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# tester AHST 2331 001

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just a test
COURSE
Understanding Art
PROF.
Dr. Brettell
TYPE
Class Notes
PAGES
3
WORDS
CONCEPTS
#tester
KARMA
25 ?

## Popular in Art History

This 3 page Class Notes was uploaded by Christina Madera on Monday August 22, 2016. The Class Notes belongs to AHST 2331 001 at University of Texas at Dallas taught by Dr. Brettell in Fall 2016. Since its upload, it has received 6 views. For similar materials see Understanding Art in Art History at University of Texas at Dallas.

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Date Created: 08/22/16
Chipola College MGF 1107 10.3 Modular Arithmetic__________________________________________________ A modulo m system consists of m elements, 0 through m­1, and a binary operation. For example, the modulo 8 system consists of the elements {0,1,2,3,4,5,6,7}.   In any modulo system we can develop a set of modulo classes by placing all numbers  with the same remainder when divided by m in the appropriate modulo class.  Our  modulo classes come from the elements in our modulo m system.  For example, in our  modulo 8 system, we have the classes 0,1,2,3,4,5,6,7.  The sets are composed in the  following manner: 0 class = {…,­16,­8,0,8,16,24,…} 1 class = {…,­15,­7,1,9,17,25,…} 2 class = {…,­14,­6,2,10,18,26,…} 3 class = {…,­13,­5,3,11,19,27,…} 4 class = {…,­12,­4,4,12,20,28,…} 5 class = {…,­11,­3,5,13,21,29,…} 6 class = {…,­10,­2,6,14,22,30,…} 7 class = {…,­9,­1,7,15,23,31,…} An integer a is congruent to an integer b modulo m, written a≡b (mod m), if a has  remainder b when divided by m.   For instance, 23≡7 (mod 8) since 23 divided by 8 gives remainder 7. Determine the modulo class in each of the following: 1.  46≡? (mod 3) 2.  112≡? (mod 13) 3.  ­13≡? (mod 37) YOU TRY: a.  18≡? (mod 7) b.  42≡? (mod 7) c.  12≡? (mod 12) e.  144≡? (mod 32) f.  ­17≡? (mod 8) g.  1001≡? (mod 35) Chipola College MGF 1107 10.3 Modular Arithmetic__________________________________________________ We can also add, subtract, and multiply in modulo systems.  In order to do this, we  compute the solution using the given operation, and then we find which modulo class the  solution belongs to. Compute the following: 4.  9­1 in mod 6 5.  14+18 in mod 15 6.  11*12 in mod 15 YOU TRY: a.  675­236 in mod 20 b.  17­20 in mod 9 c.  55+19 in mod 18 e.  1050+67 in mod 25 f.  6*7 in mod 20 g.  ­2*­5 in mod 7 For the following exercises, assume that Sunday is represented by day 0, Monday is  represented by day 1, and so on.  If today is Thursday (day 4), determine the day of the  week it will be at the end of each period.  Assume no leap years. 1.  161 days 2.  2 years YOU TRY: a.  463 days b.  3 years, 27 days Chipola College MGF 1107 10.3 Modular Arithmetic__________________________________________________

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