The following list contains some potential topics for bachelor, masters, or phd theses. Students interested in any of these topics (or related topics) are encouraged to get into contact with the listed topic proposer.
| Topic | Contact | |
|---|---|---|
| Symbolic and Algebraic Methods for Linear Partial Differential Operators (phd thesis) | Franz Winkler | |
| Computer Algebra Tools for Special Functions in Numerical Analysis (phd thesis) | Peter Paule | |
| Analysis of Algorithms by Automated Reasoning and Algebraic Methods (phd thesis) | Tudor Jebelean | |
| Rational Parametric Algebraic Curves (phd thesis) | Franz Winkler | |
| Integraldarstellungen zur Berechnung von kombinatorischen Summen in Mathematica (master thesis) | Peter Paule | |
| Automated Computing Time and Complexity Analysis of Programs (master thesis) | Bruno Buchberger | |
| Symbolic Computation for Differential Equations (master thesis) | Bruno Buchberger | |
| Euler-Maclaurin Expansion von Symbolischen Summen (master thesis) | Peter Paule | |
| Symbolisches Lösen von Differentialgleichungen a la Frobenius (master thesis) | Peter Paule | |
| Nullstellenberechnung mittels Mellin-Reihen (master thesis) | Peter Paule | |
| Contributions to the ISAC-Project Bachelor/Master Thesis (master thesis) | Wolfgang Schreiner |
The following list contains a selection of topics that are currently being investigated by a RISC student in the frame of a bachelor, masters, or phd thesis. This list might not be complete.
The following list contains all bachelor, masters, and phd theses that have been completed at RISC or by a RISC member.
| 1. | Computer Algebra Algorithms for Special Functions in Particle Physics. J. Kepler University Linz. PhD Thesis. April 2012. [pdf] [bib] |
| 2. | Video Tracking of Humans in Robotic Environments. Internationaler Universitätslehrgang Informatics: Engineering & Management (ISI Hagenberg). Diploma Thesis. September 2011. [pdf] [bib] |
| 3. | Algebraic extensions for summation in finite terms. RISC, Johannes Kepler University, Linz. PhD Thesis. February 2011. [pdf] [bib] |
| 4. | Combinatorial Sums: Egorychev's Method of Coefficients and Riordan Arrays. RISC, Johannes Kepler University Linz. Diploma Thesis. March 2011. [pdf] [bib] |
| 5. | A computational view on normal forms of matrices of Ore polynomials. Research Institute for Symbolic Computation (RISC). PhD Thesis. July 2011. RISC Technical Report 11-10. [pdf] [bib] |
| 6. | Rational General Solutions of First-Order Algebraic ODEs. Research Institute for Symbolic Computation (RISC). PhD Thesis. October 2011. RISC Technical Report 11-12. [pdf] [bib] |
| 7. | Remotely Controlling a Mechanical Laboratory via the Internet. Internationaler Universitaetslehrgang Informatics: Engineering & Management. Diploma Thesis. Johannes Kepler University, Linz, Austria, July 2010. [pdf] [bib] |
| 8. | Differential aspects of differential characteristic set computations. Johannes Kepler University, Linz, Austria. PhD Thesis. June 2010. [pdf] [bib] |
| 9. | Relations between Groebner bases, differential Groebner bases, and differential characteristic sets. Johannes Kepler University, Linz, Austria. Diploma Thesis. December 2010. [pdf] [bib] |
| 10. | An automated induction prover for finite sets implemented in the Theorema system. RISC, Johannes Kepler University Linz. Diploma Thesis. October 2010. [pdf] [bib] |
| 11. | Algorithms for Special Functions: Computer Algebra and Analytical Aspects. RISC, Johannes Kepler University Linz. PhD Thesis. June 2010. RISC technical report 10-19. [pdf] [bib] |
| 12. | An algorithmic approach to Ramanujan's congruences and related problems. RISC Linz. PhD Thesis. 2010. [bib] |
| 13. | Closed Form Solutions of Linear Difference Equations. Florida State University. PhD Thesis. 2010. [url] [bib] |
| 14. | Re-engineering of a Grid Aware Medical Database System Based on a Metamodel. Internationaler Universitätslehrgang Informatics: Engineering & Management (ISI Hagenberg). Diploma Thesis. July 2009. [pdf] [bib] |
| 15. | Retrieval and Structuring of Large Mathematical Knowledge Bases in Theorema. Research Institute for Symbolic Computation, Johannes Kepler University of Linz, Austria. PhD Thesis. Available as RISC Technical Report 09-04, February 2009. [pdf] [bib] |
| 16. | Advanced Applications of the Holonomic Systems Approach. RISC-Linz, Johannes Kepler University. PhD Thesis. September 2009. [url] [pdf] [bib] |
| 17. | Symbolic Computation Prover with Induction. Johannes Kepler University. Diploma Thesis. September 2009. [pdf] [bib] |
