|aMathematics :|ba minimal introduction /|cAlexandru Buium, University of New Mexico, Albuquerque, USA.
|aBoca Raton :|bCRC Press,|cc2014.
|aBoca Raton :|bCRC Press,|c
|axviii, 208 pages ;|c26 cm.
|aIncludes bibliographical references (page 205) and index.
|a"Minimizing the role of intuition, this text provides an introduction to pure mathematics for a one-semester undergraduate-level course. It builds on topics in algebra, geometry, and calculus from scratch in a non-circular way using many examples and exercises. Remarks scattered throughout the text address various philosophical and historical issues, putting the mathematics into context. The author uses easy-to-follow language and avoids overwhelming students with unnecessary material"--|cProvided by publisher.
內容簡介top Mathematics 簡介 Bridging the gap between procedural mathematics that emphasizes calculations and conceptual mathematics that focuses on ideas, Mathematics: A Minimal Introduction presents an undergraduate-level introduction to pure mathematics and basic concepts of logic. The author builds logic and mathematics from scratch using essentially no background except natural language. He also carefully avoids circularities that are often encountered in related books and places special emphasis on separating the language of mathematics from metalanguage and eliminating semantics from set theory.The first part of the text focuses on pre-mathematical logic, including syntax, semantics, and inference. The author develops these topics entirely outside the mathematical paradigm. In the second part, the discussion of mathematics starts with axiomatic set theory and ends with advanced topics, such as the geometry of cubics, real and p-adic analysis, and the quadratic reciprocity law. The final part covers mathematical logic and offers a brief introduction to model theory and incompleteness.Taking a formalist approach to the subject, this text shows students how to reconstruct mathematics from language itself. It helps them understand the mathematical discourse needed to advance in the field.