Questions related to the teaching and learning of mathematics.

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1answer
174 views

How much math is there? [closed]

Among other things I teach high school-level math, and one question that often comes up is: "How long would I have to study math in order to know all of it?" I usually tell them that it's like ...
7
votes
4answers
906 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 ...
7
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3answers
750 views

Masters' thesis in group theory [closed]

I would like some ideas on topics in group theory which would be suitable for a masters' thesis. What sort of problems would be suitable for this level? Because it is at masters' level, no original ...
7
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5answers
310 views

Simplest error detecting/correcting codes for math newbies

Suppose you have been given the task of teaching some basic coding theory to folks who are interested in math but have not taken algebra, number theory, etc. If you want to introduce codes, you might ...
7
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6answers
345 views

Evaluating the reception of (epsilon, delta) definitions

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in real analysis and the student reception of it. ...
7
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4answers
631 views

How to convince a high school student that differentials don't work like fractions in general?

It all started when I tried to convince a 10th grader that if $f$ is a function defined on $\mathbb{R}^n$ the differential is defined by: $\large \displaystyle df = ...
7
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3answers
1k views

Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...
7
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6answers
2k views

What is the best base to use?

When I typed this question in google I found this link: http://octomatics.org/ Just from the graphic point of view: this system seems to be easier (when he explains that you can overlap the line). He ...
7
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3answers
1k views

Experiences with Kumon

We have enrolled our 5 year old son in Kumon which is an after school math and reading enrichment program of Japanese origin. While he is learning lots of things (currently learning how to add i.e., ...
7
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6answers
626 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 ...
7
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6answers
458 views

Thinking of mathematics in terms of analogs

I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical ...
7
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4answers
238 views

Mathematical news sources.

I'm studying my high school right now but I really like math and it would be great for me if I could find a place where I can find about what is going on in the math world nowadays. About a year ago I ...
7
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5answers
477 views

Math book for an eager learner with non-mathematical background

I was reading answers to How do you explain the concept of logarithm to a five year old? and realized that I really don't understand mathematics. Okay, I lied when I said that I had no mathematical ...
7
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3answers
347 views

Does this class of cipher have a name? What weaknesses does it have?

Some Background In October I have been asked by the school I teach at to organise and lead 'a hands-on cryptography session' for a bright group of 13 year olds to follow a talk on Enigma by an ...
7
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3answers
294 views

Is formal logic necessary for pure/“higher” mathematics?

I'm asking this as an autodidact who wants to learn math rigorously for its own sake. And I was just wondering if understanding proofs could be achieved without a formal grounding in symbolic logic. I ...
7
votes
1answer
374 views

Why do professors sometime hide the book from which they are really teaching? [closed]

Well, the title is almost self explanatory. I am in a graduate school and have two professors this semester both of who are telling me that they are not following any particular book, and yet when I ...
7
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4answers
2k views

Degree choice — Math or physics

I realize that it is of bad form to cross-post. However, on this matter I very much hope to hear arguments from all sides... I hope to become a physicist focusing mainly on the theoretical side in ...
7
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2answers
520 views

Historical basis and mathematical significance of Riemann surfaces

It is written in Riemann Surfaces (Oxford Graduate Texts in Mathematics) by Simon Donaldson, that: "[t]he theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination ...
7
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2answers
383 views

Too many topics taught in class? Frustrated student in need of advice and encouragement. [closed]

Location: New York CUNY (as education systems might be different in other places) I started my life studying philosophy and psychology and then at 22 transitions to computer science. It took me a ...
7
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3answers
211 views

Graduate School?

I'm completely clueless on the process, but on track to graduate in two years, so I have a few questions about what I should do. 1) What's the difference between a Master's degree in Mathematics and ...
7
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1answer
263 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 ...
7
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2answers
410 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; ...
7
votes
6answers
487 views

Up-to-date advice on the best way to take notes (maths)

I have read some old discussions about this topic and would like to get some up-to-date advice if possible. I'm going to start university next year (maths), and I know how important is to have a set ...
7
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2answers
430 views

How to teach a High school student that complex numbers cannot be totally ordered?

