Professor: Jeff Johannes
Section 1
MWF 1:30-2:20p Welles 26
Office: South
326A
Telephone: 245-5403
Office Hours: Monday 10:30 - 11:20a in Fraser 104,
Tuesday 12:30 - 1:30p in Welles 123, Wednesday 3:30 - 4:30p in
Welles 128, Thursday 8:00 - 9:00p in South 336, Friday 12:30 - 1:20p
in South 336, and by appointment or visit.
Email Address: Johannes@Geneseo.edu
Web-page:
http://www.geneseo.edu/~johannes
Textbooks
There are many resources for our course
material. I am likely to most often be preparing from Finite
Mathematics, Maki & Thompson, 4th edition, and the
section numbers and titles come from there. There are many
books in the library at QA39.2. There are some reasonable
online books. Here is what looks to me to be the best online
choice at open staxx. Here's another
online book.
Course Goals
"Finite Mathematics" means mathematics without
calculus. In fact, it is further without anything but linear
algebra (algebra of lines). We will look at sets as preparing
us for probability study. For the second half of the course we
will consider linear algebra and see what applications we can
find. It's a gentle exploration, but sometimes we will be
surprised what we can do without getting into much
background. I am trying to update this with current
social applications. At times it may be a bit rough, but I
hope you will forgive that in an attempt to make it more interesting
and relevant. It's a tradeoff.
Learning Outcomes
Upon successful completion of Math 113 - Finite
Mathematics for Social Sciences, students will be able to
- engage in analyzing, solving, and computing real-world
applications of finite and discrete mathematics,
- set up and solve linear systems/linear inequalities
graphically/geometrically and algebraically (using matrices),
- formulate problems in the language of sets and perform set
operations, and will be able apply the Fundamental Principle of
Counting, Multiplication Principle,
- compute probabilities and conditional probabilities in
appropriate ways, and
- solve word problems using combinatorial analysis.
GLOBE Learning Outcomes
Students will demonstrate mathematical skills and quantitative
reasoning, including the ability to
• interpret and draw inferences from
appropriate mathematical models such as formulas, graphs, tables,
or schematics;
• represent mathematical information
symbolically, visually, numerically, or verbally as appropriate;
and
• employ quantitative methods such as
arithmetic, algebra, geometry, or statistics to solve problems.
Grading
Your grade in this course will be
based upon your performance on various aspects. The weight
assigned to each is designated below:
Problem Sets
(11) 40% 4% each, drop the
lowest
Exams (4)
40% 10% each
Quizzes (4)
20%
5% each
Optional Final Exam 0-20% replaces
half of each lesser individual exam
There will be eleven
assignments. Each assignment will constitute five exercises of your choosing from any
source on the topics of the associated sections and five problems
of my designation. Assignments are due on the scheduled
dates. You are encouraged to consult with me outside of
class on any questions toward completing the homework. You
are also encouraged to work together on homework assignments, but
each must write up their own well-written solutions. A good
rule for this is it is encouraged to speak to each other about the
problem, but you should not read eachother's solutions. A
violation of this policy will result in a zero for the entire
assignment and reporting to the Dean of Students for a violation
of academic integrity. Each assignment will be counted in
the following manner: the exercises will be checked for
completeness and will be worth four points each if
completed. The problems will be scored out of four points
each:
0 - missing question
or plagiarised work
1 -
question copied
2 - partial question
3 -
completed question (with some solution)
4 -
completed question correctly and well-written
Each entire problem set will then
be graded on a 90-80-70-60% (decile) scale. Late items will
not be accepted. Solutions to the problems (not to
exercises) will be posted at the time they are submitted.
Assignments will be returned on the following class day.
Because solutions will be provided, comments will be somewhat
limited on individual papers, and late papers will not be
accepted. Please feel free to discuss any homework with me
outside of class or during review. The lowest problem set score will
be dropped.
Solutions and Plagiarism
There are
plenty of places that one can find all kinds of solutions to
problems in this class. Reading them and not referencing
them in your work is plagiarism, and will be reported as an
academic integrity violation. Reading them and referencing
them is not quite plagiarism, but does undermine the intent of the
problems. Therefore, if you reference solutions you will
receive 0 points, but you will *not* be reported for an academic
integrity. Simply - please do not read any solutions for
problems in this class.
Quizzes
There will be
short quizzes as scheduled, covering the material at the level of
the exercises from the homework. Quizzes will consist of
routine questions, and will have limited opportunity for partial
credit. Because quizzes will consist of routine questions, they
will be graded on a decile scale. There will be no makeup
quizzes.
Opening
Meeting
Students
will earn one extra point on the first quiz set by visiting office
hours during the first two weeks of classes, i.e. no later than 5
February.
Exams
There will be
four exams during the semester (the fourth will be on the day of
the final exam) and a final exam during finals week. If you
must miss an exam, it is necessary that you contact me before the
exam begins. The bulk of the exam questions will involve
problem solving. Exams will be graded on a scale approximately (to be precisely
determined by the content of each individual exam) given by
100 - 80% A
79 - 60% B
59 - 40% C
39 - 20% D
below
20% E
For your interpretive
convenience, I will also give you an exam grade converted into the
decile scale. The exams will be challenging and will require
thought and creativity (like the problems). They will not
include filler questions (like the exercises) hence the full usage
of the grading scale.
