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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Literature for ODE undergrad class

I am teaching a undergrad ODE class. I am looking for some good (introductory) articles with applications of ODE's. In particular I would like some motivations for some special functions (Legendre, ...
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2answers
117 views

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 ...
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://...
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 ...
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1answer
45 views

Proving that there exists $w$ such that $4x < 6w < 6x$ and $\gcd(w,\frac{x\#}{6})=1$ where $x \ge 7$ and $x\#$ is the primorial

I am trying to show that for any integer $x \ge 7$, there exists $w$ with the following properties: $4x < 6w < 6x$ $\gcd\left(6w,\frac{x\#}{6}\right)=1$ I thought that this would be pretty ...
2
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1answer
274 views

Motivations for Prime Factorizaton

I'm at the beginning of some middle school math sessions on divisors, gcd, lcm, and prime numbers. It's the first place in the curriculum that the students encounter the three latter concepts ...
2
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2answers
128 views

Pre Algebra Text book or online

I have a kid who just started middle school. I would like to introduce them to pre algebra. I would like her to know the fundamental concepts. Just like "What is mathematics" book, if there is a book ...
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1answer
334 views

Book about Tensor Product of Vector Spaces

This subject is very commun for any book about modules. However, some undergraduate majors have Linear Algebra course before the Abstract Algebra one (where we treat about modules) and it is not ...
2
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1answer
120 views

How to document undergrad math knowledge?

If you did a degree which is low on math (read economics, psychology), but want to proceed to a more mathematically loaded master, how would you document your knowledge? Are there standarized ...
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3answers
166 views

Derivative in interesting way

I am supposed to give a 15-20 minutes math lecture, where I am expecting around 20-30 people. The lecture is about derivative. Since this would be my first "class", I would appreciate any suggestions ...
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2answers
3k views

Number of Lines Passing Through a Given Point in the Plane

How can one prove that infinite number of lines pass through a given point in plane, using Euclid's axioms (or Hilbert's, if necessary)?
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2answers
99 views

What are some good games for teaching maths to children?

I am due to teach maths to a ten-year-old. I'd like to try out some games such as Nim and Conway's Soldiers. I've found this list on Wikipedia but Googling for more just gives me a load of Flash games....
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1answer
167 views

What is a Math Learning Graph?

I went through may topics on learning maths effectively, learning math at later years (I am 30, so I read it to get motivated) One thing I missed is a natural flow of topics that one must learn to ...
2
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3answers
209 views

Learning times tables?

I have some weird gaps in my learning, I can do lambda calculus and some basic category theory, but I do not know how to do some of the most basic of arithmetic. (I am in my mid 20s) Seeing this gap ...
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2answers
21k views

Why are prime numbers important in real life? [duplicate]

What practical use are prime numbers? Why do we emphasise the teaching of prime numbers?
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1answer
245 views

4 big ideas in algebra that have rich connections to other fields? [closed]

In his controversial post criticizing high school algebra, Grant Wiggins issued a challenge to his readers: Can you identify 4 big ideas in algebra, ideas that not only provide a powerful set of ...
2
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1answer
374 views

What textbook should I get to self-learn Calculus? [duplicate]

I did not have the option to take calculus during high school. I would like to pick up this subject during my free time. I am a software engineer. I would like to improve my understanding of maths. ...
2
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2answers
172 views

At what education level is this “simple” problem adequate?

Given the following problem: Alice, Bob and Carl stand on a straight line. Alice is one rod away from Bob. Dana stands one rod away from both Bob and Carl. Carl is as far from Alice as Alice ...
2
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1answer
65 views

Any comprehensive material to revise the mathematics

I left school long back and so my mathematics knowledge also fades out. I am trying hard to re-collect the basics about log / permutaion / combination / probability / polynomial equations. I tried ...
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1answer
1k views

Complex division: polar form vs complex conjugate

The original problem In an electricity course which I volunteered to help with, the students solve circuits using phasors. Using phasors requires a good knowledge of complex numbers arithmetics, ...
2
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1answer
362 views

any Math game for kids?

I need to plan a "game" for kids about 10-11 years old that involves mathematics and some physical activity or game. It must be short-time and not very difficult because it's a stage of a big game. ...
2
votes
1answer
612 views

General definition of growth in mathematics

From high school math one knows "linear growth", "exponential growth", "logistic growth", "bounded growth" etc., but is there a common accepted general definition of "growth" which covers the special ...
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2answers
388 views

Good math software [closed]

I have finally decided to go more deep into math and cs, so to do that I will need proper tool, math tool. Could you please tell me what's the best open source math tool on the web today, since as far ...
2
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1answer
117 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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3answers
327 views

I would like to buy references in order to review and study mathematics [closed]

I am an ESL learner and most of the time I am able to understand English but In my courses, we don't study mathematics, and I think that it is a mistake or wrong. 1-What are really the best sources (...
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0answers
46 views

Online Video Lectures for Graduate Level Mathematics?

I am wondering if there is a nice compilation of good video lectures in graduate level mathematics? I mean a website, or a forum, or maybe something like course-era (which is mostly undergraduate ...
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0answers
82 views

Is group theory and in general pure maths useful in applied mathematics?

