Material to Support Promotion to Professorpeople.uwec.edu/smithaj/PromoMain.pdfdent studies,...

Material to Support Promotion toProfessor

Alexander J. SmithDepartment of Mathematics

University of Wisconsin-Eau Claire

November 10, 2002

Contents

Educational Background and Professional Appointments 4

1 Teaching and Advising 51.1 Research and Special Work with Students . . . . . . . . . . . 5

1.1.1 Funded Student-Faculty Collaborations . . . . . . . . . 51.1.2 Independent Studies Conducted . . . . . . . . . . . . . 71.1.3 Seminars Taught . . . . . . . . . . . . . . . . . . . . . 101.1.4 Capstone Projects and Seminars . . . . . . . . . . . . . 121.1.5 UWEC Student Research Day Poster Session Sponsor-

ships . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.1.6 UWEC Spring Math Retreat Sponsorships . . . . . . . 14

1.2 Curricular Initiatives and Innovations . . . . . . . . . . . . . . 161.2.1 Calculus Reform . . . . . . . . . . . . . . . . . . . . . 161.2.2 Integration of Technology into Modern Geometry . . . 181.2.3 Instructional Use of Networking and Online Technologies 191.2.4 Computational Science Minor . . . . . . . . . . . . . . 23

2 Professional Scholarship 252.1 Invited or Peer Reviewed Scholarship . . . . . . . . . . . . . . 252.2 Contributed Scholarship . . . . . . . . . . . . . . . . . . . . . 29

3 Service 323.1 Service to the Department . . . . . . . . . . . . . . . . . . . . 323.2 Service to the College of Arts and Sciences, the University,

UW System and Profession . . . . . . . . . . . . . . . . . . . 34

Appendices 38

A Letters from Students 38A.1 Jeffrey Clay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A.2 Alex Johnson . . . . . . . . . . . . . . . . . . . . . . . . . . . 40A.3 Peter Misurek . . . . . . . . . . . . . . . . . . . . . . . . . . . 42A.4 Nicholas Marti . . . . . . . . . . . . . . . . . . . . . . . . . . 43A.5 Leon Buck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44A.6 Molly Craker . . . . . . . . . . . . . . . . . . . . . . . . . . . 45A.7 Amanda Potts . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

B Cornulets 48B.1 Tentative Letter of Acceptance from Mathematics Magazine

Editor Frank Farris . . . . . . . . . . . . . . . . . . . . . . . . 48B.2 Revised Paper . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

C Correspondence relating to rejections of NSF CCLI grant pro-posals for FY1999 and FY2000 Programs, and acceptance of Pro-posal for FY2001 65

D Correspondence relating to work on review panel for the NSFComputer Science, Engineering and Mathematics Scholarship Pro-gram, including news releases for award of CSEMS grant proposaland congratulations letter from the Governor 73

E Miscellaneous correspondence relating to faculty-student collab-oration projects 78

F Other miscellaneous correspondence 86

3

4 Alexander J. Smith

Educational Background and

Professional Appointments

Dr. Alexander John Smith439 Summit Ave.Eau Claire WI 54701

EDUCATIONPh.D. in MathematicsUniversity of California-Berkeley1987

B.A. in MathematicsOxford University1982

B.S. in Mathematics, PhysicsNew Mexico State University1980

PROFESSIONAL APPOINTMENTSAssociate Professor of MathematicsUniversity of Wisconsin-Eau Claire1995-present

Assistant Professor of MathematicsUniversity of Wisconsin-Eau Claire1990-1995

G.C. Evans Instructor of MathematicsRice University1987-1990

Promotion Documentation 5

1 Teaching and Advising

1.1 Research and Special Work with Students

As described in Criteria for Promotion to Professor, “highly ef-fective teaching may include activities such as leading seminars, supervisingindependent studies and supervising projects involving student-faculty col-laboration.”

Below are listed various funded student-faculty collaborations, indepen-dent studies, capstone projects, seminars, math retreat sponsorships and stu-dent research day poster session sponsorships that I have been involved withsince submitting documentation to support promotion to Associate Professorin September 1994.

1.1.1 Funded Student-Faculty Collaborations

1. Modeling the Europan Ice LayerAlex Johnson, Brad Barth and Leon Buck2001-2

(With Marc Goulet and Paul Thomas)

Alex Johnson and Brad Barth were supported as BlugoldScholars and Leon Buck was supported by a Zivnuska Schol-arship. (Alex Johnson has been working as a Blugold Scholarunder my direction, and Brad Barth under Marc Goulet’s.)In addition to the products mentioned in 1.1.1 and 1.1.2, thestudent aspect of this research culminated in the three stu-dents presenting a talk at the 2002 Spring Wisconsin meetingof the MAA in Ripon, WI. Additionally, Leon Buck is a coau-thor on a paper mentioned in section 2.1.

2. Entropy of DNAAlex Johnson, Brad Barth, Peter Misurek and Nick Saeger2000-01

(With Marc Goulet)

Alex Johnson and Brad Barth were supported as BlugoldScholars (Alex under my direction and Brad under Marc’s).


We met with the students weekly and studied papers by TomSchneider of the National Cancer Institute. The papers wereabout the information content (in the sense of Shannon) ofgenetic sequences. The work culminated in the poster andretreat presentation mentioned in sections 1.1.5 and 1.1.6.

3. Computer Algebra Computations of Bargmann-Fok-Segal Inner Prod-uctsNick SaegerSummer 2000

(With Michael Howe)

The work was funded by a Faculty/Student Research Collabo-ration grant. My expertise in Maple and a basic understand-ing of Michael Howe’s work provided the necessary bridgebetween Michael Howe and Nick Saeger.

4. Modeling the Ice Layer on EuropaJon Mitchell1999-01

This work was funded by a Faculty/Student Research Collab-oration Grant. One outcome was a student presentation atthe Wisconsin Section of the MAA annual meeting in UW-Superior on April 14, 2000.

