Mathematics

A Minimal Introduction
1. Auflage 2013
ISBN: 978-1-4822-1600-4
Verlag: Apple Academic Press Inc.

Buch, Englisch, 226 Seiten, Format (B × H): 179 mm x 254 mm, Gewicht: 485 g

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.

Zielgruppe

Undergraduate students taking one of the following courses: transition to advanced mathematics, introduction to logic, or introduction to real analysis.

Autoren/Hrsg.

Buium, Alexandru

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematik Allgemein Mengenlehre

Inhaltsverzeichnis

Pre-Mathematical Logic. Mathematics. Mathematical Logic. Bibliography. Index.

Über Autor(innen)

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.