I've just finished the first year of Mathematics at University. I've already encountered groups, in a soft mini-course that took around half semester. My idea would be to study applied mathematics, ...
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0answers
59 views

Where to start with Euler and Ramanujan?

What are the specific qualifications for directly studying Euler and Ramanujan's works.Is Hardy's "A Course in Pure Mathematics" a good start?
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0answers
25 views

Which FOL consequence relation is better (to teach)?

Backstory: I had problems of accepting Mendelson's rule of Generalization (it's $(A(x) \vdash \forall x, A(x)$). Surfing around the net, I found this post which explained the situation for me: http:/...
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45 views

Methods for solving for partial fraction coefficients.

When I present partial fraction decomposition, there are typically two approaches to solve for the coefficients of the fractions: Clear the fractions, multiply out the products, and equate ...
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0answers
31 views

E versus e when using scientific notation

When I was calculating pressures in different units, I decided to use Google out of laziness. First I tried: 1.013e-10 mbar and received a result of: ...
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0answers
63 views

Increased Math Productivity on Mobile Devices [closed]

I have been answering questions on Math.SE for a (relatively) short time now, and I have found that answering questions on my Android phone is somewhat of a nightmare. I end up commenting much of the ...
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2answers
42 views

Proving of this trigonometric identity

$$\frac{\cot \beta}{\csc \beta - 1} + \frac{\cot \beta}{\csc \beta + 1} = 2 \sec \beta$$ What I've done: $$\frac{\frac{\cos \beta}{\sin \beta}} {\frac{1}{\sin \beta} +1} + \frac{\frac{\cos \beta}{\...
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55 views

What makes a good mathematical poster? [closed]

During my second year of university I have done some assignments and some papers, but this is my first time I have to make a mathematical poster. What could make my poster stand up. So up to now I ...
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0answers
25 views

What is a point to give the Abel's Test for product series convergence a place in introductory textbooks?

One of the hypotheses of the Abel's test for product series convergence is stronger than the corresponding Dirichlet's test; that is, the former imposes the convergence of one of the series and the ...
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0answers
52 views

What to do when finding “complex” result by accident?

This happened a couple of times today. While working on some problems, you find unexpected relationship between objects, which are not obvious to find directly. For example today I found out that $$\...
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0answers
31 views

Powerful pictures or plain proceedings?

After tutoring someone about polynomial manipulation, my mind went back to this equivalence: $(a+b)\times (c+d)=ac+ad+bc+bd$ I realized that, while it can be memorized as it is, it has a very simple ...
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40 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
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0answers
53 views

Circular Logic and Continuity

So, I was doing a Calculus problem a few minutes ago and just recalled something that my real analysis professor said during a lecture years ago... To provide context, take the function $f$ defined ...
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0answers
55 views

Is the precise definition of a limit worth covering in Calc 1?

I'm teaching calc 1 this semester and am trying to decide if I should cover the precise definition of a limit. My first impression was that I should. It helped me to gain a deeper understanding of ...
2
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1answer
91 views

Alternative proof that base angles of an isosceles triangle are equal

The "classic textbook proof" of equality of base angles of an isosceles triangles which I studied in my school days is as follows: Let $\Delta ABC$ be a triangle with $AB = AC$ and let $D$ be the mid ...
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2answers
202 views

What do we mean by 'defining a function'?

First I will start by quote from Wikipedia about function's defining methods : There are many other ways of defining functions. Examples include piecewise definitions, induction or recursion, ...
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37 views

How should the topic of frequency domain be taught?

This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics, Digital Signal and image Processing. Some of concepts which are very ...
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0answers
90 views

Argument for the zero vector not being defined as an eigenvector

Two days ago, my lecturer of Advanced Numerical Methods gave a review on the topic about eigenvalues and eigenvectors. Just as the lecturer presented the definition of eigenvalues and eigenvectors, a ...
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0answers
24 views

Learning Logic and Metric Spaces

I want to learn how to manipulate metric spaces. I have been reading this book about metric spaces. http://www.amazon.com/Metric-Spaces-Springer-Undergraduate-Mathematics/dp/1846283698/ref=sr_1_1?ie=...
2
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3answers
128 views

Good math books to get on with my education? [closed]

im looking for a set of good math books. Since i live in norway im going through the norwegian school system, where i choose to go whats called a electrical line. Im not gonna go to deep into the ...
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0answers
36 views

Determine the set of points $M$ of affix of $z\in\mathbb{C}$

Determine the set of points $M$ of affix of $z\in\mathbb{C}$ such that there exists at least one real $t$ satisfying $z^2=t(t-i)$ My attempt: We look for the form $z=x+yi$ and we want there is a ...
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0answers
77 views

How to decide which theorems from textbook to prove

I've noticed that theorems in textbooks roughly come in two varieties: those that are worth trying to prove yourself, and those that aren't. I'm not going to try and give criteria for "worth trying" ...
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0answers
45 views

Ratio Question (Primary School)

Now, there are 6 students who are sharing 4 desks at the library. While 4 of them are using the desks, the other 2 students have to wait and watch. If they have to use the desk for the same amount of ...
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1answer
269 views

Solve a problem using vectors

The purpose of this problem is to use vectors to show that the medians of a triangle all meet at a point. First, I have to show that $P$ (see the picture below) must lie two-thirds of the way from $B$ ...