Silvia Heubach

Professor Silvia Heubach
College of Natural & Social Sciences
Department of Mathematics
Office ST201
Phone
323-343-2162
Email
sheubac@calstatela.edu

INTRODUCTION

I am originally from Germany and came for a one-year student exchange. Life intervened and I decided to stay and do a Ph.D. at USC (University of Southern California in Los Angeles). I graduated in 1992 and then had two one-year visiting appointments, at Colorado College in Colorado Springs and at Humboldt State University in Arcata. I came to Cal State LA in the Fall of 1994 and have been here ever since. In my free time I like to read, watch foreign and independent movies, hike, camp, dance and stand on my head on an almost daily basis.

 

TEACHING INTERESTS

I teach courses ranging from general education to graduate level courses, mostly statistics, probability, modeling and the Mathematica course. I use Mathematica in most of my courses to visualize concepts and algorithms. My most recent focus has been the redesign and teaching of the new mathematics sequence for life sciences majors, Math 1050/1085, Math 2040/41, and Math 2050/51. These courses were developed with an NIH grant that had the goal to strengthen the quantitative skills of life sciences majors. In these courses, mathematics is taught in the context of life science and biological applications, and the course topics are those that life science makors will see in the applicaitons in their major courses. Another aspect of the grant was the introducation of a minor in bioinformatics. I have contributed two chapters on probability and its applications in bioinformatics to a textbook used at Cal State LA, Concepts in Bioinformatics and Genomics, authored by Cal State LA faculty Drs. Momand and McCurdy, with additional contirbutions by Dr. Warter-Perez.

 

GRANTS AND INITIATIVES

  • I was the faculty learning community coordinator on the First In The World grant on flipped learning. This grant provides funding for faculty from STEM disciplines to try out flipped teaching in bottle-neck courses. The grant was active from 2014 - 2019.
  • I was one of the leads for the course redesign of General Education courses in response to EO 1110. Information about the changes can be found at the math department advisement webpage.

 

HONORS AND AWARDS

  • Recipient of 2018 CSU Chancellor's Office Faculty Innovation and Leadership Award.
  • CSULA Distinguished Woman Award 2013
  • PI, Co-Director and Project Manager on NIH MARC curricular grant (July 2008-June 2014, $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 calculat

 

RESEARCH

My research spans a number of areas, ranging from operations research to modeling to combinatorics. My Masters thesis investigated 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 Raj Pamula, I have worked on a model of a system of parallel processes to compare different methods of error recovery. Work on (enumerative) combinatorics, in particular questions related to tilings and compositions with a number of collaborators has culminated in a book entitled Combinatorics of Compositions and Words, which is a resource for research in this area. Most recently, I am working on questions related to combinatorial games, an area that lends itself to student research. If you want to find out more about Combinatorial Game Theory, check out Kyle Burke's blog or the website on combinatorial games.

 

INTERVIEWS

Listen to my interview with Bonnie Stachowiak of the Teaching in Higher Ed podcast.

 

PUBLICATIONS

I had the pleasure of writing joint research articles with the following individuals (roughly in reverse chronological order): Richard Nowakowski, Craig Tennenhouse, Valdimir Gurvich, Nhan Bao Ho, Nikolay Chikin, Sharona Krinsky, Kyle Burke, Melissa Huggan, Svenja Huntemann, Urban Larsson, Eric Duchène, Matthieu Dufour, Arnold Knopfmacher, Michael Mays, Sergey Kitaev, Augustine Munagi, N.Y. Li, Toufik Mansour, Patrick Callahan, Phyllis Chinn, Ralph Grimaldi, Raj Pamula, and Joseph Watkins.

We are looking for integers n whose squares have an average of their digits that is 8.25 or bigger. If you find any, we will post the new record here. To find more about this challenge, read the article in CRUX Mathematicorum Vol 45(8), October 2020, a special edition in honor of Richard Guy, one of the founders of combinatorial Game theory.

