Conjecture and Proofs: An Introduction to Mathematical Thinking

Rating:
Summary: Review for "Conjecture & Proof" by D.D. Schwartz
Review: This book is primarily designed as a textbook for a "transition" college course (the kind of course at the sophomore level that helps students make the transition from calculus and calculation intensive courses to more abstract mathematics), and it does an excellent job. While the structure of the book is quite standard for a text of this kind, students find it accessible and user-friendly. To achieve the goal of helping students grow comfortable with abstract mathematical structures, Dr. Diane Driscoll Schwartz presents at first an introduction to logic and its use in the construction of mathematical proofs. The topics included in the two chapters cover several standard proof techniques, such as the use of the contrapositive and of the principle of mathematical induction. This part is followed by the discussion of a number of mathematical topics such as sets, functions, relations, groups, modular arithmetic, combinatorics and cardinality. While the sets of exercises include a sufficient number of problems, it would be nice to see this number increased. Some of the problems are designed for group-work and provide a good starting point for classroom discussion and for "non standard" homework assignments. The book is accompanied by an Instructor's Guide, which includes suggestions for class preparation and hints for some of the problems. For those schools that provide a technology-intensive environment, the text can be use with the computer language ISETL. The software can be downloaded from the Web Sites indicated in the book.

Rating:
Summary: Review for "Conjecture & Proof" by D.D. Schwartz
Review: This book is primarily designed as a textbook for a "transition" college course (the kind of course at the sophomore level that helps students make the transition from calculus and calculation intensive courses to more abstract mathematics), and it does an excellent job. While the structure of the book is quite standard for a text of this kind, students find it accessible and user-friendly. To achieve the goal of helping students grow comfortable with abstract mathematical structures, Dr. Diane Driscoll Schwartz presents at first an introduction to logic and its use in the construction of mathematical proofs. The topics included in the two chapters cover several standard proof techniques, such as the use of the contrapositive and of the principle of mathematical induction. This part is followed by the discussion of a number of mathematical topics such as sets, functions, relations, groups, modular arithmetic, combinatorics and cardinality. While the sets of exercises include a sufficient number of problems, it would be nice to see this number increased. Some of the problems are designed for group-work and provide a good starting point for classroom discussion and for "non standard" homework assignments. The book is accompanied by an Instructor's Guide, which includes suggestions for class preparation and hints for some of the problems. For those schools that provide a technology-intensive environment, the text can be use with the computer language ISETL. The software can be downloaded from the Web Sites indicated in the book.