1187 North Cherry Street
Galesburg, IL 61401
(309) 342-1961
aleahy@knox.edu
Department of Mathematics
Knox College
2 East South Street
Galesburg, IL 61401
(309) 341-7439
Education
Ph.D., Mathematics, Rutgers University, October 1995.
Thesis Title: Multiplicity Free Representations.
Thesis Advisor: Professor Friedrich Knop.
Studies include advanced courses in geometry, algebra, and
analysis.
B.A., summa cum laude, St. Olaf College, 1989.
Majors in Mathematics, Philosophy, and Latin.
Studies include the year 1987-1988 at the University of East
Anglia in Norwich, England.
Teaching Experience
Associate Professor, Knox College (1996-2002). I currently hold a
position in the department of mathematics. Teaching experiences
include:
Fundamentals of Mathematics (Math 121). A mathematics
course for students in the liberal arts based on The Heart of
Mathematics by Burger and Starbird.
Functions (Math 131). A pre-calculus course. I made use of
Mathematica for lectures and assignments. One section of the
course was taught using a collaborative-learning approach based on
Precalculus: Concepts in Context.
Functions and Calculus I and II (Math 140-141). An
integrated calculus-precalculus sequence: the first term reviews
equation-solving techniques and polynomial and rational functions
followed by an introduction to differential calculus and its
applications; the second term reviews trigonometric, logarithmic,
and exponential functions and their derivatives as well as basic
integration theory.
Calculus I and II (Math 151-152). An introductory calculus
sequence which depended heavily on the use of Mathematica.
I used Mathematica for class lectures and wrote
Mathematica notebooks for computer-based exercises.
Statistics (Math 160). An introductory statistics
course (non-calculus based).
Calculus III (Math 205). A multivariable calculus
course with a strong Mathematica component.
Introduction to Numerical Mathematics (Math 214). An
elementary numerical methods course targetted at sophomore-level
mathematics students. (Calculus II pre-requisite.)
History of Mathematics (Math 218). A history of
mathematics course for students with an understanding of
mathematics up to the level of calculus.
Differential Equations (Math 230). An introductory course
in differential equations. I developed exercises which used
Mathematica to study numerical methods and qualitative
approaches to equations.
Mathematical Structures (Math 300). A course aimed at
familiarizing students with the foundations of set theory, while
honing their skills in mathematical proof.
Numerical Analysis (Math 311). An introductory course in
numerical analysis. I developed material for explaining the use of
parallel algorithms for solving numerical problems.
Mathematical Statistics (Math 321). The first term of a
two-term introductory probability and statistics sequence.
Analysis I and II (Math 331-332). A two-term advanced
sequence covering algebraic and topological properties of the real
number line, function spaces and abstract topological spaces, and
differentiation and integration of functions of a real variable.
Complex Analysis (Math 333). An introductory complex
analysis course.
Abstract Algebra II (Math 342). The second term of a
two-term introductory sequence in abstract algebra. Topics
included modules and Lie groups and algebras.
Senior Seminar (Math 399). A capstone course for
mathematics majors. The course was centered around Euclid's
Elements. Students were required to give class lectures
and write a research paper with a significant mathematical content
in the history of mathematics.
Independent Study/Student Research. I have supervised
student independent studies in the following areas:
point set and algebraic topology
analysis/advanced calculus
history of mathematics (on Apollonius' Conics)
elementary cryptography
mathematics methods in secondary education
mathematical methods in middle school education
numerical analysis
parallel computing and numerical methods
history of geometry
advanced calculus (from Loomis and Sternberg)
geometric algebra
game theory
projective geometry
I have also supervised a year-long senior thesis on the
representation theory of Lie algebras and the work of another
student on the mathematics of Isaac Barrow during a
post-Baccalaureate fellowship. (This student is now a
Ph.D. candidate in the History and Philosophy of Science Program at
Notre Dame University.)
I am capable of teaching any mathematics course currently available
in the Knox curriculum. I have also worked on interdisciplinary
courses taught outside of the mathematics department:
First-Year Preceptorial (Prec 100). A first-term liberal
arts seminar for all incoming students centered around questions
concerning human identity. I led daily discussions, developed
writing assignments for students, and worked with students to
improve their writing and communicating skills.
Advanced Preceptorial: Science, Science Fiction, and the Future
(Prec 334). An interdisciplinary seminar for students in
their senior year with an emphasis on using readings from science
fiction to explore contemporary issues in science. Developed in
conjunction with a member of the physics department.
Assistant Professor, Knox College (1996-2002). Courses taught
are included in the above list.
include:
Visiting Assistant Professor, Knox College (1995-1996). I held
a visiting appointment for one year. Courses taught are included in
the above list.