5. Assessment of a Constructivist Based Calculus SequenceJeff Clay1997-8

(With Andrew Balas and Marc Goulet)

This work was funded by two Summer Research Experiencefor Undergraduates grants [Summer of 1997 and 1998] andinvolved the design of a research based assessment of theC4L calculus project at UWEC. This work resulted in Jeffbeing a coauthor on a paper (see section 2.1) presented at theFirst International Conference on the Teachingof Undergraduate Mathematics held in Samos, Greecein July 1998.


1.1.2 Independent Studies Conducted

1. Creating Learning Objects using MapletsDave WattenfordFall 2002

This independent study is a follow up of a UW System grantI received and describe in section 1.2.3 for Summer 2002. Inthe independent study, we will develop ways to create javaapplets with Maple8.

2. Scientific VisualizationPeter MisurekSpring 2000

The student took a look at the so-called Lewis Carroll PillowProblem: What is the probability that a random triangle isobtuse? The problem is made interesting by the fact that itis ill-posed. He considered several ways of generating a “ran-dom triangle.” He then used Maple to assemble the resultsinto striking visual displays comparing the methods.

3. The Connected Mathematics ProjectTodd SalisburyWinterm 1999

Todd was planning to be a middle school teacher, and CMP isa middle school mathematics curriculum that is being usedwidely across the Wisconsin as well as across the nation.Since Todd would be more employable if he could documentknowledge of the Connected Mathematics Project, we choosethis topic, and he did a detailed study of its pedagogy, im-plementation and assessment. In addition, he interviewedteachers, parents and students in Eau Claire who have beeninvolved in CMP.


4. Non-Euclidean GeometryJason WendtlandSpring 1998

Jason was an elementary education student who was turnedon to geometry by Geometer’s Sketchpad in math 330 andwanted to pursue more geometry. In the independent study,he explored hyperbolic geometry via the Poincare model us-ing Sketchpad scripts.

5. Technology in MathematicsKathy ElliottSpring 1998

Kathy was an MEPD student who was referred to me byMona Majdalani. Kathy was teaching middle school in Koreaand took some time off to get her MEPD degree. The purposeof the independent study was for her to develop ideas on waysto make effective use of graphing calculators, spreadsheetsand Geometer’s Sketchpad in her school.

6. Random Gaussian SurfacesMichael DunniganFall 1997

Michael had done a physics internship at Cornell Univer-sity during summer 1997 and wanted to pursue some of themathematics involved in the project. In the project, we usedMaple to model the formation of a certain type of “fractal”surface that arose in his internship.

7. Constructivist Methods for AP CalculusJohn SchmidtSummer 1997

John was one of our MAT students who had taken my Math751 course a few years before and wanted to follow up withsome ideas from the course and focus on adapting materialfor his AP calculus course in Arcadia, WI.


8. Transformational GeometryKelly BaarsSummer 1997

Kelly confided that she had a difficult time relating to herwork in Math 426 (abstract algebra) but that she related wellto ideas in Math 330 (geometry). I suggested that an inde-pendent study focusing on the three-dimensional group oftransformations of the Euclidean plane and the larger groupof inversions would help her to better appreciate abstractgroup theory.

9. Solving Differential Equations With Random WalksMichael Dunnigan and Holly HauschildSpring 1997

The mathematical content of this independent study was in-spired by a 1996 UWEC Spring Math Retreat talk by Dr.Fern Hunt of the National Institute of Standards. The talkwas titled Random Walk Solution of a Fluid Flow Equation.

Mike was able to use his progress in the independent study to securea Summer 1997 physics internship at Cornell University. In this sum-mer internship, he used similar mathematical methods with a physicistdoing research into thin film phenomena.

Holly presented results of the independent study at the Spring 1997State Pi Mu Epsilon meeting at St. Norbert’s College.

10. From Clifford Parallels to TwistorsAnne DaveySpring 1996, Fall 1995

In these independent studies, Anne Davey investigated thefollowing topics:

• Parallelism in elliptic space and Clifford parallels

• The Hopf fibration of the three-sphere

• The topology of the rotation group SO(3)


11. Assessing Calculus Reform EffortsDaniel WalkerFall 1995

As a result of a National Science Foundation initiative, con-siderable resources have been devoted to what is often termedthe “calculus reform movement” and various calculus reformprojects have emerged from this initiative. One aspect ofmost of these projects is an attempt to integrate technol-ogy intelligently into the teaching of calculus. Another as-pect involves pedagogy: for example, some of the projectsare problem driven, others are laboratory courses and someare activity-based. As a result of the movement, some 600universities came to adopt one of the various calculus reformtextbooks by the 1993-94 academic year. In this independentstudy, Daniel delved into details of many of the projects andstudied the Mathematical Association of America’s publica-tion titled Assessing Calculus Reform Efforts (the so-calledACRE report).

Daniel presented results of his independent study at a UWEC MathDepartment Colloquium titled A Survey of Calculus Reform Efforts onDecember 14, 1995.

12. Creating Opportunities for Using Computers in Math ClassroomsRandy DrostFall 1994

13. Technology in MathematicsJoanne PulvermacherFall 1994

1.1.3 Seminars Taught

1. Public Key CryptographyFall 1996

See item 3 below.There were nine students enrolled in this seminar.


2. Turing MachinesSpring 1995

A major goal of the seminar was to introduce some of AlanTuring’s main ideas on computation, and to foster an appre-ciation for the very subtle ideas behind Hilbert’s Tenth Prob-lem (the so-called “Halting Problem”) and Turnings solutionto the problem. In the seminar, students used spreadsheetmacros to emulate certain Turing Machines and to make theirown.

There were eight students in the seminar. Some of the com-puter science majors in the seminar became so interested inthe subject that they entered “Busy Beaver Contests” wherepeople submit candidates for a so-called busy beaver. (Itis proven that the maximal number of 1’s produced by aTurning Machine that halts when fed the blank tape is anon-computable function of the number of states. One withn states which maximizes the number of 1’s among all suchn-state machines is called a busy beaver.) These studentsused Mathematica for this extension.

