Tutor profile: Neil P.
How does one's way of thinking about things change once they master statistics?
Statistics is the ultimate tool for making predictions and decisions. Mastering this subject grants the master with the intuition to analyze risk and reward before making a decision. The master of probability and statistics would never play the lottery, for example. Although they would never gamble at the casino with a game such as blackjack, they might learn to count cards or decide to play poker. They would never commit fallacies such as the gambler's fallacy or its inverse. Instead they would put their faith in the law of large numbers as it is ingrained in their heads and they would conduct their lives with patience for it.
How does one's way of thinking about things change once they master physics?
Physics forces its masters to think in a "first principles" way. Those who have mastered this subject approach problems from the ground up. They do not memorize equations, they derive them from the most basic and fundamental equations. Even those equations are not memorized, rather they are recalled from intuitive reasoning. This way of thinking gives rise to the strongest problem solving skills as it allows for very creative solutions since the problem solver is not distracted by previously established conventions.
How does one's way of thinking about things change once they master algebra?
Once algebra is mastered, one's approach to solving a problem, any problem be it math or otherwise, may be shifted. In algebra, one does not guess a solution and see if it works. One logically deduces the missing piece of an equation by working backwards starting from the answer. Certain problems or puzzles call for this way of thinking, which algebra introduces in the simplest and most direct way.
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