How does advancing through the math major work? [closed]

Solution 1:

Questions like the OP's aren't rare, especially among maths majors (or simply bright young students interested in mathematics). The truth is that you've been lied to for most of your life as to what mathematics are. Mathematics aren't a bunch of formulae or dry steps that you must memorise, or tedious calculations that you have to perform for hours on end.

That "lot of proofs and logic" is what mathematics are. Those formulae and calculations weren't just given to us by Prometheus; they were discovered, over hundreds and thousands of years, by great minds labouring within the frameworks of logic and pattern-seeking that have come to be known as mathematics. Each time you perform a calculation, you aren't really doing mathematics...you're applying the mathematical work of someone who's gone before. Every math problem you've ever solved up to this point was really a specific example of a more general theorem, which you can only rely on to be true because someone verified it by a proof.

Real mathematics is just that: going from a small set of rules (often called axioms), constructing objects that fit those axioms, and seeing what patterns emerge when those objects are manipulated. When solid patterns can be verified by logical steps, we call these patterns theorems, and use them to refine the framework we're working with, build new objects, and survey new patterns.

If that's not your cup of tea, it's perfectly alright; if you really are interested in calculation, there are lots of engineering disciplines that will give you as many hours of algebraic recitation as you could ever want. And it isn't really your fault for having this impression...the entire public school system of North America (if not the whole of the world) is geared toward instilling this gross misapprehension of mathematics into all students' minds. If you like patterns and solving puzzles, stick with mathematics...if not (and, again, that's fine!), you may want to find a discipline more suited to your tastes.

EDIT: Here is a link to an excellent paper by William P. Thurston, which gives a much greater insight into the workings of real mathematics (and the thinking of real mathematicians) than I have here exposed. I heartily recommend reading it if you want to get a better feel for what you're setting yourself up for with a mathematical education.

Solution 2:

Did you sign up to be a math major hoping that you would be doing tedious computations all day? If so, why?

Math is all about logic and proving things in a rigorous way. What you're seeing in discrete math is a taste of what true math is really about. Maybe if you go down the applied track there are more computational things (I honestly don't really know, I just do pure). But you should get used to the idea of proving things, it's much more fulfilling than just performing computation once you get into the swing of things.