Current Record for Square with Largest Digit Average, DAve
Name & Affiliation n n2 DA(n) Date
Matthieu Dufour & Silvia Heubach

707,106,074,079,263,583

499,998,999,999,788,997,978,888,999,589,997,889

 8.25 6/23/20

Tomas Rokicki

943,345,110,232,670,883

889,899,996,999,889,979,488,999,999,795,999,689

8.25

1/30/23

Matthieu Dufour & Silvia Heubach

893,241,282,627,485,818,275,387

797,879,988,989,995,997,899,989,877,988,999,997,998,969,999,769

8.25

 10/10/20

Tomas Rokicki

989,898,919,026,382,208,216,803,790,139,943,167

979,899,869,889,599,999,789,989,999,899,659,988,889,797,488,898,989,989,999,989,949,989,989,889

 8.25 4/20/23

Tomas Rokicki

296,630,559,600,488,563,517,139,286,187

87,989,688,888,898,997,898,978,579,999,898,999,999,987,799,879,999,888,998,969

487/59=

8.25424

4/17/23

Tristrom Cooke, Adelaide

314,610,537,013,606,681,884,298,837,387

98,979,789,999,989,979,988,999,999,989,499,999,797,975,998,897,999,868,987,769

 487/59=

8.25424

 4/11/23

Tomas Rokicki

312,713,447,088,224,669,275,583

97,789,699,989,799,889,886,988,697,997,987,998,989,999,989,889

388/45=

8.25532

1/31/23

Tomas Rokicki

2,976,388,751,488,907,738,914

8,858,889,999,989,698,989,999,979,889,997,999,989,899,396

355/43=

8.25581

1/31/23

Tomas Rokicki

9984,988,582,817,657,883,693,383,344,833

99,699,996,998,998,979,989,989,997,788,978,889,798,779,999,999,969,798,987,797,889

513/62=

8.27419

 4/13/23

Matthieu Dufour & Silvia Heubach

94,180,040,294,109,027,313

8,869,879,989,799,999,999,898,984,986,998,979,999,969

8.275

7/25/20

Tomas Rokicki

2,982,951,558,104,653,129,433,595,167,102,567

8,897,999,997,998,977,794,997,988,999,999,989,979,999,899,769,898,988,999,997,897,989,489

556/67=

8.29851

 4/21/23

Tomas Rokicki

264,575,104,459,943,243,164,050,883,010,583

69,999,985,899,989,878,999,999,889,799,898,899,975,978,988,897,889,989,989,689,999,889

108/13=

8.30769

4/14/23

  • M. Dufour, S. Heubach, and A. Vo,  Circular Nim games CN(7, 4). In R. Nowakowski, B. Landman, F. Luca, M. Nathanson, J. Nešetřil & A. Robertson (Ed.), Combinatorial Game Theory: A Special Collection in Honor of Elwyn Berlekamp, John H. Conway and Richard K. Guy, (2022), pp. 139-156. Berlin, Boston: De Gruyter. https://doi.org/10.1515/9783110755411-009

  • M. Dufour, S. Heubach, and A. Vo, Circular Nim games CN(7, 4), INTEGERS, Vol 21B (2021): To the Three Forefathers of Combinatorial Game Theory: The John Conway, Richard Guy, and Elwyn Berlekamp Memorial Volume, article #A9

  • M. Dufour and S. Heubach, Squares with Large Digit Average, Crux Mathematicorum, Vol. 46, No. 8 (2020), pages 384 - 389

  • S. Heubach, M. A. Huggan, R.J. Nowakowski, and C. Tennenhouse, Cyclic Subtraction Set Games, Crux Mathematicorum, Vol. 46, No. 8 (2020), pages 413 - 414
  • V. Gurvich, S. Heubach, N.B. Ho, N. Chikin, Slow K-Nim, INTEGERS, Vol 20 (2020), article #G3
  • K. Burke, S. Heubach, M. Huggan and S. Hunteman, Keeping your Distance is Hard, to appear in Games with No Chance 6. Preprint at arXiv:1605.06801
  • M. Dufour, S. Heubach and U. Larsson, (2017) A Misère-Play *-Operator. In: Nathansson M. (Eds) Combinatorial and Additive Numebr Theorey II. CANT 2015, CANT 2016. Springer Proceedings in Mathematics & Statistics , Vol 220. Springer, Cham. DOI: https://doi.org/10.1007/978-3-319-68032-3_12
  • E. Duchene, M. Dufour, S. Heubach and U. Larsson, Building Nim, International Journal of Game Theory, 2016, vol. 45, issue 4, pages 859-873. DOI 10.1007/s00182-015-0489-3
  • M. Dufour and S. Heubach, Circular Nim Games, Electronic Journal of Combinatorics, 20:2, (2013) P22 (26 pages

PRESENTATIONS

Expect additional links to some of these presentations soon.

