Concrete Approach to Abstract Algebra (eBook)

W. W. Sawyer (Autor)

eBook Download: EPUB

2018
240 Seiten
Dover Publications (Verlag)
978-0-486-83331-6 (ISBN)

Infos

Brief, clear, and well written, this introductory treatment bridges the gap between traditional and modern algebra. Includes exercises with complete solutions. The only prerequisite is high school-level algebra. 1959 edition.

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Brief, clear, and well written, this introduction to abstract algebra bridges the gap between the solid ground of traditional algebra and the abstract territory of modern algebra. The only prerequisite is high school–level algebra.Author W. W. Sawyer begins with a very basic viewpoint of abstract algebra, using simple arithmetic and elementary algebra. He then proceeds to arithmetic and polynomials, slowly progressing to more complex matters: finite arithmetic, an analogy between integers and polynomials, an application of the analogy, extending fields, and linear dependence and vector spaces. Additional topics include algebraic calculations with vectors, vectors over a field, and fields regarded as vector spaces. The final chapter proves that angles cannot be trisected by Euclidean means, using a proof that shows how modern algebraic concepts can be used to solve an ancient problem. Exercises appear throughout the book, with complete solutions at the end.

Autor

Walter Warwick Sawyer (1911–2008) studied mathematics at St. John's College, Cambridge, and taught all over the world, starting at the universities of Dundee and Manchester and later at the University of Ghana and Canterbury College in New Zealand. He was Professor of Mathematics at Wesleyan University in Connecticut and on the faculty at the University of Toronto. His 11 books include the Dover publications Prelude to Mathematics, Mathematician's Delight, Vision in Elementary Mathematics, and A First Look at Numerical Functional Analysis.

Inhalt

Introduction1. The Viewpoint of Abstract Algebra2. Arithmetics and Polynomials3. Finite Arithmetics4. An Analogy Between Integers and Polynomials5. An Application of the Analogy6. Extending Fields7. Linear Dependence and Vector Spaces8. Algebraic Calculations with Vectors9. Vectors Over a Field10. Fields Regarded as Vector Spaces11. Trisection of an AngleAnswers to ExercisesIndex

Produkt-Details

• Erscheint lt. Verlag: 10.8.2018
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Schlagworte: Abstract • Analogy • ancient problem • angles • basic viewpoint • Brief • clear • Complex • Elementary algebra • euclidean means • exercises and solutions • extending fields • finite arithmetic • high school level algebra • integers • Linear dependence • Math • Mathematics • Modern Algebra • polynomials • prerequisite • simple arithmetic • traditional algebra • vector spaces • well written
• ISBN-10: 0-486-83331-3 / 0486833313
• ISBN-13: 978-0-486-83331-6 / 9780486833316