A Friendly Introduction to Abstract Algebra
American Mathematical Society (Verlag)
978-1-4704-6881-1 (ISBN)
A Friendly Introduction to Abstract Algebra offers a new approach to laying a foundation for abstract mathematics. Prior experience with proofs is not assumed, and the book takes time to build proof-writing skills in ways that will serve students through a lifetime of learning and creating mathematics.
The author's pedagogical philosophy is that when students abstract from a wide range of examples, they are better equipped to conjecture, formalize, and prove new ideas in abstract algebra. Thus, students thoroughly explore all concepts through illuminating examples before formal definitions are introduced. The instruction in proof writing is similarly grounded in student exploration and experience. Throughout the book, the author carefully explains where the ideas in a given proof come from, along with hints and tips on how students can derive those proofs on their own.
Readers of this text are not just consumers of mathematical knowledge. Rather, they are learning mathematics by creating mathematics. The author's gentle, helpful writing voice makes this text a particularly appealing choice for instructors and students alike. The book's website has companion materials that support the active-learning approaches in the book, including in-class modules designed to facilitate student exploration.
Ryota Matsuura, St. Olaf College, Northfield, MN.
Preliminaries: Introduction to proofs
Sets and subsets
Divisors
Examples of groups: Modular arithmetic
Symmetries
Permutations
Matrices
Introduction to groups: Introduction to groups
Groups of small size
Matrix groups
Subgroups
Order of an element
Cyclic groups, Part I
Cyclic groups, Part II
Group homomorphisms: Functions
Isomorphisms
Homomorphisms, Part I
Homomorphisms, Part II
Quotient groups: Introduction to cosets
Lagrange's theorem
Multiplying/adding cosets
Quotient group examples
Quotient group proofs
Normal subgroups
First isomorphism theorem
Introduction to rings: Introduction to rings
Integral domains and fields
Polynomial rings, Part I
Polynomial rings, Part II
Factoring polynomials
Quotient rings: Ring homomorphisms
Introduction to quotient rings
Quotient ring $/mathbb{Z}_7[x]/ /langle x^2-1/rangle$
Quotient ring $/mathbb{R}[x]/ /langle x^2 +1/rangle$
$F[x]/ /langle g(x)/rangle$ is/isn't a field, Part I
Maximal ideals
$F[x]/ /langle g(x)/rangle$ is/isn't a field, Part II
Appendices: Proof of the GCD theorem
Composition table for $D_4$
Symbols and notations
Essential theorems
Index: Index of terms
| Erscheinungsdatum | 17.08.2022 |
|---|---|
| Reihe/Serie | AMS/MAA Textbooks |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 708 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-6881-6 / 1470468816 |
| ISBN-13 | 978-1-4704-6881-1 / 9781470468811 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
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