  • How to Win in Circular Nim, Mathematics Colloquium West Chester University, September 2024
  • How to Win in Slow Exact k-Nim, Combinatorial Game Theory Colloquium IV, Azores, Ponta Delgada, Portugal, January 2023
  • Play to Win - How to win in Combinatorial Games, Cal State LA Honor's Colloquium, November 20, 2019
  • Combinatorial Games, Lightning Fast Talk at the Natural and Social Sciences College Retreat, Cal State LA, May 25, 2017. The video of the talk starts at time point 42:09.
  • New Results on Circular Nim, 48th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 6-10, 2017
  • The Game Creation Operator (for general audiences; expanded), Cal State LA Math Club, March 2, 2017
  • Keeping your Distance is Hard, Recreational Mathematics Colloquium V and Gathering for Gardener (Europe), January 28 - 31, 2017, Lisbon, Portugal.
  • The Game Creation Operator, Combinatorial Game Theory Colloquium II, January 25 - 27, 2017, Lisbon, Portugal.
  • The Game Creation Operator (for general audience), invited talk at the SoCal-Nevada MAA Section meeting, October 22, 2016
  • The Misère Star Operator, 47th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 7-11, 2016
  • Keeping your Distance is Hard, 47th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 7-11, 2016
  • The Misère Star Operator, Mathematics Colloquium, Dalhousie University, Halifax, NS, March 4, 2016
  • Keeping your Distance is Hard, Discrete Mathematics and Computer Science Seminar, University of Quebec at Montreal, QC, February 19, 2016
  • Building Nim, 46th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 2-6, 2015
  • Nim on a Tetrahedron, Recreational Mathematics Meeting, Weizman Institute, Rehovot, Israel, June 20, 2014
  • Building Nim, Second Joint Meeting of the Israel Mathematical Union and the AMS, Tel Aviv, Israel, June 16 - 19, 2014
  • Nim on a Tetrahedron, 45th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 3-7, 2014
  • Building Nim, Integers Conference 2013, Carrolton, GA, October 24-27, 2013
  • Building Nim, Women in Mathematics Symposium, UCSD, April 21, 2013
  • A generalization of Nim, 44th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 4-8, 2013
  • Nim, Wythoff and Beyond - Let's Play, Math Club CSU Los Angeles, February 27, 2013
  • A Generalization of Nim and Wythoff games, SIAM DM 12, Halifax, Nova Scotia, June 18-22, 2012
  • Circular Nim Games, Combinatorics Seminar, UQAM, Montreal, May 24, 2011
  • 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
  • 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
  • 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

 

 

Expect additional links to some of these presentations soon.

  • Inversions in compositions of integers, Permutation Patterns 2011, San Luis Obispo, June 20-24, 2011
  • Avoiding Substrings in Compositions, 41st Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 8-12, 2010
  • 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
  • Avoidance of partially ordered patterns in compositions, 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
  • 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 (invited speaker)
  • Tiling with Ls and Squares, 36th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 7-11, 2005
  • 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, CSU Dominguez Hills, Carson, 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
  • 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, 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
  • 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 13-17, 2000
  • Tiling an m-by-n Area with Square of Site up to k-by-k (m5), 30th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, Florida, March 8-12, 1999
  • 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

Expect additional links to some of these presentations soon.

  • Do the flip! – Using guided practice for Active Student Engagement, Interactive Workshop, ASEE PSW Conference at Cal State LA, April 2019.
  • How to flip Calculus One Lesson at a Time, Lilly Anaheim, March 2, 2019
  • Facilitating Flipped Learning: Utilizing Cross-Campus Learning Communities, Lilly Anaheim, March 1, 2019
  • Developing a Flipped Lesson Plan: Planning for Active Engagement, Lilly Anaheim, March 1, 2019 (50 minute workshop)
  • Mastery-based grading at scale in GE Statistics, CSU Chancellor Office First-Term Reflections: Restructuring First-Year Writing, Mathematics and Quantitative Reasoning, Long Beach, CA, February 1, 2019
  • Coordination and Professional Development at Cal State LA, CSU Chancellor Office First-Term Reflections: Restructuring First-Year Writing, Mathematics and Quantitative Reasoning, Long Beach, CA, February 1, 201