| 18. | A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics. Johannes Kepler University. Diploma Thesis. February 2009. [pdf] [bib] |
| 19. | Power Series Solutions to Holonomic Differential Equations and the General Algebraic Equation. Johannes Kepler University Linz. Diploma Thesis. 2009. The thesis also appeared as RISC report 09-15.. Diploma thesis. [pdf] [bib] |
| 20. | Contributions to MacMahon's Partition Analysis. Johannes Kepler University. Diploma Thesis. January 2009. RISC Report 09-05. [pdf] [bib] |
| 21. | Evaluation of Cluster Middleware in a Heterogeneous Computing Environment. Internationaler Universitätslehrgang Informatics: Engineering & Management (ISI Hagenberg). Diploma Thesis. July 2009. [pdf] [bib] |
| 22. | Supporting Exploration in Elementary Analysis by Computational, Graphical and Reasoning Tools. Research Institute for Symbolic Computation, Johannes Kepler University of Linz, Austria. PhD Thesis. June 2009. [pdf] [bib] |
| 23. | Interactive Tools for Inspecting Proofs in Theorema. International Studies in Informatics: Engineering & Management (ISI Hagenberg). Diploma Thesis. July 2009. Master's Thesis. [pdf] [bib] |
| 24. | Lazy Thinking Algorithm Synthesis in Gröbner Bases Theory. Research Institute for Symbolic Computation (RISC). PhD Thesis. 2008. [pdf] [bib] |
| 25. | Compilation of Theorema Programs. RISC, Johannes Kepler University Linz. PhD Thesis. May 2008. [pdf] [bib] |
| 26. | Grid-aware Database Support for Medical Software. Internationaler Universitätslehrgang Informatics: Engineering & Management (ISI Hagenberg). Diploma Thesis. July 2008. [pdf] [bib] |
| 27. | Investigations on Improving the SEE-GRID Optimization Algorithm. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Diploma Thesis. June 2008. [pdf] [bib] |
| 28. | Parallel Algorithms for Sparse Matrices in an Industrial Optimization Software. Internationaler Universitätslehrgang Informatics: Engineering & Management (ISI Hagenberg). Diploma Thesis. July 2008. [pdf] [bib] |
| 29. | Automated Formal Static Analysis and Retrieval of Source Code. International School for Informatics - Johannes Kepler University . Diploma Thesis. August 2008. in RISC Raport Series 08-21. [pdf] [bib] |
| 30. | Integration von Entscheidungsprozeduren in einen interaktiven Beweisassistenten. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. Diploma Thesis. June 2008. [pdf] [bib] |
| 31. | Functional Program Verification in Theorema. RISC, Johannes Kepler University. PhD Thesis. July 2008. Technical report no. 08-12 in RISC Report Series. [pdf] [bib] |
| 32. | Computer Algebra Tools for Special Functions in High Order Finite Element Methods. Johannes Kepler University Linz. PhD Thesis. 2008. [ps] [pdf] [bib] |
| 33. | Comprehensive Groebner bases in various domains. RISC-Linz. PhD Thesis. April 2007. [ps] [pdf] [bib] |
| 34. | Automated Invariant Generation by Algebraic Techniques for Imperative Program Verification in Theorema. RISC, Johannes Kepler University Linz, Austria. PhD Thesis. October 2007. RISC Technical Report No. 07-16. [pdf] [bib] |
| 35. | Symbolic-Algebraic Methods for Linear Partial Differential Operators. University of Linz, Austria. PhD Thesis. July 2007. [pdf] [bib] |
| 36. | Symbolic Methods for Factoring Linear Differential Operators. RISC. PhD Thesis. February 2006. [ps] [pdf] [bib] |
| 37. | Logic Foundation of Geometry and Didactics. RISC, Johannes Kepler University Linz. PhD Thesis. 2006. [bib] |
| 38. | Parametrizing algebraic varieties using Lie algebras. RISC, JKU Linz. PhD Thesis. 2006. [pdf] [bib] |
| 39. | A Framework for Publishing and Discovering Mathematical Web Services.. RISC, Johannes Kepler University Linz. PhD Thesis. 2006. [bib] |
| 40. | Contributions to the Parametrization of Algebraic Varieties.. RISC, Johannes Kepler University Linz. PhD Thesis. 2006. [bib] |
| 41. | A generic implementation of differential characteristic set algorithms in Aldor. Johannes Kepler University, Linz, Austria. Diploma Thesis. December 2005. [pdf] [bib] |
| 42. | Regular Languages and Their Generating Functions: The Inverse Problem. Friedrich-Alexander-Universität Erlangen-Nürnberg. Diploma Thesis. August 2005. [url] [pdf] [bib] |
| 43. | Solving and Simplifying the Propositional Satisfiability Problem by Sub-Model Propagation. RISC, Johannes Kepler University, Linz, Austria. PhD Thesis. 2005. [bib] |
| 44. | Symbolic-Numeric Techniques for Cubic Surfaces. RISC-Linz. PhD Thesis. July 2005. PhD Thesis. [pdf] [ps] [bib] |
| 45. | Special Functions, Computer Proofs and the DLMF. RISC, J. Kepler University Linz. Diploma Thesis. 2005. [bib] |
