INTRODUCTION
I am originally from Germany and came for a oneyear 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 oneyear 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 a 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 ahttps://www2.calstate.edu/csusystem/news/Pages/26CSUFacultyRecognizedforInnovativePracticesImprovingStudentAchievement.aspxdditional contirbutions by Dr. WarterPerez.
GRANTS AND INITIATIVES
 I am the faculty learning community coordinator on the First In The World grant on flipped learning. More details about the grant can be found here. This grant provides funding for faculty from STEM disciplines to try out flipped teaching in bottleneck courses.
 I am 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; Background on the award can be found here.
 CSULA Distinguished Woman Award 2013
 PI, CoDirector and Project Manager on NIH MARC curricular grant (July 2008June 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
 199798 Innovative Teaching Award, An Introductory Course in Mathematica, Released Time, Student Assistant and Services $4,600
 NSFCourse and Curriculum Development Grant, An Innovative Approach at the Freshman/Sophomore Level, $121,366 (3/97  11/01);
 199596 Proposal Development and GrantinAid Award, Seed Project to develop an NSF Proposal for the Creation of a New Interdisciplinary Modeling Course, Released Time (4 units)
 199596 Discretionary Lottery Funds, Technology Oriented Curriculum for Differential Equation Course, $1000 for purchase of software
 199596 Innovative Instruction Awards, Technology Oriented Curriculum for Differential Equation Course, Released time (4 units), Mini grant $594
 199596 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
I was interviewed for the Teaching in Higher Ed podcast. You can listen to the interview here.
PUBLICATIONS
I had the pleasure of writing joint research articles with the following individuals (roughly in reverse chronological order): 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.
Combinatorial Games
 K. Burke, S. Heubach, M. Huggan and S. Hunteman, Keeping your Distance is Hard, preprint. arXiv:1605.06801
 M. Dufour, S. Heubach and U. Larsson, (2017) A MisèrePlay *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/10.1007/9783319680323_12
 E. Duchene, M. Dufour, S. Heubach and U. Larsson, Building Nim, International Journal of Game Theory, 2016, vol. 45, issue 4, pages 859873. DOI 10.1007/s0018201504893
 M. Dufour and S. Heubach, Circular Nim Games, Electronic Journal of Combinatorics, 20:2, (2013) P22 (26 pages)
Enumerative Combinatorics
 S. Heubach, A. Knopfmacher , M.E. Mays & A. Munagi.: Inversions in compositions of integers, Quaestiones Mathematicae, 34:2, (2011), 187202.
 S. Heubach, S. Kitaev, Avoiding Substrings in Compositions, Congressus Numerantium, 202 (2010), 8795.
 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 kCatalan Structures, Discrete Mathematics, 308:24 (2008), 59545953.
 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 3Letter Patterns in Compositions, Combinatorial Number Theory in Celebration of the 70th Birthday of Ronald Graham, 2007, 243264, de Gruyter.
 S. Heubach, S. Kitaev and T. Mansour, Partially ordered patterns and compositions, Pure Mathematics and Applications, 17:12 (2006), 123134
 P. Callahan, P. Chinn, and S. Heubach, Graphs of Tilings, Congressus Numerantium, 183, (2006), 129138
 S. Heubach and T. Mansour, Staircase Tilings and Lattice Paths, Congressus Numerantium, 182 (2006), 97109
 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), 241255.
 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. 3351.
 P. Chinn and S. Heubach, (1,k)Compositions, Congressus Numerantium 164 (2003), pp. 183194.
 P. Chinn and S. Heubach, Integer Sequences Related to Compositions without 2's, Journal of Integer Sequences, Vol 6 (2003), Article 03.2.3
 P.Z. Chinn, R. Grimaldi, and S. Heubach, Rises, Levels, Drops and "+" Signs in Compositions, The Fibonacci Quarterly , 41 (2003) No 3, 229239.
 P.Z. Chinn, R. Grimaldi, and S. Heubach, The Frequency of Summands of a Particular Size in Palindromic Compositions, Ars Combinatoria 69 (2003), 6578.
 P.Z. Chinn, R. Grimaldi, and S. Heubach, Patterns Arising From Tiling Rectangles with 1x1 and 2x2 Squares, Congressus Numerantium 150 (2001), pp. 173192
 S. Heubach, Tiling an nbym Area with Squares of Size up to kbyk (m <= 5), Congressus Numerantium 140 (1999), pp. 4364.
Modeling
 S. Heubach, Comparison of Recovery Schemes through a Mathematica Simulation, Mathematica in Education and Research, Vol 8, No 34, pp.2836, 1999
 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 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 (EuroPDS '98), IASTED/ACTA Press, pp 29  35, 1998
 S. Heubach and J. Watkins, A Stochastic Model for the Movement of a White Blood Cell, Advances in Applied Probability 27, pp. 443475, 1995
 Thesis: Lagerhaltung unter Unsicherheit, University of Ulm, Germany, 1986
Curriculumrelated
 S. Heubach and E. Torres. A New Mathematics Course Sequence for Life Sciences Majors: A progress report, Proceedings of the Sixth Annual International Symposium on Biomathematics and Ecology: Education and Research. Web. 23 April 2014, (13 pages)
 Silvia Heubach and Elizabeth Torres. Improving Quantitative Skills of CSULA Life Science Majors. Vision and Change in Undergraduate Biology Education – A view for the 21^{st} Century.
