Department of Mathematical and Digital Sciences
Bloomsburg University of Pennsylvania

Mathematical Thinking
MATH 101

Summer 2018
Section 31: Mo-Th, 9:50-11:30 in Bakeless 104

Professor: Drue Coles
Phone: 570-389-4626
Office: 235 Ben Franklin Hall
Office Hours: Mo-Th, 9:00-9:45 and 11:30-12:00

Text: For All Practical Purposes, 10th edition, Comap, W.H. Freeman and Company, 2016.

Prerequisites: There are no college-level prerequisites for this course.

Course Description.   If you have studied arithmetic and geometry during your K-12 years and decided that mathematics is uninteresting, you are among the majority. But that is like studying the rules of spelling to the point of boredom and deciding that literature is uninteresting. The rules of spelling are important, but they tell you nothing about novels and poetry. In the same way, your early exposure to practical arithmetic and geometry was important, but it probably did not reveal to you anything about the scope and character of modern applied mathematics. That is exactly what this course is about.

Mathematical thinking is explored in this course through a variety of interesting ideas from different areas of applied mathematics. For example, we will learn about common voting methods and see how each of them can lead to paradoxical outcomes. We will also study methods for the fair division of property and goods among parties with conflicting interests. And we will discover that the movement of objects through a network can be modeled mathematically in order to investigate everything from the efficient routing of delivery trucks to the propagation of rumors through a social network.

Schedule and Reading (numbers refer to sections in the book)

  1. Graphs and Euler Circuits (1.1-1.4)
  2. Hamiltonian Circuits and Spanning Trees (2.1-2.4)
  3. Voting Systems (9.1-9.5)
  4. Fair Division (13.1-13.8)
  5. Linear Programming (4.1-4.4)
  6. Tilings (20.1-20.5)

Articles: Graph TheoryMathematical BiologyTraveling Salesman Problem

Grading.  Course grades are determined by chapter quizzes, a midterm exam, and a comprehensive final exam.

Quiz Average
Midterm Exam
Final Exam

Your weighted total will be converted to a letter grade using the following scale:


Exams.  No electronic devices of any kind may be used for any reason during an exam. If you must miss class on the day of a quiz or exam in order to participate in a university-sponsored event, attend a job interview, or fulfill some other serious commitment, let me know in advance. I will be happy to accommodate reasonable requests for alternative testing arrangements in such cases. If a medical emergency or other serious dilemma makes it impossible for you to inform me in advance, notify me by email prior to class upon your return.

The final exam will be on Thursday, August 9, our last scheduled class meeting. Please note that the exam will not given on other dates to accommodate individual vacation plans, so be sure not to book a flight until classes are officially over.

Homework.  I assign plenty of homework from each chapter to prepare you for the quizzes and exams. I do not collect the homework but we will review solutions together in class. If you have any trouble completing the assigned problems, I will be glad to help you during office hours. There is a very high correlation between (a) completion of the homework problems with genuine understanding and (b) performance on the quizzes and exams, so do not hesitate to ask for help if you need it.