Del i serien Undergraduate Texts in Mathematics

Fundamental Theorem of Algebra

Häftad, Engelska, 2012

AvBenjamin Fine,Gerhard Rosenberger

819 kr

Beställningsvara. Skickas inom 10-15 vardagar. Fri frakt för medlemmar vid köp för minst 249 kr.

Finns i fler format (1)

Inbunden

1 149 kr

Skickas inom 10-15 vardagar

The purpose of this book is to examine three pairs of proofs of the theorem from three different areas of mathematics: abstract algebra, complex analysis and topology. It is ideal for a "capstone" course in mathematics for junior/senior level undergraduate mathematics students or first year graduate students. It could also be used as an alternative approach to an undergraduate abstract algebra course.

Produktinformation

Utgivningsdatum2012-10-30
Mått155 x 235 x 13 mm
Vikt353 g
FormatHäftad
SpråkEngelska
SerieUndergraduate Texts in Mathematics
Antal sidor210
FörlagSpringer-Verlag New York Inc.
ISBN9781461273431

Tillhör följande kategorier

1 Introduction and Historical Remarks.- 2 Complex Numbers.- 2.1 Fields and the Real Field.- 2.2 The Complex Number Field.- 2.3 Geometrical Representation of Complex Numbers.- 2.4 Polar Form and Euler’s Identity.- 2.5 DeMoivre’s Theorem for Powers and Roots.- Exercises.- 3 Polynomials and Complex Polynomials.- 3.1 The Ring of Polynomials over a Field.- 3.2 Divisibility and Unique Factorization of Polynomials.- 3.3 Roots of Polynomials and Factorization.- 3.4 Real and Complex Polynomials.- 3.5 The Fundamental Theorem of Algebra: Proof One.- 3.6 Some Consequences of the Fundamental Theorem.- Exercises.- 4 Complex Analysis and Analytic Functions.- 4.1 Complex Functions and Analyticity.- 4.2 The Cauchy-Riemann Equations.- 4.3 Conformal Mappings and Analyticity.- Exercises.- 5 Complex Integration and Cauchy’s Theorem.- 5.1 Line Integrals and Green’s Theorem.- 5.2 Complex Integration and Cauchy’s Theorem.- 5.3 The Cauchy Integral Formula and Cauchy’s Estimate.- 5.4 Liouville’s Theorem and the Fundamental Theorem of Algebra: Proof Ttvo.- 5.5 Some Additional Results.- 5.6 Concluding Remarks on Complex Analysis.- Exercises.- 6 Fields and Field Extensions.- 6.1 Algebraic Field Extensions.- 6.2 Adjoining Roots to Fields.- 6.3 Splitting Fields.- 6.4 Permutations and Symmetric Polynomials.- 6.5 The Fundamental Theorem of Algebra: Proof Three.- 6.6 An Application—The Transcendence of e and ?.- 6.7 The Fundamental Theorem of Symmetric Polynomials.- Exercises.- 7 Galois Theory.- 7.1 Galois Theory Overview.- 7.2 Some Results From Finite Group Theory.- 7.3 Galois Extensions.- 7.4 Automorphisms and the Galois Group.- 7.5 The Fundamental Theorem of Galois Theory.- 7.6 The Fundamental Theorem of Algebra: Proof Four.- 7.7 Some Additional Applications of Galois Theory.- 7.8Algebraic Extensions of ? and Concluding Remarks.- Exercises.- 8 7bpology and Topological Spaces.- 8.1 Winding Number and Proof Five.- 8.2 Tbpology—An Overview.- 8.3 Continuity and Metric Spaces.- 8.4 Topological Spaces and Homeomorphisms.- 8.5 Some Further Properties of Topological Spaces.- Exercises.- 9 Algebraic Zbpology and the Final Proof.- 9.1 Algebraic lbpology.- 9.2 Some Further Group Theory—Abelian Groups.- 9.3 Homotopy and the Fundamental Group.- 9.4 Homology Theory and Triangulations.- 9.5 Some Homology Computations.- 9.6 Homology of Spheres and Brouwer Degree.- 9.7 The Fundamental Theorem of Algebra: Proof Six.- 9.8 Concluding Remarks.- Exercises.- Appendix A: A Version of Gauss’s Original Proof.- Appendix B: Cauchy’s Theorem Revisited.- Appendix C: Three Additional Complex Analytic Proofs of the Fundamental Theorem of Algebra.- Appendix D: Two More Ibpological Proofs of the Fundamental Theorem of Algebra.- Bibliography and References.

Mer från samma författare

Introduction to Abstract Algebra

Benjamin Fine, Anthony M. Gaglione, Gerhard Rosenberger

Inbunden, 2014

1 509 kr

Elementary Theory of Groups

Benjamin Fine, Anthony Gaglione, Alexei Myasnikov, Gerhard Rosenberger, Dennis Spellman

Inbunden, 2014

3 369 kr

Course in Mathematical Cryptography

Gilbert Baumslag, Benjamin Fine, Martin Kreuzer, Gerhard Rosenberger, Gilbert Baumslag, Benjamin Fine, Martin Kreuzer, Gerhard Rosenberger

Häftad, 2015

849 kr

Abstract Algebra

Celine Carstensen-Opitz, Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger

Häftad, 2019

939 kr

Elementary Theory of Groups and Group Rings, and Related Topics

Paul Baginski, Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Vladimir Shpilrain

Inbunden, 2020

2 489 kr

Topics in Infinite Group Theory

Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Leonard Wienke

Häftad, 2021

1 239 kr

Geometry and Discrete Mathematics

Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Annika Schürenberg, Leonard Wienke

Häftad, 2022

919 kr

Algebra and Number Theory

Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Annika Schürenberg, Leonard Wienke

Häftad, 2023

1 059 kr

Topics in Infinite Group Theory

Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Annika Schürenberg, Leonard Wienke

Häftad, 2024

1 419 kr

Number Theory

Benjamin Fine, Gerhard Rosenberger

Inbunden, 2016

969 kr

Mer från samma serie

Linear Algebra Done Right

Sheldon Axler

Inbunden, 2023

699 kr

Ideals, Varieties, and Algorithms

David A. Cox, John Little, Donal O'Shea

Inbunden, 2025

1 149 kr

Understanding Analysis

Stephen Abbott

Inbunden, 2015

669 kr

Undergraduate Analysis

Serge Lang

Inbunden, 1996

869 kr

Calculus and Analysis in Euclidean Space

Jerry Shurman

Inbunden, 2016

869 kr

Introduction to Linear Algebra

Serge Lang

Inbunden, 1985

809 kr

Linear Algebra

Serge Lang

Inbunden, 1987

709 kr

Rational Points on Elliptic Curves

Joseph H. Silverman, John T. Tate

Inbunden, 2015

719 kr

Understanding Analysis

Stephen Abbott

Häftad, 2016

599 kr

Applied Linear Algebra and Matrix Analysis

Thomas S. Shores

Inbunden, 2018

869 kr

Du kanske också är intresserad av

Topics in Infinite Group Theory

Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Annika Schürenberg, Leonard Wienke

Häftad, 2024

1 419 kr

Del 1

ASPECTS OF INFINITE GROUPS: A FESTSCHRIFT IN HONOR OF ANTHONY GAGLIONE

AL BENJAMIN FINE ET, Benjamin Fine, Gerhard Rosenberger, Dennis Spellman

Inbunden, 2008

2 259 kr

Geometry and Discrete Mathematics

Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, Annika Schürenberg, Leonard Wienke

Häftad, 2022

919 kr