Introduces students to the important mathematical foundations and tools in AI and describes their application to the design of AI algorithms. The book presents an introductory AI course based on the most important mathematics applications, while focusing on important topics that are proven useful in AI and involve the most broadly applicable mathematical methods. The book explores AI from three different viewpoints: goals, methods or tools, and achievements and failures. Its goals of reasoning, planning, learning, or language understanding and use are centered around the expert system idea. The tools of AI are presented in terms of what can be incorporated in the data structures. The book examines the concepts and tools of limited structure, mathematical logic, logic-like representation, numerical information, and nonsymbolic structures. Many introductory texts give the impression that AI is just a collection of heuristic ideas, data structures, and clever hacks. Fortunately, AI researchers use mathematics and are developing new tools. Since much of the mathematics used in AI is not part of standard undergraduate curriculum, the student will be learning mathematics and seeing how it is used in AI at the same time. A diskette containing solutions to many of the exercises is available for instructors.