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Aug

03

2020

We will talk about two of the coolest classes of objects in all of mathematics -- groups and elliptic curves -- and explore some of the connections between them. We will aim for Mordell's theorem about elliptic curves over rationals.

Aug

05

2020

We will explore the ideas of binary words, balanced (or Sturmian) sequences, and a binary tree that stems from an algorithmic approach to creating a list of all Sturmian words of a particular “height”. Connections between symbolic dynamical systems and number theory will be briefly discussed.

Aug

06

2020

We examine a recursive sequence in which s_n is a literal description of what the binary expansion of the previous term s_{n−1} is not. By adapting a technique of Conway, we determine limiting behavior of \{s_n\}_{n=1}^\infty and dynamics of a related self-map of 2^{\NN}. Our main result is the existence and uniqueness of a pair of binary sequences, each the compliment-description of the other.

Aug

07

2020

Is this the most elementary presentation topic you have ever seen? You

may be surprised.

What method might someone choose for determining whether or not two

fractions are equal, and is it valid? There are several possibilities

that are a priori varyingly credible or conclusive.

Sep

08

2020

We will hold a review of material needed for first year core courses. There will be 2 daily sessions from 9:00 am - 11:30 am and 1:00 pm - 3:30 pm. The "boot camp" review will include topics from Advanced Calculus, Linear Algebra, and (time permitting) Complex Variables, to ensure that everyone shares the same vocabulary and problem solving skills necessary for MTH 511-2, MTH 543, and MTH 611. Attendance is not required, but is recommended for all incoming students.

Sarah Hagen has just published "Active Learning and the Transformation of a Graduate Student Instructor" in the AMS Blog on Teaching and Learning Mathematics at https://blogs.ams.org/matheducation/.

The article is about her own transformation from lecturer to facilitator of student active learning in the classroom, and her insights about it, in the context of teaching the OSU Math boot camp for incoming graduate students.