Presentation Abstracts - MAA Sections

INQ.4 Ryan Brown Georgia College
An IBL algebraic geometry course for undergraduates
In this talk we examine an inquiry based learning model for teaching an undergraduate course in algebraic geometry using
the book {\em Algebraic Geometry: A Problem Solving Approach}. The course is suitable for both mathematics majors
who intend to pursue graduate study and future secondary school teachers. We discuss the specifics of how the course was
run and include a description of a typical class day. We also address how problems were assigned to students, how
students were motivated to present solutions to selected problems, and how student work was assessed. We conclude with
remarks on course revisions for Fall 2013.
UGG.3 Megan Bryant Clemson University
Carl Mummert (Clemson University), Roger Garcia (Kean University), James Figler, and Yudhishthir Singh
How many mates can a latin square have?
We study the number of mates that a latin square may possess as a function of the size of the square. We performed an
exhaustive computer search of all squares of sizes 7 and 8, giving the exact value for the maximum number of mates for
squares of these sizes. The squares of size 8 with the maximum number of mates are exactly the Cayley tables of Z3 = Z2
×Z2 ×Z2 ,
and each such square has 70, 272 · 8! mates. We obtain a combinatorial proof that, for every k ≥ 2, the square obtained
from a Cayley table of Zk has a mate. This research was partially supported by NSF grants OCI-1005117 and EPS-
0918949.
UGB.1 Abdoulie Ceesay Methodist University
Shivappa Palled
The Second Derivative Test and Its Applications
The second derivative test determines the nature of a critical point of a function. That is whether the critical point is a
local minimum, local maximum, a saddle point or none of these. Generally, for a function of n variables, it is determined
by the algebraic sign of a certain quadratic form, which in turn is determined by eigenvalues of the Hessian matrix. The
general second derivative test states that:
Suppose f(x) is a function of x that is twice differentiable at a stationary point x0.
1. If f”(x)> 0, then f(x) has a relative minimum at x0 .
2. If f”(x)< 0, then f(x) has a relative maximum at x0.
The extremum test gives slightly more general conditions under which a function with is a maximum or minimum. If is
a two-dimensional function that has a relative extremum at a point (x0, y0) and has continuous partial derivatives at this
point, then fx (x0,y0) = 0 and fy (x0, y0) = 0. The second partial derivatives test classifies the point as a local maximum or
relative minimum. Defining the second derivative test discriminant as
fxx fyy - fxy fyx
fxx fyy - f2xy
Then,
1. If D > 0 and fxx (x0, y0) > 0, the point is a relative minimum.
2. If D >0 and fxx (x0, y0) < 0, the point is a relative maximum.
3. If D < 0, the point is a saddle point.
4. If D = 0, higher order tests must be used.
Thus, in this paper the focus will be on the second derivative test applied to functions of 1, 2, 3….n variables. This test
can be applied to a variety of functions ranging from quadratic to multivariable functions that are used in Physics,
Computer Science and Chemistry. Additionally, the second derivatives form the bases in many symbolic computational
work and advanced computational techniques in fluid dynamics.
UGH.6 Moses Chandiga Methodist University
Shivappa Palled
Famous Bridges and Mathematics: Is there a connection between Mathematics and Bridges?
Bridging the gap between disjoint places has taken up an ingenious turn in recent years. In the historical world, obstacles
have been bypassed by various bridges whether complex or simplistic in construction is not the question as long as they
serve their purposes. We have always tended to ignore the questions that lead to the understanding of their constructions.
In other words, perception precedes mathematical reasoning like we only notice the magnificence of bridges, stop and
wonder how such innovative structures were built. If we look at the history of bridges, with the advancement of