Mathematics

A Minimal Introduction

Alexandru Buium

$389

Hardback

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English

CRC Press
25 September 2017

Set theory; Discrete mathematics; Calculus & mathematical analysis

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.

By: Alexandru Buium
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 453g
ISBN: 9781138466845
ISBN 10: 1138466840
Pages: 226
Publication Date: 25 September 2017
Audience: College/higher education , General/trade , Primary , ELT Advanced
Format: Hardback
Publisher's Status: Active

Alexandru Buium is a professor of mathematics at the University of New Mexico. He is the author of four monographs and over 70 research papers in the areas of number theory and algebraic geometry. He has held visiting positions at Columbia University, the Institute for Advanced Study, Max Planck Institute for Mathematics, University of Paris-Sud, and IHES.

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Mathematics

A Minimal Introduction

Alexandru Buium

$389

Hardback

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