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    Introductory Mathematics: Algebra and Analysis (Springer Undergraduate Mathematics) (Paperback) By (author) Geoff Smith

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    DescriptionThis text provides a lively introduction to pure mathematics. It begins with sets, functions and relations, proof by induction and contradiction, complex numbers, vectors and matrices, and provides a brief introduction to group theory. It moves onto analysis, providing a gentle introduction to epsilon-delta technology and finishes with continuity and functions. The book features numerous exercises of varying difficulty throughout the text.


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  • Full bibliographic data for Introductory Mathematics

    Title
    Introductory Mathematics
    Subtitle
    Algebra and Analysis
    Authors and contributors
    By (author) Geoff Smith
    Physical properties
    Format: Paperback
    Number of pages: 231
    Width: 164 mm
    Height: 242 mm
    Thickness: 18 mm
    Weight: 381 g
    Language
    English
    ISBN
    ISBN 13: 9783540761785
    ISBN 10: 3540761780
    Classifications

    BIC E4L: MAT
    B&T Book Type: NF
    DC21: 510
    Nielsen BookScan Product Class 3: S7.9T
    DC22: 510
    LC subject heading:
    B&T Modifier: Academic Level: 01
    B&T Merchandise Category: SCI
    B&T General Subject: 710
    B&T Modifier: Region of Publication: 04
    Abridged Dewey: 510
    Ingram Subject Code: MA
    B&T Modifier: Text Format: 06
    LC subject heading:
    BIC subject category V2: PBF
    B&T Approval Code: A51350000
    Warengruppen-Systematik des deutschen Buchhandels: 16240
    LC subject heading:
    BISAC V2.8: MAT002000
    B&T Approval Code: A51400000
    BIC subject category V2: PBK
    LC subject heading:
    BISAC V2.8: MAT000000
    Libri: ANAL8000, CALC4500
    LC subject heading:
    Libri: ALGE3000
    LC classification: QA154.2 .S546 1998, QA1-939, QA299.6-433, QA150-272
    Thema V1.0: PBK, PBF
    Edition
    1
    Edition statement
    1st ed. 1998. Corr. 3rd printing 2000
    Illustrations note
    1 black & white illustrations, biography
    Publisher
    Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
    Imprint name
    Springer-Verlag Berlin and Heidelberg GmbH & Co. K
    Publication date
    02 February 2000
    Publication City/Country
    Berlin
    Table of contents
    1. Sets, Functions and Relations.- 1.1 Sets.- 1.2 Subsets.- 1.3 Well-known Sets.- 1.4 Rationals, Reals and Pictures.- 1.5 Set Operations.- 1.6 Sets of Sets.- 1.7 Paradox.- 1.8 Set-theoretic Constructions.- 1.9 Notation.- 1.10 Venn Diagrams.- 1.11 Quantifiers and Negation.- 1.12 Informal Description of Maps.- 1.13 Injective, Surjective and Bijective Maps.- 1.14 Composition of Maps.- 1.15 Graphs and Respectability Reclaimed.- 1.16 Characterizing Bijections.- 1.17 Sets of Maps.- 1.18 Relations.- 1.19 Intervals.- 2. Proof.- 2.1 Induction.- 2.2 Complete Induction.- 2.3 Counter-examples and Contradictions.- 2.4 Method of Descent.- 2.5 Style.- 2.6 Implication.- 2.7 Double Implication.- 2.8 The Master Plan.- 3. Complex Numbers and Related Functions.- 3.1 Motivation.- 3.2 Creating the Complex Numbers.- 3.3 A Geometric Interpretation.- 3.4 Sine, Cosine and Polar Form.- 3.5 e.- 3.6 Hyperbolic Sine and Hyperbolic Cosine.- 3.7 Integration Tricks.- 3.8 Extracting Roots and Raising to Powers.- 3.9 Logarithm.- 3.10 Power Series.- 4. Vectors and Matrices.- 4.1 Row Vectors.- 4.2 Higher Dimensions.- 4.3 Vector Laws.- 4.4 Lengths and Angles.- 4.5 Position Vectors.- 4.6 Matrix Operations.- 4.7 Laws of Matrix Algebra.- 4.8 Identity Matrices and Inverses.- 4.9 Determinants.- 4.10 Geometry of Determinants.- 4.11 Linear Independence.- 4.12 Vector Spaces.- 4.13 Transposition.- 5. Group Theory.- 5.1 Permutations.- 5.2 Inverse Permutations.- 5.3 The Algebra of Permutations.- 5.4 The Order of a Permutation.- 5.5 Permutation Groups.- 5.6 Abstract Groups.- 5.7 Subgroups.- 5.8 Cosets.- 5.9 Cyclic Groups.- 5.10 Isomorphism.- 5.11 Homomorphism.- 6. Sequences and Series.- 6.1 Denary and Decimal Sequences.- 6.2 The Real Numbers.- 6.3 Notation for Sequences.- 6.4 Limits of Sequences.- 6.5 The Completeness Axiom.- 6.6 Limits of Sequences Revisited.- 6.7 Series.- 7. Mathematical Analysis.- 7.1 Continuity.- 7.2 Limits.- 8. Creating the Real Numbers.- 8.1 Dedekind's Construction.- 8.2 Construction via Cauchy Sequences.- 8.3 A Sting in the Tail: p-adic numbers.- Further Reading.- Solutions.