Final Examination
The final exam is optional. It will contain
questions from throughout the course. If you earn a higher
score on the final than any of the individual exams throughout the
semester, the score on the final will replace half of the score on
the individual exam.
This center is located in South Hall 332 and is
open during the day and some evenings. Hours for the center will be
announced in class. The Math Learning Center provides free tutoring
on a walk-in basis.
Feedback
Occasionally you will be given anonymous feedback
forms. Please use them to share any thoughts or concerns for
how the course is running. Remember, the sooner you tell me
your concerns, the more I can do about them. I have also
created a web-site
which
accepts anonymous comments. If we have not yet discussed
this in class, please encourage me to create a class code.
This site may also be accessed via our
course page on a link entitled anonymous
feedback. Of course, you are always welcome to approach
me outside of class to discuss these issues as well.
Disability Accommodations
SUNY Geneseo will make reasonable accommodations
for persons with documented physical, emotional or learning
disabilities. Students should consult with the Office of
Disability Services (105D Erwin) and their individual faculty
regarding any needed accommodations as early as possible in the
semester.
Religious Holidays
It is my policy to give students who miss class
because of observance of religious holidays the opportunity to make
up missed work. You are responsible for notifying me no later
than 5 February of plans to observe the holiday.
Tentative Schedule subject to change
Date
Topic
Due
January 22 Introduction,
24
1.1 Sets and Set
Operations
Set, subset, union, intersection, empty set,
disjoint, universal set and complement, Cartesian product
26
1.2 Venn Diagrams and Partitions
Venn diagrams, deMorgan’s laws, distributive
laws, pairwise disjoint, partition, size of a partition, size of a
Cartesian product.
29
1.3 Sizes of Sets
PSA
Size of a union, using 3-set Venn diagrams to
find sizes of sets.
31
1.4 Sets of Outcomes and Trees
sample space, tree diagrams, multiplication
principle
February 2 Q1 (1.1-4) 2.2 Counting
Arrangements: Permutations
permutation, number of permutations
5
2.3 Counting Partitions:
Combinations
PSB
combination, number of combinations, Pascal’s
triangle
addition for cases or partition, multiplication
for stages or steps
7
2.1 Probabilities, Events, and
Equally Likely Outcomes
event, probability assignment (weight),
probability of an event, complimentary events, equally likely
outcomes
9
2.4 Computing Probability Using Equally
Likely Outcomes
computation of probabilities using
permutation and combinations
12
review
PSC
14
review
16
XM12
19
3.1 Probability Measures: Axioms and
Properties
axioms for probability measure, complement
probability, pairwise disjoint probability, union probability
21
3.2 Conditional Probability and Independence
conditional probability, independence
23
3.3 Stochastic Processes and Trees
multistage experiments, conditional
probability and trees
26
3.4 Bayes Probabilities
PSD
Bayes’ formula
28
Q3 (3.1-4) 3.5 Bernoulli Trials
March 1 applications of probability to policing
4
review
PSE?
6
review
8
XM34
18
and school discipline questions
20
5.1 Equations and Graphs of Lines
equations of lines: standard form,
x-intercept, y-intercept, slope, vertical lines, parallel
22
5.2 Systems of Linear Equations of Two Variables
formulation and solution of systems of linear
equations in two variables - graphically and algebraically
25
5.3 Systems of Linear Equations of Three
or More Variables PSF
27
5.3 Systems of Linear Equations of
Three or More Variables
graphing planes in three dimensions.
Standard form. x, y, z-intercepts, solution of a system,
consistent v. inconsistent, coefficient matrix, row reduction,
augmented matrix; connections among number of variable, number of
equations, free variables and infinitely many
solutions
29
Q5 (5.1-3) 6.1 Matrix Notation and Algebra
matrix, vectors, equal matrices, addition,
scalar multiplication, matrix multiplication, properties of
addition, scalar multiplication, and matrix
multiplication, identity matrix
Matrices
and MLK
April 1 6.2 Matrix Inverses
PSG
3
6.2 Matrix Inverses
inverse of a matrix, computing inverses by
row reducing the identity matrix
Social matrices?
5
review
PSH
8
Solar Eclipse
10
review
12
XM56
15
7.1 Formulation of Linear Programming Problems
setting up linear programming problems:
constraints, feasible sets, objective function
17
7.2 Systems of Linear Inequalities in Two
Variables
graph the set of points satisfying a
system of linear inequalities
19
22
7.3 Graphical Solution of Linear Programming Problems
with Two Variables PSI
solving linear programming problems by finding corner
points (including methods for bounded and unbounded feasible sets)
24
GREAT Day
26
Q7 (7.1-3) Voting (maybe not) and Gerrymandering
29
PSJ
May 1
3
May 6 review
PSK
8
review
Thursday, May 16 XM710 12N-12:50p, optional final
1-2:20p