Math 2001 - Assignment 9
Due October 30, 2015
(1) Compute:
(a) 3 4 mod 7
(b) 2 9 mod 11
(c) 26 mod 9
(d) Solve for x Z: 13x 3 mod 31
Hint for (d): First solve the equation 13x + 31y = 3 using the
extended Euclidean algorithm.
(2) Prove: Let a, b, c, d Z a
Math 2001 - Assignment 4
Due September 23, 2015
(1) Are the following equalities true for all statements P, Q, R?
(a) P Q = P Q
(b) (P Q) R = P (Q R)
(2) Find a statement in P, Q and R that is true exactly for the
following instances:
(3)
(4)
(5)
(6)
P Q
Math 2001 - Assignment 6
Due October 9, 2015
Please explain your reasoning for your answers to the following problems.
I would like to discuss and compare solutions in class. Please indicate
on your handin whether it is ok to use an anonymous copy of your
Math 2001 - Assignment 13
Due December 4, 2015
(1) Let A, B be finite sets. How many functions from A to B are
there? How many bijective functions from A to B?
(2) (a) Read the proof of Theorem 12.2 in [1].
(b) Find an example of functions f : A B, g : B
Math 2001 - Assignment 3
Due September 16, 2015
(1) Are the following statements? If so, determine whether they
are true or false.
(a) Some swans are black.
(b) Every real number is an even integer.
(c) If x is an even integer, then x + 1 is odd.
(d) 2x =
Assignment 1
MATH 2001
DUE DATE: Thursday, September 18, at the beginning of class.
Please write out complete solutions for each of the following problems. You may,
of course, consult with your classmates, the textbook or other resources, but please
write
Math 2001 - Assignment 7
Due October 14, 2016
Be careful to write down every step in the proofs of 3,4 and reduce
every statement to definitions or other statements that were already
proved in class.
(1) How many different seating arrangements are there o
Math 2001 - Assignment 1
Due September 2, 2016
(1) Are the following true for A = cfw_1, 2, cfw_3, 4 or not?
(a) cfw_3, 4 A (b) cfw_3, 4 A (c) A (d) |A2 | = 16.
(2) [1, Section 1.1]: Exercises 2,4,16
(3) [1, Section 1.1]: Exercises 20,24,26
(4) [1, Sectio
Math 2001 Assignment 16
October 1, 2014
Problem 1. Scheinerman, 6, #2.
Problem 2. Scheinerman, 6, #10.
Problem 3. Scheinerman, 6, #11.
Problem 4. Scheinerman, 6, #13.
Problem 5. Explain why proving x Z, P (x) is equivalent to proving both
of the following
Math 2001 - Assignment 2
Due September 9, 2016
(1) Describe the following using set builder notation:
(a) A = the set of points in R2 on the line through (2, 3) that
is parallel to the y-axis
(b) B = the set of points (x, y) R2 on the line through (1, 2)
Math 2001 Assignment 20
Your name here
October 13, 2014
Problem 1. Scheinerman, 22, #12
Problem 2. Scheinerman, 22, #16cf
Problem 3. In its usual form, induction says that one may demonstrate a
sentence of the form n N, P (n) by proving the following two
The heart is actually (one, two, or three) pumps?
The heart is actually (one, two, or three) pumps?
three pumps
two pumps
one pump
Correct
Yes, the right side of the heart pumps to/from the lungs (pulmonary circuit) and the left side of the heart
pumps to
Capter 13 fecal occult blood
1. List 5 causes for blood in the stool
1. Hemorrhoids
2. Peptic ulcers and gastrointestinal ulcers
3. Diverticulitis
4. Polyps
5. Colitis
6. Colorectal cancer
2. Define the term melena and explain what causes it
Melena is whe
1
Chapter 18: Hematology
1. List the tests generally included in a CBC
White blood cell count
Red blood cell count
Platelet count
Hemoglobin
Hematocrit
Differential white blood cell count
Red blood cell indices
2. Where are erythrocytes formed in t
Blood Study Guide
The major role of the blood is transportation through an intricate system of channels blood vessels that reach
virtually every part of the body. Blood constantly courses through the vessels, carrying gases, fluids, nutrients,
electrolyte
Math 2001 - Assignment 5
Due October 2, 2015
(1) [1, Section 3.1]: Exercise 3
(2) [1, Section 3.1]: Exercise 4
(3) How many standard Colorado license plates (3 numbers followed
by 3 letters) have at least one number or letter repeated?
(4) How many differ
Math 2001 - Assignment 10
Due November 4, 2016
(1) Prove by induction that for every q R with q 6= 1 and for
every n N0 :
1 q n+1
1
2
n
1 + q + q + + q =
1q
(2) [1, Chapter 10, exercise 8] Show that for every n N:
1
2
3
n
1
+ + + +
=1
2! 3! 4!
(n + 1)!
(n
Math 2001 Assignment 23
Your name here
October 17, 2014
Problem 1. Scheinerman, 12, #21. Note that Problem 12.21c should read
(A B) C = (A C) (B C).
Problem 2. Suppose that A and B are finite sets. Prove by induction on the
cardinality of A that |A B| = |
Math 2001 Assignment 19
Your name here
October 8, 2014
Problem 1. Scheinerman, 22, #4e
Problem 2. Scheinerman, 22, #9
Definition
3. When n and k are natural numbers such that k n, we define
n
n!
=
k
k!(nk)! .
Problem 4. Prove that
n
n+1
n
+
=
k+1
k+1
Math 2001 Assignment 15
September 29, 2014
Problem 1. Scheinerman, 5, #2.
Problem 2. Scheinerman, 5, #6.
Problem 3. Scheinerman, 5, #7. Hint: Use the previous problem.
Problem 4. Scheinerman, 5, #18.
Problem 5. Scheinerman, 5, #21.
1