01-intro-RME.student

01-intro-RME.student - Agenda: * Who am I? * What is this...

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Agenda: * Who am I? * What is this course about? * What will we be doing in this course? * Describing functions with contracts ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Big ideas: thinking before hacking is important dealing with complexity is the #1 problem in programming. this class is all about that. Course Manifesto: Mathematics--especially as used by physics--is the formalism we use to describe "what is" -> we model the physical world with equations -> solutions to those equations give us insight into the physical reality around us But, classical mathematics does not say anything about how these processes unfold. For that, we need something else. Computer science is the formalism we use to describe "how to". Algorithm: An abstract sequence of actions composed to solve a problem. example: walking put left foot in front of right foot. put right foot in front of left foot. repeat. :) Program: concrete set of *program statements*, expressed in some *formal language*, which *implements* some algorithm. The task of programming: 1) Given a (possibly incomplete/imprecise) specification 2) Design an *effective* algorithm 3) Implement that algorithm *correctly* and *efficiently* An algorithm is *effective* if: - it correctly satisfies the specification - it is efficient in its (asymptotic) usage of *space* and *time* Note: "asymptotic" performance does not prescirbe a particular running time or size. Rather, it tells us how running time/space requirements grow every time we e.g. double the size of the problem to which the algorithm is applied.
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An implementation of an algorithm is *correct* if it behaves as the alogorithm is intended for all inputs/in all situations. Correctness is never negotiable. There are three notions of *efficient* implementations - the implementation has (concrete) space/time requirements "similar to" the abstract requirements of the corresponding algorithm. - of all of the "asymptotically good" possible implementations, this one is among the better ones in absolute, concrete terms. - it does not take an undue amount of programmer effort to (a) write the implementation in the first place (simplicity) or (b) improve/adapt the implementation to more general/closely related algorithms. (elegance) So, efficient can mean fast, simple and/or elegant This doesn't seem that difficult. What's the big deal? Several big problems: - Engineering: faster, better, cheaper: pick two Unfortunately, our goals are often in conflict. The easiest programs to understand/modify are often not the easiest to write. Programs that are simple to write/understand are often not the absolute fastest possible solution to a problem. The most efficient algorithms for a given problem are often subtle and difficult to implement correctly. - the *languages* in which we program have only a small number of
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01-intro-RME.student - Agenda: * Who am I? * What is this...

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