**Emily Stone**

Email

# 2007 Colloquia

**Friday, April 27**: Departmental Picnic & Softball Game

## Spring 2007

### August 1 - Mathematical Modelling: Linking Mathematics, Science, and the Arts in the Primary Curriculum

**Mathematical Modelling: Linking Mathematics, Science, and the Arts in the Primary Curriculum**This paper presents one approach to incorporating interdisciplinary experiences in the primary school mathematics curriculum, namely, the creation of realistic mathematical modelling problems that draw on other disciplines for their contexts and data. The paper first considers the nature of modelling with complex systems and how such experiences differ from existing problem-solving activities in the primary mathematics curriculum. Principles for designing interdisciplinary modelling problems are then presented, with reference to two mathematical modelling problems, one based in the scientific domain and the other in the literary domain. Examples of the models children have created in solving these problems follow. Finally, a reflection on the differences in the diversity and sophistication of these models raises issues regarding the design of interdisciplinary modelling problems.

Wednesday, 1 August 2007

Math 109

### July 30 - Using Software in Solving Mathematical Modeling Problems

**Using Software in Solving Mathematical Modeling Problems**The presentation will focus on the emerging role of new technological tools in the teaching and learning of mathematical problem solving, through modeling, in elementary and secondary school. Recent research in the field has shown that the availability of technological tools, such as computer software or graphic calculators, not only change the way students solve a problem but also improve students' explorations and discovery in the context of the problem. Specifically, in the context of modeling problems, what is expected is that the use of appropriate tools can enhance students' work and therefore result in better models and solutions. During the presentation the following software will be presented and examples of using the software in solving modeling problems will be discussed. Specifically, I will present Geogebra (www.geogebra.org), a software for creating dynamic geometry constructions with computer algebra system (CAS) capabilities, a set of math applets for the teaching and learning of spatial geometry concepts and for improving students' visualization skills (www.ucy.ac.cy/dalest) and a spreadsheet software. The presentation will discuss findings from a number of recent research studies, related to the software presented earlier. Related to the use of dynamic geometry software, a modeling problem derived from Christou, Mousoulides, Pittalis and Pitta (2004) will be discussed. The problem asks students to decide on the optimal location for building an airport that will serve the needs of four cities. The second modeling problem is retrieved from Mousoulides, Pittalis, Christou, Boytchev, Sriraman and Pitta (2007). In this problem, students need to develop a model for constructing the best possible bottle for a soft drink. The third problem comes from Mousoulides, Sriraman, Pittalis and Christou (2007), is on selecting the "best" six vendors among a number of vendors for working in a university cafeteria. In the last part of the presentation the audience will have the opportunity to further explore and discuss the possibilities of the presented software.

**References**

- Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D. (2004). Proofs through exploration in dynamic geometry environments.
*International Journal of Science and Mathematics Education*, 2(3), 339-352. - Mousoulides, N., Pittalis, M., Christou, C., Boytchev, P., Sriraman, B., & Pitta, D. (2007). Mathematical modelling using technology in elementary school. Submitted to the 8th
*International Conference on Technology in Mathematics Teaching*. University of Hradec Králové: Czech Republic. - Mousoulides, N., Sriraman, B., Pittalis, M., & Christou, C. (2007). Students' Modeling Abilities in Problem Solving.
*Proceedings of the 13th International Conference on the Teaching of Mathematical Modeling and Applications*(ICTMA). Bloomington: US.

Monday, 30 July 2007

9:30 a.m. in Math 109

### May 11 - â€śComparison of Trend Detection Methodsâ€ť

Doctoral Dissertation Defense

**“Comparison of Trend Detection Methods”**Trend estimation is important in many fields, though arguably the most important applications appear in ecology. Trend is difficult to quantify; in fact, the term itself is not well-defined. Often, trend is quantified by estimating the slope coefficient in a regression model where the response variable is an index of population size, and time is the explanatory variable. Linear trend is often unrealistic for biological populations; in fact, many critical environmental changes occur abruptly as a result of very rapid changes in human activities. My PhD research has involved formulating methods with greater flexibility than those currently in use.

Penalized spline regression provides a flexible technique for fitting a smooth curve. This method has proven useful in many areas including environmental monitoring; however, inference is more difficult than with ordinary linear regression because so many parameters are estimated. My research has focused on developing methods of trend detection and comparing these methods to other methods currently in use. Attention is given to comparing estimated Type I error rates and power across several trend detection methods. This was accomplished through an extensive simulation study. Monte Carlo simulations and randomization tests were employed to construct an empirical sampling distribution for the test statistic under the null hypothesis of no trend. A likelihood ratio test for trend was shown to be more powerful than other methods for detecting trend.

