# Mathematics Educators Stack Exchange 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

### 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

### 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 ...

### 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

### 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 ...

### 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)...

### (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 ...

### 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

### 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 ...