Instructor, Rutgers University (1989-1995). As a graduate
student, I taught the following courses:
Differential Equations for Engineering and Physics. A
fourth semester calculus course. I used Maple for class
lectures and designed Maple-based computer laboratories.
Topics in Mathematics for the Liberal Arts. (Two
Semesters.) An entry-level course for students with an interest
in the liberal arts.
Calculus. A beginning calculus course primarily for
students with an interest in business or the liberal arts.
Mathematical Theory of Probability. A fourth-year
probability course for students with a strong background in
mathematics.
Introductory Linear Algebra. An introductory course in
linear algebra for students with an interest in the sciences.
Teaching Assistant, Rutgers University (1989-1995). As a
graduate student, I was a teaching assistant for the following
courses:
Intensive Calculus. (Three semesters.) An
experimental workshop- and lecture-based introductory calculus
sequence modeled on courses developed by Uri Treisman at Berkeley and
UT-Austin. I met with students three times a week in workshops to
solve moderate to difficult calculus problems. Students presented
these solutions in formal write-ups. Professor Amy Cohen-Corwin and
Professor Richard Lyons, supervisors.
Advanced Calculus. An introductory course in the
theory of real analysis. I graded homework and exams and held office
hours.
Elementary Differential Equations. An introductory course
in the theory of differential equations. I graded homework and
exams.
Graduate Assistant, Rutgers University (1993-1994). I conducted
research in integral geometry.
Research Interests
The history of mathematics: the historical development of
calculus, applications to teaching.
Technology in mathematics education: the uses of distributed
computing in teaching college-level mathematics
Representation theory: finite-dimensional representations of
semisimple lie algebras, applications of multiplicity free
representations.
"An Introduction to James Gregory's Geometriae Pars
Universalis". Proceedings of the Eighth Midwest History of
Mathematics Conference (2000).
"History of Mathematics on the Web" Focus22:2
(2002) 12.
"A Classification of Multiplicity Free
Representations". Journal of Lie Theory8 (1998)
367-391.
Grants, Awards, and Honors
Philip Green Wright/Lombard College Award for for Distinguished
Teaching. Knox College, 2003.
NSF/CCLI grant (#0089045), "Distributed Computation, Numerical
Methods, and Scientific Computing for Mathematics and Science
Students in an Undergraduate Mathematics Department", 2000-2004.
(Co-principal investigator.)
NSF/ILI grant (#9751141), "Enhancing the Educational Impact
of Technology", 1997. (Co-principal investigator.)
"Pioneers of Representation Theory: Frobenius, Burnside,
Schur, and Brauer by Charles W. Curtis." MAA Online.
http://www.maa.org/reviews/pioneers.html (September, 2000).
"The Contest Problem Book V, by George Berzsenyi and
Stephen B. Maurer and Critical Thinking Puzzles, by Michael
A. DiSpezio." MAA Online:
http://www.maa.org/reviews/problembooks.html (July, 1998).
Presented Papers
"James Gregory's Proof of the FTC" at the annual meeting of the
Illinois Section of the Mathematical Association of America,
Galesburg, Illinois, April 8-9, 2005.
"Distributed Computing in the Numerical Analysis Curriculum" at
the annual meeting of the Illinois Section of the Mathematical
Association of America, Schaumburg, Illinois, April 2-3, 2004.
"Turning your Computing Lab into a Supercomputer" with Dennis
Schneider, at the contributed paper session on "The Creative Use of
Technology in Teaching Mathematics," Mathfest: The Annual Summer
Meeting of the Mathematical Association of America, the
University of Colorado-Boulder, July 31, 2003.
"A Student-Centered History Course Taught Through Original
Sources" at the Contributed Paper Session on The Use of History in
the Teaching of Mathematics at Mathfest: The Annual Summer
Meeting of the Mathematical Association of America, Madison,
Wisconsin, August 2-4, 2001.
"An Introduction to the Geometriae Pars Universalis" at the
Midwest History of Mathematics Conference, Northern Kentucky
University, October 13-14, 2000.
"A senior project on the geometric construction of tangents" at
the Pew Consortium Workshop on Using History in the Teaching of
Mathematics, Colorado College, Colorado Springs, Colorado, September
18-20, 1998.
"Prelude to the Hilbert Basis Theorem (or how abstract algebra
became abstract)" at the annual meeting of the Illinois state
section of the Mathematical Association of America, Lebanon, Illinois,
March 27-28, 1998.
"Barrow's Geometrical Methods for Finding Tangents" at the AMS-MAA
Special Session on The Uses of History in the Teaching of Mathematics
at the Joint Meeting of the American Mathematical Society and
Mathematical Association of America, Baltimore, Maryland,
January 7-10, 1998. (Presented jointly with Knox College student Nahyan
Fancy.)
