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# 508 Review Sheet for CS 18200 with Professor Szpankowski at Purdue

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Purdue University taught by a professor in Fall. Since its upload, it has received 39 views.

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Date Created: 02/06/15
Things to Know77 Existential Quanti er There exists an x such that Pm is true 3P Universal Quanti er For all m Pm is true WWW Binomial Coe icient The number of m combinations of a set of n distinct objects n 71 m mln 7 m H fjfifi1 fk iSiSk Product Sum Z f0fifi1fk iSiSk Logarithm De nition Formgt07 log xyltgt 2ym Properties L1 Log is a strictly increasing function Vz7 gt y a log z gt log y L2 Log is a oneto one function Vz7 ylog z log y a m y L3 log 1 0 L4 Va logz 2 a L5 Vzhy logm y log z log y L6 Vz a lo z alo z g g L7 V7ymlog y ylog m L8 1 N long Ogc logcb Summation Properties L1 L2 L3 L4 L5 L6 Let f be any function7 then n 1 Z112n 71 11 2 Proof by induction Base Step for n 17 1 2i 11 1 1 11 2 Induction Hypothesis Assume that for some 1 gt 07 n 1111 1 1 V lt 7 11 7 k 21 2 11 Inductive Step n1 11 i inn1 in1n2 Z1lt21gtn1 2 n1 2 11 11 n 21 2711 1 10 11 Ziz 1111121117 n 1 11 6 Proof by Induction Base Step for n 17 1 1 11121 1222 Inductive Step Assume for some 1 gt 0 that 11 6 then lgg izi niz wy n1gt6lt2n1gt 12n1gtltn2gt 2ltn1gt1gtgtt

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