Method of Mathematical Reasoning and Aptitude for Paper 1 Unit V (Mathematical Reasoning and Aptitude) as Per New 2020 Syllabus

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Mathematical Reasoning and Aptitude

  • Mathematical reasoning is the process of thinking about things in a logical, rational way.

  • It is considered an innate human ability that has been formalized by field such as logic, mathematics & artificial intelligence.

  • The process of reasoning is used to make decisions, solve problems & evaluate things.

  • It can be formal or informal, top-down or bottom-up & differs in terms of handling of uncertainty & partial truths.

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Types of Mathematical Reasoning

The following are the few major types of reasoning.

  • Deductive reasoning

    • Deductive reasoning is a formal method of top-down logic that seeks to find observation to prove a theory.

    • It uses formal logic & allows for uncertain but likely results.

  • Abductive reasoning

    • Like induction, abductive reasoning seeks theories to explain observation. It is less rigorous & allows for best guesses.

    • Abductive reasoning is typical used in the context of uncertainty. It is associated with decision making & making trouble shooting.

  • Backward induction

    • Backward induction is a top-down approach that starts with theories or end-states & works backwards to explain them.

    • It allows for uncertainty & is commonly used in artificial intelligence.

    • For example, it’s a classical way for a computer to pay chess by considering game end-states & working backwards to evaluate moves.

  • Critical thinking

    • Critical thinking is a process of rational thought that seeks to draw conclusions in an objective, thorough & informed manner.

    • It’s a products of human thought & is influenced by factors such as culture & language.

    • Human thought is based on natural language that allows for a great range of ideas to be contemplated.

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    • For example, humans can easily process partial truths, commonly known as grey areas, which tend to be a challenge in the field of logic.

    • Critical thinking can also examine complexities such as emotion.

    • For example, critical thinking can be used to critique a film or book.

  • Counterfactual thinking

    • Counterfactual thinking is considering things that are known to be impossible.

    • The most common example of this is evaluating past decisions that were once possible but are now impossible as their time horizon has passed.

    • Considering how past decisions might have worked out is a common human thought process that may improve decision making abilities.

  • Intuition

    Intuition are judgements that are made by the mind that are perceived by the unconscious. Such judgement exhibit intelligence but the processes by which they are generated aren’t well understood. Although intuitions is sometimes taken lightly, it has played a significant in scientific discovery.

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