"What I didn't teach in the history seminar" at the
Institute on the History of Mathematics and Its Use in Teaching,
Washington, D.C., June 2-20, 1997.
"The History of Mathematics and its Use in Teaching: A Report
on the IHMT" at the annual meeting of the Illinois state section of
the Mathematical Association of America, Rockford, Illinois, March
21-22, 1997. (Presented jointly with Herb Kasube of Bradley
University and Diann Porter of the University of Illinois at
Chicago.)
"Cayley's Invariant Theory: The Impact of Group Theory?" at
the Institute on the History of Mathematics and Its Use in
Teaching, Washington, D.C., June 3-21, 1996.
"Orbit Structures on Multiplicity Free Representations" at the
Special Session on Representation Theory and Harmonic Analysis of
Topological Groups at the Joint Meeting of the American
Mathematical Society and the Mathematical Association of America,
Orlando, Florida, January 10-13, 1996.
"The Classification of Multiplicity Free Representations" in
the Lie Groups Seminar, Rutgers University, Mathematics Department,
October 20, 1994.
Institutes, Seminars, and Significant Off-Campus Work
Oak Ridge National Laboratory, visiting scientist and
Resident Faculty Director of the Oak Ridge Science Semester. Fall
2002 (five months).
Park City Mathematics Institute, Undergraduate Faculty
Program participant. Summer 1998 (three weeks).
Institute on the History of Mathematics and Its Use in
Teaching. Summer 1996-1997 (three weeks each summer).
AMS-SIAM Summer Seminar in Applied Mathematics, The
mathematics of tomography, impedance imaging, and integral
geometry. Summer 1993 (two weeks).
Conferences Attended
Annual Meeting of the Illinois Section of the Mathematical
Association of America, Knox College, Galesburg,
Illinois, April 8-9, 2005.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, Roosevelt University, Schaumburg,
Illinois, April 2-3, 2004.
Mathfest: The Annual Summer Meeting of the Mathematical
Association of America, Boulder, Colorado, July 29-31, 2003.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, Illinois College, Jacksonville,
Illinois, March 28-29, 2003.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, McKendree College, Lebanon, Illinois,
April 5-6, 2002.
Mathfest: The Annual Summer Meeting of the Mathematical
Association of America, Madison, Wisconsin, August 2-4, 2001.
Linux Clusters: The High Performance Computing Revolution
(sponsored by NCSA: The National Center for Supercomputing and its
Applications), Urbana, Illinois, June 26-27, 2001.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, University of Illinois, Urbana,
Illinois, March 23, 2001.
ACM Conference: Information Literacy and Liberal
Education, Lake Forest College, Lake Forest, Illinois, March
9-10, 2001.
VIP Seminar: webMathematica (sponsored by Wolfram
Research), Chicago, Illinois, March 9, 2001.
Midwest History of Mathematics Conference, Northern
Kentucky University, October 13-14, 2000.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, North Central College, Naperville,
Illinois, March 31, 2000.
Strengthening Faculty Development at Liberal Arts
Colleges, Rollins College, Winter Park, Florida, March 2-3,
2000.
GLCA/ACM Mathematicians Meeting, Lake Forest College,
Lake Forest, Illinois, April 10, 1999.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, Augustana College, Rock Island,
Illinois, April 9, 1999.
Pew Consortium Workshop on Using History in the Teaching of
Mathematics, Colorado College, Colorado Springs, Colorado, September
18-20, 1998.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, McKendree College, Lebanon, Illinois, March
27-28, 1998.
Joint Meeting of the American Mathematical Society and the
Mathematical Association of America, Baltimore, Maryland, January
7-10, 1998.
Annual Meeting of the Illinois Section of the Mathematical
Association of America, Rockford College, Rockford, Illinois, March
21-22, 1997.
Pew Workshop on General Education Mathematics and Science
Courses, Hope College, Holland, Michigan, March 7-9, 1997.
Connections in Science: A Workshop on Undergraduate Science
and Mathematics Education, University of Chicago, Chicago, Illinois,
April 12-14, 1996.
Joint Meeting of the American Mathematical Society and the
Mathematical Association of America, Orlando, Florida, January
10-13, 1996.
Third International History, Philosophy, and Science
Teaching Conference, University of Minnesota, Minneapolis,
Minnesota, October 29-31, 1995.
Joint Meeting of the American Mathematical Society and the
Mathematical Association of America, San Francisco, California,
January 11-14, 1995.
Other Professional Activity
Illinois Section of the Mathematical Association of America
(ISMAA). Extensive involvement:
Chair. 2005-. (Responsible for coordinating the activities of
the 1000+ member regional organization.)
