About this Database

This database aims to be launch point for studying/reviewing university level mathematics topics. It does not aim to replace class notes or textbooks but instead aims to organize the material taught in those courses by topic, allowing the user to very quickly review find and review specific material.

How to use this database:

It is recommended that you use Obsidian to view this database, but its not necessary
View the index file to search via topics.
Use a file search function to find specific files.

This database as a concept

When working on a math problem I often find that most of my time is spent struggling with one of two problems:

Trying to learn or remember or find a necessary concepts and material needed to solve the problem at hand
Struggling to make connections between concepts that are necessary to solve the problem on my own

For example, lets say I was trying to figure out if a matrix was invertible or not and I've found my notes on the subject but I don't remember what means so now I need to find out what the symbol means and then where that was covered in my notes. Once I figure out that means determinate and find that I'll find that I don't remember what , , , or are, and I'll continue on in this way.

This cycle is exhausting and frustrating and unfortunately the shear magnitude of information available on the internet and the inconsistent use of terms and topic names make using the internet less than ideal at times. Thus this database was created to solve this problem.

Think about a topic or area you really understand, that you've mastered, and take a step back. How is your understanding and knowledge of that subject laid out? Does it look like pages in a book or slides in a presentation? Of course not, each concept is intertwined with all the others in a giant web of ideas and knowledge.

Layout

This database is made up of three elements:

Notes - any file that ends in .md and is written by us
Links - this includes any link found on a note
Source Material - class notes, outside websites, textbook references, etc

Notes

Notes in this database should represent a concept. Notes should explain the concept they represent, have some kind of graphic (an equation, graph, or image), examples, and links to both the source material the note was taken from and any related topics.

Guidelines:

Layout (for a finished note)
- An intro sentence/paragraph that explains the basics of the concept in plain terms
- A graphic to represent the topic, this can be as simple as an equation or as complicated as a three dimensional graph. Together with the intro these two elements serve as "symbols" of the topic, a logo of sorts. This helps jog the reader's memory and establish connections quicker, or establish a something to represent the topic.
- A full explanation of the concept, generally with an example or two.
- A link to the source material
- Subtopics (ex. on triple integrals we list how to use them with polar coordinates)
- Applications
- Related Topics
Writing Guidelines
- You don't need to cover a topic completely, trying to do so requires that you cover all subtopics, and this means that you will quickly find yourself 3-4 topics away from your original document. It is encouraged that when you encounter a topic that hasn't been covered in the database simply make a note for it, put an incomplete tag on it, and link it to Wikipedia or another source instead.
- If you are unsure about how accurate a topic is simply throw down an applicable tag and note that it might be incorrect. If that topic is important enough it will be fixed later down the line.
New notes
- Add new notes when they are referenced by other topics, our website generator literally doesn't add a file unless another file links to it.
- Don't get tunnel vision, make sure you spend time on the note you want to, follow the writing guidelines above.

Links

Links should be everywhere. Links are what gives this database it's value, it cannot solve it's original purpose without heavy use of links. Links should be used in sentences and explanations primarily then lists.

Guidelines:

Lots of links. Each note should adequately link to other notes and source material.
But not too many. Each reference to a topic should be linked only once within a note or subject. You may add more that 1 link to a note if you believe material the previous link is in might be skipped.
Links should be fluid. A topic is represented by a word, and a note is represented by a link. We want to emphasize this relationship by using links in our explanations rather than in lists such that we create a more organic experience.

Source material

Source material needs to be included as this database will never cover everything, nor will it explain concepts in a way that everyone will understand. Quick access to material that explains things differently, more comprehensively, and gives more examples is invaluable.

Notes should be organized by the branch of mathematics they are apart of primarily, then as they become more specific they should be placed under their prerequisite material. For example Jacobian Matrices falls under calculus (as most of its applications and prerequisite material are calculus concepts), then under multivariable calculus as it requires knowledge of multivariable calculus.

Guidelines:

Still working through this stuff, just make sure to site you sources when possible.

Notes and other stuff

The website generator is a bit picky with the latex stuff so:

When using math blocks (the centered equations that are contained inside of the $$ tags) make sure there is an empty line before and after the block.
Make sure that there are no empty newlines within a math block.
Tabs vs spaces may also effect the math blocks, although not fully tested

Writing Notes

LaTeX to png
LaTeX to svg
To set tool defaults in inkscape double click on the tool icon.
Computer Modern is the name of the LaTeX default font
pdfgrep to search pdfs forum
Use heading ## Related Topics at the bottom of notes to list related topics

Todo

add graphics to most of the notes in the calculus folder
add calc3 notes - ch 14 sect 5-6
add diffeq notes week 11 - 1 - 1- Introduction Sect 4.6 Complex Eigenvalues Part 1
add diffeq notes week 11 - 4 - 4-Sect 4.7 Defective Matrix
add diffeq notes week 12 - 1
add diffeq notes week 13 - 1
fix the general-solutions source diffeq notes - written examples are incorrect
add linear-definition and others

Obsidian Specific

ctrl+e - toggle edit/view mode
ctrl+shift+e - toggle live preview/static edit modes
ctrl+o - open quick switcher
ctrl+k - insert markdown link
[[ - insert link
ctrl+[ and ctrl+] toggle left and right sidebars respectively
ctrl+shift+F - search all files
ctrl+alt+left/right arrow - navigate backward or forward

Vim Specific

Mode related:

I - insert mode at beginning of line
A - insert mode at end of line

Editing:

x - delete character

Moving:

$ - move to end of line
b - move one word back (left)
w - move one word forward (right)

Latex Specific

\equiv - triple equal
\langle \rangle - angle brackets
\pm - plus minus
\mathbb{N} - real and natural numbers
\big( \Big( \bigg( \Bigg( - makes parentheses large
\bigg\rvert_{h=0} - "evaluated at" bar
\| - double vertical bars
\ne - not equal sign
\begin{cases}\end{cases} - add left bracket only