Math 180 Name (Print):
5/5/2016 NetID:
Time Limit: 120 Minutes
This exam contains 14 pages (including this cover page) and 16 problems. After starting the exam, check
to see if any pages are missing. Enter all requested information on the top of this pa
Worksheet 9
Math 181: Fall 2015
For the following two order requirement digraphs, use critical path scheduling to write a priority
list and then use that priority list and the list processing algorithm to schedule the tasks on two
processors.
1.
T2
T1
3
8
Chapter 22: Borrowings Models
October 21, 2013
Chapter 22: Borrowings Models
Last Time
The Consumer Price Index
Real Growth
Chapter 22: Borrowings Models
The Consumer Price index
The ocial measure of ination is the Consumer Price Index (CPI)
which is the
Homework 3
Math 181: Fall 2015
Due: Wednesday, September 23rd
About this homework assignment:
If you write your answers on multiple pieces of paper, please staple them together. Remove
any fringe from notebook paper.
You are welcome to work with other s
Chapter 13: Fair Division
October 7, 2013
Chapter 13: Fair Division
Motiving Question
In 1991 Ivana and Donald Trump divorce. The marital assets
included a 45-room mansion in Greenwich, Connecticut; the
118-room Mar-a-Lago mansion in Palm Beach, Florida;
Review for Exam 1
September 25, 2013
Review for Exam 1
Exam 1
Exam 1 will be over chapters 1,2,3, and 9.
It will be in class. Be on time.
There will be 8 Questions.
Review for Exam 1
Chapter 1 Review
Terms to know:
Graph
Edge
Vertex
Valence
Path
Circuit
E
Worksheet 13
Math 181: Fall 2015
Simplify your answers. (You can use a calculator on this worksheet.)
1. Suppose you open an IRA with an initial principal of $ 5,000 and nominal interest rate of 6%
annually. After 40 years, what would the balance be if th
Chapter 19: Symmetry and Patterns
October 30, 2013
Chapter 19: Symmetry and Patterns
Question
Lets consider the population growth of rabbits. Assuming that: a
newly born pair of rabbits, one male, one female, are put in a eld;
rabbits are able to mate at
Chapter 9:Social Choice: The Impossible Dream
September 16, 2013
Chapter 9:Social Choice: The Impossible Dream
This time
Today, we will talk about
Social Choice
Majority Rule
Condorcets Method
Voting systems for Three or More Candidates
Chapter 9:Social C
Worksheet 7
Math 181: Fall 2015
Consider the order-requirement digraph below:
T4
T1
11
12
T5
T2
12
T3
T7
9
8
T6
10
12
1. Schedule these tasks on two processors using the list algorithm with each of these priority lists:
(a) T1 , T2 , T3 , T4 , T5 , T6 , T
Homework 1
Math 181: Fall 2015
Due Friday, August 28
On an index card, write the following:
your name
your year (freshman, etc.)
your major (if you have one) or what majors you are interested in
the last math class you took and when
I have extra index
Worksheet 11
Math 181: Fall 2015
For each of the following graphs
Using Brooks theorem, give an upper bound on the chromatic number of the graph.
Use the greedy algorithm to nd a vertex coloring of the graph.
Can you nd a vertex coloring that uses fewe
Worksheet 4
Math 181: Fall 2015
1. What are some real world problems that can be modeled by a traveling salesman problem?
2. In each of the following graphs, use the brute force algorithm to nd the Hamiltonian circuit with
smallest possible cost.
A
6
A
5
Worksheet 5
Math 181- Fall 2015
In each of the following complete graphs
1. Write down the path and cost you would get by applying the Nearest Neighbor Algorithm for each
possible starting vertex.
2. Write down the path and cost you would get by applying
Notes
Math 181: Fall 2015
Disclaimer: This is just a summary of what we covered in class. It wont
include the full details or all the examples we discuss in class.
