# Questions tagged [axioms-foundations]

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### Would teaching nonstandard calculus in an introduction calculus course make it easier to learn?

Nonstandard calculus is a reformulation of calculus that is based on infinitesimals instead of epsilon-delta definitions. Of course, people had tried to use infinitesimals in calculus before; in fact, ...
254 views

### Introducing an axiomatic method to high-school students

As well as mathematics I teach IB Theory of Knowledge, which includes mathematics as an area of knowledge. The class are mainly not students with a maths focus, although they all study at least some ...
1k views

### Book request: teaching proving and reasoning at an American university

I am a European postdoc who recently teaching at a large public university in the United States. I will have to teach a course for undergraduate students that introduces them to proving and reasoning ...
276 views

### Is there a resource that formally develops the topics of elementary algebra?

Let's say you're a university lecturer who regularly teaches remedial and/or college algebra courses. A standard textbook for such a course usually starts out with a series of facts about real number ...
274 views

### Mathematics Branches and Foundation

Hi I hope every one is fine , I am an Electrical Engineer. I asked before about real and complex analysis because I am interested in Signal Processing also I am interested in coding theory and ...
188 views

### Has someone written an essay on the role of axioms in mathematics (suitable for undergrads)?

I'm just starting up the academic year (yes, it starts in February here in the Southern Hemisphere) teaching a 2nd-year Introduction to Pure Mathematics class. For general background, I would like to ...
340 views

### Why is the axiom of choice not taught from the start to mathematics undergraduates?

I've recently discovered that the following theorems require the axiom of choice to be proven: every surjective function has a right inverse. a real-valued function that is sequentially continuous ...