Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

How to Figure Things Out

This page describes some proven ways in which you can be more efficient and effective when actually doing mathematics with paper and pencil. It focuses on how to do what you do. (Almost all the of other pages in this course focus on what to do.)

Students often think that the only purpose of figuring things out is to get the answer with the minimum amount of fuss and effort, and to get it over with. Actually there are several objectives:

Luckily, the last objective is perfectly consistent with the others if you think in terms of the whole set of problems and exercises that you do in the course of the semester. If you guard carefully against errors and ensure that you can correct them easily soon after they occur you save time. If you learn what there is to learn in each problem then you have to do fewer problems and exercises overall, and you are able to do future exercises more quickly and with less frustration.

Of course, how to figure things out is a highly personal process, and what works for you may not work for somebody else, and vice versa. However, I wrote this page because over and over I see students approach problems in a way that does not work at all, for them, or anybody else. So here are some suggestions:

You'll find examples for many of these techniques throughout these web pages and the solutions of the homework problems.