Friday, May 11, 2007

8:10 a.m. in Math 109

### May 8 - Towards an Axiomatic Theory of the Category of Graphs

Presentation of Master’s Project

**Towards an Axiomatic Theory of the Category of Graphs**William Lawvere and Myles Tierney gave six axioms for an abstract category to be the category of sets. Since a graph can be viewed as a set with a special structure, these six axioms seem a natural point for beginning an investigation of the category of graphs. I will describe the categorial structures I’ve discovered when trying to determine if these axioms were satisfied.

Tuesday May 8, 2007

1:10 p.m. in Math 109

### May 3 - The Ubiquitous Newton Diagram

**The Ubiquitous Newton Diagram**Introduced by Isaac Newton in 1669 to study algebraic functions, the convex polygon known as the Newton diagram has emerged as an object of importance in many central problems of harmonic analysis. We will provide a gentle introduction to some of these problems, describe the relevance of the Newton diagram in their context, and mention some of the deeper open questions they lead to. The talk is intended for a general mathematical audience.

Thursday, 3 May 2007

4:10 p.m. in Math 109

### May 3 - An Exploratory Study of First-Year Students' Math Experinces At The Univerity of Montana

### April 27 - â€śLobachevski Illuminated: Content, Methods, and Context of the Theory of Parallels.â€ť

Doctoral Dissertation Defense

**“Lobachevski Illuminated: Content, Methods, and Context of the Theory of Parallels.”**In the 1820’s, Nikolai Ivanovich Lobachevski discovered and began to explore the world’s first non-Euclidean geometry. This crucial development in the history of mathematics was not recognized as such in his own lifetime. When his work finally found a sympathetic audience in the late 19th century, it was reinterpreted in the light of various intermediate developments (particularly Bernhard Riemann’s conception of geometry), which were foreign to Lobachevski’s own way of thinking about the subject.

Because our modern understanding of his work derives from these reinterpretations, many of Lobachevski’s most striking ideas have been forgotten. Recovering this “lost mathematics” is not easy: Lobachevski's original works, which even his contemporaries failed to grasp, are still more difficult for the modern reader, who may lack training in subjects and techniques that Lobachevski took for granted in his audience.

Accordingly, I have produced an “illuminated” version of Lobachevski’s most accessible exposition of his work, a German book that he published in 1840 entitled *Geometrische Untersuchungen zur Theorie der Parallellinien* (Geometric Investigations on the Theory of Parallels). I have produced a new English version of this work, together with extensive mathematical, historical, and philosophical commentary. The commentary expands and explains Lobachevski’s often cryptic statements and proofs, while linking the individual propositions of his treatise to the related work of his predecessors (including Gerolamo Saccheri, J.H. Lambert, and A.M. Legendre), his contemporaries (including János Bolyai and Karl Friedrich Gauss), and his followers (including Eugenio Beltrami, Henri Poincaré, and David Hilbert). This dissertation thus supplies the contemporary reader with all of the tools necessary to unlock Lobachevski’s rich, beautiful, but generally inaccessible world.

A copy of the dissertation is available in the Math Office (MA 105) for public inspection.

Friday, April 27, 2007

3:10 p.m. – 5:00 p.m. in Math 109

### April 26 - Semigroups and controllability in distributed parameter systems: some examples

**Semigroups and controllability in distributed parameter systems: some examples**We develop some linear and nonlinear examples of distributed parameter control systems from a semigroup point of view, and describe how function space theory plays a pivotal role in the controllability of these systems.

This talk is intended to be at the interface of mathematics and engineering and will be accessible to a broad mathematical audience.

Thursday, 26 April 2007

4:10 p.m. in Math 109

### April 23 - The Effect of Killer Virus on Competition in S. Cerevisiae (Baker's Yeast)

Presentation of Master’s Project

**The Effect of Killer Virus on Competition in S. Cerevisiae (Baker's Yeast)**In today's society with the high demand for fuel, the emphasis on production of alternative fuels, such as ethanol, is growing. Yeast is used to produce ethanol in a chemostat environment. Both situations can be modeled with dynamical systems, but become interesting when we introduce the concept of infection. Like any other eukaryote, yeast is susceptible to certain viruses. In this presentation we will explore the effect of "Killer- K1" virus, and how different scenarios in a chemostat can end up. In addition, biological experiments were performed and the results of the data will be discussed.

