11/13/2022 0 Comments Number of text blocks in thomasThe UI of the text is amazingly clean and efficient. The exceptions aren't detractions, though, and allow for modularity or digressions to applications. The text has a relatively linear progression, with some exceptions. Or omit the chapters on integral domains (with some minimal adjustment), lattices, and linear algebra if one is making a push to fields and Galois theory. For instance, it's easy to cover the material on matrix groups and symmetry (chapter 12) right after the intro coverage of groups (chapter 3) if you want more concrete examples. Many sections and some chapters are written in a way that relies minimally on previous material which allows one to omit them or change the order of presentation without too much fuss. So it's quite easy to divide the material into tight, bite-sized portions along the sections of the book, with a few exceptions, i.e., sections that run -much- longer and denser than average, like the section on field automorphisms. Moreover, many sections are punctuated, perhaps including no more than several definitions and propositions along with a historical note. Judson is very direct, and so his chapters are very focused. Still, it can make it hard to locate the precise definition quickly by scanning the section, but happens so rarely I won't detract a point. Defined terms _are_ still shown in bold, though. The only inconsistencies I've noticed involve the occasional definition appearing inline (usually in a sentence motivating the definition) instead of set aside in a text box. The book is consistent in language, tone, and style. NUMBER OF TEXT BLOCKS IN THOMAS HOW TOFor instance, there is a dearth of examples of how to compute minimal polynomials and extension degrees (and the subtleties involved), and so the instructor has to provide the strategies necessary to solve parts of the first two problems. However, there are instances where there are big jumps between what some beginning exercises assume and what was presented explicitly in the chapter which confused many of my students. I find his style clean and easy to follow. Judson's writing is direct and effective. Judson does this in practical ways given that Sage is such a big component of the book, and so there are many exercises and descriptions that stress this relevance. Modern applications are sprinkled throughout the text that informs the students of the value of the material beyond theoretical. But I came across very few of these in my problem sets. There _are_ some errors in the exercises, however, like the inclusion of unnecessary or irrelevant parts, or typos. All of the exercises use this definition as well, and so I chose to (mostly) avoid the chapter on Galois theory in favor of a more standard presentation. He defines this before he's defined fixed fields (ala Artin), or normal/separable extensions. However, of primary note is Judson's non-standard (in my experience) definition of Galois group as the automorphism group Aut(E/F) of an arbitrary field extension E/F. I've noticed very few outright errors in the text proper. Since Judson includes _a lot_ of Sage which he uses to expand, clarify, or apply theory from the text, a fairly standard presentation of the theory, and includes hints/solutions to selected exercises, the textbook is very comprehensive. Given the searchability, the index style is an interesting choice. There are no pages displayed, but there is a google search bar to scan the book with. The index uses a similar approach, choosing to display a collapsed link to the first paragraph in which the term is used, which is often a formal definition. NUMBER OF TEXT BLOCKS IN THOMAS FULLFor example, Judson leverages HTML so that proofs are collapsed (but can be expanded) which allows him to clean up the presentation of each section and include full proofs of earlier results when useful as references. The coverage is all fairly standard, with excepting the definition of Galois group (see accuracy), and the referencing system in the HTML version is extremely convenient. I will note here that Judson avoids generators and relations. Three chapters on rings, one on lattices, a chapter reviewing linear algebra, and three chapters on field theory with an eye towards three classical applications of Galois theory. The coverage of ring theory is slimmer, but still relatively "complete" for a semester of undergraduate study. That is, some review from discrete math/intro to proofs (chapters 1-2), and elementary group theory including chapters on matrix groups, group structure, actions, and Sylow theorems. Judson covers all of the basics one expects to see in an undergraduate algebra sequence. Reviewed by Malik Barrett, Assistant Professor, Earlham College on 6/24/19 Journalism, Media Studies & Communications +.
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