Welcome to the Rough Guide Project

This is the homepage of the Rough Guides to Mathematics project, a collection of mathematical summaries.

The articles are intended to provide motivation and an overview for the topic, serve as a reference for non-experts who have seen the topic before, highlight some interesting "detours" provided by the subject, and provide directions for related material and future study.

Articles may be browsed by the menu at top, by MSC (mathematics subject classification) tags, or by level tags. You can also use the search box at the top right of the page.

Featured Articles

Abstract Algebra I

The main goal in abstract algebra is extending the operations and properties we take for granted on sets we're used to working with (like integers, reals, complex numbers, etc.) to arbitrary sets. This requires precise definitions and requirements on the structure of the set in order to ensure the desired properties are present.


algebra fields general-algebra groups level2 msc12 msc20 rings

last edited 19 Sep 2009 21:32

Point-Set Topology

Point-set topology is the study of the intrinsic properties of surfaces that are independent of distance. The classic example is the donut and the coffee cup, which, from our point of view, will be the same object.


general-topology level3 msc54 topology

last edited 19 Sep 2009 21:33

Glossary of Abstract Algebra

This glossary lists common terms in abstract algebra, at a level typical for graduate school qualifying exams.


algebra general-algebra level4 msc08 msc12 msc13 msc15 msc16 msc17 msc18

last edited 07 Oct 2009 00:25

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