April 23, 2007

4:10 pm in Math 311

### April 19 - Nonisotropic Balls and Metrics

**Nonisotropic Balls and Metrics**One standard type of singular integral is one whose integral kernel *K* satisfies the estimate ∣*K(x _{1}y)*∣≤

*c*∣

*B(x,δ)*∣

^{-1}, where

*B(x,δ)*is the ball centered at

*x*with radius

*δ*equal to the distance between

*x*and

*y*. Such estimates help one obtain boundedness properties of the operator. The distance, and hence the ball, may be Euclidean, or it may be nonisotropic, with different directions carrying different weights. We will discuss how to derive the appropriate family of balls based on vector fields associated to the problem.

Thursday, 19 April 2007

4:10 p.m. in Math 109

### April 18 - Departmental Awards Ceremony

Dell Brown Room, Turner Hall

3:30 p.m.

### April 17 - Synaptic clearance of neurotransmitter and asymptotic reduction of neuroscience models

**Synaptic clearance of neurotransmitter and asymptotic reduction of neuroscience models**Chemical signaling in the brain involves electrically triggered release of neurotransmitter from presynaptic nerve terminals. The neurotransmitter then diffuses across a 20 nm wide synaptic cleft and is detected and converted back into electrical signals by receptors on the postsynaptic neuron. Glutamate is the most abundant neurotransmitter, and specific transporter proteins in cell membranes mediate its uptake following release. Transporters modulate the time course of signaling, so characterizing their functional kinetics and mechanism may shed light on fundamental properties of brain function. The first part of the presentation will describe some techniques for measuring transport and the second part will describe the development of models of transporter function. Neuroscience models are generally extremely complex and contain a large number of parameters that must be determined using experimental data. One of the questions that often arises may be formulated as follows: How can one find a model with the minimal number of parameters that can be reliably estimated from the available data. We will discuss the general idea of asymptotic model reduction approach that addresses this question. We will illustrate this general idea with a particular example of a complex model reduction.

**Asymptotic reduction of neuroscience models**Neuroscience models are extremely complex, they usually contain a large number of parameters that must be determined using experimental data. One of the questions that often arises may be formulated as follows: How can one find a model with the minimal number of parameters that can be reliably estimated from the available data. We will discuss the general idea of asymptotic model reduction approach that addresses this question. We will illustrate this general idea with a particular example of a complex model reduction.

Tuesday, 17 April 2007

4:10 p.m. in Math 109

### April 17 - 8th Annual Math Film Festival

### April 12 - Debugging the Neural Code

Cosponsored by the Center for Structural & Functional Neuroscience

**Debugging the Neural Code**What is the meaning associated with a single action potential in a neural spike train? The answer depends on the way the question is formulated. One general approach toward formulating this question involves estimating the average stimulus waveform that leads up to each spike generated by a nerve cell: presumably, the mean of all of these pre-spike waveforms is a good estimate of the "best stimulus" or "optimal feature" for that neuron. Many different algorithms have been used to obtain such estimates, ranging from spike-triggered averaging of stimuli to correlation-based extraction of "stimulus-reconstruction" kernels or spatiotemporal receptive fields. We demonstrate that all of these approaches miscalculate the stimulus feature selectivity of a neuron. Their errors arise from the manner in which the stimulus waveforms are aligned to one another during the calculations. Specifically, the waveform segments are locked to the precise time of spike occurrence, ignoring the intrinsic "jitter" in the stimulus-to-spike latency. We present an algorithm that takes this jitter into account. " Dejittered" estimates of the feature selectivity of a neuron are more accurate (i.e., provide a better estimate of the mean waveform eliciting a spike) and more precise (i.e., have smaller variance around that waveform) than estimates obtained using standard techniques. Moreover, this approach yields an explicit measure of spike-timing precision and, therefore, and estimate of the "temporal resolution" of a neuron.

These results will be discussed within the context of our group's general research into the functional organization and operation of one specific sensory system: the cricket cercal system. This system functions as a low-frequency, near-field extension of the cricket's auditory system, and mediates the detection, localization and identification of signals generated by predators, mates and competitors. The sense organ for this system consists of a pair of antenna-like 'cerci' at the rear of the cricket's body, each of which is covered with approximately 1000 mechanosensory hairs. Each of these hairs is innervated by a single receptor neuron. The working hypothesis is that the anatomical, biomechanical and neurophysiological characteristics of the cerci are optimized for the sensory processing operations they mediate. The group of researchers working on this general project include four MSU faculty (2 neurophysiologists and 2 applied mathematicians), 5 grad students and 1 postdoc, and a slew of advanced undergrads.

