Questions tagged [education]

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.

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9
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2answers
734 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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2answers
1k views

How should I teach a high school student about inverse functions?

Today I tried to teach a high school student about inverse functions. I gave him this problem and defined the parts that he didn't understand: Let $f: \mathbb{R} \to \mathbb{R}$, $x \mapsto x^...
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3answers
333 views

Practical implementation of Mathematics

I am 21 years old now. I have been studying Mathematics in school, college and now in university but I simply feel that I don't practically understand it. For example, I can solve complex questions on ...
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2answers
6k views

Books to study for Math GRE, self-study, have some time.

I just graduated from a regional university in the US with a minor in mathematics. There is a masters program overseas, for economics, that I want to attend but they require applicants to take the ...
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3answers
1k views

How can I find videos of mathematics at graduate level, especially on linear algebraic groups

I am studying mathematics by myself, and I find it very helpful to watch online course videos. There are many such videos on undergraduate courses, such as elementary calculus, abstract algebra, ...
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3answers
273 views

diversity and teaching [closed]

I recently attended a discussion about interviewing for math jobs, and apparently a question that is coming up frequently is something like this: "We have a culturally diverse student body. How does ...
6
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3answers
405 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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2answers
387 views

Elementary arguments concerning the stereographic projection

How does one give a proof that is short; and strictly within the bounds of secondary-school geometry that the stereographic projection is conformal; and maps circles to circles?
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4answers
3k views

Motivation behind the definition of GCD and LCM

According to me, I can find the GCD of two integers (say $a$ and $b$) by finding all the common factors of them, and then finding the maximum of all these common factors. This also justifies the ...
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3answers
5k views

Why the emphasis on Projective Space in Algebraic Geometry?

I have no doubt this is a basic question. However, I am working through Miranda's book on Riemann surfaces and algebraic curves, and it has yet to be addressed. Why does Miranda (and from what little ...
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4answers
224 views

Two questions related to probability theory and pedagogy

A housemate of mine and I disagree on the following question: Let's say that we play a game of yahtzee. Of the five dice you throw, two dice obtain the value 1, two other dice obtain the value 2, ...
3
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1answer
184 views

Ways to teach fractions

I'm tutoring elementary-level kids on equivalent fractions and am not doing a very good job of explaining it. I've tried using the example of a pizza or a pie and have shown them how they can come up ...
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4answers
2k views

Random variables: How would you explain it to a beginner?

Different types of random variables: (discrete) Binomial, hypergeometric, geometric, Poisson (continuous) Uniform, normal, exponential Random variables are very useful tools when solving simple and ...
2
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1answer
141 views

weakly locally one-to-one?

Is there any standard name for this concept that is weaker than local one-to-one-ness? In some open neighborhood of $x_0$ there is no point $x\ne x_0$ such that $f(x)=f(x_0)$. Or, if you like: In ...
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2answers
611 views

Programs for precocious prodigies

I am the director of my university's mathematics honors program, and we just had an inquiry from the parent of a 15 year old who has already completed most of the math courses for a standard ...
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12answers
2k views

Resources for a curious beginner mathematician [closed]

I have a friend whose experience of math in school was horrible (each teacher, she says, either left or was fired the year after she had them). I've been teaching her about various things: cantor's ...
1
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1answer
378 views

Mathematical disciplines [closed]

Once I spoked to a mathematician about mathematics and he asked me what was my favourite area in Maths. My answer was "Chaos Theory" and he said this is not a discipline in Mathematics. What is a ...
3
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1answer
761 views

what is teaching kids the rules and exceptions in multiplication called?

I recall reading a website quite some time ago about the rules and exceptions of multiplication with regards to teaching children. For instance: ...
3
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2answers
169 views

Advice for Calculus Tutoring

I am tutoring a friend in calculus. Right now, she is working on finding relative maxima and minima as well as Rolle's theorem. While she gets how to find relative maxima and minima she does not get ...
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6answers
6k views

What does Khan Academy have to offer? Depth? Rigor?

Khan Academy - http://www.khanacademy.org/ - is often cited as a great online resource for learning mathematics and other subjects. I have heard many good things about this website and was wondering ...
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5answers
1k 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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4answers
2k views

“Best practice” innovative teaching in mathematics

Our department is currently revamping our first-year courses in mathematics, which are huge classes (about 500+ students) that are mostly students who will continue on to Engineering. The existing ...
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4answers
275 views

Looking for a simple problem for math demonstration

I'm holding a 3-5 minute speech next week on mathematical problem solving, and how it makes me happy, to 15-20 non-mathematicians. As a part of it, I had thought about demonstrating two problems, but ...
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3answers
2k 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., ...
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4answers
2k 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 ...
5
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3answers
537 views

