MATH 420 — FINITE MATHEMATICS
Spring 2011
Welcome to the Spring 2011 Finite Mathematics course! This course description provides
extensive information about this semester’s Math 420. Read it thoroughly and refer to it the entire
semester. Throughout the semester, there will be additional handouts that will supplement this
information.
COURSE CONTENT AND GOALS
The course Math 420 (Finite Mathematics) is designed to examine and develop the concept of
“quantitative reasoning” by introducing you to some of the topics and methods from basic
mathematics that are widely used in everyday life. We will consider how some fundamental
impulses of human nature have inherently quantitative aspects, and we will explore how
mathematics provides a precise and effective language with which goals generated by these
impulses can be expressed and achieved. We study different types of real-world quantitative
problems which arise, in one way or another, from human needs and self-interest.
Course Context. We take as a context for the course our everyday human behavior, both
individually and in groups. We constantly encounter situations, such as the weather or the stock
market, which have a “quantitative” nature. We certainly know that each of these is “measured”
by various numbers, and we’re equally aware that these numbers reflect some underlying reality
that may affect us. What are our needs and wants with respect to this reality? As we plan how we
will go about our day and week, we would like to know what the weather will be. As we consider
our financial well-being, we would like to (and perhaps need to) maximize our investment return
in the stock market. These two impulses – toward prediction and optimization – are always
present in our approach to the world. When we pursue these impulses in a particular situation, the
question arises: how are we able to predict or to optimize?
“Quantitative reasoning” can be described as that reasoning which is involved in achieving these
goals. Of course, the answer to the “how?” question above depends very much on the situation –
the earth’s atmosphere and the stock market are quite different things. But certainly the answer
must involve more than just the numbers which measure. It involves understanding the situation’s
internal mechanics, and understanding them in quantitative terms.
We gain this understanding by constructing a mathematical model of the situation. With a valid
model, we can now apply various mathematical procedures (whose choice depends on the type of
model) to determine how the original situation can be predicted or optimized. In this course our
primary focus will be on these mathematical models and how to use them to gain
information.
Course Goals. The goals of this Math 420 course are for students
• to learn and retain the mathematical content presented in the course;
• to apply correctly the appropriate procedures and techniques to solve word problems;
• to develop an understanding and appreciation of mathematics as the language of quantitative
reasoning and as a means toward decision-making.
The first and second of the above goals will be the basis for student assessment in the course;
homework, quizzes and exams will consist of (i) problems related directly to the
mathematical techniques of the course and (ii) application-based word problems.
Course Overview. The course falls into six natural units. These are given below, with a summary
description of mathematics topics in each unit. We will also be applying these modeling
techniques to numerous real-world problems.
Counting Techniques.
We present a straightforward, practical approach to the basic counting techniques needed for the
concepts and methods used in Probability. We also point out some practical applications of the
counting techniques themselves: Sets and set operations; Venn diagrams; counting elements in
sets; multiplication principle; permutations; combinations; numerous applications.
Probability: Quantifying Uncertainty.
We present a concrete, practical approach to Probability that makes the concepts transparent:
Experiments and sample spaces; events; probability distributions; probability of an event;
uniform sample spaces; rules of probability; counting techniques in probability; conditional
probability; independent events; numerous applications.
Statistics.
This material will help prepare you for an introductory statistics course in your major, if it has
one: Distributions of random variables; histograms; expected value, mean, median, mode;
variance and standard deviation; binomial distribution; normal distribution
Linear Functions, Linear Models and Systems of Linear Equations.
Straight lines; linear functions; Economics applications (cost/revenue functions with break-even
points; demand/supply equations with market equilibrium); method of least squares; systems of
linear equations; Gauss-Jordan solution method; consistent and inconsistent systems; matrices
and matrix algebra; applications.
Financial Mathematics: Modeling with Exponential Functions.
Simple and compound interest; present value; annuities; present and future values of annuities;
amortization of loans; sinking funds; applications to loan financing , retirement funds, etc.
“Blackboard”. Math 420 will be a Blackboard course, using that Web-based tool for
announcements, for dissemination and archiving of course materials such as this hand-out, the
syllabus and any other course materials that will be distributed to you during the semester, as well
as for recording and displaying grades. (Most of you will see two locations for 420 on your
Blackboard site. The unified location will be for all the sections in your lecture and will contain
all announcements and course information made available to you. The section specific location
will contain your grades.)
GRADING: EXAMS, QUIZZES AND HOMEWORK
Your grade in this course will be determined in very large part by your performance on the three
“hour” exams and the final exam. Your progress between exams will be assessed through weekly
quizzes, which will also contribute to your course grade. You will build a firm foundation of
knowledge and skills for each exam by mastering a portion of it each week for that week’s quiz.
Mastery of material for the quizzes is obtained by working through problems and actively
discussing these solutions, both right and wrong, with instructors, TAs, tutors and fellow
students. Your work on turned-in homework problems will also count toward your course grade.
The course instructors and TAs wish for every student to succeed in Math 420. Your diligence in
attendance and in working outside of class is necessary for success. Your instructor and TA are
available to give out-of-class help. Each of them will announce office hours when you can drop
by for help; these will also be posted on Blackboard.
