Main Page

Making full use of the site

The best interface by far is the search box this project is intended to create a queriable resource for looking up things and learning from them (and those pages will link to related and required topics), for some examples try searching for the following:

• Norm
• Inner product
• Category
• Linear map
• Dynkin system

Some pages may be rather sparse, containing little more than a definition, but there is always some information even if it is minimal. This site follows the doctrines of monotonic definition and of least surprise. For example the term "ring without unity" violates monotonic definition, we only ever add properties. And the notation [ilmath]\mathbb{R}_+[/ilmath] is ambiguous and can violate the doctrine of least surprise.

This site goes through great effort to use a consistent, natural and unambiguous notation for everything, it also aims to document alternate notations

This site uses MathJax for mathematical rendering, which uses vector fonts to create sharp and all round superb renderings of mathematical equations. This site also uses XyJax for diagrams, (see Xypic for an example) allowing large diagrams, state machines and so forth to be rendered.

First years

Topics which first years are likely to cover (for example sequences, equivalence relations and so forth) are so called "first-year friendly" pages. This means they are written verbosely and with plenty of explanation in order help those new to the topic. A good example is the limit of a sequence page which gives two almost identical definitions, the experienced mathematician will both not care about the difference and also not need help interpreting the definition, the newcomer will need help, so very clear hand-holding proofs are presented (in a collapsed section, click expand to show) as well as an extended discussion as to why the definition works, including an animated diagram (albeit a low-res capture from a graphic calculator (at the time of writing))

• The category Category:First-year friendly contains 18 pages, this number is lower than the actual number as not all first-year friendly pages have been categorised. If you're a first year, and you search for stuff, it should be friendly.

Undergraduates

This resource is useful to check definitions and theorem statements, to see discussion of notation, and to understand dependencies of a definition, for example if you encounter a Dynkin system you can see other names for it, but also 2 distinct definitions (with references) which are proved equivalent. Thus saving you the work of doing it yourself

Postgraduates

Definitions and theorem statements are always at the top of the page and not verbose, describing the conditions followed by the name of the object or outcome of the theorem. It will be very useful as a "refresher" or checking terminology, however it may not contain some of the rare material you look for. Feel free to request material or add to the project.

Lists of covered items

(All the following statistics are as of Friday, 1/Nov/2024 at 03:37)

• Definitions - contains 819 pages (across 24 subcategories)
• Theorems - containing 239 (across 16 subcategories) (this is difficult to count, see Category:Theorems, lemmas and corollaries for more, there are many more, some trivial and not worthy of their own page)

Slightly related is the category of exemplary pages (containing 7 pages), which showcases the best pages of this site.

In the spirit of openness there is also the category of dire pages (containing 18 pages), which contains pages that are not short, but woefully incomplete and in dire need of content.

Index category

This category contains indexing pages, these are used for things like notation, operators, structures and objects, so forth. This project is always changing, if you make particular use of something or think the current way is good, please comment on the appropriate talk page.

• Index of notation

Mathematical subject index

(Note, if a link is read, it does not mean this site doesn't cover the subject, it just means that there is no introductory page to the subject

• Abstract Algebra
  • Group Theory (see Group Theory for branches)
  • Linear Algebra (see Linear Algebra for branches)
  • Order Theory (see Order Theory for branches)
  • Ring Theory (see Ring Theory for branches)
• Algebraic Topology
• Analysis
  • Complex Analysis
  • Real Analysis
    • Differentiation (see: Linear Algebra → Normed Spaces → Differentiation for branches)
    • Integration (see: Measure Theory → Integration)
• Category Theory
• Combinatorics
• Differential Geometry
• Differentiation (see: Linear Algebra → Normed Spaces → Differentiation for branches)
• Functional Analysis (see also: Linear Algebra → Normed Spaces)
• Group Theory
• Linear Algebra
  • Normed Spaces
    • Differentiation
    • Inner Product Spaces
• Manifolds
  • Smooth Manifolds
    • Differential Geometry (see Differential Geometry for branches)
  • Topological Manifolds
• Metric Spaces (see also: Linear algebra → Normed Spaces)
• Measure Theory
  • Integration
• Number Theory
• Order Theory
  • Lattice Theory
• Ring Theory
  • Module Theory
• Set Theory
  • Order Theory (see Order Theory for branches)
• Smooth Manifolds
• Topological Manifolds
• Topology
  • Metric Spaces (see Metric Spaces for branches) (see also: Linear algebra → Normed Spaces)

OLD STUFF

Old list of "areas"

• Topology
• Linear Algebra
• Set Theory
• Differential Geometry
• Abstract Algebra
• Measure Theory
• Manifolds
• Notation

Commonly needed things

• Shorthands
• Definitions
• Theorems
• Subjects
• Motivations
• All pages
• Useful inequalities
• Index of notation
• Index of terms

Good (finished) pages

• Compactness
• Topology - Motivation for topology - Continuity definitions are equivalent

Editing tips

• Editing guide