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INTRODUCTION
Originally from Germany, I came for a one-year student exchange at
the University of Southern California, Los Angeles. I stayed on and
graduated with a Ph.D. in Probability Theory in 1992. After one-year
appointments at Colorado College in Colorado Springs and Humboldt State
University, I came to CSLA in Fall of 1994. In my free time I like to
read, watch movies, hike, camp, and stand on my head on a daily basis.
TEACHING INTERESTS
I am interested in exploring ways to improve students' understanding
of the material taught, as well as to raise their interest in mathematics.
This may take the form of showing videos, using calculators or computers,
and assigning projects when appropriate. My areas of interest are probability,
modeling and differential equations. Currently I am working with faculty
from biology, chemistry, physics and computer science on integrating
the curriculum from these disciplines for life science majors as part
of an NIH grant. Find out more about these activities on the webpage
of the Center for Interdisciplinary Quantitative Analysis (CINQA).
I used to be the faculty advisor for the Math
Club, but Dr. Krebs and Dr. Shaheen have taken over.
If you are interested in being active in the Math club, contact Dr.
Krebs and Dr. Shaheen or just show up at one of the meetings, usually
Wednesdays from 3-4:15. We also have a MAA
student chapter on campus. If you want to find out more about how
to become a member and receive discounts for books and meetings, stop
by my office. For a list of events click here.
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RESEARCH INTERESTS
I have a number of research interests. My Masters' thesis was on a
stochastic model for inventory control (Operations Research), while
in my Ph.D. thesis, I developed a stochastic model for the movement
of a white blood cell. With Dr. Pamula, I have worked on a model of
a system of parallel processes to compare different methods of error
recovery. Most recently, my focus is on (enumerative) combinatorics,
in particular questions related to tilings and compositions. This work
has culminated in a book
which brings together the research on combinatorics of compositions
and words.
Publications
and Preprints
An interactive Java program that counts and produces
tilings of n-by-m rectangles with square tiles of size 1-by-1, 2-by-2,
...,k-by-k can be found here.
Book:
I had the pleasure of writing joint research articles with the following
individuals (roughly in reverse chronological order): Matthieu Dufour, Arnold Knopfmacher, Michael Mays, Sergey
Kitaev, Augustine
Munagi, N.Y. Li, Toufik
Mansour, Patrick Callahan, Phyllis
Chinn, Ralph
Grimaldi, Raj
Pamula, Joseph Watkins.
- M. Dufour and S. Heubach, Circular Nim Games, preprint.
- S. Heubach , A. Knopfmacher , M.E. Mays & A. Munagi.: Inversions in compositions of integers, Quaestiones Mathematicae, 34:2, (2011), 187-202.
- S. Heubach, S. Kitaev, Avoiding
Substrings in Compositions, Congressus Numerantium, 202 (2010), 87-95.
- S. Heubach, T. Mansour, and A. O. Munagi, Avoiding
Permutation Patterns of Type (2,1) in Compositions, Online
Journal of Analytic Combinatorics, 4 (2009)
- S. Heubach, N. Y. Li and T. Mansour, Staircase
Tilings and k-Catalan Structures, Discrete Mathematics, 308:24
(2008), 5954-5953.
- P. Chinn, R. Grimaldi, and S. Heubach, Tiling
with Ls and Squares, Journal of Integer Sequences, 10
(2007), Article 07.2.8
- S. Heubach and T. Mansour, Enumeration
of 3-Letter Patterns in Compositions, Combinatorial Number
Theory in Celebration of the 70-th Birthday of Ronald Graham, 2007,
243-264, de Gruyter.
- S. Heubach, S. Kitaev and T. Mansour, Partially
ordered patterns and compositions, Pure Mathematics and Applications,
17:1-2 (2006), 123-134
- P. Callahan, P. Chinn, and S. Heubach, Graphs
of Tilings, Congressus Numerantium, 183,
(2006), 129-138
- S. Heubach and T. Mansour, Staircase
Tilings and Lattice Paths, Congressus Numerantium, 182
(2006), 97-109
- S. Heubach and T. Mansour, Avoiding
patterns of length three in compositions and multiset permutations
, Advances in Applied Mathematics 36:2 (2006), 156
- 174.
