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CS 2100 Week 1 Class notes

by: Nick

CS 2100 Week 1 Class notes CS 2100

Marketplace > University of Utah > Computer science > CS 2100 > CS 2100 Week 1 Class notes
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About this Document

Administrative issues, number sequences, recursive formulas, closed formulas, propositional logic
Discrete Structures
Zvonimir Rakamaric
Class Notes
Discrete Structures, Math, logic




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This 4 page Class Notes was uploaded by Nick on Saturday August 27, 2016. The Class Notes belongs to CS 2100 at University of Utah taught by Zvonimir Rakamaric in Winter 2016. Since its upload, it has received 111 views. For similar materials see Discrete Structures in Computer science at University of Utah.

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Date Created: 08/27/16
CS 2100 homework is due at the beginning of class if come to friday sessions will get answers to the homework can work with others best 3 out of 4 quizzes final exam is Dec 12 at 1030am there will be bonus points for participating in class or on canvas discussions.  homework is not graded heavily. no late homework.  can work with each other on the HW   don’t allow people to copy from you.  this class is about solving problems. So, practice solving problems.  everyone will struggle with some part of this class the sections of this class connect to each other only slightly instead of building upon each other. You should read before class  do not need to bring the textbook to class.  lectures will be a lot of problems ­­ sequences only 2 ways to represent patterns in numbers: recursive formula, closed formula.  5,7,9,11,13,15 = An = A n­12 A1 = 5  don’t forget to write the base case! or = An = 2*n + 3 there are a few patterns that cannot be written in both forms.  1,9,17,25,33,41, __49 = An = A n­18 A1 = 1 or = An = 8*(n­1) + 1 An = 8*n ­ 7 constant amount added: n * constant + starting number ­ constant?  1,4,9,16,25,36 = An = n^2 An = A ^2 n+1 A1 = 1 An = An­1 + (2n­1) An = (sqrt(An­1+ 1)^2 2,4,8,16,32,64 = a1= 2 An = 2A n­1 recursive formula must refer to previous terms not future terms.  there are some things in this class that don’t have a recipe to doing them. so Practice, practice,  practice. But can always use ones you know to figure out ones you don’t.  know how to use the Sigma notation for sums propositional logic preposition is a statement that can be either true or false.  we will use T = true and F = false or 1 , 0 x<4 is not a preposition, it is a predicate 3<4 is a preposition solve HW1 is not a preposition, it is an order we will use propositional variables (lower case letters)  binary operator AND = ^ = && OR   = v = || unary operator NOT = ­, Ex: ((p ^ q) v (­, q)) truth table is presents all possible values. We will need to know the truth tables for basic operations by memory.  2^n number of rows in table, so don’t forget any rows. Good to use a pattern like binary  counting.  AND p q p^q pvq F F F F F T F T T F F T T T T T NOT p ­,p F T T F will not be penalized for using different symbols commonly used.  (p v q) ^ (­,p V q) p q pVq ­,p ­,pVq all F F F T T F F T T T T T T F T F F F T T T F T T break up the equation into parts doing inside of () first. This is very mechanical and logical two statements are logical equivalent if always evaluate to the same truth table in every row (p v q) ^ (­,p V q) = q properties  p ^ q= q ^ p p V q = q V p


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