Logic and Reasoning in the 21st Century

In clearly written prose and examples, Logic and Reasoning in the 21st Century presents contemporary real-world applications of mathematics that provide the student with a fresh look at math. Using examples as starting points, the text explores symbolic logic, deductive reasoning, set theory, making decisions under uncertainty, and analyzing two-person games. The text opens with symbolic logic and binary arithmetic, used to design circuits for everyday devices such as warning buzzers in cars and adders for calculators. Simplifying Boolean expressions is then presented, using traditional equivalences and Karnaugh maps. In the section on logical deductions, the book introduces a visual interpretation of the resolution method that is used by computers in artificial intelligence applications. The ensuing chapter on set theory is strongly grounded in modern applications, while the concluding chapters treat two reasoning topics often absent from similar texts: decision trees and game trees. Logic and Reasoning in the 21st Century is intended for use in a general liberal arts math course, typically with high-school algebra as a prerequisite. The authors catch students' attention by presenting what seems to be a nonmathematical corner of everyday modern life and then systematically introducing the mathematics behind the application. In this way, students get a fresh start in mathematics rather than simply building on recalled - and not necessarily mastered or enjoyed - topics from high-school math. Instructors have praised prepublication editions of Logic and Reasoning in the 21st Century for its clarity of presentation - especially the interesting, accessible, modern examples worked out in detail - while students at both two-year and four-year colleges have said the text represents the first mathematics course they have liked and were able to master.