Katherine Bird - Academia.edu (original) (raw)
Papers by Katherine Bird
This report is a continuation of the proof of Dade’s Ordinary Conjecture (DOC) for the finite spe... more This report is a continuation of the proof of Dade’s Ordinary Conjecture (DOC) for the finite special unitary groups. Several reductions of the main alternating sum were completed in Part I [1] resulting in an important reformulation of the main theorem. The alternating sum in this theorem was immediately decomposed into two sub alternating sums. The aim of this paper is to prove the second of these sub alternating sums, completing the proof of DOC for the finite special unitary groups in the defining characteristics. Let us recall the context from [1]. Let G be a finite group. An ordinary character of G is the character of a representation of G over a field of characteristic 0. In the p-modular representation theory of G,where p is a prime dividing the order of G, the ordinary irreducible characters of G are divided into disjoint sets called p-blocks which reflect the decomposition of the group algebra of G over a field of characteristic p into indecomposable two-sided ideals. An i...
The Learning Assistance Review, 2016
This paper describes the development, results, and future directions of the mathematics component... more This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants’ mathematical foundations, mathematical confidence, and ability to successfully place into higher-level mathematics coursework in the subsequent fall semester. Mathematics participants attended mini-lectures, participated in group activities, and completed online MyMathLab modules. Mathematics component results indicate that 73% and 71% of summer 2014 and 2015 participants, respectively, placed up at least one course level in mathematics in the fall semester. There has been heightened attention placed on postsecondary developmental education in the U.S. (Attewell, Lavin, Domina, & Levey, 2006; Bonham & Boylan, 2011; Grubb & Oakes, 2007; Hall & Ponton, 2005; Parsad and Lewis...
This paper describes the development, results, and future directions of the mathematics component... more This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations, mathematical confidence, and ability to successfully place into higher-level mathematics coursework in the subsequent fall semester. Mathematics participants attended mini-lectures, participated in group activities, and completed online MyMathLab modules. Mathematics component results indicate that 73% and 71% of summer 2014 and 2015 participants, respectively, placed up at least one course level in mathematics in the fall semester.
This report is a continuation of the proof of Dade’s Ordinary Conjecture (DOC) for the finite spe... more This report is a continuation of the proof of Dade’s Ordinary Conjecture (DOC) for the finite special unitary groups. Several reductions of the main alternating sum were completed in Part I [1] resulting in an important reformulation of the main theorem. The alternating sum in this theorem was immediately decomposed into two sub alternating sums. The aim of this paper is to prove the second of these sub alternating sums, completing the proof of DOC for the finite special unitary groups in the defining characteristics. Let us recall the context from [1]. Let G be a finite group. An ordinary character of G is the character of a representation of G over a field of characteristic 0. In the p-modular representation theory of G,where p is a prime dividing the order of G, the ordinary irreducible characters of G are divided into disjoint sets called p-blocks which reflect the decomposition of the group algebra of G over a field of characteristic p into indecomposable two-sided ideals. An i...
The Learning Assistance Review, 2016
This paper describes the development, results, and future directions of the mathematics component... more This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants’ mathematical foundations, mathematical confidence, and ability to successfully place into higher-level mathematics coursework in the subsequent fall semester. Mathematics participants attended mini-lectures, participated in group activities, and completed online MyMathLab modules. Mathematics component results indicate that 73% and 71% of summer 2014 and 2015 participants, respectively, placed up at least one course level in mathematics in the fall semester. There has been heightened attention placed on postsecondary developmental education in the U.S. (Attewell, Lavin, Domina, & Levey, 2006; Bonham & Boylan, 2011; Grubb & Oakes, 2007; Hall & Ponton, 2005; Parsad and Lewis...
This paper describes the development, results, and future directions of the mathematics component... more This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations, mathematical confidence, and ability to successfully place into higher-level mathematics coursework in the subsequent fall semester. Mathematics participants attended mini-lectures, participated in group activities, and completed online MyMathLab modules. Mathematics component results indicate that 73% and 71% of summer 2014 and 2015 participants, respectively, placed up at least one course level in mathematics in the fall semester.