There are additional resources available to you:
• The Mathematics Center (MaC) is located in the basement of Christiansen Hall Room G33 (in
Tower B) and is staffed by undergraduates whose job is to help students with Math 420 and other
math courses. The times for this service will be as follows:
Mon.,Wed., 1-9 pm., Tue,Thurs., 9 am.-5 pm., Fri., 1-5 pm., Sun., 2-5 pm.
• Randy Schroeder of the UNH Center for Academic Resources will once again offer his popular
Math 420 review sessions on Wednesdays, 4:00-6:00 PM. The beginning date of the weekly
review sessions is February 2 and the room will be announced.
Other help opportunities which arise will be announced and posted on Blackboard.
Exams. There will be three “hour exams” in the course. Their dates are
R, 17 February, 12:40 – 2:00 PM
R, 24 March, 12:40 – 2:00 PM
R, 28 April, 12:40 – 2:00 PM
Each exam will be 75 minutes long. Room assignments will be made prior to the exam date,
announced in lecture, in recitation sections and posted on Blackboard. Recitation sections do not
meet on exam days. The final exam is two hours long and will be scheduled by the UNH
Registrar sometime near mid-semester.
Quizzes. There will be nine quizzes, given in recitation sections on the following dates (all
Thursdays ):
3, 10, 24 February; 3, 10, 31 March; 7, 14, 21 April.
Quizzes will average 20 minutes in length. Please do not ask your TA to give the quiz at some
point in the class other than what he or she has indicated. A quiz on a given Thursday will
typically cover lecture material from the Monday three days prior, the Friday six days prior and
the Wednesday eight days prior.
Homework/Written Homework. Working regularly – daily! – on homework is essential in order
to keep up in the course and to succeed in the course’s assessments (quizzes and exams). On most
lecture days you will be assigned a set of problems related to that day’s material. You will be
required to turn in some of these called written homework (WRH) and homework (HW); the
others are “practice” problems. [All of these will be on the course syllabus, available on
Blackboard (and in hard-copy if you print it).] Homework will be collected via WebAssign on
Tuesdays and Thursdays. Approximately every other Tuesday Written Homework will be
turned-in problems and must be fully worked out with your work shown in an organized
and legible way; problems with answers only will be marked down. No late homework nor
written homework will be accepted. In general, between the lecture covering the homework
material and the due date for its homework, you will have one recitation section in which that
material can be discussed.
Example: In a Monday lecture, topic “X” is covered, and problems on it are assigned.
The “turn-in” portion of this assignment will usually be due on Thursday, which means
that the Tuesday recitation will be the only one available for discussion of the problems
before the Thursday due date. In this scenario, you will get the most out of the Tuesday
recitation if you work on the practice problems sometime between Monday lecture and
Tuesday recitation.
COURSE GRADES
Your course grade will be determined by your work on hour exams, the final exam, quizzes,
homework, and class participation, weighted in the proportions below.
Hour exams (3)
Final exam
Quizzes (best 8 of 9)
Homework (best 25)
Written Homework
(best 5 of 6)
Class Participation
15% each
20%
20%
12.5%
2.5%
1% (bonus)
As is customary, your performance on these assessments will be reported as a numerical score.
The number of points available on each assessment will be chosen so that exactly 1000 points are
available in the complete course. So, for example, the final exam will be worth 200 points (20%
of 1000), each quiz will be worth 25 points, and so on. This will enable you to estimate your
grade at any time during the course by totaling your points to that time, dividing that total by the
points available to that time, interpreting the result as a percentage and locating that percentage in
the table below.
Course grades will be based on points awarded as follows:
A: 930-1000 pts. (93.0%-100%)
A–: 900-929 pts. (90.0%-92.9%)
B+: 870-899 pts. (87.0%-89.9%)
B: 830-869 pts. (83.0%-86.9%)
B–: 800-829 pts. (80.0%-82.9%)
C+: 770-799 pts. (77.0%-79.9%)
C: 730-769 pts. (73.0%-76.9%)
C–: 700-729 pts. (70.0%-72.9%)
D+: 670-699 pts. (67.0%-69.9%)
D: 630-669 pts. (63.0%-66.9%)
D–: 600-629 pts. (60.0%-62.9%)
F: 0-599 pts. (0%-59.9%)
A reminder: In May, when calculating your final grade, drop the following from your total on
Blackboard (any un-graded item will count as a zero):
(1) The lowest Quiz Grade
(2) The two lowest HW Grades, and lowest WRH grade
(3) Depending on your lecture section you will need to know how to account for the class
participation grade.
The resulting number will be your final grade (out of 1000 points) and it will be converted to a
letter grade as indicated on the previous page.
COURSE POLICIES
Attendance. You are expected to attend all lectures and recitations, and to attend for the entire
50- minute period. There is a class participation component in the course grade; you cannot
accumulate credit for this component when absent from class.