- S. Heubach, P. Chinn, and P. Callahan, Tiling
with Trominoes, Congressus Numerantium 177
(2005), 33 - 44.
- S. Heubach and T. Mansour, Counting
Rises, Levels and Drops in Compositions, INTEGERS: Electronic
Journal of Combinatorial Number Theory 5 (2005),
#A11
- R. Grimaldi and S. Heubach, Binary
Strings without Odd Runs of Zeros, Ars Combinatoria 75
(2005), 241-255.
- S. Heubach and T. Mansour, Compositions
of n with parts in a set , Congressus Numerantium 168
(2004), 127 - 143.
- P. Chinn and S. Heubach, Compositions
of n with no occurrence of k,, Congressus Numerantium, 164
(2003), pp. 33-51.
- P. Chinn and S. Heubach, (1,k)-Compositions,
Congressus Numerantium 164 (2003), pp. 183-194.
- P. Chinn and S. Heubach, Integer
Sequences Related to Compositions without 2's,
Journal of Integer Sequences, Vol 6 (2003), Article 03.2.3
- S. Heubach, Using
The TI-89 To Convey Mathematical Concepts: An Introductory Modeling
Course For Non-Science Majors, Proceedings of the 14th International
Conference on Technology in Collegiate Mathematics (ICTCM), Addison
Wesley, 2003, pp. 107-111.
- P.Z. Chinn, R. Grimaldi, and S. Heubach, Rises,
Levels, Drops and "+" Signs in Compositions, The Fibonacci
Quarterly , 41 (2003) No 3, 229-239.
- P.Z. Chinn, R. Grimaldi, and S. Heubach, The
Frequency of Summands of a Particular Size in Palindromic Compositions,
Ars Combinatoria 69 (2003), 65-78.
- P.Z. Chinn, R. Grimaldi, and S. Heubach, Patterns
Arising From Tiling Rectangles with 1x1 and 2x2 Squares, Congressus
Numerantium 150 (2001), pp. 173-192
- S. Heubach, Using
Mathematica To Convey Mathematical Concepts: An Introductory Modeling
Course For Non-Science Majors, Proceedings of the 12th International
Conference on Technology in Collegiate Mathematics (ICTCM), Addison
Wesley, 2000, pp.160-165.
- S. Heubach, Tiling
an n-by-m Area with Squares of Size up to k-by-k (m <= 5),
Congressus Numerantium 140 (1999), pp. 43-64.
- S. Heubach and R.S. Pamula, Implementing
an Approximate Probabilistic Algorithm for Error Recovery in Concurrent
Processing Systems, AoM/IAoM 1999 Proceedings: Computer Science,
Vol 17, No 1, pp. 50 - 55.
- S. Heubach, An
Innovative Approach to Modeling at the Freshman/Sophomore Level,
Proceedings of the 11th International Conference on Technology in
Collegiate Mathematics, Addison Wesley, pp. 166 - 170, 1999
- S. Heubach, Comparison of Recovery Schemes through a Mathematica
Simulation, Mathematica in Education and Research, Vol 8, No 3-4,
pp.28-36, 1999
- S. Heubach, An
Innovative Modeling Approach at the Freshman/Sophomore Level,
Proceedings of the 3rd Asian Technology Conference in Mathematics,
Springer Verlag, 1998
- S. Heubach and R. Pamula, Modeling and Simulation of Error Recovery
in a Concurrent Processing System, Proceedings of the 2nd IASTED
International Conference: European Parallel and Distributed Systems
(Euro-PDS '98), IASTED/ACTA Press, pp 29 - 35, 1998
- CC. Edwards, S. Heubach, V. Howe, and G. Klatt, Floppy
Grids: Discovering the Mathematics of Grid Bracing, to appear
as a COMAP module.
