Meserve, Bruce E. Fundamental Concepts of Algebra

# Fundamental Concepts of Algebra

## Meserve, Bruce E.

Uncommonly interesting introduction illuminates complexities of higher mathematics while offering a thorough understanding of elementary mathematics. Covers development of complex number system and elementary theories of numbers, polynomials and operations, determinants, matrices, constructions and graphical representations. Several exercises — without solutions.

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Contenuti:

CHAPTER 1. OUR NUMBER SYSTEM 1-1 Sets 1-2 Cardinal numbers 1-3 Equivalence relations 1-4 Peano's postulates 1-5 Addition and multiplication 1-6 Order relations 1-7 Inverses 1-8 Positive raional numbers 1-9 Negative numbers 1-10 Real numbers *1-11 Postulates for real numbers 1-12 Properties of real numbers 1-13 Transfinite cardinal numbers 1-14 Group; number system 1-15 Complex numbers 1-16 Properties of complex numbers 1-17 De Moivre's Theorem *1-18 Fields and number systems CHAPTER 2. THEORY OF NUMBERS 2-1 Divisibility 2-2 Division Algorithm 2-3 Prime numbers 2-4 Unique Factorization Theorem 2-5 Euclidean Algorithm 2-6 Bases 2-7 Decimal notation *2-8 Congruences *2-9 Residue classes. Euler's F-function *2-10 Evaluation of F(m) *2-11 Linear congruences *2-12 Diophantine problems CHAPTER 3. THEORY OF POLYNOMIALS 3-1 Polynomials 3-2 Rings of polynomials 3-3 Rational functions 3-4 Divisibility 3-5 Division Algorithm 3-6 Irreducible polynomials 3-7 Euclidean Algorithm 3-8 Change of variable *3-9 Ideals 3-10 Functions 3-11 Limits 3-12 Continuity 3-13 Continuous functions 3-14 Derivatives *3-15 Taylor's series *3-16 Analytic functions CHAPTER 4. THEORY OF EQUATIONS 4-1 Zeros of a polynomial 4-2 Synthetic division 4-3 Change of variable 4-4 Number of roots 4-5 Determination of the roots 4-6 Conjugate imaginary roots 4-7 Elementary symmetric polynomials 4-8 Transformations of roots *4-9 Cubic equations *4-10 Quartic equations 4-11 Descartes' Rule of Signs 4-12 Sturm's Theorem 4-13 Multiple roots 4-14 Approximate solutions CHAPTER 5. DETERMINANTS AND MATRICES 5-1 Historical development 5-2 Matrices 5-3 Permutations 5-4 Inversions 5-5 Transpositions 5-6 Even and odd permutations 5-7 Determinants 5-8 Properties of determinants 5-9 Expansion of determinants 5-10 Minors 5-11 Cramer's Rule 5-12 Systems of linear equations 5-13 Linear dependence 5-14 Applications in analytic geometry 5-15 Geometric transformations CHAPTER 6.CONSTRUCTIONS 6-1 Classical constructions 6-2 Elementary classical constructions 6-3 The algebraic viewpoint 6-4 Basic classical constructions 6-5 Construction of roots of equations 6-6 Famous construction problems 6-7 Nonclassical geometric trisections 6-8 Mechanical angle trisectors 6-9 Linkages 6-10 Summary CHAPTER 7. GRAPHICAL REPRESENTATIONS 7-1 Euclidean and complex spaces 7-2 Polynomials 7-3 Conic sections 7-4 Quadric surfaces 7-5 Higher plane surves 7-6 Rational functions 7-7 Algebraic functions 7-8 Curve tracing 7-9 Special graphs 7-10 Graphical solutions 7-11 Curve fitting 7-12 Conclusion BIBLIOGRAPHY SYMBOLS AND NOTATIONS INDEX

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## 1.Fundamental Concepts of Algebra (Paperback)

