Curriculum Vitae

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Corner Brook, Newfoundland, Canada
March 23, 1969
Canadian
30 Charles St. W., Apt. 1417, Toronto, ON, M4Y 1R5
Dept. of Mathematics, University of Toronto, 100 St. George St., M5S 3G3
(416) 927-1128
(416) 978-3646
(416) 978-4107
madore@math.toronto.edu
www.math.toronto.edu/~madore

Ph.D. in Mathematics "Rank-one group actions with simple Z sub-actions." University of Toronto	Slated Completion - Spring 1999 Supervisor: A. del Junco Toronto, Ontario
M.Sc. In Mathematics "Commutant of Chacon’s Transformation." University of Toronto	1993 Supervisor: A. del Junco Toronto, Ontario
B. Math. In Co-op Pure Math and Combinatorics & Optimization University of Waterloo	1992 Waterloo, Ontario

U of T Departmental Fellowship September 98-August 99 ($3900).
U of T Open Fellowship, September 96-September 98 ($3600 per year).
Daniel B. Delury Teaching Award, 1995.
Junior Fellowship at New College, University of Toronto, 1994-99.
National Science and Engineering Research Council (NSERC) Scholarships:
    PGSB September 94-September 96 ($17400 per year).
    PGSA September 92-September 94 ($17400, $15600 per year).
    Summer Research Award 1991 and 1992.
University of Toronto Entrance Award 1992 ($2500).

Ergodic Theory Session - AMS Regional Meeting University of Florida	March 12, 1999 Gainsville, Florida
I was asked to speak at this session on a problem solved in my thesis "A transformation with square roots of all orders but no infinite square root chain."
Ontario Association of Math Educators (OAME) Nipissing University	May 22-24, 1998 North Bay, Ontario
The OAME is an annual meeting of math educators from elementary to college level. A series of math fair project outlines for high school students I am developing was the subject of my talk to a group of 50 high school teachers entitled "A Plethora of problems for projects."
Ergodic Theory / History of Math Software Brock University	January 15, 1998 St. Catherines, Ontario
I gave a colloquium to the Math Department on Ergodic Theory from its origins to modern developments. I was also asked to speak with the concurrent B.Sc./B.Ed students at Brock University about the uses of math software in education and how this has developed in the last 30 years.

Ergodic Theory

For my thesis I solved a problem posed by Jonathan King [1], about measure preserving transformations of a probability space and their roots. Write T Ť S, if S is a square root of T. If S is a 2^{n^th} root of T, then we have a square root chain of length n:

T Ť S^{2^n-1} Ť S^{2^n-2} Ť S^{2^n-3} ..... Ť S .

King’s Question: Are there any measure preserving transformations which have arbitrarily long square root chains but no (non-trivial) infinite square root chains?

I was able to answer this question in the affirmative by constructing a rank 1 action of a group where an element has arbitrarily long root chains but no infinite root chain. The transformation in the action corresponding to that element only commutes with the action and thus solves King’s question. The construction is an interesting extension of Ornstein’s rank 1 mixing example and joinings are used to show it has the desired properties.

This construction was part of a general program that has produced several interesting examples especially [2]. It will produce even more exciting examples with further work. Please see my research statement for more details.

[1] J. King, "The generic transformation has roots of all orders", preprint.
[2] A. del Junco, "A simple map with no prime factors", to appear in Israel J. of Math.

Combinatorics

Worked collaboratively with Professors Steve Tanny and Ed Barbeau on the Lyness recurrence relation:

X[n+1] = ( c + X[n]) / X[n-1].

We used Maple to further our exploration and examined relations to Ergodic Theory and Differential Geometry.

Symbolic Computation

I am currently News and Book Reviews editor for the refereed journal MapleTech which is devoted to symbolic computation developments, and applications of Maple to sciences and education.

From 1990-1992 I was a co-op student in the Symbolic Computation Group, a research project in the Department of Computer Science at the University of Waterloo. My contributions to basic research at the lab included programming, bug fixing, and documentation. I also organized our summer research retreat.

A rank 1 Z^2 mixing action where all times are simple, preprint, 22 pages.

Book Review of "Calculus Labs for Maple V" in MapleTech Vol. 3 No. 3, 1996. Birkhauser pp:3-4.

Maple in Science Education with T.C. Scott and R.M. Corless. MapleTech Vol. 1 No. 3, 1994 Birkhauser pp:58-68.

Report on 10^th Annual Maple Retreat. SIGSAM Bulletin August 1992. ACM Press.

