This short introduction explains the aim and structure of this book How to Study as a Mathematics Major, and suggests that different groups of readers might like to approach the chapters in different orders. For those who have not yet begun their undergraduate studies, it also explains some useful vocabulary.
This book is about how to make the most of a mathematics major. It is about the nature of undergraduate mathematics, about it, and about how to keep on top of stuyding while enjoying undergraduate life. It is written for those who intend to study for a mathematics major, and for those who have already started.
If you are among the first group, you are probably in one of two positions. Youmight be a bit nervous about the whole business. Perhaps you have done well in mathematics so far, but you think that your success is mostly down to hard work. Perhaps you believe that others have some innate mathematical talent that you lack, and that in upper-level courses you will be in classes full of geniuses and will end up being found out as a fraud. As a mathematics professor, I meet quite a lot of students like this. Some of them always doubt themselves, and they get their degrees but they don’t really enjoy their studies. Others do come to realize that their thinking is as good as that of anyone else. They develop more faith in themselves, they succeed, and they enjoy the whole process of learning. If you are a bit nervous, I hope that this book will help you to feel prepared, to make good progress, and to end up in this latter group.
You might, on the other hand, be confident that you are goingtosucceed. That’s how I felt when I began my undergraduate studies in the UK. I’d always been the best student in my mathematics classes, I had no problems with the extra mathematics I took in high school, and I was pretty sure I wanted to be a mathematician. But when I arrived at college and began taking the equivalent of upper-level mathematics courses, I was forced to adjust my expectations. For a while I thought that I would only barely merit a degree and that I should seriously downgrade my career aspirations. Then, in a very gratifying turnaround, I got the hang of advanced mathematics and was eventually awarded what is known as a “first class” degree. This was largely due to a few key insights that I gained from some excellent teachers. In fact, these insights prompted me to decide that studying how people think about mathematics is even more interesting than studying mathematics, so I went on to do a PhD in Mathematics Education. These days I give lectures on undergraduate mathematics, and spend the rest of my time conducting research studies to investigate how people learn and think about it.
One simple but important thing I have learned is that, whatever their feelings on declaring mathematics as their major, most students have a lot to learn about how to study it effectively. Even those who end up doing very well are usually somewhat inefficient to start with. That’s why I’m writing this book: to give you a leg-up so that your academic life is easier and more enjoyable than it would otherwise be.
Some pictures from How to Study as a Mathematics Major :
However, this book is How to Study as a Mathematics Major not about some magical easy way to complete a mathematics major without really trying. On the contrary, a lot of hard work will be required. But this is something to embrace. A mathematics major should be challenging—if it were easy, everyone would haveone. And, if you’ve got this far in your studies, you must have experienced the satisfaction of mastering something that you initially found difficult. The book is, however, about how to make sure that you’re paying attention to the right things, so that you can avoid unnecessary confusion and so that your hard work will pay off.