# Foundations Of Higher Mathematics Exploration And Proof Pdf

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View larger cover. Foundations of Higher Mathematics: Exploration and Proof is the ideal text to bridge the crucial gap between the standard calculus sequence and upper division mathematics courses. The book takes a fresh approach to the subject: it asks students to explore mathematical principles on their own and challenges them to think like mathematicians.

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A mathematical proof is an inferential argument for a mathematical statement , showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems ; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms , [2] [3] [4] along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in all possible cases. An unproven proposition that is believed to be true is known as a conjecture , or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols, along with natural language which usually admits some ambiguity. In most mathematical literature, proofs are written in terms of rigorous informal logic.

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or encountered a mathematical proof of any kind. As a consequence title like “Foundations for Higher Mathematics”, taken by students who have completed.

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