- S. Heubach, Introducing Laboratories into a Differential Equations
Course - How to get started!, Proceedings of the 9th Annual International
Conference on Technology in Collegiate Mathematics, Addison Wesley,
pp. 232 - 236, 1997
- S. Heubach and J. Watkins, A Stochastic Model for the Movement
of a White Blood Cell, Advances in Applied Probability 27, pp.
443-475, 1995
- Thesis: Lagerhaltung unter
Unsicherheit, University of Ulm, Germany, 1986
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- Presentations
Improving Quantitative Skills of Life Science Majors at CSULA, CSUPERB Quantitative Biology Network Meeting, January 3, 2013, Anaheim, CA
Improving Quantitative Skills of Life Science Majors at CSULA, Biomathematics and Ecology: Education and Research 2012, St. Louis, MO, November 9-11, 2012
A Generalization of Nim and Wythoff games, SIAM DM 12, Halifax, Nova Scotia, June 18-22, 2012
Nim, Wythoff and Beyond - Let's Play, Mathematics Colloquium CSU Long Beach, April 29, 2011
A Generalization of the Nim and Wythoff games, 42nd Southeastern International Conference on
Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 7-11,
2011
Circular
(n,k) games, Graduate Seminar, CSU Channel Island, September 8, 2010
Circular
(n,k) games, Math Colloquium, Cal Poly San Luis Obispo, May 7, 2010
Avoiding Substrings in Compositions, 41st Southeastern International Conference on
Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 8-12,
2010
Circular
(n,k) games, 41st Southeastern International Conference on
Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 8-12,
2010
Circular
(n,k) games, MAA Mathfest, Portland, OR, August 6-8, 2009
Analyzing ELLIE - the story of a combinatorial game, San
Jose State University, San Jose, CA, May 13, 2009 (slides,
handout for printing)
Pattern avoidance
of type (2,1) multi-permutation patterns in compositions, 40th
Southeastern International Conference on Combinatorics, Graph Theory
and Computing, Boca Raton, FL, March 2-6, 2009
Circular
(n,k) games, 40th Southeastern International Conference on
Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 2-6,
2009
Analyzing ELLIE - the
story of a combinatorial game, Humboldt State University, Arcata,
CA, October 23, 2007
Avoidance of Partially
ordered patterns in compositions (long version), Dalhousie
University, Halifax, NS, August 27, 2007
Avoidance
of Partially ordered patterns in compositions, International
Conference on Graph Theory and Combinatorics & Fourth Cross-strait
Conference on Graph Theory and Combinatorics, National Taiwan University,
Taipei, June 24-29, 2007
Avoidance
of Partially ordered patterns in compositions, 38th Southeastern
International Conference on Combinatorics, Graph Theory and Computing,
Boca Raton, FL, March 5-9, 2007
Do
you Sudoku? Math Club, Cal Poly Pomona, May 4, 2006
Staircase
Tilings and Lattice Paths, 37th Southeastern International
Conference on Combinatorics, Graph Theory and Computing, Boca Raton,
FL, March 6-10, 2006
Enumeration
of 3-Letter Patterns in Compositions, Integers Conference 2005,
University of West Georgia, Carrollton, GA, October 27 – 30, 2005
Compositions
and Multisets Restricted by Patterns of Length 3, Workshop
on Permutation Patterns, University of Haifa, Israel, May 29 - June
3, 2005
Tiling
with Ls and Squares, 36th Southeastern International Conference
on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March
7-11, 2005
Tiling
with Ls and Squares, Meeting of the Southern California-Nevada
Section of the MAA, Las Vegas, NV, October 10, 2004
Counting
Rises, Levels and Drops in Compositions , 35th Southeastern
International Conference on Combinatorics, Graph Theory and Computing,
Boca Raton, FL, March 8-12, 2004
Binary Strings Without Odd Runs of Zeros, 34th Southeastern