We started class by discussing the syllabus (which is linked from the course
website) and e
SolwlrIMJ
Math 180 Name (Print):
3/09/2016 NetID:
Time Limit: 90 Minutes
This exam contains 10 pages (including this cover page) and 10 problems. After starting the exam, check
to see if any pages are missing. Enter all requested information on the top of
Math 180 Name (Print): 30 LOTION 5
Exam #2 UIN:
10/21/2015 Email:
Time Limit: 2 Hours
This exam contains 8 pages (including this cover page) and 8 problems. After starting the exam1 check to
see if any pages are missing. Enter all requested information
Solwi'ims
Math 180 Name (Print):
Exam #1 UIN:
9/23/2015 Email:
Time Limit: 2 Hours
This exam contains 8 pages (including this cover page) and 8 problems. After starting the exam, check to
see if any pages are missing. Enter all requested information on th
Math 181, Exam 1, Fall 2013
Problem 1 Solution
1. Compute the integrals
Z
(a)
sin1 (x) dx
Z
(b)
dx
+ 1)
x2 (x
Z
(c)
3
9 x2 dx
0
Solution:
(a) Use Integration by Parts to evaluate the integral. Letting u = sin1 (x) and dv = dx
yields
1
du =
dx, v = x.
1 x
Math 181, Exam 2, Spring 2010
Problem 1a Solution
Z
1a. Compute the improper integral:
0
1
x2 dx
.
1 x3
Solution: The integral is improper because the integrand is undefined at x = 1. We evaluate
the integral by turning it into a limit calculation.
Z 1
Z
Math 180
Final Exam
12/10/2015
Time Limit: 2 Hours
Name (Print):
UIN:
UIC Email:
This exam contains 12 pages (including this cover page) and 13 problems. After starting the exam, check
to see if any pages are missing. Enter all requested information on th
Math 180, Exam 1, Fall 2013
Problem 1 Solution
1. Calculate each limit below.
14
2
(a) lim
x7 x2 7x
x7
19x4 + 2x 1
x 3x4 + 16x2 + 100
(b) lim
Solution:
(a) The least common denominator of the function is x2 7x. Thus, the function can be written
as follows
Math 180, Exam 2, Fall 2013
Problem 1 Solution
1. Compute each derivative below.
(a)
d x
(2 arcsin(x3 )
dx
(b)
d
(sin(x)x
dx
[Note: arcsin(x) = sin1 (x)]
[Hint: Logarithmic differentiation may be useful.]
Solution:
(a) Using the Product Rule and the deriv
Math 180, Final Exam, Fall 2012
Problem 1 Solution
1. Find the derivatives of the following functions:
(a) ln(ln(x)
(b) x6 + sin(x) ex
(c) tan(x2 ) + cot(x2 )
Solution:
(a) We evaluate the derivative using the Chain Rule.
d
1
d
1
1
ln(ln(x) =
ln(x) =
dx
l
Math 180, Final Exam, Fall 2013
Problem 1 Solution
1. Compute each limit or explain why it does not exist.
(a) lim
cos2 (x) 1
x
(b) lim
|x 3|
x3
x
x3
(c)
lim
x+
3x2 + 2x 1
[Justify your answer using calculus.]
4 + 3x + 5x2
Solution:
(a) This limit is of t
Chapter 10: The Manipulability of Voting Systems
October 3, 2013
Chapter 10: The Manipulability of Voting Systems
Last Time
1
An Introduction to Manipulability
2
Majority Rule and Condorcets Method
3
The Manipulability of Other Voting systems for Three or
Math181:Worksheet1
1. Trytoanswer(a)and(b)ownyourown,thencompareyouranswerswithyourgroupand
discuss(c)
a. WhichofthefollowinggraphshaveanEulerpath?
b. WhichofthefollowinggraphshaveanEulercircuit?
c. Whatdothegraphsin(a)haveincommon?Whatdothegraphsin(b)hav