Abstract
- Systematic way of solving a given problem
9 Tips
1. Use the defining features of the set-up
- Look at what is given
- Ask the definition of each term
- How the ideas piece up together (infer)
Example 1: Approaching a problem related to Circle, Inscribed Angle Theorem.excalidraw
- We are given a Circle
- Definition of Circle
- It has a radius which is a line from the center of circle to its circumference
- Piece the ideas up
- Any lines from the center of circle to its circumference is the same length
2. Giving things (meaningful) names
- Give names to objects that describe its properties (Or to differentiate each one)
- It is like forming an Abstraction (抽象) over something, then we have more brain power to build on top of it
Example 1: Approaching a problem related to Circle, Inscribed Angle Theorem.excalidraw
- Give Θ (Theta) a name
3. Leverage symmetry
- Obtaining another piece of information based on reflection/symmetry, basically using reflection/symmetry to generate more useful information
Example 1: Approaching a problem related to Circle, Inscribed Angle Theorem.excalidraw
- Since the angle is 90degrees, 2 out 3 sides are the same. The 2 triangles obtained after divided are basically the same triangle, symmetry of each other
- Thus, we can conclude that a b, d e
4. Try describing 1 object 2 ways
- Explaining something in 2 different perspectives. 2 different paths to the same object, likely to have some different knowledge points. This helps to have more connections. Thus, coming out with more creative ideas
- For example, counting the possible permutation of a string of 5 bits. 1) Count the exponential 2) Count the possible permutation one by one
Example 1: Approaching a problem related to Circle, Double-angle Formula for cosine.excalidraw
- Proof cos2(a) == 1/2 * (1 + cos(2θ)) by describing the cos2(a) & cos(2θ) on the graph
5. Draw a picture
- This helps with Visualisation
- One way to visualise numbers is to associate they with coordinates, then we can present the numbers & their relationship in graph format
6. Ask a simpler version of the problem
- Find a problem that has the similar setup, but easier to solve or more approachable to get more sense/clue of the original problem
7. Read a lot, and think about problems a lot
- Insights & ingenuity is basically pattern recognition
- Using obsidian to connect the ideas, structure messy knowledge nodes, let nodes interconnect with each other, form a network of pattern recognition, so each node has a lot of contact points via directly and indirectly connected nodes
- With connections and repetitions, the knowledge points will be embedded into sub-conscious which is much more efficient than and powerful than conscious
8. Always gut-check your answer
- There isn’t perfection, the ability to identify mistakes & give fixes is golden
9. Learn at least a little bit of programming
- Helps to provide a different perspective to math which is very abstracted
- We can also take advantage of its ability to generate a massive set of numbers to get a rough estimation trend or pattern