3. Public Key CryptographyFall 1995

In this seminar, I implemented, at the undergraduate level,the ideas I had been developing for having students use spread-sheets to create a miniature RSA public-key network. (Pre-viously I had only implemented the idea of the spreadsheetnetwork with a class of academically talented high schoolstudents.) In this seminar, I worked with some interestedstudents in creating other types of public-key networks withspreadsheets, such as the “knapsack cipher,” with which Ihad been previously unfamiliar. Together with the nine stu-dents, I extended many of the spreadsheets described in mypaper Using Spreadsheet to Emulate the RSA Method. Forexample, we extended the simple primality testing spread-sheet (based solely of Fermat’s Little Theorem) into a spread-sheet based on Euler’s criterion for quadratic reciprocity.


(This is the primality test mentioned in the previous de-scription of my work with Daniel Walker on the distributionof quadratic residues.) Some students in this seminar sub-sequently enrolled in M. Wick’s Mathematica seminar andconverted some of the spreadsheets they designed in thisPublic-Key Cryptography seminar into their Mathematicaproject. In addition, with the insight and spreadsheet skillof a student name Rebecca Peer, I was able to extend thebasic RSA spreadsheet described in the aforementioned pa-per into a more elaborate one involving linked spreadsheetsthat encrypts and decrypts longer blocks of text.

1.1.4 Capstone Projects and Seminars

1. Assessing a Combined Laboratory/Classroom Environment for Calcu-lus InstructionCapstone Project: Brianna PowersFall 2002

2. Exploring Hyperbolic Geometry with Geometer’s SketchpadCapstone Project: Nick MartiFall 2000

3. Mathematical WritingCapstone Project: David Berger, Keith Bellows and Casey WrightFall 1999

The model for this capstone project was based on the coursetitled Mathematical Writing that was designed by the pre-eminent computer scientist Donald Knuth. His course hasbeen used as a capstone course at Stanford University and hedescribes the course in Mathematical Writing (MAA NotesNumber 14, 1989).

4. Modelling the Ice Layer on EuropaCapstone Project: Jon MitchellFall 1999


5. Mathematical WritingCapstone SeminarSpring 1999

There were four students enrolled in this capstone seminar.

For this seminar and the following two capstone projects,issues of technical writing and the effective presentation ofmathematics were studied. The projects were a mixtures ofmathematical content with techniques of writing and rewrit-ing. The students learned to typeset mathematics using TEX,which is the professional mathematician’s typesetting lan-guage. This capstone experiences provided the students withexcellent opportunities to create good, final copies of earlierwork to include in their portfolios documenting work in themajor.

6. Mathematical WritingCapstone Project: Holly HauschildFall 1998

7. Mathematical WritingCapstone Project: Kelly BaarsSpring 1998

1.1.5 UWEC Student Research Day Poster Session Sponsorships

1. Refreezing of the Ice Sheet on Europa After a Melt-Through EventLeon Buck, Brad Barth, Alex JohnsonApril 2002

This poster was awarded Honorable Mention.

(With Marc Goulet and Paul Thomas)

2. Computational BiologyBrad Barth, Alex Johnson, Peter Misurek and Nick SaegerApril 2001

(With Marc Goulet)


3. Computer Algebra Computations of Bargmann-Fock-Segal Inner Prod-uctsNick SaegerApril 2001

(With Mike Howe)

1.1.6 UWEC Spring Math Retreat Sponsorships

1. The Application of Fractal Geometry to Sound SynthesisAmanda PottsSpring 2002

2. Refreezing of Ice After Melt-Through Events on EuropaLeon Buck, Alex Johnson and Brad BarthSpring 2002

3. Computational Biology and MathematicsBrad Barth, Alex Johnson, Peter Misurek and Nick SaegerSpring 2001

4. Modeling the Ice Layer on EuropaJon MitchellSpring 2000

5. The Artistic and Linguistic Beauty of MathematicsMark AverySpring 1998

An outstanding 40-minute presentation.

6. Primeless ExpansesLarry CornellSpring 1998

7. Stochastic Differential EquationsMichael Dunnigan and Holly HauschildSpring 1997

8. The Dirac Scissors ProblemAnne DaveySpring 1996

An outstanding 40 minute presentation.


9. The RSA CryptosystemJason KlovningSpring 1996

10. Using Mathematica to Explore the Randomness of Quadratic ResiduesDaniel WalkerSpring 1995

If one can prove the existence of “small” quadratic non-residues for general primes, then it follows that a determinis-tic, polynomial-time primality test exists. On the other hand,if for some prime, “small” quadratic non-residues do not ex-ist, then the generalized Riemann hypothesis is false. In orderto prepare for the presentation, I spent approximately twentyhours either teaching Mr. Walker about quadratic residues,randomness and Mathematica or writing Mathematica pro-grams for his use in the presentation.

Special Note: In August 2002, Agrwal, Kayal and Saxenaannounced a deterministic polynomial time algorithm to testprimality.

11. A Survey of Calculus Reform EffortsDaniel WalkerSpring 1995


1.2 Curricular Initiatives and Innovations

My personal philosophy of teaching centers on one main tenet:

Mathematical ideas can only be learned if certain mental construc-tions are already in place.

Concerning this tenet, in The Feynman Lectures on Physics, Feynman as-sesses the effectiveness of his infamous lecture series for Cal Tech freshmenand sophmores in the preface by reminding us of the famous quote attributedto Edward Gibbon:

The power of instruction is seldom of much efficacy except inthose happy dispositions where it is almost superfluous.

Feynman then goes on to write

There isn’t any solution to this problem of education other thanto realize that the best teaching can be done only when thereis a direct individual relationship between a student and a goodteacher – a situation in which the student discusses the ideas,thinks about the things, and talks about the things. It’s impos-sible to learn very much by simply sitting in a lecture, or even bysimply doing problems that are assigned.

