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Zusatztext "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 Informationen zum Autor 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. Zusammenfassung 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 Inhaltsverzeichnis IDEASThe 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 THEORIESNumber 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 ...
