How to Study as a Mathematics Major
Format: PDF / Kindle (mobi) / ePub
Every year, thousands of students declare mathematics as their major. Many are extremely intelligent and hardworking. However, even the best will encounter challenges, because upper-level mathematics involves not only independent study and learning from lectures, but also a fundamental shift from calculation to proof.
This shift is demanding but it need not be mysterious -- research has revealed many insights into the mathematical thinking required, and this book translates these into practical advice for a student audience. It covers every aspect of studying as a mathematics major, from tackling abstract intellectual challenges to interacting with professors and making good use of study time. Part 1 discusses the nature of upper-level mathematics, and explains how students can adapt and extend their existing skills in order to develop good understanding. Part 2 covers study skills as these relate to mathematics, and suggests practical approaches to learning effectively while enjoying undergraduate life.
As the first mathematics-specific study guide, this friendly, practical text is essential reading for any mathematics major.
fast, 234 feedback, 181, 185 feeling guilty, 211 filing, 220 finishing things, 221 first class marks, 236 flexibility, 7 for all, 70 for every, 50, 81 forces, 146 formal, 76, 77, 91, 104 formulas, 8, 10, 84 Foundations, 94 fractions, 22 friction, 146 functions, 21, 29 piecewise-defined, 53, 164 further reading, xiv general results, 82, 132 generality, 83 generalization, 49, 50 genius, 194, 237 getting behind, 224, 233 graduate jobs, 246 grammar, 189 graph, 44 partial
times x differentiated, plus x times v differentiated. That does indeed come out as stated, because v is a function of x. Notice that this is important—if v were just a constant, it would differentiate to 0, so we need to keep track of what is being treated as a function of what. Then I can look at the next equation and see that this simply involves replacing dy/dx with f(v). I was expecting it to be replaced with f(y/x), but with a moment’s thought I can see that the substitution y = vx does
work. This means that you should always go to recitations and make the most of what is on offer. If your instructor is a professor, there is also another, more prosaic reason you should always go: at some point you might want this person to write a recommendation for you. If you ask them to do so and their first thought is, “Oh yes, Martin, he’s the one who rarely showed up and was always ill-prepared,” that doesn’t put them in a great frame of mind for writing about how brilliant you are.
other students. Doing so can make learning more enjoyable and can improve everyone’s skills in talking about mathematics, but make sure that you are not just getting distracted. • Colleges have many support services. Everyone should go to the careers service early. Hopefully you won’t need to use the other services very much, but it is probably worth familiarizing yourself with how they work. FURTHER READING For more on interacting with others and managing the practical aspects of college
even if you only take up a couple of practical tips, you’ll be better off than if you’d never thought about it at all. Certainly it is easier to stay on track, or to get back on track, if you have some idea of where the track is. Before we get into the advice, though, I’ll start with a short cautionary section on what you’re aiming for and what you’re aiming to avoid. 11.2 Aims and things to avoid First, it’s important to have a sense of what qualifies as a particular level of achievement