theory course?

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. ...
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1answer
267 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 ...
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1answer
149 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 ...
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1answer
391 views

Where can I find the 1960s New Math syllabus?

I've been looking everywhere for even a short summary of the content of the 1960s New Mathematics Math education reform in the US but I cannot ;-; Does anyone know?
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1answer
254 views

Publishing mathematics

How or where does one express work they've done to others? What does it mean formally to 'publish' mathematical work you've done? How do you know if your work is any good? Or if someone has already ...
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1answer
88 views

Education: Reading Proofs

I am finishing my undergraduate degree and one thing I've noticed is how little weight has been placed upon the ability to read proofs, in basically all of my math courses. In first year calculus you ...
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5answers
223 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 ...
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3answers
321 views

Examples of useful, insightful, and interesting hand-waving [closed]

It seems to me that some hand-waving (by which I mean some arguments that aim at giving some form of intuition on the problem even at expenses of complete rigour [and not mnemonics for high-schoolers ...
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4answers
3k views

What are the prerequisites for taking introductory abstract algebra?

I am a maths student in my second year of university. I have taken and done quite well in Calculus I, II, III as well as a linear algebra (application focused) class. I have not worked much with ...
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4answers
852 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"?
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Where to go after calculus?

Ok this is a bit of an unanswerable question, but hopefully someone will answer. As I have been going through college & high school there has been a kind of "path" through which you learn math. ...
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4answers
386 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 ...
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3answers
454 views

Mathematics Style Guide - l vs 1 vs |

I had a quick look around here and google before, and didn't find any answer to this particular question, and it's beginning to really irritate me now, so I'm asking here: How is one supposed to ...
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9answers
1k views

Educational Math Software

What is the the most educational software for high school and college math? Not the one that just gives you the answer, but has any of the following: Edit: Software mentioned in answer added in ...
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6answers
663 views

What we're never taught explicitly

I would like to make a complaint really. School math(s) can be the most boring way to learn: sitting down and rote learning binomial expansion or the volume of a cylinder is just not interesting. It ...
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3answers
2k views

Why is 1 raised to infinity Not defined and not “1” [duplicate]

$1$ square is $1$, so is raised $1$ to $123434234$. My maths teacher claims that $1$ raised to infinity is not $1$, but not defined. Is there any reason for this? I know that any number raised to ...
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5answers
3k views

Are there any memorization techniques that exist for math students?

I just watched this video on Ted.com entitled: Joshua Foer: Feats of memory anyone can do and it got me thinking about memory from a programmers perspective, and since programming and mathematics ...
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3answers
2k views

Reviews/comparison of Python vs Matlab for teaching Linear Algebra

I am wondering about advantages of using Python for teaching introductory linear algebra. I have been using Matlab and I became interested in Python mainly because of several resources, e.g., ...
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5answers
2k views

Experiences with Rudin?

So I am trying to tutor a friend in analysis. This is her first time with proofs. We are on chapter 2 – the topology chapter – of Rudin's Principles of Mathematical Analysis and ...
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3answers
675 views

Which of these courses to take if one intends to go to grad school in pure math (rank please)

could you rank these classes in terms of necessity to take if I intend to pursue a Ph.D in pure math? I don't know if I can fit everything, but I want to make sure I take the most important ones: ...
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3answers
836 views

What is the probability that GCD of $(a,b)$ is $b$?

My question is quite simple. I have been googling a lot lately trying to find a solution to this: Given a sequence of n integers $[1,2,...,n]$. If we pick two numbers randomly from the set say, a and ...
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4answers
637 views

Is there any good reason why a protractor starts from right to left, unlike a scale, which starts from left to right?

While studying through the number system, i notice that positive side is from 0 to +ve infinity. The direction is left to right. However, this is opposite in case of angles. The sort of curved number ...
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3answers
430 views

(translated)Russian mathematics books?

