An Introduction to Abstract MathematicsBond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. |
Contents
1 | |
Sets
| 49 |
Functions
| 81 |
Binary Operations and Relations
| 123 |
The Integers
| 151 |
Infinite Sets
| 209 |
The Real and Complex Numbers
| 235 |
Polynomials
| 263 |
Answers and Hints to Selected Exercises | 295 |
317 | |
319 | |