Abstract


  • Systematic way of solving a given problem

9 Tips


1. Use the defining features of the set-up

  1. Look at what is given
  2. Ask the definition of each term
  3. How the ideas piece up together (infer)

Example 1: Approaching a problem related to Circle, Inscribed Angle Theorem.excalidraw

  1. We are given a Circle
  2. Definition of Circle
  3. It has a radius which is a line from the center of circle to its circumference
  4. Piece the ideas up
  5. 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 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

  1. 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

Reference