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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Why doesn't this work? — The V.I. Arnold Primary School Problem (Two women started at sunrise…)

I've got a, perhaps silly, question. I understand the various solutions to this problem: Two women started at sunrise and each walked at a constant velocity. One went from A to B and the other ...
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1answer
178 views

Interpretation of First Isomorphism Theorem

I understand that the first isomorphism theorem basically says that any homomorphism f from group G to group G' induces an isomorphism from G/Ker(f) to the f(G). What I don't quite understand is the ...
39
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7answers
3k views

Why is there antagonism towards extended real numbers?

In my backstory, I was introduced to the geometric concept of infinity rather young, through reading about the inversive plane. In the course of learning calculus, I'm pretty sure I formed a concept ...
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3answers
1k views

How to explain to a small child that the area of a square of side a is a²?

I have a small child and I am always trying to find the best way to explain new things to her. The area of a square is a very basic concept that is related to the idea of area unity and can be used to ...
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4answers
220 views

Primary/Elementary Pedagogy: What is the rationale for the absent '+' in mixed fractions?

Why are elementary students taught to represent one and a half as 1 1/2 rather than 1 + 1/2? This mode of expression seems standard throughout at least North America. I think it is bad pedagogy for a ...
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2answers
39 views

Getting the Amps from Watts, Amps and the voltage of a line

What amperage capacity should the supplied wired be rated for a refrigerated fixture which has a 208V power supply and the following loads? 4 Evaporator fan motor rated at 9W each 4 Evaporator fan ...
6
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2answers
664 views

How to explain lagrange multipliers to a lay audience?

So I will be giving a seminar to a scientifically mature lay audience (think bio/social science undergrad level). I have been told that I should count on less than half the audience to have experience ...
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6answers
564 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. ...
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6answers
659 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 ...
3
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3answers
149 views

What Will Happen Without Decimal Expansion?

After a discussion on the complexity of decimal expansion (such as $0.\bar{9}=1$), some of my students (middle school) decided to throw away the decimal expansion of some numbers! Namely, the numbers ...
7
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1answer
409 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 ...
0
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2answers
263 views

What exactly do math education PhDs do?

I have been researching this for the past hour or so, but I have not really found a sufficient answer. What I have found is that vaguely, math education PhDs set policies for math education. However,...
2
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1answer
120 views

Bridge the gap to university mathematics [closed]

Can anyone suggest some good books to help an high school student to "bridge the gap" to university math? I've heard of http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316 and http://...
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votes
4answers
1k views

Solve without a calculator: What is the possible value of 2*((1+1/100)^100)?

What is the possible value of $2·((1+\tfrac{1}{100})^{100})$? Google will give $2·((1+\tfrac{1}{100})^{100}) = 5.40962765884$. How can I find the possible value without Google or a calculator? How ...
28
votes
8answers
3k views

Active learning vs Passive learning in Math

I am trying to improve how I learn in general but specifically in math and a common suggestion I keep coming across is the difference between active learning and passive learning. The problem is, most ...
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1answer
54 views

Variational characterization of gradient?

Let $f: \mathbb{R}^n \to \mathbb{R}$ be a differentiable function. One way to define the gradient of $f$ is as the vector whose inner product with any other vector gives the directional derivative in ...
4
votes
2answers
189 views

Is there a systematic way to detect overcounting in simple combinatorics?

TL;DR: In simple combinatorics problems, is there a systematic way to detect overcounting before computing the counts and comparing them? Is it simple enough to be taught to undergrads: At my ...
1
vote
1answer
111 views

maths for a strong visual spatial thinker with sequential processing weakness?

Can someone with superior visual spatial thinking ability but weak sequential/word ability be successful in university maths and beyond? For example, for real analysis, would definitions with lots of ...
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votes
4answers
1k views

Most useful books for a math undergrad

What are the most useful books an undergraduate in math should read? I found Alock's "How to study as a math major" and "how to study for a math degree" very useful. Are there any other good readings ...
0
votes
1answer
542 views

Max(x,y) and argmax(x,y)

I am writing my report and I got confused on this simple maths concept. What I need is: I have 2 values i.e x and y and I want to use the maximum of either x or y as my length. So which statement is ...
0
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1answer
46 views

How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
-1
votes
1answer
1k views

Determine sin cos and tan from slope? NON CALCULator

I am used to finding this by drawing the triangle and knowing the angle measurement. With the angle measurement i can find sin cos and tan. But i dont have angle all I have is line. I have put a ...
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1answer
92 views

The right angled triangles ABD and BCD?

