[copperx]

I've always been intrigued by higher math, but I never got further than Calculus III, differential equations, and proofs by induction in discrete math.

Do you have a suggestion on how to get into real math?

Could taking a class in Abstract Algebra be a first step? I've thought about auditing the class at a local college, but the syllabus scared me. Groups? Rings? I've never heard about these things in any class.

Any suggestions?

[BeetleB]

If you've already done diff eq and calculus, you're ready for real analysis.

Abstract algebra has little prerequisites, so you can definitely do that. However, if calculus clicked with you, then you may find real analysis more to your liking. If you've done enough physics/engineering that requires calculus, you probably won't have trouble connecting the analysis material to your experience.

For me (engineering/physics), abstract algebra was ... abstract. It felt like a bunch of abstract ideas and structures that mathematicians invented to occupy themselves. Of course, that's not at all true in reality, but it was mostly irrelevant to my real world problems.

PS: If you've forgotten your calculus, don't worry - most real analysis courses/books start from scratch and don't assume prior knowledge.

[bkallus]

Taking a course in abstract algebra is a good first step. A first course in abstract algebra is supposed to introduce you to groups and rings, so you won't be out of place.

You might also consider taking a proof-based course in linear algebra.