Editore: Dover Publications Inc., United States (1983)
ISBN 10: 0486614700 ISBN 13: 9780486614700
Nuovi Paperback Quantità: 1
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Descrizione libro Dover Publications Inc., United States, 1983. Paperback. Condizione libro: New. New edition. 213 x 137 mm. Language: English . Brand New Book. This uncommonly interesting volume has been a favorite for 30 years, and is now available for the first time in a modestly priced paperback edition. Beginning with the fundamentals of numbers and sets, the author clearly guides the reader through the often discouraging complexities of algebra. Meserve presents the fundamental concepts of algebra illustrated by numerous examples- and, in many cases, the theory is further explicated by suitable sequences of exercises. The author s aim is to introduce the concepts of higher mathematics while bringing the reader to a more thorough understanding of elementary mathematics. His lucid explanations cover these major areas: OUR NUMBER SYSTEM: Sets, Cardinal Numbers, Order Relations, Real Numbers, Fields and Number Systems, more. THEORY OF NUMBERS: Divisibility, Prime Numbers, Bases, Division Algorithm, Decimal Notations, Linear Congruences, more. THEORY OF POLYNOMIALS: Rational Functions, Irreducible Polynomials, Functions, Limits, Continuity, Derivatives, more. THEORY OF EQUATIONS: Zeros of a Polynomial, Change of a Variable, Number of Roots, Quartic Equations, more. DETERMINANTS AND MATRICES: Historical Development, Permutations, Inversions, Transpositions, Cramer s Rule, more. CONSTRUCTIONS: The Algebraic Viewpoint, Classical Constructions, Mechanical Angle Trisectors, Linkages, more. GRAPHICAL REPRESENTATIONS: Euclidean and Complex Spaces, Conic Sections, Quadric Surfaces, Curve Tracing, more. While intended for students who have previously studied college mathematics through calculus, this book has also been successfully used where calculus was not a prerequisite. It provides a very easily followed presentation and may also be used as an introductory or supplementary textbook. For prospective teachers of secondary mathematics, for students preparing for specialized advanced undergraduate courses in mathematics, and for the general reader in search of a firmer grasp of the essentials of algebra, there is no better, more helpful guide than Meserve. Codice libro della libreria AAC9780486614700

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## 2.Fundamental Concepts of Algebra (Paperback)

Editore: Dover Publications Inc., United States (1983)
ISBN 10: 0486614700 ISBN 13: 9780486614700
Nuovi Paperback Quantità: 1
Da
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(London, Regno Unito)
Valutazione libreria

Descrizione libro Dover Publications Inc., United States, 1983. Paperback. Condizione libro: New. New edition. 213 x 137 mm. Language: English . Brand New Book. This uncommonly interesting volume has been a favorite for 30 years, and is now available for the first time in a modestly priced paperback edition. Beginning with the fundamentals of numbers and sets, the author clearly guides the reader through the often discouraging complexities of algebra. Meserve presents the fundamental concepts of algebra illustrated by numerous examples- and, in many cases, the theory is further explicated by suitable sequences of exercises. The author s aim is to introduce the concepts of higher mathematics while bringing the reader to a more thorough understanding of elementary mathematics. His lucid explanations cover these major areas: OUR NUMBER SYSTEM: Sets, Cardinal Numbers, Order Relations, Real Numbers, Fields and Number Systems, more. THEORY OF NUMBERS: Divisibility, Prime Numbers, Bases, Division Algorithm, Decimal Notations, Linear Congruences, more. THEORY OF POLYNOMIALS: Rational Functions, Irreducible Polynomials, Functions, Limits, Continuity, Derivatives, more. THEORY OF EQUATIONS: Zeros of a Polynomial, Change of a Variable, Number of Roots, Quartic Equations, more. DETERMINANTS AND MATRICES: Historical Development, Permutations, Inversions, Transpositions, Cramer s Rule, more. CONSTRUCTIONS: The Algebraic Viewpoint, Classical Constructions, Mechanical Angle Trisectors, Linkages, more. GRAPHICAL REPRESENTATIONS: Euclidean and Complex Spaces, Conic Sections, Quadric Surfaces, Curve Tracing, more. While intended for students who have previously studied college mathematics through calculus, this book has also been successfully used where calculus was not a prerequisite. It provides a very easily followed presentation and may also be used as an introductory or supplementary textbook. For prospective teachers of secondary mathematics, for students preparing for specialized advanced undergraduate courses in mathematics, and for the general reader in search of a firmer grasp of the essentials of algebra, there is no better, more helpful guide than Meserve. Codice libro della libreria AAC9780486614700

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## 3.Fundamental Concepts of Algebra

Editore: Dover Publications Inc. 1983-06-01 (1983)
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Descrizione libro Dover Publications Inc. 1983-06-01, 1983. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-ING-00310342

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## 4.Fundamental Concepts of Algebra (New edition)

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Descrizione libro Dover Publications Inc. Paperback. Condizione libro: new. BRAND NEW, Fundamental Concepts of Algebra (New edition), Bruce E. Meserve. Codice libro della libreria B9780486614700

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## 5.Fundamental Concepts of Algebra

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Descrizione libro Dover Publications Inc., 1983. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486614700

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## 6.Fundamental Concepts of Algebra

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Descrizione libro Dover Publications Inc., 1983. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486614700

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## 7.Fundamental Concepts of Algebra (Dover Books on Mathematics)

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## 10.Fundamental Concepts of Algebra (Dover Books on Mathematics)

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