I once again need your precious knowledge! I am not sure which is the best pedagogic way to teach a High school student about why complex numbers cannot be totally ordered. When I was in High school ...
7
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2answers
98 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, ...
7
votes
1answer
135 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 ...
7
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2answers
260 views

Enlightening misunderstandings of test questions

What enlightening misunderstandings of test questions have you encountered? Of course, there are jokes about this, such as literal (graphic) “expansion” of the power of a binomial, but I am asking ...
7
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2answers
582 views

Mathematics Article Collection Books for Talented High School Students

I'm looking for some good books including mathematics articles which are appropriate for talented high school students. I'm NOT looking for puzzle or Olympiad problem books. Here are some of my ...
7
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0answers
632 views

Learning higher-mathematics on your own

I was hoping someone had an opinion on how to learn higher-mathematics (specific fields that could be of use to me) outside of a classroom setting. I graduated with an M.S. in Computer science about ...
7
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0answers
336 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 ...
6
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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
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4answers
195 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?
6
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4answers
2k 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 ...
6
votes
3answers
459 views

Why $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?

First I have checked the search option but found nothing relevant to my problem and also level of math. I just started learning the language of mathematics, on my own and I have trouble understanding ...
6
votes
5answers
915 views

discrete math book suitable for younger person?

When I took discrete math as an adult I realized that this was a subject I would have enjoyed and done well at much earlier in life, even in my early teens. Does anyone know if there are good books, ...
6
votes
3answers
491 views

The Importance Of Good Teachers and Guidance In the Academics

I'm a first year student for a math degree. I'm very curious on how good students overcome their bad teachers in the journey of learning and grasping the courses material fully, all in the pressure of ...
6
votes
4answers
371 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 ...
6
votes
3answers
308 views

Foreign undergraduate study possibilities for a student in Southeastern Europe

In the (non-EU) country I live in, the main problem with undergraduate education is that it's awfully constrained. I have only a minimal choice in choosing my courses, I cannot take graduate courses, ...
6
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4answers
376 views

How should I grade my students?

Anyone who is interested in my experience as a grader in the past can check this thread. This semester I was assigned a grader for a certain class, which runs two sections. There are two professors, ...
6
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5answers
3k 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 ...
6
votes
4answers
648 views

Teaching irrational numbers?

I'm interested in teaching the irrational numbers to high-school students, and I need your ideas on how to do in an 'optimal' and innovative way. And my question is: What should the teacher know ...
6
votes
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 ...
6
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3answers
793 views

Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
6
votes
2answers
427 views

Self-Teaching: Is Geometry the Nexus of all Mathematics?

Necessary prologue: I'd really like to become more fluent in the language of mathematics. I don't have a schedule that permits me taking a class and any on-line tutors that I find seem relatively ...
6
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2answers
179 views

Teaching algebra in a culturally relevant way while fitting Common Core standards

I've been assigning algebra textbook and worksheet problems (from the publishers and my own) that look like this: Simplify the following expressions. $x^{- 3} y^2$ $c^2 d^{-5}$ ...
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3answers
707 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 ...
6
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2answers
555 views

Personal advice ragarding Qualifying Exams

I am a Graduate student in Mathematics and in second Year. I have three qualifying exams in topics Abstract algebra, Real and Complex Analysis and Algebraic and differential topology.I already ...
6
votes
1answer
303 views

What pure mathematics foundations should an applied mathematician have?

I'm studying mathematics, with some statistics also, and I've always chosen applied courses. I'm getting to the point where I'm studying 3rd year undergraduate to graduate level material. My first ...
6
votes
1answer
162 views

How to combat memorization

As a student in high school, I never bothered to memorize equations or methods of solving, rather I would try to identify the logic behind the operations and apply them. However, now that I've begun ...
6
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3answers
689 views

Teaching the concept of a function.

I am doing a class for at risk high school math students on the concept of a function. I have seen all the Internet lesson plans and different differentiated instruction plans. The idea of a ...