300 conceptos

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almost three-hundred concepts to know for a pre-mathematician Rate This Elementary maths (nowadays dubbed precalculus) are those that you are learning s ince the awakening of your conscience and anyone should master no matter what pr ofession. After you learn those elementary maths that each human mind should lea rn to perform diligently in a competitive and cruel society, you would be prepa red to begin to learn a set of concepts that serve to you to be considered a pro fessional mathematician, a list of concepts and results is offered to do a contr ast against you think you know or should know. Independently of the flavor or kind of mathematician you gonna be, the following list is aimed for a universal person which is an aspirant mathematician who cla im to be useful in the whatever environment where he or she evolves. Remember th at as an amateur mathematician you are fated to be abstract minded and perhaps t o apply these techniques to th e reality, to model matter and energy as well as all its tangible instances. Abstract reasoning is our essential spirit. For a beginning professional mathematician an incomplete list of modern concepts and results is: sets and maps set operations symmetric difference basic types of maps: constant, injective, surjective, bijective image, pre-image, rank and fiber of a mapping equivalence relation equivalence class partitions abstraction lemma combinations binomial theorem division algorithm Euclides algorithm prime numbers arithmetic fundamental theorem coprime integers modular arithmetics mathematical logic propositional and predicative calculus axiomatics deduction theorem Zorn lemma Zermelo-Fraenkel set theory axiomatics binary operation in a set algebraic structure semigroup monoid group ring field skewfield module vector space algebra groupoide subgroup normal subgroup coset quotient set quotient group or factor group

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