I am a first year CS undergraduate taking a module on differential equations. For part of this module I did a personal project on the motion of simple harmonic systems (damped and undamped) which I recently found out was in fact something we would briefly cover at the end of the module. From my project I have a very nice set of interactive graphs which I made to aide my learning and understanding of the subject. When I found out that the subject of my project was something that would be covered in the module it occurred to me that this might be worth offering to my professor to possibly share with other students or something to that end. However as soon as I thought this I realised that it might come across as arrogant and I'm now unsure of what to do. Would it be worth emailing my professor about this?
Providing material to your teachers is all about HOW and WHY you provide that material. If you're providing this material purely as an extra resource than provided you approach it as that, you shouldn't appear arrogant. If you are doing this to prove your knowledge of the topic or to try and 'one up' the instructor, then yes this is gonna be seen as arrogance.
I suggest an email similar to the one below: "Dear xxxx, Looking ahead in the topic I noticed that we are covering yyyyyyy. I have previously done a project on this topic and thought that it might be useful in trying to explain the concepts. I have attached all documents on the project for you to review and would love an opportunity to discuss my work with you.
Thank-you for your time, I look forward to hearing from you, " Etc...
That should get your point across without portraying arrogance. How you conduct yourself in any meetings or class however, that is really up to you.
Also be aware that the teacher may choose not to use your project or other materials. That is their choice and their right. They may choose to include it in subsequent versions of their topic.