## Research and Academic Work

Until March 2008 I was a research assistant at the Department of Mathematics at the University of Salzburg, working for Wolfgang Schmid on a project supported by the Austrian Science Fund (FWF), Grant P18455-N18. I am a former member of the Ganesh Research Group located at the Department of Computer Science.

My work focused on high-dimensional numerical integration with a special interest in low discrepancy point sets, digital nets, (ordered) orthogonal arrays, coding theory, and related computer implementations.

I was the main developer of MinT,
the database of optimal
(*t*, *m*, *s*)-net parameters.
I am also the developer of
HIntLib
(High-dimensional Integration Library), a C++ library providing
high-performance implementations of all major algorithms
used for numerical integration in medium and high dimensions.
Integration routines based on
interpolatory cubature rules as well as Monte Carlo and quasi-Monte Carlo
algorithms are taken into account.

In addition to my work in this project I gave lectures and was the administrator of the web server of the GeoGebra project.

### Awards

**Hans-Stegbuchner-Award**from the Department of Mathematics at the University of Salzburg. November 2007. For an exceptional Ph.D. thesis.**Hans-Stegbuchner-Award**from the Department of Mathematics at the University of Salzburg. June 2000. For exceptional achievements during the curriculum.

### Degrees

**Ph.D. in Mathematics**(“Dr. rer. nat.”), October 2006, University of Salzburg, Austria.**M.S. in Mathematics**(“Mag. rer. nat.”), April 2002, University of Salzburg, Austria.**M.S. in Applied Computer Science**(“Dipl.-Ing.”), September 2001, University of Salzburg, Austria.**M.S. in Computer Science**, August 1998, Bowling Green State University, Ohio.

### Publications

Publications are listed here in the order they were written (most recent first)—which is not necessarily the order of their publication!

- R. Schürer and W. Ch. Schmid.
**MinT – New Features and New Results.**In P. L’Ecuyer and A. B. Owen, editors,*Monte Carlo and Quasi-Monte Carlo Methods 2008*, pages 171–189. Springer-Verlag, 2010. © Springer-Verlag. doi:10.1007/978-3-642-04107-5_10 - R. Schürer.
**Construction of Digital Nets based on Propagation Rules for OOAs.***Proceedings in Applied Mathemtics and Mechanics*,**7**(1), pages 1022601–1022602, 2007. doi:10.1002/pamm.200700314 - R. Schürer and W. Schmid.
**MinT – Architecture and Applications of the (***t*,*m*,*s*)-Net and OOA Database.*Mathematics and Computers in Simulation*,**80**(6), pages 1124–1132, February 2010. © Elsevier Science B.V. on behalf of IMACS. doi:10.1016/j.matcom.2007.09.010 - R. Schürer.
**A New Lower Bound on the**In A. Keller, S. Heinrich, and H. Niederreiter, editors,*t*-Parameter of (*t*,*s*)-Sequences.*Monte Carlo and Quasi-Monte Carlo Methods 2006*, pages 623–632. Springer-Verlag, 2008. © Springer-Verlag. doi:10.1007/978-3-540-74496-2_37 - R. Schürer.
**Ordered Orthogonal Arrays and Where to Find Them.**PhD thesis, University of Salzburg, Austria, August 2006. Errata Corrected version - W. Schmid and R. Schürer.
**Shift-Nets and Salzburg Tables: Power Computing in Number-Theoretical Numerics.**In H. Efinger and A. Uhl, editors,*Scientific Computing in Salzburg—Festschrift on the Occasion of Peter Zinterhofs 60*, volume 189 of^{th}Birthday*books@ocg.at*, pages 175–184. Oesterreichische Computer Gesellschaft, 2005. - R. Schürer and W. Schmid.
**MinT: A Database for Optimal Net Parameters.**In H. Niederreiter and D. Talay, editors,*Monte Carlo and Quasi-Monte Carlo Methods 2004*, pages 457–469. Springer-Verlag, 2006. © Springer-Verlag. doi:10.1007/3-540-31186-6_28 - R. Schürer.
**Optimal Communication Interval for Parallel Adaptive Integration.***Parallel and Distributed Computing Practices*,**5**(3), pages 269–278, 2002. - R. Schürer.
**Adaptive Quasi-Monte Carlo Integration Based on MISER and VEGAS.**In H. Niederreiter, editor,*Monte Carlo and Quasi-Monte Carlo Methods 2002*, pages 393–406. Springer-Verlag, February 2004. © Springer-Verlag. - R. Schürer.
**Optimal Communication Frequency for Parallel Adaptive Integration Routines.**In R. Trobec, P. Zinterhof, M. Vajteršic, and A. Uhl, editors,*Parallel Numerics ’02: Theory and Applications*, pages 29–38, University of Salzburg, Austria and Jožef Stefan Institut, Ljubljana, Slovenia, October 2002. - R. Schürer.
**A Comparison between (Quasi-)Monte Carlo and Cubature Rule Based Methods for Solving High-dimensional Integration Problems.***Mathematics and Computers in Simulation*,**62**(3–6), pages 509–517, 2003. © Elsevier Science B.V. on behalf of IMACS. doi:10.1016/S0378-4754(02)00250-1 - R. Schürer and A. Uhl.
**An Evaluation of Adaptive Numerical Integration Algorithms on Parallel Systems.***Parallel Algorithms and Applications*,**18**(1–2), pages 27–47, March 2003. doi:10.1080/1063719031000088012 - R. Schürer.
**High-Dimensional Numerical Integration on Parallel Computers.**Master’s thesis, University of Salzburg, Austria, May 2001. - R. Schürer.
**Parallel High-dimensional Integration: Quasi-Monte Carlo versus Adaptive Cubature Rules.**In V. N. Alexandrov, J. J. Dongarra, B. A. Juliano, R. S. Renner and C. J. K. Tan, editors, Proceedings of the International Conference on*Computational Science – ICCS 2001*, volume 2073 of*Lecture Notes in Computer Science*, pages 1262–1271. Springer-Verlag, San Francisco, CA, USA, May 2001. © Springer-Verlag. - R. Schürer.
**Adaptive Numerical Integration on Message-Passing Systems.**In G. Okša, R. Trobec, A. Uhl, M. Vajteršic, R. Wyrzykowski, and P. Zinterhof, editors,*Proceedings of the International Workshop on Parallel Numerics (ParNum 2000)*, pages 93–102, Bratislava, Slovakia, September 2000.

