عنوان

Mathematics :

1482216019

9781482216011

b552508

Mathematics :

[Book]

a minimal introduction

Alexandru Buium, University of New Mexico, Albuquerque, USA.

Boca Raton

CRC Press

[2014]

pt. 1 Pre-mathematical logic --;ch. 1 Languages --;ch. 2 Metalanguage --;ch. 3 Syntax --;ch. 4 Semantics --;ch. 5 Tautologies --;ch. 6 Witnesses --;ch. 7 Theories --;ch. 8 Proofs --;ch. 9 Argot --;ch. 10 Strategies --;ch. 11 Examples --;pt. 2 Mathematics --;ch. 12 ZFC --;ch. 13 Sets --;ch. 14 Maps --;ch. 15 Relations --;ch. 16 Operations --;ch. 17 Integers --;ch. 18 Induction --;ch. 19 Rationals --;ch. 20 Combinatorics --;ch. 21 Sequences --;ch. 22 Reals --;ch. 23 Topology --;ch. 24 Imaginarles --;ch. 25 Residues --;ch. 26 p-adics --;ch. 27 Groups --;ch. 28 Orders --;ch. 29 Vectors --;ch. 30 Matrices --;ch. 31 Determinants --;ch. 32 Polynomials --;ch. 33 Congruences --;ch. 34 Lines --;ch. 35 Conics --;ch. 36 Cubics --;ch. 37 Limits --;ch. 38 Series --;ch. 39 Trigonometry --;ch. 40 Integrality --;ch. 41 Reciprocity --;ch. 42 Calculus --;ch. 43 Metamodels --;ch. 44 Categories --;ch. 45 Functors --;ch. 46 Objectives --;pt. 3 Mathematical logic --;ch. 47 Models --;ch. 48 Incompleteness.

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--

Mathematics -- Textbooks.

Mathematics.

Alexandru Buium, University of New Mexico, Albuquerque, USA.

Alexandru Buium

[Book]

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