Towards a comprehensive graph of mathematical domains and topics.
Math.mx (mathematics) is a zoomable tree map of hierarchical mathematical topics (a navigatable taxonomy of math). It's goal is to give one a holistic mechanism for exploring all of math, to learn what they don't know, to discover and see how fields are related, and to contribute/associate resources to help others better undestand each topic. Its data set is the American Mathematics Society (AMS) MSC2010 taxonomy classifications.
Imagine your own personalized learning graph which showed you a visual map of the topics you wished to learn. When fully zoomed out, you see a map of top level concepts, represented as rectangles. And each each rectangle in the map is colored with hue and saturation whose intensity varies from grey to pink to red, indicating an average representation of how many sub topics in this field you have learned. Each topic's rectangle may be clicked, entered, and zoomed in to, revealing it's related child subtopics. In a recursive manner, each of these topical rectangles too are colored, giving the learning an understanding of their knowledge or familiaritry of this topic's sub-topics. And in clicking any given topic, eventually the learner will reach a base case where there is no sub-topic, but instead a resource -- a wikipedia article, a khan academy quiz, a youtube video, a book chapter -- capable of informing your challenging your understanding.. And upon learning this material, your learning graph becomes updated and through this process, the colors of the map update at each level.
On top of this map, similar to google maps, researchers can plan a trail towards learning a specific discipline of math or perhaps the shortest path to acquiring the knowledge dependent on solving a specific problem. And with each learner who uses the map, the map evolves and learns, providing better resources, predictions, and feedback to all who might enjoy it.
python -m SimpleHTTPServer 8000 index.html
- Here's my 1st announcement of math.mx on facebook + goals
- Here's an idea + complimentary initiatives you may want to explore
- Wiki Data Support: Resolve every math topic to a wikidata ID
- Entity Resolve w/ Wikipedia: Extend the math.mx DAG (which is from the AMS MSC2010 taxonomy -- query it here) with https://en.wikipedia.org/wiki/Category:Fields_of_mathematics (iterate over wikipedia math categories)
- Allow Users to Edit: CRUD (create, read, update, delete) (i.e. back with a database, like s3)
- Allow each box/cell to be annotated with users' resources (academic papers, videos)
- Allow users to add children or neighbors to a specific cell
- Improve Granularity: Make root nodes in the graph not be "domains", but be so granular they resolve to specific formula.
- Curricula Generation: From any given box/cell, allow the user to click a link which generates a (shortest path, ordered) list of dependencies (walks the graph) to learn/understand the selected formula or topic
- User accounts:
- Visualize your comprehension: imagine if each cell in math.mx was colored with a shade of red showing users w/ accounts how well they comprehend a cell (and all its dependencies).
- http://mathworld.wolfram.com/letters/
- http://www.math.niu.edu/~rusin/known-math/index/
- https://www.khanacademy.org/exercisedashboard
- http://jeffbaumes.github.io/standards/#
- https://dl.dropboxusercontent.com/u/11459286/ccssmgraph.pdf
- http://meta.math.stackexchange.com/questions/6479/a-graph-map-of-math-se
- http://forums.xkcd.com/download/file.php?id=29015&sid=8ae1604e5e548bed844ae0f1275bad43&mode=view
- http://www.aaamath.com/grade6.htm#topic1 - elementary
- https://github.com/stared/tag-graph-map-of-stackexchange
- http://www-old.newton.ac.uk/preprints/NI12010.pdf
Insofar as interesting data sets go, you may also be interested in https://michaelkarpeles.com/curations/the-foundation (which I hope becomes like the future math.mx described above)
The objective of this repository is to outline a comprehensive graph (currently a tree) of mathematics and mathematical subtopics, to keep track of which domains or principles I have converage (understanding), and to attach/associate resources with, in order to evaluate and effectively improve my holistic understanding.
Imagine if we could map each rectangle to a color who saturation intensity represents our degree of mastery of the underlying topics/skills.
This experiment could be extended such that, each box at the most zoomed setting directly maps to a wikipedia article containing e.g. equations. If/once one "checks" or asserts their understanding of the concepts of this article, the box becomes checked / colored. As you zoom out, the color of the box becomes the average saturation intensity of its children.
At the top-most level, a map of our ignorance.