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.
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.
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.
Über den Autor
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.
Klappentext
This second edition gives a thorough introduction to the vast field of Abstract Algebra with a focus on its rich applications. It is among the pioneers of a new approach to conveying abstract algebra starting with rings and fields, rather than with groups. Our teaching experience shows that examples of groups seem rather abstract and require a certain formal framework and mathematical maturity that would distract a course from its main objectives. Our philosophy is that the integers provide the most natural example of an algebraic structure that students know from school. A student who goes through ring theory first, will attain a solid background in Abstract Algebra and be able to move on to more advanced topics. The centerpiece of our book is the development of Galois Theory and its important applications, such as the solvability by radicals and the insolvability of the quintic, the fundamental theorem of algebra, the construction of regular n-gons and the famous impossibilities: squaring the circling, doubling the cube and trisecting an angle. However, our book is not limited to the foundations of abstract algebra but concludes with chapters on applications in Algebraic Geometry and Algebraic Cryptography.
