(math professor here) > I worry there are some dots I never connected This will always be true for anyone learning math in any circumstances. The beauty of t

(math professor here) > I worry there are some dots I never connected This will always be true for anyone learning math in any circumstances. The beauty of the subject is that there is always more to unravel, always more connections to make. Don't worry about what you didn't learn -- although follow-up classes to pick up some of the loose ends are always recommended :) I don't believe that there is any one royal road to mathematics. Different people learn in different ways, and come with different backgrounds. For example, some people like to learn all the foundations and formalism up front, and then build on it. Personally, I like to learn a bunch of examples first, so that when I see the formalism I can relate it to what I already know. Personally, I definitely appreciate foreshadowing (as you do) and try to incorporate it in my own teaching. You'll find a lot of good math materials out there at higher levels, but generally speaking they will cover one subject at a time, as this is what creators enjoy creating. For example one book I like is Underwood Dudley's Elementary Number Theory (can be bought cheaply online) -- and one reason is that the author gives elementary proofs which mimic the structure of the higher-level formalism (i.e. abstract algebra), so that this formalism feels familiar by the time you actually learn it. This somewhat aligns with your request for "foreshadowing". One of my colleagues said that this book drives him crazy for the same reason -- he thinks you should learn the higher-level formalism up front, so you can put it to good use. No one can say that one approach is better or worse than the other, just that it worked better for them.