Background



Researchers have identified many factors affecting undergraduate engineering students' achievement and persistence. Yet, much of this research focuses on persistence within academia, with less attention to career plans after graduation. Furthermore, the relative influence of expectancy-versus value-related beliefs on students' achievement and career plans is not fully understood.



Purpose (Hypothesis)



To address these gaps, we examined the relationships among the following motivation constructs for female and male first-year engineering students: (a) expectancy-related constructs that included engineering self-efficacy (i.e., a judgment of one's ability to perform a task in engineering) and expectancy for success in engineering (i.e., the belief in the possibility of success in engineering); (b) value-related constructs that included identification with engineering (i.e., the extent to which one defines the self through a role or performance in engineering) and engineering values (i.e., beliefs related to engineering interest, importance, and usefulness); (c) engineering achievement; and (d) engineering career plans.



Design/Method



Participants included 363 first-year engineering students at a large state university. The students completed an online survey instrument in the first and second semester of their first year.



Results



Students' expectancy- and value-related beliefs decreased over the first year for both men and women. Men reported higher levels for expectancy-related beliefs than women. Expectancy-related constructs predicted achievement better than the value-related constructs, whereas value-related constructs predicted career plans better for both men and women.



Conclusions



Expectancy- and value-related constructs predicted different outcomes. Thus, both types of constructs are needed to understand students' achievement and career plans in engineering.

An Analysis of Motivation Constructs with First-Year Engineering Students: Relationships Among Expectancies, Values, Achievement, and Career Plans

The cyclic sieving phenomenon

This paper is primarily intended as an introduction for mathematicians to some of the rich algebraic combinatorics arising in for instance conformal field theory (CFT). It tries to refine, modernise, and bridge the gap between papers [6] and [55]. Our paper is essentially self-contained, apart from some of the background motivation (Section 1) and examples (Section 3) which are included to give the reader a sense of the context. Detailed proofs will appear elsewhere. The theory is still a work-in-progress, and emphasis is given here to several open questions and problems.

/pdf/modular-data-the-algebraic-combinatorics-of-conformal-field-1t2fifuld8.pdf

Modular Data: The Algebraic Combinatorics of Conformal Field Theory

A construction of admissible -modules of level

We prove a generalized rationality property and a new identity that we call the ''Jacobi identity'' for intertwining operator algebras. Most of the main properties of genus-zero conformal field theories, including the main properties of vertex operator algebras, modules, intertwining operators, Verlinde algebras, and fusing and braiding matrices, are incorporated into this identity. Together with associativity and commutativity for intertwining operators proved by the author in [H4] and [H6], the results of the present paper solve completely the problem of finding a natural purely algebraic structure on the direct sum of all inequivalent irreducible modules for a suitable vertex operator algebra. Two equivalent definitions of intertwining operator algebra in terms of this Jacobi identity are given.

Generalized Rationality and a "Jacobi Identity" for Intertwining Operator Algebras

We describe an initiative to investigate how institutional practices implementing information technology can promote retention of women in engineering through enhancing their self-perceptions and motivations. The initiative uses the self-efficacy theory to implement teaching techniques designed to promote educational attributes: greater motivation, effort, and persistence. The particular method we chose was to design and teach a course to educate women in the area of computer problem diagnosis and repair. Continued demonstration and reinforcement of the proficiency attained by the women throughout the course in computer technology distinguished them among colleagues and established an environment conducive to enhancing students’ feelings of self-efficacy and associated control beliefs.

https://www.ijee.ie/articles/Vol18-4/IJEE1289.pdf

Thinking Inside the Box: Self-Efficacy of Women in Engineering*

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting multinomial formula for the binomial coefficients. The inverse relation is deduced from a parametrization of suitable identities that facilitate dealing with nested compositions of partial Bell polynomials.