Thursday, 12 April 2007

4:10 p.m. in Math 109

### April 11 - Phase-locking in electrically coupled networks of cortical neurons

Cosponsored by the Center for Structural & Functional Neuroscience

**Phase-locking in electrically coupled networks of cortical neurons**Electrical coupling between inhibitory interneurons appears to be ubiquitous in the brain. Because inhibitory interneurons are thought to play a fundamental role in generating cortical oscillations, phase-locking dynamics of electrically coupled interneurons has received considerable interest. In this talk, I will discuss collaborative work with the experimental lab Dr. Barry Connors at Brown University (Mancilla et al. 2007) in which we examine phase- locking in both real and model pairs of electrically cortical interneurons. By using the theory of weakly coupled oscillators and phase-response curves (PRC), we identify some of the intrinsic properties of neurons that determine the stability of phase-locked states and describe the underlying dynamical mechanisms.

Wednesday, 11 April 2007

4:10 p.m. in Skaggs 117

### April 6 - The Road to Mathematics Reform: One State's Perilous Journey

**The Road to Mathematics Reform: One State's Perilous Journey**Washington State embarked on a journey of educational reform thirteen years ago, only to find itself bogged down by unacceptable high school exit exam scores in mathematics. This talk highlights a number of the pitfalls in the process of reform, while considering the effects of the reform effort on curricular rigor, educational resources, and college readiness.

Friday, 6 April 2007

4:10 p.m. in Math 109

### April 5 - Teaching with Classroom Voting

**Teaching with Classroom Voting**Classroom voting can be a very powerful tool for teaching mathematics that we have successfully integrated into our calculus classes at Carroll College. This technique involves posing multiple-choice questions to the class and having them discuss the issue with their peers before voting on the right answer with a set of hand-held "clickers." Their votes are recorded and tabulated with a computer, giving the instructor almost instantaneous feedback on student understanding. After the vote, we then ask individual students to explain and defend their answers, to justify their vote. Sometimes the answer quickly becomes clear, but the best questions result in an extended debate, as students who chose different answers explain their thoughts. Research on this method indicates that the most powerful effect on student learning comes from these classroom discussions, both before and after the vote. With some organization we have found that classroom voting requires no additional class time, allowing us to cover exactly the same syllabus and give similar exams to what we covered before classroom voting. Instead we replace many of the examples that would be done on the board with similar problems that the students do themselves, as well as use voting questions to provoke common misconceptions and bring up issues that would otherwise be dealt with in a lecture format. We have recently received an NSF grant to develop a library of classroom voting questions for differential equations and linear algebra classes and are looking for colleagues who might be interested in testing these materials.

Thursday, 5 April 2007

4:10 p.m. in Math 109

### March 20 - Linearity in non-linear situations.

**Linearity in non-linear situations.**In surprisingly many instances, one encounters not only one function exhibiting ``odd'' behavior, but large vector spaces of such functions.

In this expository talk, we will describe a number of occurrences of this situation.

Tuesday, 20 March 2007

4:10 p.m. in Math 109

### March 16 - Change of Settings and Row-Reduction Process in Undergraduate Linear Algebra

**Cancelled**

**Change of Settings and Row-Reduction Process in Undergraduate Linear Algebra**Since the formation of the Linear Algebra Curriculum Study Group in 1990, there has been considerable interest in studying the teaching and learning of undergraduate linear algebra. This talk outlines a dissertation aimed at understanding how undergraduate linear algebra students are often able to implement a computational algorithm such as row-reduction, but later encounter great difficulty with changes in context. The talk will discuss the research question in the context of constructivist encapsulation theories, as well as a methodological framework influenced by work done in experimental psychology. Emerging results concerning the Gaussian elimination algorithm in different settings will be presented; which describe relevant procedural and conceptual links in connection with Piaget’s (1989) notion of "reflective abstraction," as well as suggest an extension of Tall’s notion of the procept.

Friday, 16 March 2007

4:10 p.m. in Math 109

### March 15 - Proof: Definitions, Difficulties, and Help

*Proof: Definitions, Difficulties, and Help*The ability to write a valid mathematical proof is a necessity for every mathematician. But, what is a proof? The definition of proof has changed throughout history and even today, remains a matter of discussion. Yet, whatever you decide it is, there is evidence that students have difficulty with it. Studies, both recent and past, have shown that a large portion of undergraduate mathematics majors have difficulties constructing, understanding, and validating proofs. However, all mathematicians were once students themselves and at some point learned how to construct a valid proof. So, how do they do it?

In this talk, I will discuss the history of proof, the definitions which were and are used, the evidence of student inabilty, and the possible heuristics which could be used to make life easier. I will also discuss briefly my ongoing research in this area.

Thursday, 15 March 2007

4:10 p.m. in Math 109

### March 13 - Peer Review of Teaching Beyond the Classroom

Teaching Excellence Series

**Peer Review of Teaching Beyond the Classroom**What other things besides performance tell us about teaching? How might these things be assessed? In this workshop, we will examine these questions within the context of mathematics. A sample syllabus for a "Contemporary Mathematics" course will be assessed using a syllabus evaluation tool. In addition, a reflective paper and a critical incident reflection will be examined to see how they influence our thinking. This will be followed by a discussion of alternative methods of assessment, such as portfolios.