I try to apply the tenet by pushing students to make mental constructions intheir own minds, in order to create dispositions where “instruction is almostsuperfluous.” Because I feel comfortable with computer technology and enjoyboth its challenges and benefits, my search to teach by this tenet tends tomanifest itself through numerous integrations of technology into my teaching.

In this section, I describe four teaching activities that I have been involvedwith since being promoted to Associate Professor, and which I feel evidencequality teaching motivated by the above tenet.

1.2.1 Calculus Reform

Since 1995, I have spent a considerable amount of my time working to inte-grate computers into calculus instruction at UWEC. This began when MarcGoulet and I attended an intensive three week workshop at Purdue Uni-versity [May 25-June 10, 1995] titled Calculus, Concepts, Computers and


Cooperative Learning (C4L). Of the various NSF-supported calculus reformprojects, this one seemed to Marc and me to have the most solid pedagogicalfoundation.

Influenced by the C4L project, we developed a “lab-based” approach tocalculus instruction where “expert system” software (eventually Maple) wasused. There were three reasons for this.

• Firstly, computers continue to change mathematics. In their profes-sions, both our education majors and liberal arts majors will need tointegrate computers with mathematical thinking skills. For example,Technology in the Wisconsin Model Academic Standards (for gradesK-12) says,

Calculators, computers, spreadsheets, graphing utilities andother forms of electronic information technology are nowstandard tools for mathematical problem solving in science,engineering, business, medicine, government, and finance.Thus, the use of technology must be an integral part of teach-ing and learning mathematics.

We should not protect our students from this reality. “Knowing themath” does not imply that they will find it natural to integrate tech-nology in the application or teaching of mathematics. This integrationis a learned skill.

• The second reason relates to a pedagogical issue. “Mapping” calculusconcepts into expert system software can foster mental construction.Initially we had students meet in the computer lab and would pushthem to grapple with ideas before formally presenting topics in class.Then in class we would spend a lot of time talking with students aboutwhat they did in lab. In the best of class meetings we would find thatwe have reached Feynman’s ideal state and that the lecture had becomesuperfluous. At other times students would rush through the computerlab activities, dividing up the work among their group members, thusfailing to make adequate mental constructions in their individual minds.

• A third reason was to use the computer as a straw-man. When agroup of students gets stuck in lab, they naturally call an instructorover for help. Almost always the reason the group is stuck is because


they are running head on into a mathematical concept that they mustgrapple with. But usually the students are not prepared to admit this tothemselves and instead suspect that there is a “syntax” error. In otherwords, they blame the computer. The instructor plays along with thefiction that it is the computer’s fault and asks the students to explainwhat they have tried. The instructor feels joy inside as the studentsverbalize. The students are glad that the instructor is forming a unitedfront with them in figuring out what’s wrong with the darn computer.Before long, the instructor has guided the students into confrontingthe mathematical issue that needs to be grappled with. In the process,the students have verbalized and formed mental constructions. Theinstructor goes away knowing precisely what issues must be broughtout in a future class and what constructs students have developed sothat those very constructs can be used to tailor the presentation ofmaterial.

One disadvantage to the instructional approach described above is thatstudents coming through the calculus sequence will have differing experi-ences; some go through taking “traditional” classes while others go throughtaking “reform” classes. This makes it difficult to design an upper divisioncurriculum for majors. In Fall 1999 I served as course coordinator for Math114. This was the first semester of the department’s attempt to strike a bal-ance between the two tracks, which we have called “hybrid” calculus. Whathas emerged from this is an agreement to provide first and second semestercalculus students with a weekly two hour laboratory experience−the imple-mentation of this experience currently taking many different forms.

An outgrowth of this curricular initiative is my scholarly interest in as-sessment of various modes of calculus instruction and involvement in thepedagogy of teaching undergraduate mathematics, documented in section2.

1.2.2 Integration of Technology into Modern Geometry

At UWEC we offer an upper division course titled Modern Geometry whichis required for students in our teaching majors and minors. In the past thecourse was taught frequently by Dr. Bierman, who retired in 1998. Orvillewas the first to use “dynamical geometry” software in the course in about1993. This type of software is best exemplified by Cabri and Geometer’s


Sketchpad. Dynamical geometry software primarily has pedagogical utility,and not research utility like expert-system software such as Maple. Dynami-cal geometry software is quite easy to learn how to use, and so it encouragesstudents to visualize and analyze problems “on the fly.” In this way, studentsgrow to make their own conjectures about various properties and objects.

I feel that I am quite proficient with using Geometer’s Sketchpad to teachgeometry, and have make extensive use of it on the many occasions that I havetaught Modern Geometry. I have also made extensive use of it in graduatelevel courses for MAT and MST students, as well as in various independentstudy projects. I find that my main tenet of teaching, i.e., that mathematicalideas can only be learned if certain mental constructions are already in place,can be applied quite effectively in courses such as these where the content canbe directly explored and demonstrated using dynamical geometry software.

In order to optimize effective use of dynamical geometry software in ourgeometry courses, I initially made use of standard resources the universityhad on hand: namely classrooms with at most a computer for the teacher,and general access labs with several computers. In this initial use, I wouldschedule my class to meet at least one hour per week in a general access labso that students could grapple with the content in a “laboratory” settingbefore lecture. After doing this several times, I began to see how effectivea combined environment could be, where computer exploration and lecturewould be woven together. This idea was the main impetus for my desireto begin writing the NSF Course, Curriculum and Laboratory Improvementgrants documented in section 2.1, and was a main component of the projectproposal which ultimately provided funding for our department’s combinedclassroom and laboratory environment.

1.2.3 Instructional Use of Networking and Online Technologies

Since the 1997-8 academic year I have made extensive use of technologies suchas curricular web pages, network file sharing, web-based learning systems andonline learning object in my classes. I describe some examples in the followingparagraphs.