/pdf/some-convolution-identities-and-an-inverse-relation-3t2xd1ql8x.pdf

Some Convolution Identities and an Inverse Relation Involving Partial Bell Polynomials

The usual spinor construction from one fermion yields four irreducible representations of the Virasoro algebra with central charge $c = 1/2$. The Neveu-Schwarz (NS) sector is the direct sum of an $h = 0$ and an $h = 1/2$ module, and the Ramond (R) sector is the direct sum of two copies of an $h = 1/16$ module. In addition to the fundamental fermions, which represent a Clifford algebra, and the Virasoro operators, there are infinitely many other vertex operators, in one-to-one correspondence with the vectors (states) in the NS sector. These give the NS sector the structure of a Vertex Operator SuperAlgebra, and the R sector the structure of a ${\bold Z}_2$-twisted module for that VOSA. Keeping both copies of the $h = 1/16$ modules in the R sector, we can define intertwining operators in one-to-one correspondence with the states in the R sector such that the usual Ising fusion rules for just three modules are replaced by a rule given by the group ${\bold Z}_4$. The main objective is to find a generalization of the VOSA Jacobi-Cauchy identity which is satisfied by these intertwining operators. There are several novel features of this new ``Matrix'' Jacobi-Cauchy Identity (MJCI), most of which come from the fact that correlation functions made from two intertwiners are hypergeometric functions. In order to relate and rationalize the correlation functions we use the Kummer quadratic transformation formulas, lifting the functions to a four-sheeted covering, branched over the usual three poles, where the Cauchy residue theorem can be applied. The six possible poles on the cover give six terms in the MJCI. Furthermore, we organize those functions into $2\times 4$ matrices and find the $2\times 2$ (fusion and braiding) matrices which relate them at the six poles. These results for intertwiners

Spinor construction of the c = 1/2 minimal model

The representation theory of affine Kac-Moody Lie algebras has grown tremendously since their independent introduction by Robert V. Moody and Victor G. Kac in 1968. Inspired by mathematical structures found by theoretical physicists, and by the desire to understand the ``monstrous moonshine'' of the Monster group, the theory of vertex operator algebras (VOA's) was introduced by Borcherds, Frenkel, Lepowsky and Meurman. An important subject in this young field is the study of modules for VOA's and intertwining operators between modules. Feingold, Frenkel and Ries defined a structure, called a vertex operator para-algebra(VOPA), where a VOA, its modules and their intertwining operators are unified. In this work, for each $l\geq 1$, we begin with the bosonic construction (from a Weyl algebra) of four level $-\shf$ irreducible representations of the symplectic affine Kac-Moody Lie algebra $C_l^{(1)}$. The direct sum of two of these is given the structure of a VOA, and the direct sum of the other two is given the structure of a twisted VOA-module. In order to define intertwining operators so that the whole structure forms a VOPA, it is necessary to separate the four irreducible modules, taking one As the VOA and the others as modules for it. This work includes the bosonic analog of the fermionic construction of a vertex operator superalgebra from the four level 1 irreducible modules of type $D_l^{(1)}$ given by Feingold, Frenkel and Ries. While they only get a VOPA when $l = 4$ using classical triality, the techniques in this work apply to any $l\geq 1$.

Bosonic construction of vertex operator para-algebras from symplectic affine Kac-Moody algebras

Introduction Bosonic construction of symplectic affine Kac-Moody algebras Bosonic construction of symplectic vertex operator algebras and modules Bosonic construction of vertex operator para-algebras Appendix Bibliography.

Michael D. Weiner

Papers

Thinking Inside the Box: Self-Efficacy of Women in Engineering*

Some Convolution Identities and an Inverse Relation Involving Partial Bell Polynomials

Spinor construction of the c = 1/2 minimal model

Bosonic construction of vertex operator para-algebras from symplectic affine Kac-Moody algebras

Bosonic Construction of Vertex Operator Para-Algebras from Symplectic Affine Kac-Moody Algebras