How to Study Mathematics | Illinois Wesleyan University

The first major difference between high school mathematics and college mathematics is the amount of emphasis on what the student would call theory---the precise statement of definitions and theorems and the logical processes by which those theorems are established. To the mathematician this material, together with examples showing why the definitions chosen are the correct ones and how the theorems can be put to practical use, is the essence of mathematics. A course description using the term ``rigorous'' indicates that considerable care will be taken in the statement of definitions and theorems and that proofs will be given for the theorems rather than just plausibility arguments. If your approach is to go straight to the problems with only cursory reading of the ``theory'' this aspect...

The first major difference between high school mathematics and college mathematics is the amount of emphasis on what the student would call theory---the precise statement of definitions and theorems and the logical processes by which those theorems are established. To the mathematician this material, together with examples showing why the definitions chosen are the correct ones and how the theorems can be put to practical use, is the essence of mathematics. A course description using the term ``rigorous'' indicates that considerable care will be taken in the statement of definitions and theorems and that proofs will be given for the theorems rather than just plausibility arguments. If your approach is to go straight to the problems with only cursory reading of the ``theory'' this aspect of college math will cause difficulties for you.