Mathematics 113:  Finite Mathematics
Spring 2024
Introduction

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

   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

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 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. 

Math Learning Center

    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 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