General Information for Your Research
Improving Your Proofs
There are a number of books on mathematical proofs. Here are two that may help:
Reading, Writing, and Proving: a Closer Look at Mathematics by Ulrich Daepp (2003)
Print version QA 13 .D34 2003, O'Meara Mathematic Library
"How can someone learn to prove mathematical results? There are many theories on this. We believe that learning mathematics is the same as learning to play an instrument or learning to succeed at a particular sport. Someone must provide the background: the tips, information on the basic skills, and the insider’s 'know how.' Then the student has to practice" (Preface).
An Accompaniment to Higher Mathematics by George Exner (1996)
QA 9.54 E96, O'Meara Mathematics Library
"Like music and athletics, the main pleasure in mathematics is in the process of doing: exploring, inventing, and discovering. You are ... intrinsically good doers of mathematics, but you may be fighting with one hand (or two hands) tied behind your backs without knowing it. This book is all about some active tools to make your doing of mathematics more effective, and thus, possibly, more enjoyable" (Introduction).
In the course of your research, you may encounter topics that are unfamiliar to you. Reading a little about these topics in an encyclopedia is a great way to get a good overview.
Here are two highly recommended general reference resources:
"MathWorldTM is the web's most extensive mathematical resource, provided as a free service to the world's mathematics and internet communities as part of a commitment to education and educational outreach by Wolfram Research, makers of Mathematica. MathWorld has been assembled over more than a decade by Eric W. Weisstein with assistance from thousands of contributors."
Encyclopaedia of Mathematics
Print version QA 5 .M3713 1987, O'Meara Mathematics Library reference
"The Encyclopaedia of Mathematics is the most up-to-date and comprehensive English-language graduate-level reference work in the field of mathematics today. [It] comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics."