Question

WHAT MAKES THAT MATHEMATICAL CONCEPT IMPORTANT TO EVERY STEP?

Answer 1

i wrote this page for students at the  You may find it useful whoever you are, and you are welcome to use it, but I'm going to assume that you are such a student (probably an undergraduate), and I'll sometimes pretend I'm talking to you while you are taking a class from me.

Let's start by me asking you some questions. If you are interested in some suggestions, comments, and elaborations, click on the Comments. Do so in particular if you answered "Yes!". (In making the comments I assume you did say "Yes!", so don't be offended if you didn't and are just curious.)

Do you feelThat being lost in mathematics is the natural state of things? Comments.That lectures and textbooks are incomprehensible? Comments.That the amount of material in any math course is so overwhelming that you (or anybody else) could not possibly absorb it? Comments.That mathematics is just a collection of formulas and theorems that one somehow has to cram into one's head? Comments.That the solution of problems requires a collection of tricks whose conception was based on a generous allowance of magic? Comments.That math courses are just hurdles one has to cross as an undergraduate student? Comments.That mathematics is irrelevant? Comments.Are you taking mathematics only because it's required? Comments.Are you frustrated working through heaps of meaningless problems that are all alike? Comments.Does the thought "I can look it up if I have to " occur to you frequently? Comments.When solving assigned problems, do you often think "What does he want us to do?"? Comments.Do you find yourself frequently searching through literature in vague hopes of finding a helpful formula or theorem? Comments.Do the proofs you find in your textbook or in the literature look contrived to you? Comments.Do you often wonder why your teachers make you study a piece of mathematics that could not possibly ever be useful? Comments.Are you upset that the teacher insists on doing proofs rather than telling you how to solve problems? Comments. >Do you often wish your teacher would do more examples? Comments.When you are trying to solve a problem, do you find yourself frequently spinning your wheels, hoping for an idea that never comes? Comments.Do you ask questions in class? Comments.Do you sell your textbook after you take a math class? Comments.Do you find it difficult to prepare for an exam? Comments.Do you worry about your grade a lot? Comments.Do you skip class a lot? Comments.Do you often leave class early? Comments.Do you often repeat courses? Comments.Do you cheat on exams? Comments.

If your answer to all of these questions is a resounding "No!" then you should read no further and return to the study of mathematics. I'd also like to meet you, please drop me an e-mail! Otherwise I'm hoping that this page has something to offer you (and of course you may send me an e-mail anyway). I believe that many students struggle with mathematics only because they don't know what it means tounderstand Mathematics and how to acquire that understanding.

The purpose of this page is to help you learn how to approach mathematics in a more effective way.