Grounded in mathematical inquiry, this introduction explores the philosophy of mathematics, emphasizing the relationship between mathematical concepts and their practical applications. It delves into the foundational questions and theories that shape mathematical thought, making it an essential resource for those interested in the philosophical underpinnings of mathematical practice.
How to write mathematical proofs, shown in fully-worked out examples.This is a companion volume Joel Hamkins's Proof and the Art of Mathematics , providing fully worked-out solutions to all of the odd-numbered exercises as well as a few of the even-numbered exercises. In many cases, the solutions go beyond the exercise question itself to the natural extensions of the ideas, helping readers learn how to approach a mathematical investigation. As Hamkins asks, "Once you have solved a problem, why not push the ideas harder to see what further you can prove with them?" These solutions offer readers examples of how to write a mathematical proofs.The mathematical development of this text follows the main book, with the same chapter topics in the same order, and all theorem and exercise numbers in this text refer to the corresponding statements of the main text.