In the late 1980's I began my efforts to increase the success rate of minorities in first semester calculus. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. These meetings with students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum.

I took over the position of Associate Head for Undergraduate Affairs in the department in 2003. I set a very modest goal for myself: to double the number of mathematics majors. With almost 600 mathematics majors I have reached that goal. I think the next doubling is going to be much harder to achieve. My work with minority students provided me with the tools to accept this new challenge of working with all students.

This talk will describe my own efforts to encourage ALL of our students that a mathematics major, or adding mathematics as a second major, is a great career choice. I will also describe the support that I have from the university and the department that enables me to carry out these tasks.

Theory of knowledge and learning spaces is used to assess readiness and de-
termine course placement for mathematics students at or below introductory calculus at
the University of Illinois. Readiness assessment is determined by the articially intelligent
system ALEKS. The ALEKS-based mechanism used at the University of Illinois eectively
reduces overplacement and is more eective than the previously used ACT-based mech-
anism. Signicant enrollment distribution changes occured as a result of the mechanism
implementation. ALEKS assessments provide more specic skill information than the ACT.
Correlations of ALEKS subscores with student maturity and performance meets explecta-
tions in many cases, and revels interesting characteristics of the student population in other
(systematic weakness in exponentials and logarithms). ALEKS revels skill bimodality in the
population not captured by the previous placement mechanism.
The data shows that preparation, as measured by ALEKS, correlates positively with
course performance, and more strongly than the ACT in general. The trending indicates
that while a student may pass a course with a lower percentage of prerequisite concepts
known, students receiving grades of A or B generally show greater preparedness. Longi-
tudinal comparison of students taking Precalculus shows that ALEKS assessments are an
eective measure of knowledge increase. Calculus students with weaker skills can be brought
to the skill level of their peers, as measured by ALEKS, by taking a preparatory course.
Interestingly, the data provided by ALEKS provides a measure of course eectiveness when
students preformance is aggregated and tracked longitudinally. The data is also used to
measure course eectiveness and visualize the aggregate skills of student populations.

Quantum resonances describe metastable states created by phenomena such as tunnelling, radiation, or trapping of classical orbits. Mathematically they are elegantly defined as poles of meromorphically continued operators such as the resolvent or the scattering matrix: the real part of the pole gives the rest energy or frequency, and the imaginary part, the rate of decay. With that interpretation they appear in expansions of linear and non-linear waves. And they can be found in other branches of mathematics and science: as poles of Eisenstein series and zeta functions in geometric analysis, scattering poles in acoustical and electromagnetic scattering, Ruelle resonances in dynamical systems, and quasinormal modes in the theory of black holes. In my talk I will present some basic concepts and illustrate recent mathematical advances with numerical and experimental examples.

Self assembly is the idea of creating a system whose component parts spontaneously assemble into a structure of interest. In this talk I will outline our research program aimed at creating self-assembled structures out of very small spheres, that bind to each other on sticking. The talk will focus on

(i) some fundamental mathematical questions in finite sphere packings (e.g. how do the number of rigid packings grow with N, the number of spheres);

(ii) algorithms for self assembly (e.g. suppose the spheres are not identical, so that every sphere does not stick to every other; how to design the system to promote particular structures);

(iii) physical questions (e.g. what is the probability that a given packing with N particles forms for a system of colloidal nanospheres); and

(iv) comparisons with experiments on colloidal nanospheres.