Math and Humanity
Math and Humanity
Credit Hours: (3)
Three hours lecture. Mathematics is studied in its historical and cultural context, as a creative human endeavor. Topics covered include numerical and geometrical ideas and their development, sets, infinity, formal logic, and applications to music and the visual arts. Will not satisfy requirements for a major in mathematics. This course has been approved for Core Curriculum credit in Mathematical Sciences.
Detailed Description of Content of Course
The course is divided into four sections. It begins with the historical development of arithmetic from simple tally systems and moves on to elementary number theory. Topics here include bases other than 10, prime numbers and their distribution, and Fermat’s Last Theorem. Simple music theory is studied as an application.
The second section of the course deals with sets and infinity. Here students learn the elements of set theory and are introduced to the fact that some infinities are larger than others.
The third section of the course is on formal logic. A bit of the history of the subject is discussed, and students are taught the basics of formal propositional logic.
The fourth and longest section is on geometry. A brief history of the early development of geometry in Mesopotamia, Egypt, and Greece is presented, including some mention of the religious and economic stimuli for that development. Some Euclidean geometry is discussed along with applications to perspective and fractals. If time permits, other applications of geometry to art are included.
Detailed Description of Conduct of Course
Lectures, group work, homework, readings, and tests are employed. A common, comprehensive final exam, constructed by all course instructors under the leadership of the course coordinator, is given.
Goals and Objectives of the Course
On finishing this course students should (i) be able to answer basic but important questions about the early history and development of mathematics; (ii) be able to apply a few techniques involving numbers and geometry; (iii) be able to symbolize a simple argument and determine whether it is valid; and (iv) know a bit about the mathematical structures in art and music.
Students will be able to use the tools of mathematics and quantitative reasoning to conceptualize and solve problems.
Students will be able to:
a. identify and interpret relationships among numeric, symbolic, and graphical information
b. generate mathematical models using numeric, symbolic, and graphical information for use in real-world applications
c. solve problems using numeric, symbolic, and graphical information
Graded tests, homework, and perhaps in-class work and presentations are used. A common, comprehensive final examination is given and determines at least 20% of each student’s course grade.
Other Course Information
Review and Approval