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Questions tagged [axioms-foundations]

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4
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4answers
211 views

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, ...
8
votes
3answers
192 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 ...
10
votes
5answers
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 ...
8
votes
3answers
249 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 ...
3
votes
2answers
231 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 ...
11
votes
1answer
181 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 ...
6
votes
2answers
334 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 ...
2
votes
1answer
186 views

Is derivation based Math a good way to teach my 5 years old daughter addition? [closed]

I love deriving formulas. I am pretty good at Math. Maybe because I have a little asperger syndrome. Most people don't learn Math that way. Why not? I recently taught peano axioms to my daughter. ...
1
vote
3answers
222 views

How to tell the Axioms from the Assumptions

Are there criteria, that allow one to decide, whether something, which isn't a consquence of a theorie's axioms, but is exploitet in a proof, is a further axiom and not an assumption? A concrete ...