## Mathematics 113:  Finite MathematicsSpring 2020Introduction

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.
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.
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