What should be the order of things on an introduction to pure maths?

[matqkks]

I want to produce a resource that has a narrative and includes the following topics:

Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation.

It is in aid as an introduction to a number theory module.

How should I order these so that the end document has a narrative and is coherent, not just disjoint set of topics?

 

[fresh_42]

I would proceed chronological and by great mathematicians: numbers, Diophant, Fermat, Euler, Gauß, Dedekind and Cantor, maybe Vieta, Abel and Galois, too. I'm not sure whether this would cover such more or less trivial things like binomial formulas or notation, i.e. whether the research to figure it out is worth it, but at least it provides a general route.

 

[fresh_42]

E.g. I once searched for the origin of $0$ which in my opinion is the crucial step: the first time we named something that isn't there! IIRC I ended up in India some 5,000 years ago. The ciphers as we write them today made their way from India over Arabia to Europe and into the world. Many think it was arabic, but this isn't true. They got it from India, e.g. from a book of Aryabhata. The ciphers as we write them are significantly older, but also from India.

Then you can decide whether you will follow their way, or make a detour to ancient Greece and geometry. I would end the story with Andrew Wiles, so it becomes a nice little narrative. However, it takes a bit of time to tell it.