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Algebra and Geometry An Introduction to University Mathematics 2nd Edition by Mark V Lawson ISBN 9781003098072 100309807X

Name: Algebra and Geometry An Introduction to University Mathematics 2nd Edition by Mark V Lawson ISBN 9781003098072 100309807X
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Algebra & Geometry: An Introduction to University Mathematics 2nd Edition Mark V. Lawson Digital Instant Download

Author(s): Mark V. Lawson

ISBN(s): 9781003098072, 100309807X

Edition: 2

File Details: PDF, 7.02 MB

Year: 2021

Language: English

SKU: EB-32409410 Category: Mathematics - Algebra Tag: Mark V. Lawson

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Algebra and Geometry An Introduction to University Mathematics 2nd Edition by Mark V Lawson – Ebook PDF Instant Download/Delivery: 9781003098072 ,100309807X
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ISBN 10: 100309807X
ISBN 13: 9781003098072
Author: Mark V Lawson

Algebra & Geometry: An Introduction to University Mathematics, Second Edition provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications. The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solutions of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra. New to the second edition Several updated chapters, plus an all-new chapter discussing the construction of the real numbers by means of approximations by rational numbers Includes fifteen short ‘essays’ that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material Expanded references Contains chapter exercises with solutions provided online at www.routledge.com/9780367563035

Algebra and Geometry An Introduction to University Mathematics 2nd Edition Table of contents:

Section I IDEAS

Chapter 1 The Nature of Mathematics

1.1 Mathematics in history

1.2 Mathematics today

1.3 The scope of mathematics

1.4 What they (probably) didn’t tell you in school

1.5 Further reading

Chapter 2 Proofs

2.1 Mathematical truth

2.2 Fundamental assumptions of logic

2.3 Five easy proofs

2.4 Axioms

2.5 Un petit peu de philosophie

2.6 Mathematical creativity

2.7 Proving something false

2.8 Terminology

2.9 Advice on proofs

Chapter 3 Foundations

3.1 Sets

3.2 Boolean operations

3.3 Relations

3.4 Functions

3.5 Equivalence relations

3.6 Order relations

3.7 Quantifiers

3.8 Proof by induction

3.9 Counting

3.10 Infinite numbers

Chapter 4 Algebra Redux

4.1 Rules of the game

4.2 Algebraic axioms for real numbers

4.3 Solving quadratic equations

4.4 Binomial theorem

4.5 Boolean algebras

4.6 Characterizing real numbers

Section II THEORIES

Chapter 5 Number Theory

5.1 Remainder theorem

5.2 Greatest common divisors

5.3 Fundamental theorem of arithmetic

5.4 Modular arithmetic

5.5 Continued fractions

Chapter 6 Complex Numbers

6.1 Complex number arithmetic

6.2 Complex number geometry

6.3 Euler’s formula for complex numbers

6.4 Making sense of complex numbers

Chapter 7 Polynomials

7.1 Terminology

7.2 The remainder theorem

7.3 Roots of polynomials

7.4 Fundamental theorem of algebra

7.5 Arbitrary roots of complex numbers

7.6 Greatest common divisors of polynomials

7.7 Irreducible polynomials

7.8 Partial fractions

7.9 Radical solutions

7.10 Algebraic and transcendental numbers

7.11 Modular arithmetic with polynomials

Chapter 8 Matrices

8.1 Matrix arithmetic

8.2 Matrix algebra

8.3 Solving systems of linear equations

8.4 Determinants

8.5 Invertible matrices

8.6 Diagonalization

8.7 Blankinship’s algorithm

Chapter 9 Vectors

9.1 Vectors geometrically

9.2 Vectors algebraically

9.3 Geometric meaning of determinants

9.4 Geometry with vectors

9.5 Linear functions

9.6 Algebraic meaning of determinants

9.7 Quaternions

Chapter 10 The Principal Axes Theorem

10.1 Orthogonal matrices

10.2 Orthogonal diagonalization

10.3 Conics and quadrics

Chapter 11 What are the Real Numbers?

11.1 The properties of the real numbers

11.2 Approximating real numbers by rational numbers

11.3 A construction of the real numbers

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