Axiomatic Arithmetic: An Introduction To Number Systems
Regular price
€92.99
A01=Amol Sasane
Author_Amol Sasane
Cardinality
Category=PB
Category=PBKA
Completeness of the Reals
Complex Numbers
Continued Fractions
Decimal Representation
eq_isMigrated=1
eq_nobargain
Euclid's Algorithm
Foundations of Algebra and Analysis
Fundamental Theorem of Algebra
Fundamental Theorem of Arithmetic
Integers
Liouville's Approximation Theorem
Modular Arithmetic
Natural Numbers
Number Systems
Number Theory
Octonions
P-adic Numbers
Peano Axioms
Quaternions
Rational Numbers
Rational Zeroes Theorem
Real Numbers
Product details
- ISBN 9789819822263
- Publication Date: 24 Oct 2025
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
The goal of this book is to construct and explore the properties of the most commonly encountered number systems, beginning with the Peano axioms for the natural numbers. The systems discussed include the natural numbers, integers, rational numbers, real numbers, and complex numbers.Along the way, the book covers a range of related topics such as the ring-theoretic properties of integers, Euclid's algorithm, the fundamental theorem of arithmetic, modular arithmetic, and cardinality. It also delves into decimal and continued fraction representations of the reals, the rational zeroes theorem, Liouville's approximation theorem, the extended real number system, and the fundamental theorem of algebra.The book contains 233 exercises with detailed solutions provided at the end, making it well-suited for self-study. These exercises also introduce additional number systems including the quaternions, octonions, and p-adic numbers.The intended audience is first- or second-year undergraduate students in Mathematics or the Applied Sciences who have completed a first course in Calculus. It may also be valuable to school teachers interested in the foundations of algebra and calculus, as well as students in teacher education programs.This book can serve as a supplementary text for introductory courses in real analysis or algebra. It also includes 57 figures to aid understanding throughout.
