Algebra and Number Theory
Description
In the two-volume set 'A Selection of Highlights' we present basics of mathematics in an exciting and pedagogically sound way. This volume examines fundamental results in Algebra and Number Theory along with their proofs and their history. In the second edition, we include additional material on perfect and triangular numbers. We also added new sections on elementary Group Theory, p-adic numbers, and Galois Theory.
- A true collection of mathematical gems in Algebra and Number Theory, including the integers, the reals, and the complex numbers, along with beautiful results from Galois Theory and associated geometric applications.
- Valuable for lecturers, teachers and students of mathematics as well as for all who are mathematically interested.
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Persons
Ben Fine was a Professor of Mathematics and Statistics at Fairfield University. He received his Ph.D. from Courant Institute in 1973. He had visiting positions at Yale University, University of California, NYU and TU Dortmund.
Anja Moldenhauer received her Ph.D. from the University of Hamburg. Her research focus lies on Mathematical Cryptology using Combinatorial Group Theory. Since 2017 she is working as a data scientist.
Gerhard Rosenberger did his doctorate in Analytic Number Theory and habilitated in Combinatorial Group Theory. Worldwide he has worked for longer terms at nine universities. At present he is at the University of Hamburg.
Annika Schürenberg studied Mathematics, Physics and German and received her teaching degree from the University of Hamburg. Since 2020 she is working as a teacher at an elementary school.
Leonard Wienke received his master degree from the University of Hamburg and is currently a Ph.D. student at the University of Bremen. His research focus lies on Combinatorial Algebraic Topology.
Content
- Intro
- Preface
- Contents
- 1 The Natural, Integral, and Rational Numbers
- 2 Division and Factorization in the Integers
- 3 Modular Arithmetic
- 4 Exceptional Numbers
- 5 Pythagorean Triples and Sums of Squares
- 6 Polynomials and Unique Factorization
- 7 Field Extensions and Splitting Fields
- 8 Permutations and Symmetric Polynomials
- 9 Real Numbers
- 10 The Complex Numbers, the Fundamental Theorem of Algebra, and Polynomial Equations
- 11 Quadratic Number Fields and Pell's Equation
- 12 Transcendental Numbers and the Numbers e and p
- 13 Compass and Straightedge Constructions and the Classical Problems
- 14 Euclidean Vector Spaces
- Bibliography
- Index