Network File Sharing Pilot Project. Fall 1997-8 was the year beforeall UWEC students were given Windows NT accounts to access shared fileson a so-called “Student Global Server,” which first appeared in 1998-9. InFall 1997-8 I was part of a pilot project that experimented with providing


file sharing by students and the instructor. In the project, students in myMath 216 class were given accounts on a Microsoft Outlook Exchange, and itwas through this medium that networking and file sharing was accomplished.Students worked collaboratively in groups of two or three using MapleV andturned in their MapleV worksheets through Outlook from a general accesscomputer lab. Then from my office, I could make substantial comments ontheir work using a keyboard, and ask students to make revisions.

The primary pedagogical advantage to this use of network file sharingwas that it can truly make it possible to have a revision component to acourse. I think that having students write sentences and paragraphs ex-plaining mathematics and using vocabulary such as “expression, equation,function, evaluate, solve, simplify, graph, level curve, slice, variables, implicit,explicit,” etc., and having them do revisions on this writing is quite necessaryin the calculus sequence. Indeed experience tells us that beginning calculusstudents do not distinguish between the actions of solving an equation andevaluating a function. This writing serves as a bridge between “computationof an answer,” which is characteristic of lower division courses and “proofwriting”, which should be an expectation in upper division courses.

There are two primary reasons why it is difficult to have a revision com-ponent to a course. These reasons are

(i) it is difficult to keep track of revision requests made by the instructor,and subsequent revisions done by the student and

(ii) it is difficult for students to revise their writing if it is done with paperand pencil (should they rewrite the entire work, or just the parts thatneed editing?).

File sharing really does simplify the logistics of having a revision componentto a course.

The time involved in setting up this pilot project was substantial. I hadseveral meetings over the course of Summer 1997, Fall 1997 and Spring 1998to set up the project, troubleshoot, and give feedback on the project.

Network File Sharing. Following the aforementioned pilot project, in1998-9 the university saw the introduction of a computing environment whereevery student was given an account on what we now call the UWEC Domain.This allowed all students access to shared files and made possible the use ofnetworking technologies in all classes. I was quick to take advantage of this


technology in order to facilitate management of laboratory sections in calcu-lus as well as in my upper division courses and faculty/student collaborationprojects. For example, I often set permissions on folders so teams of stu-dents can share files for collaboration in calculus labs when Maple files needto be shared, or in geometry classes when Geometers’ Sketchpad files needto be shared. Moreover, I frequently provide assistance to colleagues in thedepartment when they want to make use of networking technology in theirclasses.

Curricular Web Pages and Web-Based Learning Technology. SinceSpring 1997 I have maintained curricular web pages for my classes, althoughas of Summer 2002 I have switched to the web-based learning technologyBlackboard. Through these technologies I make available basic course docu-ments such as syllabi, assignments and old exams.

When I teach a class in “lecture format” I make frequent use of Mapleto enhance the lecture, especially in Math 216. Initially students expressedfrustration with this because, of course, it was difficult for them to “takenotes.” So I started saving the Maple worksheet from the lecture to makeit available on the web in both html and maple-worksheet formats. Muchto my surprise, these “Maple lecture summaries on the web” proved to bevery popular with students. If I did not get links made in a timely fashion,I would start getting email messages reminding me to do so.

In general, after passing a learning curve, I have found that maintainingthese curricular web pages becomes routine and not overly time consuming,and that they provide a certain cohesiveness and structure to the class thatstudents like to take advantage of from their residence.

Math 216 email Reading Assignments. Since Fall 2001 I have postedreading questions on my course web site for Math 216 students. Before a classmeeting when a new section from the textbook is to be taken up, studentsare required to email me their answers to my reading questions a couple ofhours before class. I then grade and email responses to their answers beforeclass. Typically the reading questions push the student to think about somestatements or figures in the new section, and there is a request to do certainodd-numbered, basic “skill” problems in the exercise set. If students have anydifficulty with the basic exercises, they are to tell me so in their email. Theidea came from the paper “How We Get Our Students to Read the Text Before


Class” by mathematicians Matt Boelkins and Tommy Ratliff. At the end ofthe course, when I ask students to evaluate the effectiveness of the readingassignments, a typical response is, “The reading assignments did push me toread the text and were beneficial because they made it easier to understandthe information that you presented even if I didn’t fully understand it whenI was reading it.”

I plan to continue using this teaching strategy in appropriate coursessuch as Math 216. It seems to be a simple and effective way to employ, at avery basic level, the main tenet mentioned at the beginning of this section:mathematical ideas can only be learned if certain mental constructions arealready in place. It sure helps to have read the textbook before listening toa lecture!

Learning Objects. In the last couple of years there has been much in-terest among professional educators in “learning objects.” These have beencharacterized as “any digital resource that can be reused to support learn-ing.”

While attending the Meeting of PIs and Other Senior Personnel NSFDUE Projects in Mathematics at the National Science Foundation buildingin Washington D.C. in March 2002, I attended several workshops on topicssuch as Mathematical Materials on the Web and Modifying and ReusingExisting Online Materials in Mathematics. At this workshop I became moreinformed about learning objects, in particular about ones available from theMathematical Sciences Digital Library (MathDL), which is an online resourcemanaged by the Mathematical Association of America with fundingby the National Science Foundation.

Upon returning from this meeting, I decided to apply for a grant from theLearning Objects and Pedagogy Grant Program of the UW System of Officeof Learning and Information Technology. My proposal titled “Digital Learn-ing Objects in a Calculus Class” was funded in June 2002. Through this work,I have experimented with making use of digital resources from MathDL, aswell as developed some beginning skills in creating my own learning objects.Professional educators of undergraduate mathematics students seem to be ina very good position relative to educators in other disciplines. This is be-cause our leading pedagogical software packages and expert system softwarepackages are beginning to make the writing of java applets quite accessibleto users such as myself who have no experience with java. For example, the


most recent version of Geometer’s Sketchpad allows good, basic exports tojava applets, and Maple8 has added a package called Maplets that allowsexperienced Maple users to create java applet learning objects from withinMaple. Currently I am conducting an independent study with a student tolearn more about Maplets.