International Conference on Combinatorics, Graph Theory and Computing,
Boca Raton, FL, March 3-7, 2003
Counting Compositions: Patterns and Combinatorial Proofs, Mathematics
Colloquium, CSU Dominguez Hills, CA, April 24, 2002
Counting Compositions with 1s and ks, 33rd Southeastern International
Conference on Combinatorics, Graph Theory and Computing, Boca Raton,
FL, March 4-8, 2002
Using The TI-89 To Convey Mathematical Concepts: An Introductory
Modeling Course For Non-Science Majors, Calculator workshop the
14th International Conference on Technology in Collegiate Mathematics
(ICTCM), Baltimore, MA, November 1-4, 2001
The Frequency of Summands of Size k in Palindromic Compositions,
Fall Meeting of the Southern California Section of the MAA, Los Angeles,
CA, October 13, 2001
Rises, Levels, Drops and "+" Signs in Compositions, 32nd Southeastern
International Conference on Combinatorics, Graph Theory and Computing,
Baton Rouge, LA, February 26 - March 1, 2001
Exact and Asymptotic Results for the Number of Tilings of Rectangles
with Squares, AMS/MAA Joint Meeting, New Orleans,LA, January 10-12,
2001
An Alternative to College Algebra- An Introductory Modeling Course
for Freshman Liberal Arts Majors, Joint Meeting of the AMS and MAA,
New Orleans, January 10-13, 2001
Exact
and Asymptotic Results for the Number of Tilings of an m-by-n Board
with Squares, Mathematical Colloquium, University of Ulm, Germany,
November 14, 2000
Tiling
Rectangles with Squares, Mathematical Colloquium, Humboldt State
University, Arcata, CA, October 19, 2000
An
Innovative Modeling Course for Freshman Liberal Arts Majors,
MAA Mathfest 2000, Los Angeles, CA, August 3 - 5, 2000
Patterns Arising From Tiling Rectangles With Squares, 10th
SIAM Conference on Discrete Mathematics, Minneapolis, Minnesota, June
12-15, 2000
Patterns
Arising From Tiling Rectangles With Squares, 31st Southeastern
International Conference on Combinatorics, Graph Theory and Computing,
Boca Raton, Florida, March 12-17, 2000
Using Mathematica To Convey Mathematical Concepts: An Introductory
Modeling Course For Non-Science Majors, Computer workshop at the
12th International Conference on Technology in Collegiate Mathematics
(ICTCM), Burlingame, CA, Nov. 4 - 7, 1999
Implementing
an Approximate Probabilistic Algorithm for Error Recovery in Concurrent
Processing Systems, 17th International AoM/IAoM Conference,
San Diego, CA, August 6-8, 1999
An Introductory Modeling Course for Liberal Arts Majors based
on Mathematica, Morsels in Math Teaching, California State University
Northridge, Northridge, CA, May 18, 1999
Tiling
an m-by-n Area with Square of Site up to k-by-k (m=<5), 30th
Southeastern International Conference on Combinatorics, Graph Theory
and Computing, Boca Raton, Florida, March 8-12, 1999
An Innovative Approach to Modeling at the Freshman/Sophomore Level,
11th International Conference on Technology in Collegiate Mathematics,
New Orleans, Louisiana, November 19 - 22, 1998
An Introductory Modeling Course for Non-Science Majors: Using Mathematica
to Convey Mathematical Concepts, Western Regional Meeting of the
American Mathematical Society, Tucson, Arizona, November 13 - 15, 1998
An Innovative Modeling Approach at the Freshman/Sophomore Level,
3rd Asian Technology Conference in Mathematics (ACTM'98), Tsukuba, Japan,
August 24 - 28, 1998
Modeling
and Simulation of Error Recovery in a Concurrent Processing System,
European Parallel and Distributed Systems (Euro-PDS '98), Vienna, Austria,
July 1-3, 1998
Using Mathematica to bring Research into the Classroom, 10th
International Conference on Technology in Collegiate Mathematics (ICTCM),
Chicago, IL, Nov. 7 - 9, 1997
Rigid or Not?, Joint Regional Meeting of the AMS/MAA, Claremont
McKenna College, Claremont, CA, Oct. 4, 1997
Introducing Laboratories into a Differential Equations Course -
