# Knowledge Graph

I am building my own knowledge graph, the areas I add to the graph are Mathematics, Physics, Computer Science and Music, but I'd like to interconnect as many areas as possible. If you'd like to contribute please let me know.

## How to use this knowledge graph to learn:

• You need to use a computer to access it, a phone will be too small.
• Use this to find an area of interest
• Once you've found a topic, search for it in the left search bar (under the focus tab) on this link
• The output will be a tree structure, the red nodes represent knowledge that you can learn, the root (aka top red node) is something that you can learn without any previous experience in the particular field.
• The layer after that represent ideas that build on that first idea, and possibly other concepts at that level. You can see what it is related to by clicking on it.
• In general the next layer represents ideas that build on the previous layers, this is how you develop advanced ideas.
• By following a top to bottom approach you are given the guarentee that there will never be a statement which you cannot comprehend, sure understanding why it's true might be harder, but you will be able to understand what the statement is, as you understand all of the definitions that this node uses!
• In order to see the content related to a knowledge node you must click on it, then follow the link that appears, if there is no link, it is a work in progress, but a link will be there soon.

# The Schema

• This defines the structure of the knowledge base
• The motivation of this schema is from a hierarchy
• Consider all of Mathematics
• There are subsections of Mathematics, say Geometry
• Inside of Geometry we have different areas, say The Constructible Numbers
• In there we would find the definition of a compass and straight edge
• In general, we notice two different things, something that is structural and something that has knowledge in it.
• Geometry in this case was structural, it may have some base definitions of it's own but mainly it is there to hold all the different areas of geometry.
• The definition of a compass is not structural, it only contains it's definition
• This gives rise two two different types
• Structure
• Knowledge
• We augment the schema further motivated by the way we learn
• Knowledge
• Will have a parent, it's parent will always be a Structure
• The definition of a Set belongs in Set Theory
• Will have outgoing edges (directed) labled "Knowledge Used" to other instances of Knowledge
• This nodes that are connected in this way is knowledge that you must understand to understand this instance of Knowledge
• Eg) You need to know what the definition a set is to understand the definition of a function
• Structure
• Will have a parent as well, this will also be a Structure
• It will have outgoing Knowledge Used edges as well, this will be the starting definitions/axioms in the particular structure

## Generalizations through a Knowledge Graph

• Think about how we learn stuff: We take simple ideas and build on them to make more advanced ones
• This is exemplified in textbooks
• Textbooks define a certain ordering when they publish their books.
• Chapters can sometimes stand independently from other chapters (eg, you do not need to know all the previous chapters to learn this chapter)
• Inside chapters there is a more particular ordering found
• Following the method in which we learn, then you can see that it makes sense that they would introduce a set of base ideas/definitions and then create more ideas/definitions that use previous ones.
• Using the above schema, we have already induced the textbook ordering
• 