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 step stone module such as number theory, group theory, combinatorics, and real analysis. What should I cover to make this 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.

Are there any good images that can be used as a hook for an elementary number theory course?

I am writing an introduction to a first course in elementary number theory. The topics are linear Diophantine equations, modular arithmetic including FLT and Euler's Generalization, quadratic residues and Non - linear Diophantine equations. How can I write an introduction to this showing linkage between the various topics and hook potential students to do this course? What is the motivation on covering these topics?