Mathematics in Decision Making
MATH 1100-02 Spring 2024
Syllabus

Dr. Michael Prophet                                                 Office Hours: M: 9-10am, T,Th: 2:30-3pm, F: 10-11am or by appointment
Office: WRT 320                       
Office Phone: 273-2104                                        
prophet@math.uni.edu
11-12:15pm T,TR; WRT 010
Office Hours
  TBA and by appointment
Introduction to this course
In these modern times, it is easier than ever to disengage from Decision Making. There are plenty of humans and robots ready (indeed eager) to make decisions for us. And perhaps just as easy (and unfortunate) are those times we find ourselves making decisions based on very little information - the dreaded uninformed decision. Yet we are called on to make important decisions all the time:  at home, on the factory floor, at the ballot box, in the corporate office and on the sports field. How can we become more engaged, better informed decision makers?
This course will give you experience with using mathematical tools and techniques that are “custom made” for gathering, organizing and utilizing information so that we become active, informed participants in the decisions that affect our lives. In short, this course provides a toolkit for Decision-Makers!

Course Description
Through this course we will see mathematics applied in a variety of settings - some of which will be familiar while others completely new and, perhaps, somewhat surprising. However, the common theme in all applications will be the utility of mathematics in decision making. Through the construction of mathematical models we will learn how complex questions can be answered in the areas of management science, data science, social choice and game theory.

Course Learning Outcomes
A student who successfully completes this course will be able to
  1. construct graphs using vertices and edges
  2. employ Euler and Hamiltonian circuits within graphs to solve traversal problems
  3. employ spanning trees to solve traversal problems
  4. execute specific algorithms to solve scheduling problems
  5. perform linear programming to solve optimization problems
  6. employ data techniques from data science to draw conclusions about population
  7. conduct selection methods (voting methods) to determine a 'winner' in an election
  8. understand and demonstrate drawbacks to voting methods
  9. employ optimal strategies in head-to-head competitions (games)

Responsibilities
There are three central expectations I have of students in this course.
  1. Students are responsible for the material covered in class. It will often happen that we are unable to discuss in class every aspect of a particular section. However, unless specifically indicated, students remain responsible for the sections in their entirety. Failure to attend class, even for a legitimate reason, does not absolve any student from the responsibility of material covered. If you miss a class, you should find out, as soon as possible, what you missed from those who attended.

  2. It is expected that students read the textbook. The book is well written and packed with information! There is a great deal of detailed explanations and lots of examples that provide particularly good guidance on solving problems. In addition to Skill Checks and Exercises, you'll find a summary of Vocabulary terms at the end of each chapter - and this is something you'll definitely want to take advantage of, as vocabulary is a crucial part of this course.

  3. It is expected that students participate, in a meaningful way, to the discussion and problem-solving effort we conduct during class. Typically our class meetings will begin with me talking about the reading you did the since our last time together. Then, as a group, we will discuss the major points of the latest material and finally work to solve exercises from our textbook. The goal is to get several problems presented and solved on the board. To encourage your participation, there will be EC Points available (see below!).

Course Organization
We will be using the (required) text For All Practical Purposes (11th Edition) by COMAP (W.H. Freeman publisher). The course is organized into 4 Units, with reading and homework Assignments within each Unit:


Unit 1: Management Science, part 1
  • Chapter 1: Urban Services
    • Assignment 1 and Quiz 1
    • Assignment 2 and Quiz 2
  • Chapter 2: Business Efficiency
    • Assignment 3
    • Assignment 4 and Quiz 3
  • Test 1


Unit 2: Management Science, part 2
  • Chapter 3: Scheduling and Planning
    • Assignment 5
    • Assignment 6
    • Assignment 7 and Quiz 4
  • Chapter 4: Linear Programming
    • Assignment 8 and Quiz 5
  • Test 2


Unit 3: Science of Data
  • Chapter 5: Data Distributions
    • Assignment 10
    • Assignment 11 and Quiz 6
    • Assignment 12 and Quiz 7
  • Chapter 6: Data Relationships
    • Assignment 13
    • Assignment 14 and Quiz 8
  • Chapter 7: Data for Decisions
    • Assignment 15 and Quiz 9
  • Test 3


Unit 4: Social Choice and Competition
  • Chapter 9: Social Choice
    • Assignment 16 and Quiz 10
  • Chapter 10: Manipulability of Voting Systems
    • Assignment 17 and Quiz 11
  • Chapter 15: Game Theory
  • Test 4

Homework
The listing of homework problems will be contained in our Assignments. While it will not be collected, it is (obviously) very important that you work through all assigned homework problems. Homework problems will appear on our quizzes and quiz problems will appear on our exams.

Quizzes
After every one or two Assignments we will have an online quiz accessed through our eLearning site. The details for quiz taking are:

Exams
There will be 4 in-class exams, with the fourth test occurring on our Final Exam day/time. There will be no make-up exams. Each exam must be taken on the scheduled day and time. A missed test is scored as a 0 without prior and proper justification from UNI Student Services or a medical office.  The details for test-taking are:

EC Points
EC points are Extra Credit points awarded for Engaged Contributions to our class. By simply participating during our class time you can earn up to 28 EC points over the course of the semester. Of course your participation must make some relevant contribution to our discussion: ask a good question; provide a good answer; present a solution to a homework problem, etc..I will be the arbiter (decider) on what constitutes an Engaged Contribution.
Blackboard Disclaimer
During the semester we will use Blackboard to access the textbook, administer quizzes and record grades. But otherwise it is a "third party" in terms of accomplishing the learning goals of this course. And Blackboard does not determine your grade. Your final grade is determined by the Grading Rubric described below and based on this rubric, you should be able to, throughout the semester, estimate your current grade without the use of Blackboard.
Grading Rubric
There are 500 points available, distributed like this:

4 Exams 400 points
Quizzes 100 points

Your final grade is determined by the percent of total points you earn out of the 500 points possible. Any extra credit points earned are simply added to your total points. Final grades will be assigned according to the standard scale:

100%-90% A
89%-80% B
79%-70% C
69%-50% D

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