Algebra & Geometry
An Introduction to University Mathematics
1st Edition
Published on 23. May 2016
Book
Paperback/Softback
384 pages
978-1-4822-4647-6 (ISBN)
Description
Algebra & Geometry: An Introduction to University Mathematics 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 several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra
The text focuses on linear equations, polynomial equations, and quadratic forms. The first several chapters cover foundational topics, including the importance of proofs and properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra
Reviews / Votes
"This book is for anyone who, having had a taste of higher school mathematics, wants to see what serious math at a university level is truly like. It introduces all the important topics in algebra and algebra as it affects geometry and does so in a totally uncompromised fashion. Professor Lawson shows respect for the subject through the patience exercised in developing the material thoroughly while keeping the reader engaged with a conversational style that never loses clarity. Along the way, there are some real novelties that will surprise even seasoned readers of mathematics."-Professor Peter M. Higgins, F.I.M.A., University of Essex
More details
Language
English
Place of publication
Oakville
Canada
Target group
College/higher education
Illustrations
50 s/w Abbildungen
89 Illustrations, black and white
Dimensions
Height: 234 mm
Width: 159 mm
Weight
544 gr
ISBN-13
978-1-4822-4647-6 (9781482246476)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Book
06/2021
2nd Edition
Chapman & Hall/CRC
€87.80
Shipment within 15-20 days
Additional editions
Book
06/2017
1st Edition
CRC Press
€252.97
Withdrawn from sale
Person
Mark V. Lawson is a professor in the Department of Mathematics at Heriot-Watt University. Dr. Lawson has published over 60 papers and has given seminars on his research work both at home and abroad. His research interests focus on algebraic semigroup theory and its applications.
Content
IDEAS
The Nature of Mathematics
MATHEMATICS IN HISTORY
MATHEMATICS TODAY
THE SCOPE OF MATHEMATICS
WHAT THEY (PROBABLY) DIDN'T TELL YOU IN SCHOOL
FURTHER READING
Proofs
MATHEMATICAL TRUTH
FUNDAMENTAL ASSUMPTIONS OF LOGIC
FIVE EASY PROOFS
AXIOMS
UN PETIT PEU DE PHILOSOPHIE
MATHEMATICAL CREATIVITY
PROVING SOMETHING FALSE
TERMINOLOGY
ADVICE ON PROOFS
Foundations
SETS
BOOLEAN OPERATIONS
RELATIONS
FUNCTIONS
EQUIVALENCE RELATIONS
ORDER RELATIONS
QUANTIFIERS
PROOF BY INDUCTION
COUNTING
INFINITE NUMBERS
Algebra Redux
THE RULES OF THE GAME
ALGEBRAIC AXIOMS FOR REAL NUMBERS
SOLVING QUADRATIC EQUATIONS
THE BINOMIAL THEOREM
BOOLEAN ALGEBRAS
CHARACTERIZING REAL NUMBERS
THEORIES
Number Theory
THE REMAINDER THEOREM
GREATEST COMMON DIVISORS
THE FUNDAMENTAL THEOREM OF ARITHMETIC
MODULAR ARITHMETIC
CONTINUED FRACTIONS
Complex Numbers
COMPLEX NUMBER ARITHMETIC
COMPLEX NUMBER GEOMETRY
EULER'S FORMULA
MAKING SENSE OF COMPLEX NUMBERS
Polynomials
TERMINOLOGY
THE REMAINDER THEOREM
ROOTS OF POLYNOMIALS
THE FUNDAMENTAL THEOREM OF ALGEBRA
ARBITRARY ROOTS OF COMPLEX NUMBERS
GREATEST COMMON DIVISORS OF POLYNOMIALS
IRREDUCIBLE POLYNOMIALS
PARTIAL FRACTIONS
RADICAL SOLUTIONS
ALGEBRAIC AND TRANSCENDENTAL NUMBERS
MODULAR ARITHMETIC WITH POLYNOMIALS
Matrices
MATRIX ARITHMETIC
MATRIX ALGEBRA
SOLVING SYSTEMS OF LINEAR EQUATIONS
DETERMINANTS
INVERTIBLE MATRICES
DIAGONALIZATION
BLANKINSHIP'S ALGORITHM
Vectors
VECTORS GEOMETRICALLY
VECTORS ALGEBRAICALLY
THE GEOMETRIC MEANING OF DETERMINANTS
GEOMETRY WITH VECTORS
LINEAR FUNCTIONS
THE ALGEBRAIC MEANING OF DETERMINANTS
QUATERNIONS
The Principal Axes Theorem
ORTHOGONAL MATRICES
ORTHOGONAL DIAGONALIZATION
CONICS AND QUADRICS
The Nature of Mathematics
MATHEMATICS IN HISTORY
MATHEMATICS TODAY
THE SCOPE OF MATHEMATICS
WHAT THEY (PROBABLY) DIDN'T TELL YOU IN SCHOOL
FURTHER READING
Proofs
MATHEMATICAL TRUTH
FUNDAMENTAL ASSUMPTIONS OF LOGIC
FIVE EASY PROOFS
AXIOMS
UN PETIT PEU DE PHILOSOPHIE
MATHEMATICAL CREATIVITY
PROVING SOMETHING FALSE
TERMINOLOGY
ADVICE ON PROOFS
Foundations
SETS
BOOLEAN OPERATIONS
RELATIONS
FUNCTIONS
EQUIVALENCE RELATIONS
ORDER RELATIONS
QUANTIFIERS
PROOF BY INDUCTION
COUNTING
INFINITE NUMBERS
Algebra Redux
THE RULES OF THE GAME
ALGEBRAIC AXIOMS FOR REAL NUMBERS
SOLVING QUADRATIC EQUATIONS
THE BINOMIAL THEOREM
BOOLEAN ALGEBRAS
CHARACTERIZING REAL NUMBERS
THEORIES
Number Theory
THE REMAINDER THEOREM
GREATEST COMMON DIVISORS
THE FUNDAMENTAL THEOREM OF ARITHMETIC
MODULAR ARITHMETIC
CONTINUED FRACTIONS
Complex Numbers
COMPLEX NUMBER ARITHMETIC
COMPLEX NUMBER GEOMETRY
EULER'S FORMULA
MAKING SENSE OF COMPLEX NUMBERS
Polynomials
TERMINOLOGY
THE REMAINDER THEOREM
ROOTS OF POLYNOMIALS
THE FUNDAMENTAL THEOREM OF ALGEBRA
ARBITRARY ROOTS OF COMPLEX NUMBERS
GREATEST COMMON DIVISORS OF POLYNOMIALS
IRREDUCIBLE POLYNOMIALS
PARTIAL FRACTIONS
RADICAL SOLUTIONS
ALGEBRAIC AND TRANSCENDENTAL NUMBERS
MODULAR ARITHMETIC WITH POLYNOMIALS
Matrices
MATRIX ARITHMETIC
MATRIX ALGEBRA
SOLVING SYSTEMS OF LINEAR EQUATIONS
DETERMINANTS
INVERTIBLE MATRICES
DIAGONALIZATION
BLANKINSHIP'S ALGORITHM
Vectors
VECTORS GEOMETRICALLY
VECTORS ALGEBRAICALLY
THE GEOMETRIC MEANING OF DETERMINANTS
GEOMETRY WITH VECTORS
LINEAR FUNCTIONS
THE ALGEBRAIC MEANING OF DETERMINANTS
QUATERNIONS
The Principal Axes Theorem
ORTHOGONAL MATRICES
ORTHOGONAL DIAGONALIZATION
CONICS AND QUADRICS