Mathematical Proofs: A Transition to Advanced Mathematics (3rd Edition)
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own.
Mathematics is beautiful--and it can be fun and exciting as well as practical. Good Math is your guide to some of the most intriguing topics from two thousand years of mathematics: from Egyptian fractions to Turing machines; from the real meaning of numbers to proof trees, group symmetry, and mechanical computation. If you've ever wondered what lay beyond the proofs you struggled to complete in high school geometry, or what limits the capabilities of computer on your desk, this is the book for you.
Our goal in this book is to explain as many important theorems, examples, and techniques as possible, as quickly and directly as possible, while at the same time giving (nearly) full details and keeping the text (nearly) selfcontained. This book contains some simplifications of known approaches and proofs, the exposition of some results that are not readily available, and some new material as well.
Intuitionism: An Introduction (Study in Logic & Mathematics)
Intuitionistic mathematics involves discerning the truth of a given statement. This high-level introductory treatment assumes a strong mathematical background, bringing readers directly to the center of several different branches of intuitionistic mathematics. The author, a leader in the field of intuitionistic mathematics, employs condensed proofs and presumes a familiarity with classical theories. 1971 edition.
Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics, and computer science. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated.