### Conferences

A list of international conferences where I gave a talk:

**6**, July 2007, Zürich, Switzerland:^{th}International Congress on Industrial and Applied Mathematics (ICIAM 2007)

*Construction of Digital Nets based on Propagation Rules for OOAs.***7**, August 2006, Ulm, Germany:^{th}International Conference on Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2006)

*A New Bound on the**t*-Parameter of (*t*,*s*)-Sequences.**16**, September 2005, Klagenfurt, Austria:^{th}International Congress of the Austrian Mathematical Society (ÖMG) (Mathematik 2005)

*MinT – The (**t*,*m*,*s*)-Net Database.**5**, May 2005, Tallahassee, Florida:^{th}IMACS Seminar on Monte Carlo Methods (MCM 2005)

*MinT – Features, Methods, and Details.***Number Theoretic Algorithms and Related Topics (NTA 2004)**, September 2004, Strobl, Austria:

*MinT – A Web Based Database for Querying Optimal (**t*,*m*,*s*)-Net Parameters.**6**, June 2004, Juan-les-Pins, France:^{th}International Conference on Monte Carlo and Quasi-Monte Carlo Methods (MC^{2}QMC 2004)

*Improving Low-dimensional Projections of Digital (t, m, s)-Nets Using Basis Supplement Algorithms.***4**, September 2003, Berlin, Germany:^{th}IMACS Seminar on Monte Carlo Methods (MCM 2003)

*Adaptive Quasi-Monte Carlo Integration.***5**, July 2003, Sydney, Australia:^{th}International Congress on Industrial and Applied Mathematics (ICIAM 2003)

*HIntLib: A Software Package for High-dimensional Integration.***5**, November 2002, Singapore:^{th}International Conference on Monte Carlo and Quasi-Monte Carlo Methods (MCQMC 2002)

*Adaptive Strategies for Quasi-Monte Carlo Integration.***International Workshop on Parallel Numerics (ParNum 2002)**, October 2002, Bled, Slovenia:

*Optimal Communication Frequency for Parallel Adaptive Integration Routines.***3**, September 2001, Salzburg, Austria:^{rd}IMACS Seminar on Monte Carlo Methods (MCM 2001)

*A Comparison between (Quasi-)Monte Carlo and Cubature Rule Based Methods for Solving High-dimensional Integration Problems.***International Conference on Computational Science (ICCS 2001)**, May 2001, San Francisco, California:

*Parallel High-dimensional Integration: Quasi-Monte Carlo versus Adaptive Cubature Rules.***International Workshop on Parallel Numerics (ParNum 2000)**, September 2000, Bratislava, Slovakia:

*Adaptive Numerical Integration on Message-Passing Systems.*

### Internal Talks

The following talks were given by me at various occasions at our university; most of them during the weekly meetings of the Ganesh Research Group or in Peter Gerl’s Mathematical Forum. PDF-files containing the slideshows used for the presentation are available.

**New Results on the Search of Shift Nets**, at the*Mathematical Forum*, May 2006.**MinT – and the Set of Possible (**, at the*t*,*m*,*s*)-Net Parameters*Mathematical Forum*, May 2005.**Factorization of Polynomials over Finite Fields**, at the*Mathematical Forum*, April 2004.**Optimizing an Algorithm in Number Theoretical Numerics**, at the*Mathematical Forum*, May 2003.**Adaptive Quasi Monte Carlo Integration**, at the*Mathematical Forum*, June 2002.**High-dimensional Well-distributed Point Sets**, at my final exam in Mathematics, April 2002.**Adaptive Monte Carlo Integration**, in PV Scientific Computing, January 2002.**Parallel Computation**(in German), at my final exam in Computer Science, September 2001.**Cubature Rules for High-dimensional Adaptive Integration**, in PV Scientific Computing, January 2001.**Parallel and Adaptive Numerical Integration on Hypercubes**, in PV Scientific Computing, June 2000.

### Course Work

This list contains a number of articles, presentations, handouts, programs and other stuff that was written by me for the classes I took during my curriculum. Even though hardly any of these items can be considered serious research, the list contains a number of neat things that may be noteworthy.

**VL Computer Algebra**(Fall 2001/01)**Seminar: What is Mathematics?**(Spring 2001):**Seminar: Topology**(Spring 2001):**Counting Mazes**- Paper containing my talk (German)
- C++ Program for counting mazes
- See also Tony Phillips’ Maze page

**Seminar: Mathemtical Methods in Astronomy**(Fall 1999/00)- Java Applet for calculating and ploting the Restricted Three Body problem
- Java Applet for calculating the path of the earth moving around the sun

**Projektpraktikum: Forschungsdokumentation der UNI Salzburg**(Spring 1997)- Diplom- und Dissertationsbörse

**VL/PS Rapid Application Development Tools**(Fall 1996/97):- My talk (in German) on Microsoft’s Webserver IIS and its interface to database systems

**PJ Practical Course in Programming II**(Spring 1996): Distributed Storys (Java-Applet)