This repository was created as a general resource to serve as a personal reference to predominantly simple, but very forgettable details specific to numerical analysis. For example, I can't tell you how many times over the years I've confused combinations and permutations and what differentiates the two. That is until I adopted The Feynman Technique in my perpetual pursuite of knowledge. The Feynman Technique is a recursive (i.e., methods called iteratively on themselves on a simpler and/or smaller subproblem with each iteration) and iterative (i.e., methods which repeat themselves repetitively such as while and/or for loops) 4-step process which is described in the hyperlink above, but in the name of redundancy goes as follows:
- Study
- Teach
- Fill the knowledge gaps
- Simplify
You first study (Step 1) material to a point you believe youreself to be capable of explaining/teaching (Step 2) it to someone else who has no prior knowledge of the topic in such a way they can understand it at a rudimentary level. After explaining/teaching it to someone else you can easily discern the specific subtopics of the primary topic you are studying by identifying the parts which were most difficult for you to explain, and/or them to understand. Then you revisit Step 1 (i.e., studying) to fill the knowledge gaps (Step 3) such that you can explain the topic in a more effective, efficient, and simpler way (Step 4). Now, we repeat the process iteratively such that we refine our understanding of the topic with each iteration (which is what makes it recursive). This method is named after the world renowned Nobel Prize winning Physicist Richard Feynman.
The order of the table of contents below is a biased (my personal opinion) indicator relative to both the complexity of the topic itself, and the recommended order to learn the topics based on dependencies from a lower ordered topic in the table. Please note there are many other topics within the Mathematics umbrella of topics, and these are simply the most prevalent from my perspective as an Electrical Engineer.
| Order | Topic | Description |
|---|---|---|
| 1 | Algebra | the study of variables (i.e., x, y, z) within expressions and the rules which govern how we may manipulate them without dimininishing the integrity of their values seen ubiquitously across all of mathematics |
| 2 | Geometry | the study of the shapes and arrangements of objects emphasizing the properties and relations of points, lines, surfaces, solids in one or more dimensions |
| 3 | Trignometry | the study of the relationship angles and the ratio of lengths with origins in maritime navigation and astronomy |
| 4 | Probability | the study of the likelihood of occurance measured by the ratio of the favorable cases to the whole number of possible cases |
| 5 | Statistics | the study of analyzing numerical data in large quantities for the purpose of inerring proportions in a whole from those in a representative sample |
| 6 | Calculus | the study of change with respect to the physical world around us emphasizing the rates of these changes, the aggregation of the parts of a whole, from both a finite and/or infinite, singular and/or multi-dimensional perspective relative to some defined condition or value (i.e., time, frequency) |
| 7 | Linear Algebra | the study of linear combinations used for solving systems of linear equations with a finite number of unknown variables |
| 8 | Differential Equations | the study of equations that relate a function with one or more of its derivatives which ultimately resolve to a function in numerical analysis; equations composed of both regular expressions and derivatives |
| 9 | Complex Analysis | the study of the analysis of functions of a complex (i.e., real and imaginary components) variable |