The vision for learning object technology is the development of large, dig-ital libraries of learning objects such as MathDL. Then instructors will beable to easily browse and select digital objects to bring into modern class-rooms equipped with computer technology. In this way students can freelyexplore and experiment with concepts in class as they are introduced, muchas students in a geometry class with access to Geometer’s Sketchpad can donow.

1.2.4 Computational Science Minor

Because of my interest and capability with symbolic computational softwaresuch as Maple, I became involved in the interdisciplinary ComputationalScience Minor program in the 1997-8 academic year. This was the first yearthe minor appeared in the university catalogue, and credit must be given toMarc Goulet, Paul Thomas, Brian Mahoney and others for working to gainSystem approval for the program.

In my way of thinking, the faculty/student research collaboration modelis an ideal way to apply the tenet mentioned at the beginning of this sectionto the teaching of more advanced undergraduates. Clearly this model sets uprather directly an individual relationship between a student and a teacher, a“situation in which the student discusses the ideas, thinks about the things,and talks about the things.” Research of this sort directly fosters mental con-structions of abstract concepts, thereby making it possible for the student tolearn more mathematics. I see the curriculum of the Computational Scienceminor as an ideal mechanism to encourage such faculty/student relationshipsand thus I have been very interested and active in the CPSC program.

In Fall 1997, Michael Penkava, Marc Goulet, Lyle Ford (physics) and Iwrote a funded $5,000 NET grant to develop the program’s curriculum. InSpring 1998, Michael Penkava and I were charged with interviewing variousfaculty members in the sciences to find out what mathematical skills andconcepts they required in their undergraduate students in order to conductcomputational science research using a faculty/student research collaborationmodel. We interviewed several such faculty including Paul Thomas, Fred


King, Warren Gallagher and Harry Jol. Then in June 1998 we attended theone-week Women and Science Curriculum Reform Institute at UW-Oshkoshin order to work on the CPSC curriculum.

Since these beginning days for the CPSC program, I have informallyconsulted with a number of CPSC students and faculty doing course workin the program. For example, in Fall 2000 Nick Saeger (a truly outstandingmathematics major and CPSC minor) was working with Jim Phillips from theChemistry Department on a CPSC 300 course project. The project involvedDr. Phillips work on solving the Schrodinger wave equation for a “Morsepotential” and integrating the eigenfunctions (which involved hypergeometricfunctions) to find transition probabilities. Because of my background inphysics and my capability with Maple, I was able to consult with them,explaining some nuances of hypergeometric functions and helping them setup the problem for a Maple solution.

One of my favorite examples of involvement in the CPSC course projectsinvolved working with Michael Penkava and Holly Hauschild on their projectto compute invariants of polynomial Poisson algebras. My contribution wasto figure out how to get Maple to compute what is called a Groebner Basisfor a polynomial ideal. They were interested in having Maple solve about3000 polynomial equations in 8 variables–a highly overconstrained system. Ispent about 15 engrossing hours on this project in March and April of 1999.


2 Professional Scholarship

As described in Criteria for Promotion to Professor, candidates forpromotion are expected to be engaged in scholarly activity which includesactivities such as publication, presentations at professional meetings such asspeeches at national, regional, state or local meetings, panel discussions atsuch meetings, or inservice programs for school district personnel. Schol-arly activities also include professionally related consulting, presentationsin department colloquia and leading department seminars. As describedin the section Goals of the Mathematics Department: Scholar-ship, the activities of grantsmanship, curriculum development and review-ing/refereeing are also considered scholarly activity. In this section of ourDepartment Evaluation Plan, various subjects of scholarly activity aredescribed, including pure and applied mathematics, the pedagogy of teachingmathematics at any level, and the development, use or study of technologyin the teaching and doing of mathematics.

Below is documentation of various such subjects of scholarly activity thatI have been engaged in since I submitted material for promotion to AssociateProfessor in September 1994. I have attempted to divide these activities into“Invited or Peer Reviewed Scholarship” and “Contributed Scholarship.”

2.1 Invited or Peer Reviewed Scholarship

1. Cornulets. Mathematics Magazine. (Tentatively to appear, see letterfrom journal editor in appendix.)

In the words of the Editor of the American Mathematical So-ciety journal Mathematics Magazine, this paper brings forththe mathematics behind a visual connection between the fa-mous Cornu Spiral and a novel discrete structure which Ihave analyzed and have called a “Cornulet.” I have submit-ted the requested revisions and anticipate that the paper willappear sometime in Spring 2003.

2. The Excellence in Mathematics and Computer Science Scholarship withMike Howe and Andrew Phillips. Computer Science, Engineering,and Mathematics Scholarships (CSEMS) Program. NationalScience Foundation, Division of Undergraduate Education, September2002 (#0220772).


This $400,000 grant proposal went through a rigorous peerreview process. The NSF says, “Each proposal was consid-ered by a panel of reviewers, each of whom received a copyof all proposals to be reviewed by that panel. Each panelmember read and wrote reviews of the proposals, and thenthe panel convened as a group to discuss the proposals underconsideration. Following these discussions, reviewers com-pleted their individual written reviews of each proposal.”

I played a central role in the writing of the grant, and was ableto provide insight that I have gained by reviewing CSEMSproposals in June 2001. See item 7 below. Andy Phillipsand I are co-principal investigators, and Mike Howe is theprincipal investigator.

3. Persistence of Thin Ice Regions in Europa’s Ice Crust with Leon Buck,Chris Chyba, Marc Goulet and Paul Thomas. To appear in Geo-physics Research Letters.

This article summarizes collaborative research done with LeonBuck (a UWEC student), Chris Chyba (A MacArthur Fellowholding positions at SETI and Stanford), and Marc Gouletand Paul Thomas (both UWEC faculty). The research re-quired modelling the freezing of the Europan ice crust aftermelt through events by using Maple to solve certain partialdifferential equations and to visualize the solutions.

4. A Case Study in the History of Calculus Reform, with Andrew Balasand Marc Goulet. Proceedings of the Second International Con-ference on the Teaching of Mathematics at the UndergraduateLevel [CD-ROM], paper 284 (2002).

