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.

It is a fascinating result of Ulmer that the elliptic curve y^2=x^4+x^3+t^d attains arbitrarily large rank over $\bar{F_q}(t)$ as d varies over the positive integers. In this talk we will provide some new examples of this phenomenon and provide an overview of previous work in this area, particularly that of Ulmer and Berger.