Math 15
Additional Exercises
February 25, 2014
1.
Prove that if n is odd, then n 2 n is odd.
2.
If a ,b , and c are odd integers, then there are no rational solutions to
ax 2 bx c 0 .
3 is irrational.
3.
Prove that
4.
If x is rational, then x 3 1 is ratio
Math 15
I.
Probability: Independent Events
March 14, 2014
Extreme Values for the Probability of an Event: Given any event E, what are the
largest and smallest values for P E ? In other words, what are the values that
belong in the boxes:
P E
Under what
Math 15
I.
The Golden Ratio and the Fibonacci Sequence
March 14, 2014
Find x, which is the ratio of the length of the long side of this triangle to the length
of its short side (and be ready to be impressed with this value). Give both an
exact value and a
Math 15
Last Chance Quiz
May 10, 2014
Determine if each of the following is an equivalence relation:
1.
l 1Rl 2 means that l 1 is not perpendicular to l 2 l 1,l 2 R 2 .
2.
l 1Rl 2 means that l 1 intersects l 2 l 1,l 2 R 2 where l 1 l 2 .
3.
l 1Rl 2 means
Math 15
Quiz 6
March 15, 2014
Show absolutely all of your work and completely simplify your answers. Give exact
values only.
1.
To reduce stress, the Republic of Algebrania has piloted a program that sends its
citizens to a one-week long camp. Because thi
Math 15
Quiz
May 4, 2014
1.
Prove that if a b mod n and b c mod n , then a c mod n .
2.
Build a logic circuit (using onlt AND gates, OR gates, and inverters only) that
directly translates the Boolean statement xy x y x y .
Math 15
Quiz 2
February 25, 2014
Use our rules of inference to verify the conclusion of the following argument:
My cat Pythagoras reads both math books and French books. My family Psychiatrist
noted that either Pythagoras does not read math books or does
Math 15
0.
Permutations and Combinations
March 14, 2014
Some useful formulas:
i)
n! n n 1 n 23 2 1 where n is an integer
ii)
P n, k
iii)
n!
This is the means by which we can compute a
n k !
permutation. Specifically, it represents the number of ways we c
Math 15
Quiz 7
March 15, 2014
Show absolutely all of your work and completely simplify your answers. Use exact
values only. Prove each of the following statements using Mathematical Induction.
1.
1
3n 2 5n
i i 2 4 n 1n 2
i 1
2.
10n 7 2n
n
n 10
n N
Math 15
Introduction to Probability
March 14, 2014
Some definitions:
i)
Experiment: an observation of a physical occurrence.
ii)
Sample Space: the set of all possible outcomes of an experiment.
iii)
Event: a subset of the sample space (a collection of out