Note: Dr. Chism is author of the book "Peer Review of Teaching" which the Department used as a Resource for the Peer Review of Teaching Program last year. (The new edition is due out in May.) Dr. Chism has agreed to serve as a consultant; to listen to our experiences and suggest directions which we might take. Please come with questions!

Tuesday, 13 March 2007

4:10 p.m. in Math 109

### March 8 - Spline Regression Techniques for Trend Detection

**Spline Regression Techniques for Trend Detection**Trend estimation is important in many fields, though arguably, the most important applications appear in ecology. Trend is difficult to quantify, in fact, the term itself is not well-defined. Commonly, trend is quantified by estimating the slope coefficient in a regression model where the response variable is an index of population size, and time is the explanatory variable. Linear trend is often unrealistic for biological populations; in fact, many critical environmental changes occur abruptly as a result of very rapid changes in human activities. My PhD research has involved formulating methods with greater flexibility and robustness than those currently in use. This is a particularly timely and important problem given rapid changes in the environment associated with change in land use, human pressures, and global warming.

Penalized spline regression provides a flexible technique for fitting a smooth curve. This method has proven useful in many areas including environmental monitoring, however, inference is more difficult than ordinary linear regression because so many parameters are estimated. My research focuses on developing a test for trend using penalized spline regression techniques. The test will be compared to other commonly used methods in trend detection such as linear regression, nonparametric correlation techniques, and other smoothing techniques. Further considerations such as autocorrelation are considered. In this presentation, penalized spline regression will be introduced and possible trend detection methods using spline regression will be discussed. Simulation results and future research will also be presented.

Thursday, 8 March 2007

4:10 p.m. in Math 109

### February 8 - Graduate Teaching Assistantsâ€™ Knowledge of Statistics and Knowledge for Teaching Statistics

**Graduate Teaching Assistants’ Knowledge of Statistics and Knowledge for Teaching Statistics**This study investigates graduate teaching assistants' (TAs) knowledge of sampling concepts and TAs' knowledge of teaching sampling concepts within the introductory statistics curriculum. For the past two decades the mathematics education community has placed increased emphasis on the teaching and learning of probability and statistics (NCTM, 2000; Ben-Zvi & Garfield, 2004). Graduate teaching assistants (TAs) teach the bulk of introductory statistics courses at many universities (Luzter, Maxwell, & Rodi, 2000); thus, they have the potential to play a vital role in undergraduate statistics education and in the promotion of statistical literacy among college students. Yet, little is known about TAs' statistical content knowledge and their knowledge for teaching statistics. This study is an important first step in creating a dialogue concerning the nature of TAs' knowledge of sampling and knowledge for teaching statistics. 68 TAs from 18 universities completed surveys containing several sampling tasks. Five of these TAs participated in a series of task-based interviews. The analysis of survey and interview data forms a basis for characterizing TAs' knowledge of sampling concepts. In particular, tension in TAs' understanding of the foundational concepts of sampling as they relate to statistical inference, a cornerstone of introductory statistics courses, will be examined.

Thursday, 8 February 2007

4:10 p.m. in Math 109

### February 6 - Pre-Algebra and the Chinese Remainder Theorem: Connections for Teachers and Students

**Pre-Algebra and the Chinese Remainder Theorem: Connections for Teachers and Students**As part of a mathematics teacher preparation program, the study of number theory is generally required. NCTM's *Principles and Standards for School Mathematics* calls for instruction enabling students in grades 6-8 to “use factors, multiples, prime factorization, and relatively prime numbers to solve problems,” and for students in grades 9-12 to “use number theory arguments to justify relationships involving whole numbers.” This talk will look at a problem from pre-algebra that an undergraduate number theory student would recognize as a Chinese Remainder Theorem problem. The talk will analyze the connections between solution methods appropriate to middle schoolers and those appropriate to undergraduates.

Tuesday, 6 February 2007

4:10 p.m. in Math 109

### February 2 - Student Obstacles and Historical Obstacles to Foundational Concepts of Calculus

**Student Obstacles and Historical Obstacles to Foundational Concepts of Calculus**240 university calculus students were given a questionnaire about foundational calculus concepts: function, limit, continuity, and the real number line. Based on their responses, and follow-up interviews with a few students, they were categorized according to the epistemological obstacles they displayed. I found that several of the clusters of obstacles commonly co-occurring in students were also prominent in the history of calculus. This indicates that one key to understanding the parallels between student thinking and historical thinking lies in shared epistemological predispositions, such as the disposition toward smooth motion or toward algebraic simplicity. These predispositions support, but do not strictly constrain, the multiple connected conceptions observed in the study.