AB=5cm BD=4cm and angle ABD=x Find the exact value of cos(ABC) this is the trangle...: https://twitter.com/JxstyBiebs/status/432919494466752514
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4answers
57 views

The graph of the function is $g(x)=x^3-2x^2+x+1$ and the tangent to the curve is at $x=2$?

a) Find the equation of the tangent to the curve at $x=2$ HELP and then b) Determine the angle that this tangent makes with the positive direction of the $x$-axis Please help I really need to ...
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vote
2answers
78 views

General solution to the integral of 4/x

A friend asked me what was the solution to the problem (which was on his test)$$\int\frac4xdx$$ I proceeded to tell him that you can take out the 4 in the numerator, and then just take the integral of ...
0
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1answer
61 views

Mean and Variance Statistics

$X_1, X_2, \dots , X_n$ ~ i.i.d $U[0,1]$ a) Find the mean and variance of $lnX_1$. b) Let $0\le a \lt b$. Find the $\lim_{n \to \infty} P(a \le (X_1,X_2, \dots ,X_n)^{(n^ -0.5)}*e^{ ( n^{0.5})}\le ...
9
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1answer
432 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 ...
4
votes
3answers
2k views

How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...
5
votes
1answer
198 views

Software for basic math notes at 5th to 10th grade level (10 to 15 years old)

So I've looked around, here and otherwise, but sadly can't seem to find quite what I'm looking for. I don't know if it even exists, I figured it was worth trying to ask, though. I've found plenty of ...
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1answer
2k views

Applications of infinity in real life [duplicate]

I am writing a mathematical essay and would like to focus on the concept of infinity. I am not sure of any real life applications of infinity to write about or some way to narrow down the topics. Does ...
1
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3answers
658 views

How would you explain confidence intervals to a beginner with very weak algebra skills

Let us say that you are taking AP Statistics. The prerequisite is a passing grade of D or above in Algebra II. The kids that you are working with struggle with algebra and do not retain information ...
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2answers
173 views

Resources for teaching introductory course in differential equations?

The first time I was assigned to teach an introductory linear algebra course, I was able to find a number of resources which were helpful. For example, Linear Algebra Gems and Resources for Teaching ...
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1answer
37 views

Teaching School Algebra via Programming

It seems that there are ideas to teach school algebra (i.e. using variables, working with algebraic expressions and solving equations) via computer programming. I need a book or a collection of ...
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2answers
368 views

How to deduce this puzzle

Every station on the railway system sells tickets to every other station. Some new stations were added. 46 sets of additional sets of tickets were required. How many new stations have been added? How ...
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2answers
278 views

Convention verses memory: The quotient rule v product rule for derivatives

I have long wondered why the product rule is taught the way it is. ${ d(UV)=Udv+Vdu}$ Don't get me wrong, I am not a complete NOB when it comes to calc, but the quotient rule states $${d(\frac {U}{V}...
4
votes
1answer
224 views

To take notes or not to [closed]

Is it really better to take notes as a maths major or are some better without them? I've never gotten used to taking notes and I've never done it. But I'm wondering if I'd improve if I'd start doing ...
0
votes
1answer
556 views

How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
1
vote
1answer
211 views

How to get a top-notch Math education (high school level) online?

For the past years, it is becoming more and more accessible to get college level content from many different sources, and, if one is willing can get very far with his math education (not only by ...
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0answers
86 views

What is the less confusing way to explain confidence intervals to a beginner

Let us say that you are back in high school and you have a friend who has missed class for a week. He needs information to be spoonfed to him, because its not his style to overthink. If you push for ...
2
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1answer
108 views

How to solve this Mystery with Mathematics

I read a mystery in a book but I can't solve it with Mathematics. The mystery is: "I have tripled my nephew's age, and 5 years ago I have 5 times from his twin brother age. What is my age now?" In ...
0
votes
3answers
114 views

Baloney detection kit for Math

There are folks who claim they proved Fermat's Last Theorem, Riemman Hypothesis offering no more than a half a dozen pages (sometimes one or two pages) of proof, very few if any citations of previous ...
16
votes
3answers
460 views

which exact integration techniques belong in a first year calculus/analysis course?

At our university we are now discussing changes to the course contents and there is some heated discussion regarding integration in the first year calculus courses. Currently, the techniques of exact ...
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1answer
63 views

How Should the First Sessions of an Undergrad. Course Be?

Form a teaching perspective, the first sessions of an undergraduate mathematics course are of a great importance. They can make clear the aims of the course, and point out to the main problems and ...
4
votes
1answer
93 views

Natural discontinuities

As I stare at a cube-shaped building whose side has length $100$ meters, while walking westward parallel to its north wall at a location $100$ meters north of the building, the distance to farthest ...
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vote
2answers
959 views

Math Riddles #10 - Car Meter Riddle

Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms I need to travel so my car meter find another palindrome?
3
votes
1answer
74 views

Figuring out deficiencies in math education.

I'm mostly self-taught and while I know (and use) many advanced mathematical topics, I often enough find holes in my understanding of lower level math. Is there an exam (or series of exams) I could ...
2
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1answer
139 views

What is the contribution of group theory to topology?

An answer for a question on MathOverflow.net which asked for some recommendations on textbooks for books in topology received the following comment: "It's a great book to introduce applied ...
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1answer
64 views

What are some helpful pre-requisites/hints/encouragement for going through Theodore Frankel's “Geometry of Physics” in a self-study?

I plan on working through "Geometry of Physics" by Frankel. I keep on running into little snags here and there, and I am wondering if that's just part of the process, or whether I am ill-prepared. ...
1
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0answers
115 views

Why are hyperbolic trigonometric functions avoided in (my) high school and early post-secondary school?

I remember seeing hyperbolic trigonometric functions (sinh, cosh, tanh, etc.) in my precalculus textbook back in high school and see them today in my calculus textbook. However, I have not had a ...
10
votes
2answers
315 views

How to introduce category theory to a high school audience?

I am a mathematician with background in Category Theory. I have been asked to give a 20 minute talk about my area of research to an audience of talented high school students and school mathematicians (...