  • Flipping Calculus at Cal State LA, AAAS Meeting at Cal Poly Pomona, June 14, 2018

  • Facilitating a Culture of Transformative Pedagogical Change in STEM via Focused Faculty Development, AAAS Meeting at Cal Poly Pomona, June 14, 2018

  • A New Mathematics Course Sequence for Life Science Majors: A Progress Report, Biomathematics and Ecology: Education and Research 2013, Arlington, VA, October 11 - 13, 2013
  • Improving the quantitative skills of life science majors at California State University Los Angeles. Poster presented at the Vision and Change conference, Washington, D.C., August 28-30, 2013
  • Improving Quantitative Skills of Life Science Majors at CSULA, Joint Mathematics Meeting, January 9-12, 2013, San Diego, CA
  • 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
  • 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
  • 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
  • An Innovative Modeling Approach at the Freshman/Sophomore Level (NSF/DUE: 9653262), MAA Poster Session of the NSF DUE CCLI Program, Joint Meeting of the AMS and MAA, New Orleans, January 10-13, 2001
  • An Innovative Modeling Course for Freshman Liberal Arts Majors, MAA Mathfest 2000, Los Angeles, California, August 3 - 5, 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
  • An Introductory Modeling Course for Liberal Arts Majors based on Mathematica, Morsels in Math Teaching, California State University Northridge, Northridge, CA, May 18, 1999
  • An Innovative Approach to Modeling at the Freshman/Sophomore Level, 11th International Conference on Technology in Collegiate Mathematics (ICTCM), New Orleans, LA, Nov. 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, AZ, Nov. 13 - 15, 1998
  • A New Introductory Modeling Course for Non-Science Majors, Regional Meeting of the Southern California Section of the Mathematical Association of America (MAA), Pepperdine University, Malibu, CA, October 19, 1998
  • An Innovative Modeling Approach at the Freshman/Sophomore Level, 3rd Asian Technology Conference in Mathematics (ATCM'), Tsukuba, Japan, August 24 - 28, 1998
  • An Introductory Modeling Course Using Mathematica, LACTE Seminar, CSLA, Feb. 19, 1998
  • Using Mathematica to bring Research into the Classroom, 10th International Conference on Technology in Collegiate Mathematics (ICTCM), Chicago, IL, Nov. 7 - 9, 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, 199

Expect additional links to some of these presentations soon.

  • Logarithms - Trick or Treat?, Cal State LA Physics Seminar, October 31, 2019
  • Do you Sudoku? Math Club, Cal Poly Pomona, May 4, 2006
  • S. Heubach and R.S. Pamula, Implementing an Approximate Probabilistic Algorithm for Error Recovery in Concurrent Processing Systems, 17th International AoM/IAoM Conference, San Diego, CA, August 6-8, 1999
  • Modeling and Simulation of Error Recovery in a Concurrent Processing System, 2nd International IASTED Conference: European Parallel and Distributed Systems (Euro-PDS'98), Vienna, Austria, July 1 - 3, 1998
  • Rigid or Not?, Joint Regional Meeting of the AMS/MAA, Claremont McKenna College, Claremont, CA, Oct. 4, 1997
  • Optimizing Rollback Schemes for Parallel Processes, 1996 Seminar on Stochastic Processes, Duke University, Durham, NC, March 14 - 16, 1996
  • 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

EDUCATIONAL BACKGROUND

  • Ph.D in Applied Mathematics, 1992. University of Southern California, Los Angeles, Los Angeles, CA.  GPA 4.0. Thesis: A Stochastic Model for the Movement of a White Blood Cell. (Advisor: Dr. Joseph Watkins)
  • M.S. in Mathematics, 1998. University of Southern California, Los Angeles, Los Angeles, CA. GPA 4.0
  • Diplom in Wirtschaftsmathematik (Masters in Mathematics and Economics), 1986. University of Ulm, Germany. Thesis: Inventory Control Under Uncertainty. (Advisor: Dr. Ulrich Rieder)
  • Vordiplom in Wirtschaftsmathematik (B.A. in Mathematics and Economics), 1986. University of Ulm, Germany