PPT-Proof Techniques and Chessboard Problems

Proof Techniques and Chessboard Problems Graph Terms informal Independent Set packing anticlique a set of nonadjacent vertices Dominating Set covering a set of vertices that together are adjacent to all the other vertices. These three techniques are used to prove statements of the form If then As we know most theorems and propositions have this conditional form or they can be reworded to have this form Thus the three main techniques are quite important But some theo Consider a chessboard and remove two diamet rically opposite corner unit squares Is it possible to cover without overlapping the remaining 62 unit squares with dominoes A domino is a rectangle Solution Two diametrically opposite corner squares that Proof If we can produce 5 strings that are pairwise distinguishable wrt then it follows by the Distinguishability Theorem that any DFA recognizing must have at least 5 states 5 such strings are 111110100000001 Now we need to check the claim by ndin (aka cs302: Discrete Mathematics II). Spring 2010. University of Virginia. David Evans. Computation is what Computers do, who needs theory?. flickr. : . gastev. [cc]. Charles Babbage’s . Difference Engine. 1. IN. THE PRESENCE OF. LIMITED. ADVERSARIES. Background – Communication Scenario. 2. Alice. Bob. 011100110110111101110011. Calvin. Bad guy. Encoder. Decoder. (Adversarial). Noisy Channel .  .  . CHESSBOARD LOCALIZATION The chessboard images have been acquired under different conditions of illumination, position, and background; they could therefore contain a frontal, rotated or tilted chessbo RECORDINGMICROPHONE TECHNIQUES 3 Microphone Techniques.............4..................................................................................5Microphone Techniques ........................... (aka cs302: Discrete Mathematics II). Spring 2010. University of Virginia. David Evans. Computation is what Computers do, who needs theory?. flickr. : . gastev. [cc]. Charles Babbage’s . Difference Engine. Can you find an ordering of all the n-bit strings in such a way that . two consecutive n-bit strings differed by only one bit?. This is called the Gray code and has many applications.. How to construct them?. Problem Solving in a Mixed Ability Classroom. Leann de Belder. @LMPeters16 . What does reasoning and problem solving look like in my classroom? . In groups, discuss what reasoning and problem solving means to you.. Basic . definitions:Parity. An . integer. n is called . even. . if, and only if. , . there exists . an integer k such that . n = 2*k. .. An integer n is called . odd. if, and only if, . it is not even.. Basic . definitions:Parity. An . integer. n is called . even. . if, and only if. , . there exists . an integer k such that . n = 2*k. .. An integer n is called . odd. if, and only if, . it is not even.. 5 Research-ByEdward KangToo often people imagine that long hours of studying are the best path to being a model straight-A student Yetresearch showsthat highly successful students actually spend less The Desired Brand Effect Stand Out in a Saturated Market with a Timeless Brand