Friday, 2 February 2007

3:10 p.m. in Math 109

### February 1 - The Best Little Horosphere in Kazan

**The Best Little Horosphere in Kazan**Trigonometry is easy to develop in Euclidean geometry. Indeed, one can summarize the process in two sentences. In a right triangle, an acute angle determines the remaining angle (since the angles must sum to ∏), which then determines the triangle’s shape (by AAA-similarity), and thus, the ratios of its sides. Once we express these ratios as functions of the acute angle, a few simple manipulations yield the laws of cosines and sines, which suffice to solve all trigonometric problems.

In the hyperbolic plane, none of this works. Here, triangles’ angle sums vary widely, similar triangles do not exist, and side-ratios cease to be functions of one acute angle. In this lecture, I shall explain the beautiful and surprising means by which N. I. Lobachevski (our hero) overcame these obstacles to derive the trigonometric formulae of hyperbolic geometry. The tale includes an unexpected excursion into three-dimensional hyperbolic space, a lovely surface therein called the horosphere, and a new definition of parallelism.

The details are prickly, but in this lecture I shall confine myself to a descriptive overview that will be accessible to all. He who has ears to hear, let him hear.

Thursday, 1 February 2007

4:10 p.m. in Math 109

## Fall 2007

### November 20 - Algebraic Literacy: Empirical Tests of an Instructional Strategy

**Algebraic Literacy: Empirical Tests of an Instructional Strategy**To advance in mathematics, students must develop fluency with algebraic computations. The development of computational fluency, however, is no easy task. Research suggests that an instructional focus on computations alone produces faulty performance and poor retention. On the other hand, holistic instructional approaches, focusing on computation and understanding, promise to improve students' success in algebra. In this presentation, I offer one holistic approach that defines algebraic understanding (and the goal of algebra instruction) in terms of six literacies. I then trace recent and ongoing efforts to gauge the impact of this approach on students' performance and understanding of algebra.

Tuesday, 20 November 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### November 15 - Standards-based or Traditional Mathematics: Does it matter?

**Standards-based or Traditional Mathematics: Does it matter?**"Math Wars" have been an ongoing event in the mathematics education community, which includes school districts, teachers, parents, mathematicians, and mathematics educators. There are questions about which curricula and pedagogy, Standards-based or traditional mathematics curricula, best support rigorous instruction that promotes students' superior mathematical understanding. The research projects in which I have been involved attempt to answer these questions by assessing student learning and understanding of mathematics at middle grades and high school levels, and, their long term course-taking patterns, and persistence in post-secondary science, technology, engineering, and mathematics (STEM) classes after participating in a traditional, University of Chicago School Mathematics Project (UCSMP), or *Standards*-based mathematics curriculum. College mathematics placement tests are included in the study as well. The findings have implications for middle grades and high school mathematics curriculum selection, post-secondary student placement, and for future research in this area.

Thursday, 15 November 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### November 13 - Middle School Teachers' Formative Use of a Feedback Guide

**Middle School Teachers' Formative Use of a Feedback Guide**As part of a professional development program focused on mathematics problem solving, middle school teachers were introduced to a feedback guide intended to help them provide feedback to students and make instructional decisions. The teachers' use of this feedback guide is the focus of this talk. I will discuss the extent to which teachers use the guide reliably, as well as the evidence of the teachers' use of the feedback guide to inform follow-up instruction. Although the subjects of the study were middle school teachers, the discussion about instructional planning has implications for all levels of instruction.

Tuesday, 13 November 2007

4:10 p.m. in Skaggs 117

3:30 p.m. Refreshments in Math Lounge 109

### November 5 - Error Estimates for Ill-Posed Problems

Department of Computer Sciences & Department of Mathematical Sciences Colloquium Series

**Error Estimates for Ill-Posed Problems**Some recent results related to estimation of errors in inverse and ill-posed problems will be discussed. The speaker is a world-renowned specialist working in the area of inverse and ill-posed problems, including general theory, numerical methods, and applications of these problems. He is the author of more than 300 scientific publications, including 12 monographs, on this topic as well as on mathematical physics, applied mathematics and science education.

