Algebra and Number Theory by Gerhard Rosenberger
Algebra and Number Theory

Algebra and Number Theory


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About the Book

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.


About the Author:

Gerhard Rosenberger did his doctorate in Analytic Number Theory and habilitated in Combinatorial Group Theory. His scientific work includes 27 published books and more than 200 articles in internationally acclaimed journals. Worldwide he has worked for longer terms at nine universities, including Dortmund, Fairfield, Jyväskylä, and Passau. At present, he is at the University of Hamburg.

Annika Schürenberg studied Mathematics, Physics, and German and received her teaching degree (with distinction) from the University of Hamburg. She has worked as a student teaching assistant and later as an academic teaching assistant at the University of Hamburg; since 2020 she a teacher of Mathematics at an elementary school. She is co-author of the two-volume set A Selection of Highlights, 2nd edition, published with De Gruyter.

Leonard Wienke has studied Mathematics and Physics at the University of Hamburg. He will obtain his Ph.D. from the University of Bremen in early 2023. He has been a teaching assistant for several courses and has given lectures in Point-Set and Algebraic Topology. He is co-author of Topics in Infinite Group Theory, published, and the two-volume set A A Selection of Highlights 2nd edition, published with De Gruyter.


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Product Details
  • ISBN-13: 9783110789980
  • Publisher: De Gruyter
  • Publisher Imprint: de Gruyter
  • Height: 244 mm
  • No of Pages: 395
  • Spine Width: 21 mm
  • Weight: 671 gr
  • ISBN-10: 3110789981
  • Publisher Date: 18 Sep 2023
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Sub Title: A Selection of Highlights
  • Width: 170 mm


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