Identifying an \u3cem\u3em\u3c/em\u3e-Ary Partition Identity through an \u3cem\u3em\u3c/em\u3e-Ary Tree

The Calkin-Wilf tree is well-known as one way to enumerate the rationals, but also may be used to count hyperbinary partitions of an integer, h2(n). We present an m-ary tree which is a generalization of the Calkin-Wilf tree and show how it may be used to count the hyper m-ary partitions of an integer, hm(n). We then use properties of the m-ary tree to prove an identity relating values of h2 to values of hm, showing that one sequence is a subsequence of the other. Finally, we give a bijection between the partitions to reprove our identity

Extending a Recent Result in Hyper \u3cem\u3em\u3c/em\u3e-ary Partition Sequences

A hyper m-ary partition of an integer n is defined to be a partition of n where each part is a power of m and each distinct power of m occurs at most m times. Let hm(n) denote the number of hyper m-ary partitions of n and consider the resulting sequence. We show that the hyper m1-ary partition sequence is a subsequence of the hyper m2-ary partition sequence, for 2 ≤ m1 \u3c m2

Clickers and Classroom Voting in a Transition to Advanced Mathematics Course

Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a Transition to Advanced Mathematics course. The clicker questions were used to initiate small group discussions in order to improve mathematical communication skills of the students. Student and instructor reactions to the clickers and group discussions are given

Collaborating with Students on Scholarly Work

Faculty and librarians in a wide range of disciplines can benefit from student collaboration in their scholarly work by including students in thoughtfully planned ways. This roundtable invites faculty and librarians in any field—whether their work regularly needs teams of student-researchers or their projects are typically solo endeavors—to engage in a discussion of how scholars in a range of disciplines can collaborate successfully with students. As the presenters’ experiences show, students can be involved in a variety of aspects of faculty/librarian scholarship, contributing as full collaborators and co-authors, or assisting in more limited modes with an individual study. The discussion will also identify challenges and share strategies for structuring a collaborative process that is productive and rewarding for both faculty/librarians and their students