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Expert: - 5/19/2010


Question

Diagrams of Question #
Question # 1

(a)   How many one-to-one functions are there from a set’X’ with four elements to a set’Y’ with five elements?
(b)   How many one-to-one functions are there from a set’X’ with six elements to a set’Y’ with four elements?
(c)     Let a bijective function f:X->Y be defined as

      Draw Inverse function of ‘f’ using arrow diagram.

Note: Arrow diagram is attached with this Email.


Question # 2

Which type of functions these arrow diagrams defines?
i)   ii)   iii)   iv)   v)


Diagrams are attached with this Email.


Question # 3

Find the sum of all the integral multiples of 6 between 5 to 99 (use formula to sum the series).

Answer
Question # 1

(a) There are 4 elements in X, each of which can have 5 choices in Y.
This makes the number of total cominations 4*5 = 20.

(b)  There are 6 elements in X, each of which can have 4 choices in Y.
This makes the number of total cominations 6*4 = 24.

(c) To make the inverse, draw the same lines with each of the arrowheads at the other ends of the line that they are on.

Question # 2

I'm not sure of the names to use, but ...
(i) is a non-invertible function;
(ii) is nothing, but when the arrows are inverted, it is a non-invertable function;
(iii) is an invertible function that is one-to-one;
(iv) is a function that is almost invertible, but the inverse has no definition for 4;
(v) is a non-invertable function that is kind of like montonic since anything maps to 6.

Question # 3

Find the sum of all the integral multiples of 6 between 5 to 99 (use formula to sum the series).
There are 16 multiples of 6, that is, 6, 12, 18, 24, 30, 35,42, 48, 54,60, 66, 72, 78, 84,90, and 96.  The sum of these would be that same as 6*sum(1 thru 16).

The sum(1 thru 16) = 16*17/2 = 136.  Multiply this by 6, and the right answer is found.

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

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