Lecturer University of Toronto	1995-Present Toronto, Ontario
Lecturing for a section of Calculus (MAT137Y) for sciences including Computer Science, Math, Astronomy and Physics, in 1998-1999. This is a difficult course for students. Topics include epsilon - delta proofs of limits and questions of integrability. Guest lectured for various courses including Calculus for Sciences (MAT 135Y - 7 lectures and MAT 137Y - 1 lecture), Calculus for Engineers (MAT187H - 1 lecture), Dynamics (MAT199H - 1 lecture) and Combinatorics (MAT344H - 2 lectures).
Teaching Assistant /Tutor University of Toronto	1992 - present Toronto, Ontario
Taught two hours of tutorials each week for courses including Calculus for Business (MAT133Y), Calculus for Science (MAT135Y, MAT 137Y) and Calculus for Math Specialists (MAT157Y). Explained problem solving techniques and difficult concepts in the course. Assisted students with homework problems. Conducted and marked quizzes and tests. Marked assignments and held contact hours for upper year courses including Linear Algebra (MAT 223H), Combinatorics (MAT 344H), Analysis (MAT 357Y, MAT 1000, MAT 338H), Abstract Algebra (MAT 300Y), and Complex Analysis (MAT 334H). Four years experience as a Math Aid Centre tutor providing students from Single and Multivariable Calculus, Linear Algebra, Differential Equations, and upper year courses with one on one help.
Junior Fellow at New College University of Toronto	1994-Present Toronto, Ontario
As the senior math tutor at the college I organized the math aid center. As a member of the college I am privileged to contribute to the academic and social atmosphere through regular interaction with faculty and students. During academic orientation I meet with students planning to study calculus in a fun session called "Coping with Calculus". I also write a puzzle page for the New College Alumni newsletter.
University of Toronto Mentorship Program University of Toronto	1998-1999 Toronto, Ontario
With a colleague, Rubén Martinez, I am mentoring a group of four advanced high school students from around Toronto. We meet with the students regularly for small lectures and problem solving. Our program is based around a reading course in knot theory.
Textbook Reviewer for MATHPOWER 12 McGrawHill-Ryerson	August 1997- Present Whitby, Ontario
As an editor I have been doing critical reviews of chapters of the MATHPOWER 12 (Western Edition) high school textbook. My reports to Melanie Myers, math publisher, examine the mathematical accuracy, pedagogy, clarity, style and the fit to the MATHPOWER learning model.
Discover Science Day University of Toronto	1997 Toronto, Ontario
To promote careers in science, the university invites Grade 9 and 10 females to meet with university researchers in small groups. I organized and ran a fun and lively two-hour session on games and strategy, whimsically entitled "How to Cheat your Friends."
SOAR - Math Summer Camp University of Toronto	1997 Toronto, Ontario
Designed and implemented computer labs as part of an integrated three-week enrichment curriculum on Symmetry Groups of the Platonic Solids. Over forty gifted high school students participated. The Maple worksheets we used were also presented to high school teachers through a workshop at the Ontario Institute for Studies in Education on how to design math enrichment programs for grades 9 to 13.
Teacher Training Seminar University of Toronto	1996 Toronto, Ontario
Prof. Joe Repka led us for eight weeks in discussing and practicing all aspects of being a university lecturer. This included presentation style, test creation, exam creation, and course administration. I taught a first year calculus course for one hour, which was videotaped for review. For further experience I taught a third year Graph Theory course for two hours.
Maple Expert	1990-Present
Member of the Symbolic Computation Group (University of Waterloo 1990-1992) and Maple Ambassador (1992-present). Lectured on Maple at University of Toronto at Mississauga, University of Waterloo and Memorial University of Newfoundland. I developed and taught a two day introductory course in Maple at John Abbott College in June of 1998. I was an instructor at a week long National Science Foundation funded summer workshop at Rose Hulman Institute in Indiana on "Reforming the Engineering, Science and Math Curriculum through Symbolic Computation" in July, 1995.
End User Analyst Ultramar Canada	1988-1989 Toronto, Ontario and Montréal, Québec
Over three work terms, of four months each, I supported the users of PCs at two different offices in English and French. Teaching standard company software to users was a major function.

Local Organizing Committee for MAA Summerfest 1998 meeting at Ryerson: I helped find, prepare, and distribute information about Toronto to the many participants.

Problem Co-ordinator for the International Mathematics Olympiad (1995) : With a partner and the team leaders from the competing countries we assigned marks for one of the six contest questions. We graded about one third of the over 400 students from 74 countries.

Secretary Graduate Student Committee for External Review of Mathematics at University of Toronto (1994) : Our committee met with a group of international mathematicians to help prepare the university for the coming of the Fields Institute - Canada’s premiere mathematics research institute.

Teaching Assistant Training Committee (1994-1997) : With a small group of faculty and staff, we organized annual training events for the math department T.A.'s. I personally organized and ran the first training event in 1994.

High School Recruitment Committee (1998-1999).

Mathematics Departmental Council (1992-1993 and 1997-1998).

Departmental Computer Committee (1995-1997).

Secretary and V.P. of Mathematics Graduate Student Association (1993-1995).

Scout Leader - helping youth (age 6-25) develop mentally, emotionally, physically and spiritually through outdoor skills (1987-Present).

St. John Ambulance Standard First Aid training.

References available from the following individuals on request.

1. Professor Andres del Junco, Ph.D. thesis supervisor.
Address: Department of Mathematics, University of Toronto, 100 St. George St., Toronto ON, M5S 3G3.
Phone: (416) 978-5165
FAX: (416) 978-4107
Email: deljunco@math.toronto.edu

2. Professor Steve Halperin, Chair Department of Mathematics, University of Toronto.
Address: Department of Mathematics, University of Toronto, 100 St. George St., Toronto ON, M5S 3G3.
Phone: (416) 978-3320
FAX: (416) 978-4107
Email: halper@math.toronto.edu

3. Professor Ed Barbeau, Professor, University of Toronto.
Address: Department of Mathematics, University of Toronto, 100 St. George St., Toronto ON, M5S 3G3.
Phone: (416) 978-7200
FAX: (416) 978-4107
Email: barbeau@math.toronto.edu

4. Abe Igelfeld, Senior Tutor and Undergraduate Advisor.
Address: Department of Mathematics, University of Toronto, 100 St. George St., Toronto ON, M5S 3G3.
Phone: (416) 978-
FAX: (416) 978-4107
Email: igelfeld@math.toronto.edu