A Pisot number is a real algebraic integer, all of whose conjugates lie strictly inside the open unit disk; a Salem number is a real algebraic integer, all of whose conjugate roots are inside the closed unit disk, with at least one of them of modulus exactly 1. Pisot numbers have been studied extensively, and an algorithm to generate them is well known. Our main result characterises all Pisot numbers whose minimal polynomial is a Littlewood polynomial, one with {+1, −1}-coefficients, and shows that they form an increasing sequence with limit 2. It is known that every Pisot number is a limit point, from both sides, of sequences of Salem numbers. We show that this remains true, from at least one side, for the restricted sets of Pisot and Salem numbers that are generated by Littlewood polynomials. Finally, we prove that every reciprocal Littlewood polynomial of odd degree n 3 has at least three unimodular roots.
A Pisot number is a real algebraic integer greater than 1, all of whose conjugates lie strictly inside the open unit disk; a Salem number is a real algebraic integer greater than 1, all of whose conjugate roots are inside the closed unit disk, with at least one of them of modulus exactly 1. Pisot numbers have been studied extensively, and an algorithm to generate them is well known. Our main result characterises all Pisot numbers whose minimal polynomial is derived from a Newman polynomial — one with {0, 1}-coefficients — and shows that they form a strictly increasing sequence with limit (1 + √5)/2. It has long been known that every Pisot number is a limit point, from both sides, of sequences of Salem numbers. We show that this remains true, from at least one side, for the restricted sets of Pisot and Salem numbers that are generated by Newman polynomials.
Information literacy (IL) is fundamentally important for CS students and graduates who are required to write research papers and stay abreast of new technologies and ideas. However, IL is absent in CS curriculum guidelines and the literature is scarce on research focused on IL skills among CS students. In this paper, we discuss aspects of IL and introduce the ACRL Framework for Information Literacy in Higher Education in the context of an undergraduate CS course covering social issues. We share how we used the Framework as the basis of our learning activities, which included lectures, a reading, and an assignment in which students reflected on core ideas pertaining to IL. We analyzed responses from the assignment to assess whether students achieved our learning outcomes. Nearly all students recognized markers of scholarly authority, but fewer students achieved learning outcomes based on more abstract concepts. We provide recommendations on incorporating IL activities in CS courses, and encourage explicit interventions to improve CS students' IL skills.
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