Introduction to Pure mathematics

[matqkks]

I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a stepping stone module such as number theory, group theory, combinatorics, real analysis.

What should I cover to make this an interesting and be used as a hook for them to be motivated to do pure mathematics? Should have an impact on them.

It will be a first-year university undergraduate module.

 

[pka]

I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a stepping stone module such as number theory, group theory, combinatorics, real analysis.
What should I cover to make this an interesting and be used as a hook for them to be motivated to do pure mathematics? Should have an impact on them.
It will be a first-year university undergraduate module

First, I would look for a textbook designed just for such a course. There is little need to reinvent the wheel.
The textbook A Transition to Advanced Mathematics by Doug Smith, et al, is such a text.