How to Get Started!, 9th International Conference on Technology
in Collegiate Mathematics, Reno, NV, Nov. 7 -10, 1996
Highlights and Pitfalls in O.D.E. Reform, 9th International
Conference on Technology in Collegiate Mathematics, Reno, NV, Nov. 7
-10, 1996
Optimizing Rollback Schemes for Parallel Processes, 1996 Seminar
on Stochastic Processes, Duke University, Durham, NC, March 14 - 16,
1996
How many ways are there to tile an n-by-m rectangle using 1-by-1
and 2-by-2 tiles?, MAA (Southern and Northern) Section Meeting,
Cal Poly, San Luis Obispo, CA, October 20 - 22, 1995
A Stochastic Model for the Movement of a White Blood Cell,
Women in Probability, Cornell University, Ithaca, NY, October 16-18,
1994
A Stochastic Model for the Movement of a White Blood Cell,
Combined MAA/AMS Western Section Meeting, University of Oregon, Eugene,
OR, June 15-17, 1994
A Stochastic Model for the Movement of a White Blood Cell,
1st IMS North American New Researchers' Meeting, UC Berkeley, Berkeley,
CA, August 4 -7, 1993
-
- Reviews
- NSF Course, Curriculum and Laboratory Improvement Program (CCLI)
grant applications, Arlington, VA, July 15 - 18, 2002
- NSF Course and Curriculum Development (CCD) grant applications,
Arlington, VA, July 21 - 24, 1997
- Interactive Differential Equations (software and lab manual), Addison
Wesley, Winter 96.
Refereed Articles
- Discrete Mathematics
- Integers Journal
- Ars Combinatoria
- Journal of Difference Equations and Applications
- Central European Journal of Mathematics
- Quaestiones Mathematicae
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-
-
- Grants and Awards
- Co-Director and Project Manager on NIH MARC curricular grant (July
2008-June 2013, $1.57 Million)
- NSF travel grant to attend FPSAC conference in Tianjin, China, July
2007, $1150
- Invited Researcher, University of Haifa, Haifa, Israel, supported
by the Department of Mathematics and the Caesarea Rothschild Institute,
$1500 travel grant + housing, March 2007
- Invited Researcher, University of Haifa, Haifa, Israel, supported
by the Department of Mathematics and the Caesarea Rothschild Institute,
$1900 travel grant + housing, September 2005
- Invited Researcher, University of Haifa, Haifa, Israel, supported
by the Department of Mathematics and the Caesarea Rothschild Institute,
$1500 travel grant + housing, May 2005
- 2003/2004 AWM Travel Grant, $1100
- 1999/2000 CSLA Outstanding Professor Award
- 1999/2000 AWM Travel Grant, $500
- 1997-98 Innovative Teaching Award, An Introductory Course in Mathematica,
Released Time, Student Assistant and Services $4,600
- NSF-Course and Curriculum Development Grant, An Innovative Approach
at the Freshman/Sophomore Level, $121,366 (3/97 - 11/01);
- 1995-96 Proposal Development and Grant-in-Aid Award, Seed Project
to develop an NSF Proposal for the Creation of a New Interdisciplinary
Modeling Course, Released Time (4 units)
- 1995-96 Discretionary Lottery Funds, Technology Oriented Curriculum
for Differential Equation Course, $1000 for purchase of software
- 1995-96 Innovative Instruction Awards, Technology Oriented Curriculum
for Differential Equation Course, Released time (4 units), Mini grant
$594
- 1995-96 Innovative Instruction Awards, $5000 for purchase of graphing
calculators
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- Educational Background
- University of Southern California, Los Angeles
Ph.D. in Applied Mathematics (1992), GPA 4.0: A Stochastic Model
for the Movement of a White Blood Cell. (Advisor: Dr. Joseph Watkins).
Masters of Science in Mathematics (1989), GPA 4.0
- University of Ulm, Germany
Diplom in Wirtschaftsmathematik (Masters in Mathematics and Economics)
(1986)
Vordiplom in Wirtschaftsmathematik (B.A. in Mathematics and Economics)
(1983)
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