Professor: Jeff Johannes
Section 1 MWF 10:30-11:20a
Fraser 108
Office: South
326A
Telephone: 245-5403
Office Hours: Monday 8:00 - 9:00p, Tuesday 11:30a - 12:30p, 1:30
- 2:30p, Thursday 1:00 - 2:30p, Friday 9:30 - 10:20a, and by appointment or
visit.
Email Address: Johannes@Geneseo.edu
Web-page:
http://www.geneseo.edu/~johannes
Skype:
mathetyes@gmail.com
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 is
another at lumen
learning.
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.
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.
Upon successful completion of the R/ requirement,
students will be able to
- convert a problem into a setting using symbolic notation;
- connect and find relationships among symbolic quantities;
- construct an appropriate symbolic framework;
- carry out algorithmic and logical procedures to resolution;
- draw valid conclusions from numeric/symbolic evidence.
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 (9) 40% 4% (now more) each, drop
the lowest
Exams (3)
40% 10% (now more) each
Quizzes (4)
20% 5% each
Optional Final Exam 0-20% replaces half of
each lesser individual exam
Problem Sets
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 each other'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.
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.
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 January 31 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
27
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 3 Q1 (1.1-4) 2.1 Probabilities, Events, and
Equally Likely Outcomes
event, probability
assignment (weight), probability of an event, complimentary events, equally
likely outcomes
5
2.2 Counting Arrangements: Permutations
PSB
permutation, number
of permutations
7
2.3 Counting Partitions: Combinations
combination, number
of combinations, Pascal’s triangle
addition for cases
or partition, multiplication for stages or steps
10
2.4 Computing Probability Using Equally Likely Outcomes
computation
of probabilities using permutation and combinations
12
review
PSC
14
review
17
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
24
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 2 4.1 Random Variables and
Probability Density Functions
random variable, binomial random variable, probability density function,
4
4.2 Expected Values and Standard Deviations of
Random Variables
expected values and variance and standard deviation of a random variable,
expected value of binomial random variable
6
review
PSE
9
review
11
XM34
13
5.1 Equations and Graphs of Lines
equations of
lines: standard form, x-intercept, y-intercept, slope, vertical lines,
parallel
… and the world changes …
All section numbers here reference these
course materials, where you can find professional videos (they are in
weeks 2-5 on this site).
23
2.1 Systems of Linear Equations of Two Variables
formulation and
solution of systems of linear equations in two variables - graphically and
algebraically
25
2.1 Systems of Linear Equations of Three or More Variables
27
review
30 2.2
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
April 1 2.3 Matrix Notation and
Algebra
matrix,
vectors, equal matrices, addition, scalar multiplication, matrix
multiplication, properties of addition, scalar multiplication, and matrix
multiplication, identity matrix
3
review PSF
6
2.4 Matrix Inverses
8
2.4 Matrix Inverses
inverse of a
matrix, computing inverses by row reducing the identity matrix
10
review
Q5 (2.1-2)
13 3.2
Systems of Linear Inequalities in Two Variables
PSG
graph the set of points satisfying a
system of linear inequalities
15 3.3
Formulation of Linear Programming Problems
setting up linear programming
problems: constraints, feasible sets, objective function
17
review
20 3.5
Graphical Solution of Linear Programming Problems with Two Variables
solving linear
programming problems by finding corner points (including methods for bounded
and unbounded feasible sets) PSH
22
GREAT Day?
24
review
Q6 (2.3-4)
27 review
29
review
May 1 review
May 4 review
PSI
6
review
Friday May 8 8a - Saturday May 9 8p XM567 75 minutes
Monday May 11 8a - Tuesday May 12 8p optional final 2.5
hours