Skip to main content ☰ Contents You! < Prev ^ Up Next > \(\def\ann{\operatorname{ann}}
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Preface How to Use This Book
I'm still in the process of figuring out exactly what this 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 analysis sequence.
Assistance in studying for the Analysis 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 .These are pretty standard and probably what you'd be expecting. 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 more technical result used specifically in the proof of a larger result.
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.
Exploration .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.
Context .Historical and etymogical origins.
Footnotes .Sometimes act like remarks. However, most are strictly for fun and add little to no educational value, at least in the traditional sense.
2
It should really be “feetnote” if you think about it.
