# Freshman Seminars

*W. Hugh Woodin*

2020 Fall (4 Credits)

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Schedule: **
W 12:00 PM - 02:00 PM

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Instructor Permissions: **
Instructor

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Enrollment Cap: **
12

Infinity captivates the imagination. A child stands between two mirrors and sees herself reflected over and over again, smaller and smaller, trailing off to infinity. Does it go on forever? Does anything go on forever? Does life go on forever? Does time go on forever? Does the universe go on forever? Is there anything that we can be certain goes on forever? … It would seem that the counting numbers go on forever, since given any number on can always add one. But is that the extent of forever? Or are there numbers that go beyond that? Are there higher and higher levels of infinity? And, if so, does the totality of all of these levels of infinity itself constitute the highest, most ultimate, level of infinity, the absolutely infinite? In this seminar we will focus on the mathematical infinite. We will start with the so-called “paradoxes of the infinite”, paradoxes that have led some to the conclusion that the concept of infinity is incoherent. We will see, however, that what these paradoxes ultimately show is that the infinite is just quite different than the finite and that by being very careful we can sharpen the concept of infinity so that these paradoxes are transformed into surprising discoveries. We will follow the historical development, starting with the work of Cantor at the end of the nineteenth century, and proceeding up to the present. The study of the infinite has blossomed into a beautiful branch of mathematics. We will get a glimpse of this subject, and the many levels of infinity, and we will see that the infinite is even more magnificent than one might ever have imagined.

- Requirements:
- Course open to Freshman Students Only

Additional Course Attributes:

Attribute | Value(s) |
---|---|

FAS Divisional Distribution | None |

Course Search Attributes | Display Only in Course Search |

All: Cross Reg Availability | Not Available for Cross Registration |

FAS: Course Level | Primarily for Undergraduate Students |

*Robin Gottlieb*

2021 Spring (4 Credits)

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Schedule: **
W 03:00 PM - 05:00 PM

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Instructor Permissions: **
Instructor

**
Enrollment Cap: **
12

What are the goals of mathematics education at the middle and high school level, and how do these goals impact our evaluation of the success or failure of math education in America? Why does math education at these levels matter? What societal structures (historic, economic, political, cultural) impact mathematics education? How does math education in turn impact societal structures? As the world changes, how do the goals of mathematics education change, and in what ways? We will explore these issues to become more educated participants in this ongoing discussion.

- Course Notes:
- A special invitation is extended to students not planning to concentrate in math.

- Requirements:
- Course open to Freshman Students Only

Additional Course Attributes:

Attribute | Value(s) |
---|---|

All: Cross Reg Availability | Not Available for Cross Registration |

FAS: Course Level | Primarily for Undergraduate Students |

Course Search Attributes | Display Only in Course Search |

FAS Divisional Distribution | None |