Mathematics 113:  Finite Mathematics
Spring 2020
Introduction

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

    Upon successful completion of the R/ requirement, students will be able to

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