MATH 102fm Contemporary Mathematics (3)

A non-technical survey of applications of contemporary mathematics, including topics such as networks, voting theory, probability, statistics and methods of counting. Develops problem-solving, analytical thinking, critical reading and writing skills. Explores the use of mathematics to better understand the world. Does not count toward the major.

This course is typically taught once per year. The semester may vary depending on scheduling issues. This course is really designed for those whose major does not require or suggest a particular mathematics course but are looking for a nontraditional view of mathematics. This will cover topics not commonly seen from the high school curriculum, though the level of difficulty is relatively low. Note that some majors may require or encourage taking Math 105 Introduction to Statistics; for students in this category, we encourage you to take that course. For all others who are looking for a way of fulfilling the m requirement, this is a great course to do so. We currently Tannebaum's Excursions in Modern Mathematics, but we have also used COMAP's For All Practical Purposes.

Upon completion of this course, students will have

• acquired a greater appreciation for the nature, beauty, and scope of mathematics as well as its ongoing development;
• been introduced to a diverse collection of mathematical topics typically not covered in the high school curriculum;
• a better understanding of how mathematical thinking and mathematical structures are useful for many things and are all around us;
• appreciated the applicability of mathematics to a wide variety of disciplines; and
• developed their reading and writing skills in the context of mathematics to help satisfy the foundations part of this course.

Content goals for the course: The philosophical goals given above are more important than the details of the particular content. Therefore, we do not prescribe a specific list of content goals. However, following the current text, choosing a subset of the following would be one way to package some content goals. With these, the students will learn to

• consider alternative methods of counting votes, including criteria to consider for a method.
• appreciate the methods of implementing weighted voting systems.
• explore the mathematics in implementing a variety of methods of fair division, both discrete and continuous.
• recognize the implementation, advantages, and disadvantages of several methods of apportionment.
• model various real-world situations using graphs and consider how to pursue circuits and paths, including both the Euler and Hamilton varieties.
• consider trees as a means of representing real-world situations and how to use these structures to solve a variety of problems.
• appreciate a simple sequence, such as the Fibonacci sequence, and explore a variety of related topics.
• appreciate both the dangers and benefits of exponential growth and recognize situations where the exponential growth model appropriately models the real-world.
• appreciate the mathematical beauty of symmetry and understand how this can be represented by various mathematical transformations.
• understand the concept of randomness and its implementation in pursuing collecting statistical data.
• recognize the various statistical tools (e.g., mean, median, standard deviation) that can be used to convey information about a set of data.
• appreciate the nature and mathematics of probability and how it impacts our lives on a daily basis.