 S. Heubach, Using The TI89 To Convey Mathematical Concepts: An Introductory Modeling Course For NonScience Majors, Proceedings of the 14th International Conference on Technology in Collegiate Mathematics (ICTCM), Addison Wesley, 2003, pp. 107111.
 S. Heubach, Using Mathematica To Convey Mathematical Concepts: An Introductory Modeling Course For NonScience Majors, Proceedings of the 12th International Conference on Technology in Collegiate Mathematics (ICTCM), Addison Wesley, 2000, pp.160165.
 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, An Innovative Modeling Approach at the Freshman/Sophomore Level, Proceedings of the 3rd Asian Technology Conference in Mathematics, Springer Verlag, 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
Books
 S. Heubach and T. Mansour, Combinatorics of Compositions and Words, CRC Press, 2009.

J. Momand and A. McCurdy, with contributions by S. Heubach, N. WarterPerez, Concepts in Bioinformatics and Genomics, Oxford University Press, 2016
PRESENTATIONS
Combinatorial Games
Expect additional links to some of these presentations soon.
 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 610, 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 SoCalNevada MAA Section meeting, October 22, 2016
 The Misère Star Operator, 47th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 711, 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 26, 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 37, 2014
 Building Nim, Integers Conference 2013, Carrolton, GA, October 2427, 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 48, 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 1822, 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 711, 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 812 2010
 Circular (n,k) games, MAA Mathfest, Portland, OR, August 68, 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 26, 2009
 Analyzing ELLIE  the story of a combinatorial game, Humboldt State University, Arcata, CA, October 23, 2007
Enumerative Combinatorics
Expect additional links to some of these presentations soon.
 Inversions in compositions of integers, Permutation Patterns 2011, San Luis Obispo, June 2024, 2011
 Avoiding Substrings in Compositions, 41st Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 812, 2010
 Pattern avoidance of type (2,1) multipermutation patterns in compositions, 40th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 26, 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 Crossstrait Conference on Graph Theory and Combinatorics, National Taiwan University, Taipei, June 2429, 2007
 Avoidance of partially ordered patterns in compositions, 38th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 59, 2007
 Enumeration of 3Letter 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 711, 2005
 Counting Rises, Levels and Drops in Compositions, 35th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 812, 2004
 Binary Strings Without Odd Runs of Zeros, 34th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, FL, March 37, 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 48, 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 1013, 2001
 Exact and Asymptotic Results for the Number of Tilings of an mbyn 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, 10^{th} SIAM Conference on Discrete Mathematics, Minneapolis, Minnesota, June 1215, 2000
 Patterns Arising From Tiling Rectangles With Squares, 31st Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, Florida, March 1317, 2000
 Tiling an mbyn Area with Square of Site up to kbyk (m5), 30th Southeastern International Conference on Combinatorics, Graph Theory and Computing, Boca Raton, Florida, March 812, 1999
 How many ways are there to tile an nbym rectangle using 1by1 and 2by2 tiles?, MAA (Southern and Northern) Section Meeting, Cal Poly, San Luis Obispo, CA, October 20  22, 1995
Curriculumrelated
Expect additional links to some of these presentations soon.
 Masterybased grading at scale in GE Statistics, CSU Chancellor Office FirstTerm Reflections: Restructuring FirstYear Writing, Mathematics and Quantitative Reasoning, Long Beach, CA, February 1, 2019
 Coordination and Profession Development at Cal State LA, CSU Chancellor Office FirstTerm Reflections: Restructuring FirstYear Writing, Mathematics and Quantitative Reasoning, Long Beach, CA, February 1, 2019
 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 2830, 2013
 Improving Quantitative Skills of Life Science Majors at CSULA, Joint Mathematics Meeting, January 912, 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 911, 2012
 Using The TI89 To Convey Mathematical Concepts: An Introductory Modeling Course For NonScience Majors, Calculator workshop the 14^{th }International Conference on Technology in Collegiate Mathematics (ICTCM), Baltimore, MA, November 14, 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 1013, 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 1013, 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 NonScience 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. 1922, 1998
 An Introductory Modeling Course for NonScience 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 NonScience 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, 3^{rd} 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, 1996
Modeling/Other
Expect additional links to some of these presentations soon.
 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 68, 1999
 Modeling and Simulation of Error Recovery in a Concurrent Processing System, 2^{nd} International IASTED Conference: European Parallel and Distributed Systems (EuroPDS'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 1618, 1994
 A Stochastic Model for the Movement of a White Blood Cell, Combined MAA/AMS Western Section Meeting, University of Oregon, Eugene, OR, June 1517, 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: 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
University of Ulm, Germany
Diplom in Wirtschaftsmathematik (Masters in Mathematics and Economics) (1986)
Vordiplom in Wirtschaftsmathematik (B.A. in Mathematics and Economics) (1983)