Good lecture optimization problem involving $\ln x$ or $e^x$

I am teaching a Calc 1 of sorts, like a slightly easier version of Calc 1 with no trig. I want a good optimization/practical problem to do in lecture that involves $\ln x$ or $e^x$, to combine review ...
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8answers
11k views

How can I read numbers and mathematical symbols comfortably, at a university level? [closed]

When I look at math, it's like my mind goes fuzzy. The only way to describe it is to relate to how when you read, you see the letters and words, but your brain picks up on the meaning? When I see ...
18
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6answers
892 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 ...
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4answers
1k views

The Power of Taylor Series

I am teaching a Calculus class and we are finishing up power/Taylor series this week. The last section of the chapter is on applications, but the only ones listed there are approximating non-rational ...
85
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8answers
5k views

A Case Against the “Math Gene”

I'm currently teaching a mathematics course for elementary educators (think of it as math methods, but with less focus on methods and more focus on content). In a student's essay, I encountered the ...
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0answers
290 views

Am I graduate if I take my bachelor degree in Italy?

I don't know if it is appropriate to ask here such a question since it doesn't involve a specific mathematical problem, but I think such information will be useful for many people like me... My real ...
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5answers
2k views

Good discrete mathematics notes?

Good morning, Do you know of a good resource for discrete mathematics notes, lectures and/or videos? I found the classes + notes given to be lacking at my university... Topics covered thus far: ...
4
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1answer
204 views

Algorithm for keeping a concrete version of Euclid's argument simple

(My actual question is at the very bottom of this posting.) Suppose you're teaching a course in mathematics-for-liberal-arts majors and it's the last math course they'll ever take. It has almost no ...
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6answers
2k 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 ...
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2answers
506 views

What is the origin of the prefix logic notation used in WFF 'N PROOF?

The classic "modern logic" game of WFF 'N PROOF uses a set of symbols to represent logical relations that I've seen used nowhere else: $C$ for then; $A$ for or; $K$ for and; $E$ for if and only if; ...
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4answers
2k views

Fun math for young, bored kids?

For 6 months, I'll be organizing, as part as my volunteer work in an NGO, math classes with small groups (~10 students, aged 16 or 17). These classes are not compulsory, but students willing to stay ...
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2answers
1k 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 ...
3
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2answers
2k views

Grad degree that mainly deals with probability/game theory/optimization?

I'm currently working but am going to take classes as a non-degree student to beef up the math part of my background. I've only taken calc 1-3, ODEs, linear algebra, logic, and decision theory so my ...
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4answers
1k views

Is there a more efficient method of trig mastery than rote memorization?

I would like to get alot better at trig than I am. What is the best/most efficient method? Thanks much in advance Joe
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0answers
392 views

Have Changes in Applications Made Linear Algebra More Central/Urgent?

In the days when my father taught civil engineering (some decades ago), mathematical applications seemed to be mainly "scientific." (This was the "space age.) Hence the most important branch of ...
10
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2answers
583 views

Is there any toy for learning algebraic manipulation of fractions?

Is there any toy for learning algebraic manipulation of fractions? If you don't know of any, how would you design one? What I'm imagining is something similar to a Rubik's cube whose manipulation ...
9
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2answers
1k 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 ...
9
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1answer
332 views

Request for “Nice” Papers in i) Differential Geometry ii)Analysis iii)Topology, to Go Over

Everyone: I am a little frustrated with the progress in my bottom-up learning process, and I think I might get better results by doing some more top-down, i.e., by reading and trying to make sense of ...
6
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2answers
714 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 ...
14
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4answers
419 views

Should the domain of a function be inferred?

It is a common practice to have students of elementary algebra infer the domain of a function as an exercise. I believe this is contrary to the spirit of the definition of a function as a collection ...
46
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7answers
29k views

How to study for analysis?

I am currently a first year undergraduate majoring in mathematics. I'm taking an introductory analysis course and find it very hard compared to other math couses. I know that the topics covered in the ...
6
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1answer
454 views

Is it ever really Pi Time?

Walking with my son at 3:14pm the other day, I mentioned to him, "Hey, it's Pi Time". My son knows 35 digits of $\pi$ (don't ask), and knows that it's transcendental. He replied, "is it exactly $\pi$...
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2answers
1k views

List of topics for a 'Quantitative Reasoning' Course

I am planning to develop a course which I tentatively call as 'Quantitative Reasoning'. The goal of the course is to equip a typical undergraduate student with sound quantitative reasoning skills so ...
75
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24answers
12k views

What is your favorite application of the Pigeonhole Principle?

The pigeonhole principle states that if $n$ items are put into $m$ "pigeonholes" with $n > m$, then at least one pigeonhole must contain more than one item. I'd like to see your favorite ...
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17answers
28k views

Mathematical equivalent of Feynman's Lectures on Physics?

I'm slowly reading through Feynman's Lectures on Physics and I find myself wondering, is there an analogous book (or books) for math?