Classroom Behavior. The classroom is a place of common purpose and of concentration on the
issue at hand. There is no reason and no excuse for audible conversation, movement around the
room, cell phone noise or any other distraction from class discussion and learning. Your
instructor and TA respect all students for their wish to learn and for their efforts in doing so.
Please extend similar respect to your fellow students, your TA and your instructor so that tension
and disruption not diminish the learning environment.
Calculators. The course has no official calculator policy – it is “calculator-neutral”. We do
suggest that you have a calculator, capable of taking powers and roots, for work in Statistics, least
squares method and Finacial Mathematics, but it is possible to do the rest of the course without
one. You can use the calculator for any of the rest of the course you wish or need to, but we
reserve the right to prohibit calculator use on certain exam and/or quiz questions. Keep in mind
that in many cases we will be grading you on your use of a particular method of solution
for a problem. In these cases, even if your calculator gives you the right answer by itself or
using another method, you won’t get credit for it. Conclusion: use your calculator wisely, and
don’t use it to avoid the solution methods introduced in the course.
Homework. Homework assignments are to be turned in to your TA in or before your own
recitation session. No late homework will be accepted.
Make-ups. There will be no make-up quizzes, except for compelling academic or non-academic
reasons supported by letters from the appropriate authority (e.g., doctor, athletic coach). Your
lowest quiz score will be dropped; this is meant, in part, to provide you with some “insurance” in
case you need to miss a quiz due to a non-excused absence. There are two valid reasons for
needing a make-up hour exam: (i) compelling non-academic reasons supported by letters from the
appropriate authority; or (ii) conflict with another course’s exam where that course has a higher
priority than Math 420. In either case, you must contact your instructor in advance of the
exam. For each hour exam, a make-up will be scheduled for the same day (probably in the late
afternoon/early evening). If you have been authorized by your instructor to take a make-up, you
may take that scheduled one. If you are authorized and cannot for any reason take the scheduled
make-up, you can make up the missed exam during the last week of classes, on a day to be
arranged .
Cancellations (Storm-related). If your recitation section in which a quiz is scheduled does not
meet due to campus operations being curtailed by the University, you will be able to make up that
quiz at the next recitation meeting. If an hour exam or final exam is similarly cancelled, alternate
arrangements will need to be made.
Academic Dishonesty. Academic dishonesty has many forms, including lying, cheating, bringing
notes or answer keys to exams, asking other students about the contents of quizzes or exams,
plagiarism and taking personal credit for the work of another. Any violations of UNH regulations
in this area will be dealt with according to UNH policy. This can include a course grade of “F”
and, in some cases, suspension from the university.
(Book: Finite Mathematics (9th edition), by S.T. Tan, (Publisher: ThomsonBrooks/Cole))
Syllabus: 25 January- 18 February
T, 25 Jan
Recit:
Introduction
W, 26 Jan
Lect: Sect 6.1
Sets: notation and operations
pp. 320-322: 5-70(multiples of 5)
HW1-Due T, 1 Feb
R, 27 Jan
Recit:
F, 28 Jan
Lect: Sect 6.2
Counting elements in a set
pp. 326-329: 1-13(odd), 19-31(odd)
HW2-Due R, 3 Feb
M, 31 Jan
Lect: Sect 6.3
Multiplication Principle
pp. 333-335: 1-25(odd)
HW3-Due T, 8 Feb
T, 1 Feb
Recit:
HW1 Due
W, 2 Feb
Lect: Sect 6.4
Permutations and Combinations
pp. 344-347: 1-9(odd), 27,31,33,35
HW4-Due R, 10 Feb
R, 3 Feb
Recit:
Quiz 1: Sect 6.1,6.2
HW2 Due
F, 4 Feb
Lect: Sect 6.4
Permutations and Combinations (continued)
pp. 344-347: 11-17(odd), 41-55(odd), 67
M, 7 Feb
Lect: Sect 7.1
Experiments, sample space and events
pp. 359-362: 1-23(odd), 27,33,35
HW5-DueT, 15 Feb
T, 8 Feb
Recit:
HW3 Due
WRH1 Due
W, 9 Feb
Lect: Sect 7.2
Probability
pp. 367-371: 1,3,7,15,19,23-33(odd)
HW6-Due T, 15 Feb
R, 10 Feb
Recit:
Quiz 2: Sect 6.3, 6.4
HW4 Due
F, 11 Feb
Lect: Sect 7.3
Rules of Probability
pp. 376-380: 1-13(odd), 15-18, 23-41(odd)
HW7-Due T, 22 Feb
M, 14 Feb
Lect: Sect 7.4
Counting Techniques in Probability
pp. 386-388: 1-19(odd)
HW8-Due T, 22 Feb
T, 15 Feb
Recit:
HW5, HW6 Due
W, 16 Feb
Lect:
Test 1- Review: Ch 1(6.1,6.2,6.3,6.4), Ch2(7.1,7.2,7.3)
R, 17 Feb
Test 1
12:40-2:00pm (note: Test 1 is during common exam
time. There are no recitations at regular time)
F, 18 Feb
Lect: Sect 7.4
Counting Techniques in Probability (continued)
pp. 368-388: 21-29(odd)
HW9-Due R, 24 Feb