APPLI DISCRETE STRUC
APPLI DISCRETE STRUC COT 3100
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This 2 page Class Notes was uploaded by Carlo Monahan on Friday September 18, 2015. The Class Notes belongs to COT 3100 at University of Florida taught by Timothy Davis in Fall. Since its upload, it has received 35 views. For similar materials see /class/206631/cot-3100-university-of-florida in OTHER at University of Florida.
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Date Created: 09/18/15
COT 3100 sec 7094X Fall 1999 Supplementary Notes on How to Write Good Proofs 1 Why is this important Some students may not at rst understand why it s important for their career that they learn how to write good mathematical proofs They might say I understand the basic concepts and properties of discrete structures and I know how to work with them why is it important that I be able to prove things about them The reason is that proofwriting teaches not only logical reasoning skills but also the critically important very general skill of knowing how to clearly communicate a logical argument Sup pose you are working at a company and you need to explain to a coworker client or supervisor the reason why you recommend a particular algorithm procedure strategy or course of action If you are able to give a clearly stated concise coherent logical argument in support of your pro posal your chances of successfully convincing your audience of the merits of your proposal and of your own competence will be greatly improved The ability to communicate effectively was recently rated the most important job skill by industries that hire our graduates http www cise ufl edudavisIABApr99Apr995urvey txt You can look at writing mathematical proofs as simply an exercise in clearly and convincingly communicating a logical argument The domain of our proofs happens to be the discrete mathe matical structures that we have been studying but many of the same skills of clear thought and clear communication that you learn when doing mathmatical proofs can carry over to improve your skills at composing persuasive rational arguments in just about any area of endeavor And of course knowing how to read and write proofs and rational arguments in general should be very helpful to you for your later classes in this degree program and it will be absolutely essential if you plan to go on to graduate school to eventually teach or do original research in any area of engineering science computer science or mathmatics Law and business graduate pro grams also require the ability to present clear arguments 2 What is a proof A proof is merely an argument that rmly establishes the validity of a statement Ideally the most effective means of proof is an interactive discussion Suppose you are trying to convince someone of the truth of a statement A They don t at rst understand why A is true so you give them an intermediate statement B in support of A They may then see why B is true but not yet why B implies A So you give them an additional intermediate step C Now maybe they
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