Course MAT189

Number, Shape and Symmetry

Calculus, while very important to scientists and engineers, is but one part of modern mathematics, and the technicality of the subject often obscures the underlying mathematical principles. In response, this course is meant to be an alternative to a first semester calculus course for non-scientists, requiring less mathematical background, but of similar depth. In particular, the course will assume only the standard material from high school algebra and geometry. Math 189 attempts to give students an understanding of what mathematics is, what mathematicians do, and the subject's history. The course emphasizes the understanding of ideas and the ability to express them through mathematical arguments.  Offered every other Spring, if staffing permits.

Topics

We will roughly cover chapters 1 - 14 of the textbook Number, Shape, and Symmetry by Dianne L. Herrmann and Paul J. Sally, Jr.  The text was not quite published in time for this first offering of the course in Spring 2012, but Chapter 0 and Chapter 1 from a preliminary version of the text are available in the Sample Materials section below.

Topics include prime numbers and divisibility, congruences, and symmetry groups. Highlights of the course include a description of RSA encryption and a solution to Rubik’s cube. 

Description of classes

There will be two interactive lectures each week, and student participation in lecture is an important component of the course. As such, attendance is required, and students who anticipate missing more than one lecture throughout the semester should discuss this with the instructor as soon as possible.  Reading material and a set of practice problems (largely from the textbook) will be assigned for each lecture. While the practice problems will not be collected and graded, there will be time in lecture to ask questions about them and to compare solutions with other students. A number of the practice problems will be designated as weekly homework, to be written up carefully and turned in at the beginning of class on Thursday of the subsequent week. Students are encouraged to collaborate with one another, but each individual student is expected write up solutions independently, and listing all collaborators.  Short weekly quizzes (largely based on the homework material) will be given at the beginning of class every Thursday.  Late assignments will not be accepted, and makeup quizzes will not be given; however, the lowest homework and quiz grades will be dropped at the end of the semester.  A midterm exam will be given midway through the semester.  However, in lieu of a Final Exam, students will be asked to choose from a number of Final Projects (see Sample Material below for more details).  After preparing a short expository paper on the topic ( due Dean's Date), students will give an Oral Presentation on the topic and their work in the course throughout the semester (a few days after the final paper is due).

  • Problem sets - 25%
  • Quizzes - 25%
  • Midterm Exam - 15%
  • Paper in lieu of Final - 15%
  • Oral Presentation - 10%
Placement and Prerequisites

An alternative to a first semester calculus course for non-scientists, requiring less mathematical background, but of similar depth. In particular, the course will assume only the standard material from high school algebra and geometry.