Programming Committee Chairman, 2004 and 2005. (Responsible for
coordinating all aspects of the annual meeting of the statewide
organization.)
Director for Private Universities. 2001-2004.
Two-Year College Committee member. 1998-2001.
Illinois Section Project NExT Fellow, 1998-1999.
Pre-publication review of Chapters 5-6 of Precalculus: A
Graphing Approach by Barnett, Ziegler, and Byleen (McGraw-Hill).
November 1999.
NSF/CCLI Grant Review Panelist. June 26-29, 1999.
Grader for the American Regions Mathematics League
(ARML) high school mathematics competition, May 30, 1998.
Computer Experience
Programming Experience. I have experience programming in C, Java,
Perl, and PHP. Some recent projects include:
C programming using MPI. In conjunction with student
research projects, I have written miscellaneous programs using MPI
to implement numerical algorithms in distributed computing clusters.
Dynamic web pages with PHP and MySQL. I developed
several dynamically-generated web pages using PHP as a scripting
language to access a MySQL database.
Dynamic web pages with Perl and LDAP. I developed
several dynamically-generated web pages using PHP as a scripting
language for accessing various LDAP directories. This project also
included the design and evelopment of schemas for encoding course
information in an LDAP database.
System administration. I currently administer a network of 41
Linux computers for the mathematics and computer science departments
at Knox College, including departmental file and web servers, faculty
desktop systems, a teaching lab and beowulf cluster, and several
small student-use computing labs. Duties include:
Administration of the primary departmental server. The
primary departmental file server is a Dell Poweredge 2650 running
Fedora Core 1. The system: maintains files for all mathematics
faculty members and students in their courses; makes these files
available to departmental and campus systems via NFS, Windows SMB,
and Appletalk protocols; serves self-developed interactive webpages
to faculty and graders for managing electronic student assignments;
acts as an LDAP server; acts as a Mathematica license
server; performs all computations for Mathematica sessions
across campus
Administration of the departmental web server. The
mathematics department web server (math.knox.edu) is wholly managed
by the mathematics department. The system: maintains web pages for
three sites (math.knox.edu, ismaa.knox.edu, cs.knox.edu, and
pcmi.knox.edu) using the Apache web server and runs a MySQL server
for displaying dynamic web pages via PHP; provides SSL-enabled
webmail to interested students and faculty.
Administration of the departmental computing labs and
distributed computing cluster. Currently based on Fedora Core
2. Duties include the development of installation and maintenance
scripts, software installation and updating, and the installation
of software for the beowulf cluster
Administrative work also includes the creation of various shell and
perl scripts, responsibility for maintaining system back-ups,
and advising on all departmental computer purchases.
Departmental Service
Administrator for Mathematics Department computer systems.
Putnam Exam coordinator, 1999-2000.
Stephens Prize Exam coordinator, 1999-2000, 1998-1999, and
1995-1996 (with Kevin Hastings).
Carr Prize Exam coordinator, Spring 1997.
Mathematica Lab Teaching Assistant Coordinator, Spring
1997.
College Committee Service
Faculty Budget and Development Committee, 2002-2005
Computer Science Tenure Review Committee (chair), Spring 2004.
Instructional Support Committee, 2001- (Chair, 2001-2002.)
Computer Science Search Committee, Spring 2001.
Life after Knox Working Group (facilitator), Spring 2001.
Computer Science Search Committee, Spring 2000.
ACE/Kellogg Working Group on Faculty Development, Fall
1999.
Admissions work: numerous individual student contacts and
classroom visitations; attended several luncheons; participated in
day-long St. Louis Informational Programs (September 1996 and 1998).
Honors committees: I have served on college honors committees
for the following students:
Hari Ramanan, 1999-2000.
Ryan Stuffelbeam, 1997-1998.
Anton Kamenov, 1997-1998.
Nate Bode, 1996-1997 (Chair).
Leonard Blackburn, 1996-1997.
McNair Research Program: I directed a McNair summer research
program undertaken by Michelle Hackman entitled "The Mathematics of
Louis Lagrange: Calculus of Variations".
ISMAA student mathematics contest supervisor: I brought groups of
2-5 students to the annual ISMAA meetings to participate in the student
mathematics contests (1997-1999 annually).
Math club talk: "The Brachistochrone Problem", October 13, 1998.
Math Colloquium lectures: "Introduction to webMathematica", 2002;
"The Mathematics of Data Compression", 2000 (3 lectures
total);"Fourier Transforms for Finite Groups", 1997 (4 lectures
total); "The Mathematics of Computer-Aided Tomography", 1998.
Phi Beta Kappa, Chapter President, 2001-2003.
Community Service
Galesburg Telecommunications Commission. Appointed by the city
council. November, 2000-. (Elected Chair, 2001-.)