Abstract Algebra
An Interactive Approach, Second Edition
Seiten
2024
|
2nd edition
Chapman & Hall/CRC (Verlag)
978-1-032-91795-5 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-032-91795-5 (ISBN)
This textbook is for a first undergraduate course in abstract algebra. It differs from the first edition in that it offers optional technology and less focus on interactivity. It has a more traditional approach where additional topics to the primary syllabus are placed after primary topics are covered, creating a more common table of contents. W
The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use.
This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered.
This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.
Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics.
This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.
The new edition of Abstract Algebra: An Interactive Approach presents a hands-on and traditional approach to learning groups, rings, and fields. It then goes further to offer optional technology use to create opportunities for interactive learning and computer use.
This new edition offers a more traditional approach offering additional topics to the primary syllabus placed after primary topics are covered. This creates a more natural flow to the order of the subjects presented. This edition is transformed by historical notes and better explanations of why topics are covered.
This innovative textbook shows how students can better grasp difficult algebraic concepts through the use of computer programs. It encourages students to experiment with various applications of abstract algebra, thereby obtaining a real-world perspective of this area.
Each chapter includes, corresponding Sage notebooks, traditional exercises, and several interactive computer problems that utilize Sage and Mathematica® to explore groups, rings, fields and additional topics.
This text does not sacrifice mathematical rigor. It covers classical proofs, such as Abel’s theorem, as well as many topics not found in most standard introductory texts. The author explores semi-direct products, polycyclic groups, Rubik’s Cube®-like puzzles, and Wedderburn’s theorem. The author also incorporates problem sequences that allow students to delve into interesting topics, including Fermat’s two square theorem.
William Paulsen, PhD, professor of mathematics, Arkansas State University, USA
Preliminaries. Understanding the Group Concept. The Structure within a Group. Patterns within the Cosets of Groups. Mappings between Groups. Permutation Groups. Building Larger Groups from Smaller Groups. The Search for Normal Subgroups. Solvable and Insoluble Groups. Introduction to Rings. The Structure within Rings. Integral Domains and Fields. Unique Factorization. Finite Division Rings. The Theory of Fields. Galois Theory. Appendix: Sage vs. Mathematica®. Answers to Odd-Numbered Problems. Bibliography.
| Erscheinungsdatum | 16.10.2024 |
|---|---|
| Reihe/Serie | Textbooks in Mathematics |
| Zusatzinfo | 41 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 1202 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 1-032-91795-4 / 1032917954 |
| ISBN-13 | 978-1-032-91795-5 / 9781032917955 |
| Zustand | Neuware |
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