The paper was peer reviewed and we presented it on July 2,2002 at this international conference in Crete, Greece.

5. A Combined Mathematics Laboratory and Classroom Environment withMarc Goulet. Poster Session of the Meeting of PIs and Other Senior Per-sonnel NSF DUE Projects in Mathematics in Washington DC on March15, 2002.


Marc Goulet and I were invited to present a poster at thismeeting held in the NSF building. The meeting was spon-sored by the Mathematical Association of America.Support for attending the meeting was provided by the MAAand the UWEC Office of Research.

6. A Combined Mathematics Laboratory and Classroom Environment withMarc Goulet. Poster Session of the Joint AMS-MAA National Meetingin San Diego, California on January 8, 2002.

Marc Goulet and I were invited to present a poster on ourproject A Combined Mathematics Laboratory and ClassroomEnvironment at this poster session. I did not attend themeeting, but worked with Marc on the preparation of theposter, who did the actual presentation of the poster.

7. Invited review panelist for the 2002 National Science Foundation Com-puter Science, Engineering and Mathematics Scholarship Pro-gram. Washington, DC from May 30-June 3, 2001.

8. A Combined Mathematics Laboratory Classroom Environment withMarc Goulet and Michael Penkava. Course, Curriculum and Labo-ratory Improvement Program of the National Science Foundation,Division of Undergraduate Education. November 2000 (#0088254).

The grant proposal for this $114,000 project underwent arigorous peer review process. The NSF says, “Proposals inCCLI are reviewed by panels of faculty within the disciplineof the proposal. Reviewers come from all over the UnitedStates, from two-year and four-year colleges and from com-prehensive and research universities.”

The program invites proposals for projects that enable agroup of faculty to explore strategies for overcoming iden-tified challenges and barriers to curricular reform.

In Summer 1998, Michael Penkava and I submitted an earlyversion of this project, and the proposal was rejected. InSummer 1999, Marc Goulet, Michael Penkava and I rewrotethe proposal, and this was also rejected. Finally, after more


rewriting in Summer 2000, the proposal was accepted. I amthe principal investigator.

9. Contributing author to Flickering Clusters: Women, Science, and Collab-orative Transformations. Cheryl Ney, Jacqueline Ross and Laura Stem-pel, editors. University of Wisconsin Press. Madison, WI (2001).

This book is about curricular reform in different sciences andthe transformations that pedagogy is going through. Onereview of the book said, “the book could be a very importantvehicle for regional and national discussion and serve as amodel for other initiatives.”

10. Consultant for Wisconsin Center for Academically Talented Youth regard-ing curriculum and instruction for the Summer Advanced Learning Pro-gram. Spring 2001.

For a number of years, the curriculum for the WCATY indi-vidually paced precalculus curriculum had been the StanfordEducation Program for Gifted Youth (EPGY) online curriculumbecause Josh Zucker, the WCATY ALP instructor, was pro-fessionally associated with EPGY. Upon his departure fromWCATY, I was asked to help design and implement a newcurriculum. I subsequently taught the curriculum in Sum-mer 2000 and Summer 2001 in the WCATY ALP program atLawrence, University.

11. P.J. Thomas, M.R. Goulet, A.J. Smith, D.G.B. Whitelaw and C.F.Chyba, Refreezing timescales following a melt-through event on Europa,Lunar Planet. Sci. Conf. [CD-ROM] XXXII, abstract 1208 (2000).

The paper was peer reviewed and we presented it at thisannual international conference in Houston, Texas on March16, 2000.

12. A. Balas, B. Basenauer, J. Clay, M Goulet, A. Smith, Assessing Cal-culus Reform at the University of Wisconsin-Eau Claire, Proceedingsof the First International Conference on the Teaching of Mathematicsat the Undergraduate Level, pages 35-37. John Wiley and Sons, 1998.


The paper was peer reviewed and we presented it at thisinternational conference in Samos, Greece on July 3, 1998.

13. The LAB Approach to Teaching Calculus with Andrew Balas and MarcGoulet. Institute at the Wisconsin Math Council Meeting in GreenLake Wisconsin on April 30, 1998.

We were invited by WMC to present this three-hour inserviceworkshop for state high school mathematics teachers.

2.2 Contributed Scholarship

1. The Grand Unitary Hypothesis Regarding Zeros of the Zeta FunctionUWEC Mathematics SeminarJanuary 26, 2001

In this talk I outlined a possible direction of research relatedto work Marc Goulet and I were conducting on the Entropyof DNA. The idea is to use certain statistical methods devel-oped by computational biologists to explain certain regularpatterns in the distribution of the zeros of the Riemann zetafunction observed by Andrew Odlyzko of Bell Labs.

2. Recent Progress in HyperKahler GeometryUWEC Mathematics SeminarSeptember 8, 2000

In this talk I described how some conjectures I made in myPh.D. thesis have recently been solved.

3. LAB Based Calculus Reform at the University of Wisconsin-Eau Claire(with A. Balas and J. Clay)July 3, 1998Poster SessionFirst International Conference on the Teaching of Undergraduate Math-ematics at the Undergraduate LevelSamos, Greece


4. The LAB Cycle (with Marc Goulet)June 14, 1998Caucus Session at the Women and Science Curricular Reform InstituteUW-Oshkosh

5. What is a Spinor?October 2, October 9, 1998UWEC Mathematics Seminar

6. Cooperative Learning and Computers (with Marc Goulet and AndrewBalas)August 28, 1997

A workshop, funded by UWEC Network for Excellence inTeaching, attended by various Math, Physics, Economics andC&I faculty.

7. Compactifying Minkowski SpaceOctober 10, October 17, 1997UWEC Mathematics Seminar

8. There is No Royal Road to Mathematics: Using Writing to DevelopCalculus ConceptsFebruary 13, 1997UWEC Mathematics Department Colloquium

9. Constructivist Based Calculus CoursesDecember 6, 1998Whitehall High School

Andrew Balas, Marc Goulet and I gave a three hour workshopto the High School Math Teacher COOP (Arcadia, Indepen-dence, Whitehall, Blair-Taylor) on calculus instruction.