Most russian mathematician(generally) are known to do and teach mathematics in a very original manner,they do in a very intuitive yet rigorous way, with/through wonderful connection to physics. ...
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2answers
576 views

Strengthening My Foundation in Mathematics

"For every equation you introduce, you cut your audience in half." This expression, which I believe came from Stephen Hawking, summarizes why I believe that I have a weak foundation in ...
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3answers
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Difficulties with Chapter 2 in Rudin

I have been reading Rudin (Principles of Mathematical Analysis) on my own now for around a month or so. While I was able to complete the first chapter without any difficulty, I am having problems ...
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2answers
337 views

How to tackle the depression and frustration regarding math? [closed]

I'm a high school student and it is my last year at school. I've always loved math from the core of my heart. Last year, I prepared a lot for the National olympiad. I cleared the regionals smoothly ...
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1answer
282 views

Are mathematics competitions important?

So I'm seventeen and currently a junior in high school. I love mathematics very much, it's developed into a strong passion over the past few years, after witnessing the president of the math club at ...
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2answers
261 views

How are more difficult proofs discovered?

Are there any resources that show how are the various proofs of important theorems in mathematics are invented? I don't understand how can anyone come up with this method for proof for example. I want ...
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1answer
427 views

The perception of mathematics

In my work I wrote the following sentence. "...there is a negative perception of mathematics and mathematicians, both within and outside of academia." Err. Right. So, I believe that this is ...
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457 views

What should be the next step?

This is a soft/educational question and I'll flag it to be made community wiki. A little bit of background, first. I am in my last undergraduate year, and I took a graduate course in category theory; ...
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1answer
180 views

How to draw greek letters on paper / blackboard?

For $\gamma$ (gamma), I've noticed people doing a sort of $\alpha$ (alpha) rotated by ninety degrees, which seems to be the standard on-paper-or-blackboard equivalent of $\gamma$. But for letters ...
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1answer
157 views

Is it a bad idea to study modern algebraic geometry without having any background in smooth manifolds?

I have a chance to take a course in algebraic geometry developed in the scheme theoretic setting and am considering my options. I have taken graduate courses in general and commutative algebra and ...
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2answers
357 views

Outline and Goals of a One-Year Calculus Sequence

Our department is considering restructuring our traditional three semester calculus sequence so that the calculus requirement for our majors is satisfied in two semesters. Does your department ...
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1answer
285 views

Journals or Magazines on Study Skills or How to Study Math

I am trying to find only journals or trustworthy magazines which can help math students to study math more efficiently and productively. I am not asking about books in this thread. In particular, I am ...
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1answer
170 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: ...
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1answer
246 views

Learning Mathematics in a Second Language

My first language is English, and since all of my formal education has been undertaken in the USA, I have learned mathematics entirely in the English language. However, I have spent a fair amount of ...
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1answer
286 views

Is making the math learning process deliberately more challenging an effective teaching strategy?

I've often come across a view on teaching/learning math to the effect that forcing students to struggle rather then "spoon-feeding them" (as they put it) makes for much more able students in the long ...
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1answer
139 views

Proof vs Practice

I've been brushing up on a lot of basic arithmetic, algebra, and logic as I work towards a review of calculus (and beyond), and I keep noticing that in order to fully understand many principles in the ...
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0answers
71 views

How to explain the topic of Fourier transform interactively? [closed]

This is a soft question . In the walk-in for the lectureship, I have decided to give demo lecture on the topic of Fourier transform. The principal of the institution ask me to take lecture ...
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0answers
159 views

Undergrad research gateways

This question is intended as public service to mathematics. It is meant to benefit undergrad research students and maybe even researchers wishing to broaden their expertise and learn something away ...
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0answers
346 views

The difference between 10 and 9.99999 … (recurring) [duplicate]

Possible Duplicate: Does .99999… = 1? At supper today my daughter was discussing her maths (she's 13) - she had been studying putting decimal numbers into what she called standard ...
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1answer
901 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 ...
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7answers
3k views

Easiest and most complex proof of $\gcd (a,b) \times \operatorname{lcm} (a,b) =ab.$

I'm looking for an understandable proof of this theorem, and also a complex one involving beautiful math techniques such as analytic number theory, or something else. I hope you can help me on that. ...
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4answers
258 views

Formality and mathematics

Why is it important to be formal in mathematics? Is formality beneficial for students? Or is it just to scare students away from mathematics?
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1k views

Expanding problem solving skill

I have a great passion for Math but my lack in problem solving skill always keeps me away from the "good stuff". I always wanted to be better at Math and one of the things I figured out was to keep ...