/sci/ - Science & Math

>>8557003

Harvard
Princeton
Yale

>>7428709
>>7428652

A standard textbook like this may be fine in a class where the professor takes the incomplete proofs presented in the book and completes them in lecture and discusses the proof techniques used and reasoning behind them and then from there answers and clarifies any questions. At this point the students in the class (that paid attention) could go back and fill in the details to the other proofs and be able to do the homework assignments. This is pretty standard at any university math class. Maybe even an independent study class where the professor guides the students through the areas she struggles in.

But:
These books don't serve so well the students that aren't in a university setting or don't have access to other classmates or professors to clarify points, or check their work. The newb math student might think he has the correct logical reasoning and correct proof but might be missing a step here or there that doesn't necessarily follow from the axioms. This student will blindly just continue through the material having no idea if they are truly understanding the concepts or not. Maybe they get stuck on a problem and can't figure it out and the "hints" section says check theorem X but they do and they can't deduce it further. A typical university student will be able to present their work to the professor and get guidance "Use theorem X, do similar argument we did in class set k equal to this and derive from there to get your result and boom student is done. But the student NOT in university doesn't have this opportunity. In more recent times this has changed with the invention of stackexchange though, but stackexchange is no substitute for an actual university professor lecturing on common theorems/proofs and from there giving out assignments. The former student will be ahead of the student that is still stuck on the most ~basic~ incomplete proof they don't understand that the former student's university professor proved in class.