Buch, Englisch, 398 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 1290 g
Buch, Englisch, 398 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 1290 g
Reihe: Graduate Texts in Mathematics
ISBN: 978-0-387-97497-2
Verlag: Springer
This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19 century. It glimpses the mystery surrounding imaginary numbers in the 17 century and views some major developments of the 20 century.
Zielgruppe
Graduate
Weitere Infos & Material
A. From the Natural Numbers, to the Complex Numbers, to the p-adics.- 1. Natural Numbers, Integers, and Rational Numbers.- 2. Real Numbers.- 3. Complex Numbers.- 4. The Fundamental Theorem of Algebr.- 5. What is ??.- 6. The p-Adic Numbers.- B. Real Division Algebras.- Repertory. Basic Concepts from the Theory of Algebras.- 7. Hamilton’s Quaternions.- 8. The Isomorphism Theorems of FROBENIUS, HOPF and GELFAND-MAZUR.- 9. CAYLEY Numbers or Alternative Division Algebras.- 10. Composition Algebras. HURWITZ’s Theorem-Vector-Product Algebras.- 11. Division Algebras and Topology.- C. Infinitesimals, Games, and Sets.- 12. Nonsiandard Analysis.- 13. Numbers and Games.- 14. Set Theory and Mathematics.- Name Index.- Portraits of Famous Mathematicians.
