# Homework 23: Section 7.2

Read Section 7.2 and complete

- Theorem 7.2.3
- Exercise 7.2.4
- Theorem 7.2.5
- Corollary 7.2.7

**Due:** Tuesday, December 2

# Homework 24: add a user profile

The first thing I want you to do is to create your own profile for the wiki; you should do this by midnight on **Wednesday, November 25**. You can include as little or as much information about yourself as you like. It might also be nice if you would post a picture of yourself so that people can put a face to your name, but you aren't required to do so if you don't like. You are, however, required to **include some mathematical expression using Wikidot's built-in LaTeX compiler**, just so you get comfortable typesetting mathematics; you are encouraged to be creative in how you make your mathematical expression tie in to the rest of your profile.

You can check out Dana's profile if you want an example of what your profile might look like. After you've created your profile, check to make sure it appears on the user profiles page.

## getting started

On the left navigation panel of this page, there's a text-entry box below "add a new page." In that box you should type

`profile:your-name-here`

though of course you should substitute your actual name in place of "your-name-here". Clicking the button "new page" then takes you to a blank page which is yours to edit; in fact, it takes you straight to the editing panel. Play around so you get comfortable with how the wiki formats text. You should **change the title of the page**. By default, the title of the page will match the title that you assigned to it when you created it, which in this case is `profile:your-name-here`. However, we don't really want the "profile" part to show up when the page displays. So, delete "profile:" in the default page title. When you are done, click "save". Don't worry if you find that you made a mistake or want to later insert something else: you can change or add to your entry by clicking "edit" on the bottom right part of the page.

## including pictures

If you want to include a picture of yourself, you can either link to a picture of yourself which is posted elsewhere on the web (in which case you need the picture's URL) or you can upload a picture from your computer to the wiki. In the latter case, just click on "files" in the bottom right corner of your page to bring up an uploading dialogue; note that this "files" link is not available when you are editing your page, so make sure you've closed the editing panel before trying to upload your picture. Either way, you can include the picture into your page by clicking on the "insert image wizard" button in the editing panel. I'd be happy to help you with this if you want.

## inserting mathematics

**Note:** The following is adopted from Andy Schultz's Quick LaTeX Guide.

Wikidot uses a markup language called $\LaTeX$ to generate properly typeset mathematics. Since you'll be posting to the forum and creating Wiki pages with serious mathematical content, it's good that you get some practice writing mathematical expressions in $\LaTeX$.

## the basics

When you're in the editing panel, you can insert mathematical expressions within your text (i.e., "inline") by using the code

`[$ your-mathematical-expression-here $]]`

For instance, this sentence — which includes the equation $x^{2}+y^{2} = r^{2}$ — is typeset as

`For instance, this sentence -- which includes the equation [[$ x^{2}+y^{2} = r^{2} $]] -- is typeset as`

You can also have your mathematical expressions separated from the text and placed on their own line for emphasis. For instance, if you wanted to type

Here's some fancy mathematics that I don't really understand

(1)Man, that's complicated!

then you'd use the code

```
----
Here's some fancy mathematics that I don't really understand
[[math]]
\log \zeta(s) = s\int_{2}^{\infty} \frac{\pi(x)}{x(x^{s}-1)}~dx = \log \prod_{p} (1-p^{-s})^{-1}.
[[/math]]
Man, that's complicated!
----
```

## more examples

Here are a few more examples that illustrate some of the mathematical notation we may want to use:

expression you want | code you type |
---|---|

$n \in \mathbb{N} \subseteq \mathbb{Z}$ | [[$n \in \mathbb{N} \subseteq \mathbb{Z} $]] |

$\sum_{i=1}^n i^2=1^2+2^2+ \cdots +(n-1)^2+n^2$ | [[$\sum_{i=1}^n i^2=1^2+2^2+ \cdots (n-1)^2+n^2 $]] |

$\sqrt{2} \notin \mathbb{Q}$ | [[$ \sqrt{2} \notin \mathbb{Q}$]] |

$2\in \{2,3,4\} \cap \{1,2,3\}$ | [[$2\in \{2,3,4\} \cap \{1,2,3\}$]] |

$f:A\to B$ | [[$f:A\to B$]] |

$f(x_1)\neq f(x_2)$ | [[$f(x_1)\neq f(x_2)$]] |

$\{a_n\}_{n=1}^{\infty}$ | [[$\{a_n\}_{n=1}^{\infty}$]] |

$(f\circ g)(x)=f(g(x))$ | [[$(f\circ g)(x)=f(g(x))$]] |

$\frac{a}{b}+\frac{c}{d}\neq \frac{a+b}{c+d}$ | [[$\frac{a}{b}+\frac{c}{d}\neq \frac{a+b}{c+d}$]] |

Wikidot also provides a brief summary of how to include mathematical expressions into the wiki.

## a few general comments

Here are a few things to keep in mind:

- All wiki commands are of the form [[blah]].
- All inline mathematical notation must be framed by dollar signs. That is, in the wiki, all inline mathematical notation is of the form [[$stuff$]].
- All displayed mathematical notation (i.e., on its own line and centered) is of the form [[math]] math-stuff-here [[/math]].
- All special symbols in $\LaTeX$ are of the form \some-command. Once you've used $\LaTeX$ enough, you can almost guess what the command is for a certain symbol.

For a list of some of the more common $\LaTeX$ symbols, see here. If you want to see a really, really, really long list of symbols, go here.

**Due:** Wednesday, November 25 at midnight