Community Digest

Top new questions this week:

College undergraduate geometry courses

I am interested in learning how a course in geometry is employed today at undergraduate colleges/universities in the U.S. On the one hand, such a course seems to serve as an optional (rarely required) ...

undergraduate-education geometry discrete-math differential-geometry  
asked by Joseph O'Rourke 8 votes
answered by amWhy 4 votes

Intuition explanation about Lebesgue measure zero of the rational numbers

This is a question about the intuition of the rational number having measure zero. Let us consider followng proof: Let $I = [0,1]$ and $Q = \mathbb Q \cap I$ and let $\lambda$ be the Lebesgue measure. ...

intuition series infinity  
asked by flawr 1 vote

How can I teach $\frac{300}{200}$ to 10 years old students while s\he knows canceling the zeroes rule?

I am teaching math to a 10 year old student. He learned that $$\frac{300}{100}=\require{cancel}\frac{3\cancel{00}}{1\cancel{00}}=3$$ and $$\frac{6000}{300}=\require{cancel}\frac{60\cancel{00}}{3\...

mathematical-pedagogy teaching fractions  
asked by C.F.G 1 vote
answered by Pedro 5 votes

Exercises for explaning homothety, homothetic center, similarity on line and plane, free vector and vector space

I need the collection of exercises for such topics as: maps and transformations, composition of maps homothety, rotation homothety, homothetic center similarities of the line and the plane free ...

undergraduate-education algebra geometry linear-algebra exercises  
asked by paus 1 vote

Greatest hits from previous weeks:

Real-World Applications of Logic

When introducing logic in a first semester university course, the examples I use are often quite artificial. One example: One of three kids (Annie, Bob, Chris) has broken a window. Annies says "it was ...

undergraduate-education examples logic  
asked by Anschewski 17 votes
answered by adamblan 12 votes

Fun set theory for kids

Are there some fun results in set theory to set as landmarks while introducing to kids? For example, while introducing graph theory to kids, I could explain isomorphism via a pentagon and pentagram, ...

secondary-education primary-education set-theory  
asked by athos 14 votes
answered by A. Goodier 21 votes

How to explain the difference between the fraction a / b and the ratio a : b?

I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the ...

undergraduate-education primary-education fractions  
asked by Abdallah Abusharekh 14 votes
answered by Burt Furuta -2 votes

Is there a simple example that empirical evidence is misleading?

Suppose that I want to show a student that empirical evidence in mathematics is not enough and we do need proofs, what kind of examples can I use? By empirical evidence, I mean that (most of the time)...

undergraduate-education  
asked by ablmf 16 votes
answered by Jasper 29 votes

(How) Do American undergraduate math programs teach complex numbers?

What kind of exposure to complex numbers can you expect in mathematics majors at American colleges? I teach at a very large public university. It occurred to me that it is possible to graduate in ...

undergraduate-education usa complex-numbers  
asked by shuhalo 16 votes
answered by Xander Henderson 28 votes

Why is learning mathematics compulsory?

In most education systems, Mathematics is a compulsory subject from primary school all the way to the start of university. A common reason given is that essential concepts like addition and ...

secondary-education curriculum  
asked by Axel Tong 40 votes
answered by Ben Crowell 68 votes

Beautiful planar geometry theorems not encountered in high school

I would like to impress college students (undergraduates in the U.S.) that there is more to planar geometry beyond what they learned in high school. I would like to show them beautiful theorems they ...

undergraduate-education geometry  
asked by Joseph O'Rourke 36 votes
answered by Jyrki Lahtonen 30 votes
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