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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.
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.
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.
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.
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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 BILIBILI解锁通 - 看国内视频 听国内音乐 回国加速器 【官方 ...:BILIBILI解锁通帮助海外华人解除IP地域限制;出国留学旅游使用国内IP上网;支持腾讯视频、乐视视频、搜狐视频、爱奇艺、PP视频、哔哩哔哩(B站)、优酷视频、土豆视频、芒果TV、华数TV、QQ音乐、企鹅FM、全民K歌、网易云音乐、虾米音乐、豆瓣FM ....
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.