Fundamentals
- A correct value system is the most important foundation (the goal to excel, the willingness to help)
- How to make decisions ? (differentiate emotional decision and strategic decision)
- How to do planning ?
- How to do reasoning, analyzing and drawing conclusion ?
- How to be open minded, humble but not blindly follow conventional wisdom ? (why human walk with 2 legs, why do we have supermarkets, how do we decide where to put a bus station, why an apple is more expensive than an orange)
- How to be patient and control emotions ?
- Develop a good sense of numbers and able to read different charts and graphs, observing relationship between variables and their trends.
- Appreciation of doing things in a smart way
Basic Math Concepts
- Numbers, counting (Integer) and quantities (Real)
- Cause and effect
- Set (belongs, union, intersect, subset)
- Function (dependent and independent variable, continuous vs discrete). Various graphing (histogram, line graph, plot), 2D curve and 3D plane
- Linear equations, degree of freedoms, relationship between number of variables and number of equations.
- Calculus (differentiation and integration), multi-variables and partial differentiation
- Logic (if/then, necessary/sufficient conditions, equivalence) and Proof establishments
- Debate and Logic fallacies
- Geometry and Vector (think 3D instead of 2D)
- Probabilities (Draw a tree of all outcomes and counting)
- Probability distribution function and expected gains
- Permutations and Combinations (how to find out "all possibilities")
- Mathematical induction, recursion in proofs.
- Digits with different bases (and their relationship with Polynomials)
- Making predictions: False positives, False negatives and how trade-off decisions should be made
Math Models
- Decision tree (decision and outcome alternations, min/max strategy). Expected gain and optimization
- Game theory (Nash equilibrium). Outcome prediction within a social group. Win/win and win/lose and lose/lose situations.
- Finding solution using Search tree, exhaustive search in all possibilities in a systematic way (tree traversal, breath-first vs depth-first vs heuristic)
- Linear programming for constraint satisfaction and optimization
- Deterministic vs Stochastic process (Markov chains), Queuing theory
- Control system (equilibrium, stability and feedback loop)
- Graph model (nodes and arcs, path finding, shortest path, minimal spanning tree)
- Finite State Machines (everything happens in a cycle)