Monday, 5 November 2007

4:10 p.m. in Math 311

3:30 p.m. Refreshments in Math Lounge 109

### October 25 - Why model malaria? Disease dynamics in a changing world.

Department of Computer Sciences & Department of Mathematical Sciences Colloquium Series

**Why model malaria? Disease dynamics in a changing world.**Malaria is a complex vector-borne disease and a major public health burden in endemic regions of the tropics. Non-endemic regions have shown pronounced patterns of increase in incidence and re-emergence in the past three decades. Despite extensive knowledge accumulated for almost a a century on the biology of both the parasite and the mosquito vector, the reasons for these patterns of exacerbation are not well understood. Climate change, human migrations, and drug resistance are different hypotheses but evaluating these mechanisms from time series data remains elusive. In this talk, by using data from East African highlands, I present ongoing work on a mosquito-human coupled model to start answering some of these questions.

Thursday, 25 October 20073:30 p.m. Refreshments in Math Lounge 109

### October 18 - A New Method of Detecting Differentially Expressed Genes through Probe Level Data from Oligonucleotide Arrays

**A New Method of Detecting Differentially Expressed Genes**

**through Probe Level Data from Oligonucleotide Arrays**Oligonucleotide arrays such as Affymetrix GeneChips use multiple probes, or a probe set, to measure the abundance of mRNA of every gene of interest. Some analysis methods attempt to summarize the multiple observations into one single score before conducting further analysis such as detecting differentially expressed genes (DEG), clustering and classification. However, there is a risk of losing a significant amount of information and consequently reaching inaccurate or even incorrect conclusions during this data reduction. We developed a novel statistical method to detect DEG for both two-group and k-group cases. It utilizes probe level data and requires no assumptions about the distribution of the dataset. The method was tested on benchmark datasets and compared with existing summarization methods (RMA, GCRMA, MAS5, PLIER, etc.). The results show that our method successfully detects DEG with positive predictive value of 94% while maintaining a low false discovery rate and consistently out performs the existing methods.

Thursday, 18 October 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### October 15 - A Centennial for Two Great Scholars: Heiberg's Translation of the Lost Palimpsest of Archimedes - 1907 and Heath's Publication on Euclid's Elements - 1908

**A Centennial for Two Great Scholars:**

**Heiberg's Translation of the Lost Palimpsest of Archimedes - 1907 and Heath's Publication on Euclid's Elements - 1908**One century ago two of the greatest classical scholars in the history of mathematics translated a lost palimpsest to try to answer the question: "Did Archimedes (ca. 250 BC) really have the fundamental concepts of infinitesimal calculus?" In this talk I will trace the search for an answer from 1907 to 2007. The materials presented have been collected at Oxford, Cambridge, London, Copenhagen, Vatican City, Jerusalem, and Constantinople as well as in cities across our country.

Monday, 15 October 2007

4:10 p.m. in Math 312

3:30 p.m. Refreshments in Math Lounge 109

### October 8 - Future Teachers' Professional Knowledge

**Future Teachers' Professional Knowledge**Teacher education has been the subject of criticism for a long time without its effectiveness ever being analysed empirically on a broader base. The International Association for the Evaluation of Educational Achievement (IEA) has therefore launched in 2006 an international study on teacher education (TEDS-M) dealing with policy, practice and teachers' readiness to teach mathematics. Due to the lack of theoretical frameworks for internationally comparative studies on teacher education, a pilot study (PTEDS) has been undertaken in the last 4 years. In this paper qualitative results of a complimentary case study embedded in the P-TEDS study about future mathematics teachers' professional knowledge will be presented. Based on interviews and the results of open questionnaires, data about what are the competencies the evaluated future teachers' have in the areas of (1)mathematical knowledge (so-called mathematical content knowledge), (2) knowledge on mathematics pedagogy (so-called pedagogical content knowledge in mathematics) and (3) general pedagogical knowledge. The study shows that in order to develop a comprehensive understanding of modelling and its pedagogical value future teachers need appropriate knowledge and competencies in mathematics, mathematics pedagogy and general pedagogy. The study underlines the central role mathematics pedagogical knowledge plays in the development of professional knowledge of teachers.

Monday, 8 October 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### October 4 - Furthering the Professional development of teachers - some observations, ideas and visions from the view point of a research mathematician at a German University

**Furthering the Professional development of teachers -**

**some observations, ideas and visions from the view point of a research mathematician at a German University**The talk starts with a short description of the system of teacher education in Germany as well as with an overview on the German school system. Presently the author is running a project entitled "Mathematik Anders Machen" which translates to "Mathematics Done Differently" to spread and to broaden existing local or regional professional development programs. This massive project is sponsored by the Deutsche Telekom Foundation (T-Mobile) in collobaration with the German Mathematicians' Association (DMV). In describing the theoretical framework of the program the author will refer to recent international research results in the area of professional development.

