A gap has long existed between basic calculus studies and abstract algebra and real analysis. Over the years, the focus of calculus instruction has become ever more computational, leaving those interested in higher mathematics somewhat ill prepared for the more advanced, abstract work which requires the ability to understand and construct proofs.
Introductory Concepts for Abstract Mathematics will help students bridge the gap between calculus and the more advanced mathematical studies. It teaches how to deal effectively with abstract ideas, comprehend the logical structure of proofs, and write mathematics using conventional terminology in an effective, logical, and comprehensible way.
• Provides die foundation required for advanced mathematical studies by including a thorough development of sets, relations, and functions.
• Imparts other important concepts, such as the development of real numbers, least upper bounds, and concepts related to, transfinite cardinal arithmetic.
• Teaches the writing of mathematics and the construction of proofs.