Exploring Mathematics - An Engaging Introduction to Proof (Relié)

A combination of creativity and rigor is essential to conducting mathematical inquiry, and this textbook gives students a comprehensive mathematics experience : interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results. This text is filled with hundreds of examples, exercises, and projects to pique the students' curiosity. Written with a minimum number of pre-requisites, this textbook : Encompasses core topics such as proof techniques, sets, functions, relations, and cardinality, with selected additional topics for further exploration.
Employs a problem-based approach to help students develop interesting examples and theorems through projects and over 600 exercises. Includes in-text exercises with complete solutions or robust hints located in an appendix, as well as end-of-chapter exercises and projects to give students the opportunity to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.
Can be used by first and second year college students as well as by independent readers who want an accessible introduction to theoretical mathematics.