Thursday, 4 October 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### September 27 - The Center Manifold

**The Center Manifold**After receiving a UM forestry degree in 1955, Al Kelley earned a doctoral degree in mathematics at the University of California, Berkeley in 1963. He joined the mathematics department at UC-Santa Cruz in 1966. He worked as a smokejumper during summers while attending UM and made his first trip to California in 1954, landing by parachute to fight a fire there. He also worked as a forester in Oregon and as a U.S. Air Force radar officer. While teaching at Berkeley in 1964, Kelley discovered and named the center manifold, and he was among the first to recognize the importance of computers in mathematical research. He is the co-author of three widely used college textbooks on the C programming language.

Kelley is returning to campus to receive a 2007 Distinguished Alumni Award from the UM Alumni Association. In this talk he will discuss the center manifold as well as his journey from forestry to mathematics to computer science.

Thursday, 27 September 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### September 20 - Mathematics Building Inauguration

**Mathematics Building Inauguration **

The Department of Mathematical Sciences will hold an open house and dedication ceremony on Thursday, Sept. 20, for the new addition to the Mathematics Building. The open house will be 3:30-5:30 pm with a short dedication ceremony taking place at 4:10 pm by the entrance to the addition. The addition houses an elevator, making the building completely accessible for the first time, in addition to new restrooms and offices. The public is welcome to attend. Cake and ice cream will be served.

Thursday, 20 September 2007

3:30 p.m. - 5:30 p.m.

### September 17 - Freeman Dyson's challenge for the future: The mock theta-functions

**Freeman Dyson's challenge for the future: The mock theta-functions**The legend of Ramanujan is one of the most romantic stories in the modern history of mathematics. It is the story of an untrained mathematician, from south India, who brilliantly discovered tantalizing examples of phenomena well before their time. Indeed, the legacy of Ramanujan's work (as a whole) is well documented and includes direct connections to some of the deepest results in modern number theory such as the proof of the Weil Conjectures, and the proof of Fermat's Last Theorem. However, one final problem remained. In his last letter to Hardy (written on his death bed), Ramanujan gave examples of 17 functions he referred to as "mock theta functions". Without a definition and without good clues, number theorists were unable to make any real sense out of these peculiar functions. Nevertheless, these examples make important appearances in many disparate areas of mathematics, a fact which inspired Freeman Dyson to proclaim:

Mock theta-functions give us tantalizing hints of a grand synthesis still to be discovered. Somehow it should be possible to build them into a coherent group- theoretical structure... This remains a challenge for the future. My dream is that I will live to see the day when our young physicists, struggling to bring the predictions of superstring theory into correspondence with the facts of nature, will be led to enlarge their analytic machinery to include not only theta-functions but mock theta-functions.

--Freeman Dyson, 1987

In this lecture I will outline the history of Ramanujan's final enigma, and I will discuss the solution obtained in joint with Kathrin Bringmann. The result appears in a series of four papers in Inventiones Mathematicae, Annals of Mathematics, Proceedings of the National Academy of Sciences, and the Journal of the American Mathematical Society.

Monday, 17 September 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109

### September 17 - Who Wants to Be a Mathematician

**10:00 am**

**Freeman Dyson's Challenge for the Future - The Story of Ramanujan's Mock Theta Functions**The In his last letter to Hardy, Ramanujan defined 17 peculiar functions which are now referred to as his mock theta functions. Although these mysterious functions have been investigated by many mathematicians over the years, many of their most basic properties remained unknown.

This inspired Freeman Dyson to proclaim:

The mock theta-functions give us tantalizing hints of a grand synthesis still to be discovered. Somehow it should be possible to build them into a coherent group theoretical structure... This remains a challenge for the future.

--Freeman Dyson, 1987

After recalling the story of the enigmatic Ramanujan, we describe the solution to Dyson's "challenge for the future", and we indicatesome of the consequences of this new theory.

Monday, 17 September 2007

10:00 a.m. in University Center North Ballroom

**11:00 am**

"Who Wants to Be a Mathematician" contest

All events are in the University Center North Ballroom (3rd floor)

### September 6 - Adventures in Finland: Mathematical and Otherwise

**Adventures in Finland: Mathematical and Otherwise**In this talk, I'll speak about my experiences in Finland during the 2006-07 academic year. I have a number of mathematical adventures to share. In particular, I'll discuss the three general problems that I worked on over the course of the year. Each was quite different, but there is a uniting theme: large-scale Bayesian estimation. I'll attempt to tie them together using this framework and hopefully give a general audience a feel for each. One of the projects was in collaboration with Finnish researchers, and this facilitated a number of travel opportunities within Finland. So, I'll also show some pictures of the Finnish country side and of Helsinki. My main goal in this talk will be to give a broad audience a feel for what was an enriching year for me, both personally and professionally.

Thursday, 6 September 2007

4:10 p.m. in Math 103

3:30 p.m. Refreshments in Math Lounge 109