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# Discrete Math for Computing | Week of March 1st, 2016 CS 2305

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This 4 page Class Notes was uploaded by Aaron Maynard on Tuesday March 1, 2016. The Class Notes belongs to CS 2305 at a university taught by Timothy Farage in Spring 2016. Since its upload, it has received 70 views.

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Date Created: 03/01/16

Discreet Math for Computing Aarst Mardard Timothy Farage March 1 – 3 , 2016 Tech Update Nuclear Power United States get 20% of its electricity from nuclear power. France gets 70% of its electricity from nuclear power. When nuclear power came along, France created a reactor design and made an approval for such design. In the 1970's, three-mile island had a nuclear meltdown and the people became nervous. Shortly after the meltdown a fictional film came out about the dangerous effects of nuclear power, and delayed the process for America because the people were scared. If you can do nuclear inexpensively, it would be the best to use because it is nonpolluting, gas emitting source of power. 0% of people have been hospitalized or killed due to nuclear radiation in the US. The only nuclear meltdown to have caused illness and death was Chernobyl. At the time this was under the Soviet Union which carries little to no standard. ^^^ Bottom line: don't work in a nuclear power plant in a communist country. Functions Definition: A function F from a set B to a set C, F: B->C, is a set of ordered pairs, such that every element of B is mapped to (or paired with) exactly one element of C. Domain Codomain Discreet Math for Computing Aastn Mrdnard Timothy Farage March 1 – 3 , 2016 Let’s say B is the set of Students in the class, and C is the set of Grades. B:{set of students in class} C:{set of grades} A+ A B F Students Grades B:{4,6,7} C:{Red, Yellow, Green, Violet} F1 = {(4,[something]), (6,[something]), (7,[something])} ^^^ There are only three sets, though they can contain any combination. To solve how many functions from B->C, we take the exponential of |C| to |B|: |B|^|C| Discreet Math for Computing Aaron Maynard Timothy Farage March 1 – 3 , 2016 F:[all real numbers] -> [all real numbers] where F(x) = x^2 A function is known to be as a one-to-one, or 1-1. In linear algebra, known as objective. If ∀ x ε B ∀ x ε B[(x1!= x 2 -> (F(x )1!= F(x ))2 Every function means: for every x, there is a y. Every one-to-one function means, for each x, there is a unique y. In a one-to-one function, if F:B -> C is 1-1, then |B| <= |C| A function F:B->C is said to be onto (surjective) if for all Y there exists a Y C B such that there exists an (x,y) in a function... or y = f(x) "There are no unused values in C" "The codomain value of C is all used up" Domain Codomain if F:B->C is onto, then |B| >= |C| Example: B would be the number of students taking a course, while C would be the number of sections of such course. Discreet Math for Computing Aaron Maynard Timothy Farage March 1 – 3 , 2016 If F:B -> C is both 1-1 and onto, then F is said to be of correspondence (pairing). Domain Codomain |B| = |C|

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