Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.
1. Let's play!
2. Discovering and presenting mathematics
3. Sets
4. The integers and the fundamental theorem of arithmetic
5. Functions
6. Relations
7. Cardinality
8. The real numbers
9. Probability and randomness
10. Algebra and symmetry
11. Projects
Appendix A. Solutions, answers, or hints to in-text exercises
Index
Bibilography.
