Skip to main content Contents Index Prev Up Next \(\DeclareMathOperator{\ann}{ann}
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Preface How to Use This Book
I’m still in the process of figuring out exactly what this text is for. Some possibilities include:
Future lecture notes for the hopeful possibility that one day I will teach a course over this material.
Current notes for students taking the first year algebra sequence.
Assistance in studying for the Algebra Qualifying Exam at UNL.
Clout.
Blocks.
Here are the types of environments you are likely to encounter throughout the text and what they are used for.
Definition .
The building blocks of what we’ll be working with.
Examples .
Specific instances of a definition. For example, the empty set, \(\emptyset\) is an example of a set, and thus would be contained within an “example” environment. At some point the line between example and definition becomes incoherently blurred, but I have done my best to keep things consistent.
Theorem .
A result.
Lemma .
A true mathematical statement that was proven mainly to help in the proof of some theorem.
Corollary .
An important result whose proof comes directly from a previous theorem.
Proposition .
Results that require proof but are more specific and/or contained in a larger result coming later.
Exercise .
Generalizations, specifics, smaller results, things are are less essential to the course or results who’s proofs are usually skipped.
Problem .
Used for qualifying exam problems.
Remark .
Providing context in the form of foreshadowing or content not covered in this text. In general, there shouldn’t be anything defined in a remark, they should be entirely optional.
Discussion .
Usually for arguing about notation.
Footnotes .
Sometimes act like remarks. However, most are strictly for fun and add little to no educational value, at least in the traditional sense.
Don’t Forget the Index! This text (and algebra in general) contains an otherworldly amount of definitions and notation, it can sometimes be overwhelming keeping track of it all, and that’s okay! The [cross-reference to target(s) "index" missing or not unique] is here to help; it contains a comprehensive list of all the terms and notation used here, as well as where to find their definition / first usage in the text. Use it, it’s here for you!
