Principles of mathematics : a primer / Vladimir Lepetic

Von:

Lepetic, Vladimir, 1950- [aut]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Verlag: Hoboken, New Jersey : John Wiley & Sons, 2016Beschreibung: 1 online resourceISBN:

9781119131656
9781119131694
9781119131649

Schlagwörter:

Andere physische Formen: 9781119131649 | Erscheint auch als: Principles of mathematics. Hoboken, NJ : Wiley, 2016. xiii, 654 Seiten | Print version: Principles of mathematics MSC: MSC: *00-01 | 00A05 | 03-01 | 15-01 | 20-01RVK: RVK: SK 399LOC-Klassifikation:

QA8.4

Online-Ressourcen:

Zugang im Netz des KIT

Inhalte:

Zusammenfassung: Cover -- Title Page -- Copyright -- Dedication -- Contents -- Preface -- Chapter 1 Set Theory -- 1.1 Introduction -- 1.2 Set Theory - Definitions, Notation, and Terminology - What is a Set? -- 1.3 Sets Given by a Defining Property -- 1.4 The Algebra of Sets -- 1.5 The Power Set -- 1.6 The Cartesian Product -- 1.7 The Sets N, Z, and Q -- 1.8 The Set R - Real Numbers I -- 1.9 A Short Musing on Transfinite Arithmetic -- 1.10 The Set R - Real Numbers II -- 1.11 Supplementary Problems -- Chapter 2 Logic -- 2.1 Introduction -- 2.2 Propositional Calculus -- 2.3 Arguments I -- 2.4 Arguments II -- 2.5 A Short Revisit to Set Theory -- 2.6 Boolean Algebra -- 2.7 Supplementary Problems -- Chapter 3 Proofs -- 3.1 Introduction -- 3.2 Direct Proof -- 3.3 Indirect Proof -- 3.4 Mathematical Induction -- 3.5 Supplementary Problems -- Chapter 4 Functions -- 4.1 Introduction -- 4.2 Relations -- 4.3 Functions -- 4.4 Supplementary Problems -- Chapter 5 Group Theory -- 5.1 Introduction -- 5.2 Fundamental Concepts of Group Theory -- 5.3 Subgroups -- 5.4 Cyclic Groups -- 5.5 Homomorphisms and Isomorphisms -- 5.6 Normal Subgroups -- 5.7 Centralizer, Normalizer, Stabilizer -- 5.8 Quotient Group -- 5.9 The Isomorphism Theorems -- 5.10 Direct Product of Groups -- 5.11 Supplementary Problems -- Chapter 6 Linear Algebra -- 6.1 Introduction -- 6.2 Vector Space -- 6.3 Linear Dependence and Independence -- 6.4 Basis and Dimension of a Vector Space -- 6.5 Subspaces -- 6.6 Linear Transformations - Linear Operators -- 6.7 Isomorphism of Linear Spaces -- 6.8 Linear Transformations and Matrices -- 6.9 Linear Space M mn -- 6.10 Matrix Multiplication -- 6.11 Some More Special Matrices. General Linear Group -- 6.12 Rank of a Matrix -- 6.13 Determinants -- 6.14 The Inverse and the Rank of a Matrix Revisited -- 6.15 More on Linear Operators -- 6.16 Systems of Linear Equations I.PPN: PPN: 832702218Package identifier: Produktsigel: ZDB-26-MYL | ZDB-30-PAD | ZDB-30-PQE

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