How to Study as a Mathematics Major

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.

Part 1: Mathematics
Introduction
1. Calculation Procedures
2. Abstract Objects
3. Definitions
4. Theorems
5. Proof
6. Proof Types and Tricks
7. Reading Mathematics
8. Writing Mathematics
Part 2: Study Skills
9. Lectures
10. Other People
11. Time Management
12. Panic
13. (Not) Being the Best
14. What Mathematics Professors Do