10. The Non-Euclidean Geometry of the Euclidean AlgorithmMarch 9, 1997UWEC Mathematics Seminar


11. The Politics of Public-Key CryptographyDecember 11, 1996Presentation to the UWEC Chapter of the Association of ComputingMachinery

12. All Infinite Dimensional Separable Banach Spaces are HomeomorphicOctober 11, 18, 25, 1996UWEC Mathematics Seminar

13. Conceptual Calculus, Computers and Cooperative LearningNovember 17, 1995UW-River Falls Mathematics Department Colloquium

14. Constructivism in the College Mathematics Classroom (with Marc Goulet)October 27, 1995UW System Women Studies Conference on The Everyday Art and Actof TeachingUW Madison

15. Conceptual Calculus, Computers and Cooperative LearningOctober 12, 1995UWEC Mathematics Department Colloquium

16. Teaching an Open Inquiry Mathematics CourseMay 12, 1995UW System Women and Science Program Spring RetreatSpring Green, WI

17. Team Teaching a Lab Based Calculus Course (with Marc Goulet)May 12, 1995UW System Women and Science Program Spring RetreatSpring Green, WI

18. The Yang-Mills Equations and the Four-Dimensional Poincare Conjec-tureMarch 10, March 24 1995UWEC Mathematics Seminar

19. Panel discussion: Science in the Classroom: An Update of the Womenand Science ProgramNovember 11, 1994UW Women’s Studies Consortium 19th Annual Women’s Studies Con-ferenceUW-Stevens Point


3 Service

3.1 Service to the Department

Elected and Appointed Committees

• 2002-3

– Department Senator

– Awards Committee

– Mathematics Graduate Curriculum Committee

– Department Technology Representative

• 2001-2

– Chair: Mathematics Department Personnel Committee

– Mathematics Graduate Curriculum Committee

– Department Technology Representative

• 2000-1

– Secretary: Mathematics Department Personnel Committee

• 1999-2000

– Student Affairs Committee

– Long Range Planning Committee

• 1998-9

– Chair: Mathematics Recruitment Committee

– Student Affairs Committee

– Library Committee

– Marketing the Graduate Program Committee

– Day of the Meet Manager for 1999 Mathematics Meet


• 1997-8

– Chair: Associate Professorship Subcommittee

– Chair: Student Affairs Committee


– Mathematics Recruitment Committee


• 1996-7

– Secretary: Associate Professorship Subcommittee




– Department Review Committee

• 1995-6

– Chair: Mathematics Department Curriculum Committee

– Chair: 1996 UWEC Math Meet Committee

– Catalogue Committee


• 1994-5

– Secretary: Mathematics Curriculum Committee

– Co-Chair: 1995 UWEC Math Meet Committee

– Catalogue Committee


3.2 Service to the College of Arts and Sciences, theUniversity, UW System and Profession

• 2002-3

– University General Education Committee

This is a new committee charged with overseeing the GeneralEducation program in wake of the recent restructuring of GEby the university senate. I was elected to the committee bythe faculty of the College of Arts and Sciences.

– Arts and Science Curriculum Committee

– University Senate Executive Committee

– University Senate Budget Committee

• 2001-2


– Distance Education Committee

– MAT Oral Exam Committee for Greg Dieckman

– MAT Oral Exam Committee for Mark Johnson

– Wisconsin INTEL Science Talent Search Committee

– Together with Don Reynolds, I worked with and mentored twomathematically talented Memorial High School students [Joe Pe-tefish and Kyle Moore]. We met with them for one hour per weekin Fall 2001, enriching their mathematical knowledge with chal-lenging and interesting topics. In Spring 2002, I was “job shad-owed” by one of the students, who is exploring career possibilitiesincluding academia.

• 2000-1


– Advisory Committee of the Graduate Council

– Computational Science Minor Committee

– UW System Symposium For Undergraduate Research and Cre-ative Activity Abstract Review Committee



• 1999-2000




• 1998-9



• 1997-8


– Service Learning Advisory Committee

– Reviewer for Kell Container Corporation Scholarship for Faculty/StudentCollaborative Work

– MEPD Oral Exam Committee for Kathy Elliot

– Wisconsin Westinghouse Science Talent Search Committee

• 1996-7

– Service Learning Advisory Committee

– Search and Screen Committee for the Service Learning Coordina-tor

– Wisconsin Westinghouse Science Talent Search Committee

– Chair of Oral Exam Committee for Daniel Walker

• 1995-6

– Service Learning Steering Committee

– Facilitator for the Fall 1995 New Student Colloquium

– Department Representative to UWEC Service Learning Retreat


• 1994-5

– UWEC Representative to the three-day NSF Project KaleidoscopeRegional Colloquium on Revitalizing Introductory Science andMathematics Courses held at Beloit College

– Consulted by the Director of La Crosse School District Math andScience Program on ways to vitalize the La Crosse School DistrictGifted and Talented Mathematics Program

– MAT Oral Exam Committee for Scott Gaulke

– Facilitator for the Fall 1994 New Student Colloquium


Appendices

38. . .AJS Appendices

A Letters from Students

A.1 Jeffrey Clay

AJS Appendices. . .39


A.2 Alex Johnson


A.3 Peter Misurek


A.4 Nicholas Marti


A.5 Leon Buck


A.6 Molly Craker


A.7 Amanda Potts


B Cornulets

B.1 Tentative Letter of Acceptance from Mathematics MagazineEditor Frank Farris


B.2 Revised Paper


C Correspondence relating to rejections of NSF CCLI grant propos-als for FY1999 and FY2000 Programs, and acceptance of Proposalfor FY2001


D Correspondence relating to work on review panel for the NSFComputer Science, Engineering and Mathematics Scholarship Pro-gram, including news releases for award of CSEMS grant proposaland congratulations letter from the Governor


E Miscellaneous correspondence relating to faculty-student collab-oration projects


F Other miscellaneous correspondence

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