| 46. | Algorithms for Nonlinear Higher Order Difference Equations. RISC-Linz. PhD Thesis. October 2005. [ps] [ps] [bib] |
| 47. | Symbolic Computation in Number Theory.. RISC, Johannes Kepler University Linz. PhD Thesis. 2005. [bib] |
| 48. | Combinatorial Sequences: Non-Holonomicity and Inequalities. RISC, J. Kepler University Linz. PhD Thesis. August 2005. [pdf] [bib] |
| 49. | Tools for Using Automated Provers in Mathematical Theory Exploration. Research Institute for Symbolic Computation, Johannes Kepler University of Linz, Austria. PhD Thesis. August 2004. Also available as RISC Tech Report no. 04-12. [url] [bib] |
| 50. | Algorithms for Change of Orderings in the Theory of Gröbner Bases.. RISC, Johannes Kepler University Linz. PhD Thesis. 2004. [bib] |
| 51. | Fault Tolerance for Distributed Maple. RISC-Linz, Johannes Kepler University, Linz, Austria. PhD Thesis. September 2004. [ps] [bib] |
| 52. | Verification of Imperative Programs in Theorema. West University of Timisoara, Romania. Diploma Thesis. 2004. [bib] |
| 53. | Representation of sari using computer-generated patterns. RISC-Linz, Johannes Kepler University, Linz, Austria. PhD Thesis. 2004. [pdf] [bib] |
| 54. | Spline Implicitization of Planar Shapes and Applications. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria. PhD Thesis. 2004. [txt] [bib] |
| 55. | Interpolation von Sobolevräumen. Joh. Kepler Univ. Linz. Diploma Thesis. January 2004. [pdf] [bib] |
| 56. | Numerical Computation of Groebner Bases. RISC, Johannes Kepler University Linz. PhD Thesis. 2003. [bib] |
| 57. | A Contribution to the Symmetry Classification Problem for 2nd Order PDEs in one Dependent and two Independent Variables. RISC, Johannes Kepler University Linz. PhD Thesis. 2003. [bib] |
| 58. | Graphical Solutions to the Plateau Problem. RISC-Linz, J. Kepler University. PhD Thesis. 2003. [bib] |
| 59. | A Symbolic Algorithm for Generating Solutions of Boundary Value Problems. RISC, Johannes Kepler University Linz. PhD Thesis. 2003. [bib] |
| 60. | Involutive Bases for Polynomial Ideals. Research Institute for Symbolic Computation. PhD Thesis. Johannes Kepler University, Linz, Austria, February 2003. [url] [bib] |
| 61. | Polynomial Arithmetic and Linear Systems in Symbolic Summation. RISC Linz. PhD Thesis. 2002. [bib] |
| 62. | Automated Geometric Theorem Proving in the Frame of the Theorema Project. RISC, Johannes Kepler University Linz. PhD Thesis. 2002. [bib] |
| 63. | Supporting User-Friendliness in the Mathematical Software System Theorema. RISC, Johannes Kepler University Linz. PhD Thesis. 2002. [bib] |
| 64. | Uncoupling Systems of Linear Ore Operator Equations. RISC, J. Kepler University Linz. Diploma Thesis. 2 2002. [ps] [ps] [bib] |
| 65. | Solving and Proving in Equational Theories with Sequence Variables and Flexible Arity Symbols. RISC, Johannes Kepler University of Linz. PhD Thesis. 2002. [ps] [bib] |
| 66. | Symbolic Summation in Difference Fields. RISC, J. Kepler University Linz. PhD Thesis. May 2001. (published as Technical report no. 01-17 in RISC Report Series.). [ps] [pdf] [bib] |
| 67. | Solutions of Difference Equations With Polynomial Coefficients. RISC, J. Kepler University Linz. Diploma Thesis. 2001. [pdf] [bib] |
| 68. | The Bézout Construction of the Resultant. RISC, Johannes Kepler University Linz. PhD Thesis. 2001. [bib] |
| 69. | Non-conventional Algorithms for Multiple Precision Arithmetic. RISC, University of Linz. PhD Thesis. December 2001. Habilitation thesis. [bib] |
| 70. | A Set Theory Prover in Theorema: Implementation and Practical Applications. RISC Institute. PhD Thesis. May 2001. [tar.gz] [bib] |
| 71. | Automated Theorem Proving by Integrating Proving, Solving and Computing. RISC, Johannes Kepler University of Linz. PhD Thesis. 2000. [zip] [bib] |
| 72. | Algorithmic Resolution of Singularities. Research Institute for Symbolic Computation, Johannes Kepler University. PhD Thesis. A-4040 Linz, 2000. [bib] |
| 73. | Functional Logic Programming with Distributed Constraint Solving. RISC, Johannes Kepler University Linz. PhD Thesis. 2000. [bib] |
| 74. | On the Computational Complexity of Resolving Curve Singularities and Related Problems. RISC, Johannes Kepler University Linz. PhD Thesis. 2000. [bib] |
| 75. | Anchored Sweep â A Paradigm. RISC, Johannes Kepler University Linz. PhD Thesis. 2000. [bib] |
| 76. | An Architecture for Combining Provers and its Applications in the Theorema System.. RISC, Johannes Kepler University of Linz. PhD Thesis. 1998. [ps] [bib] |
| 77. | Periodic Interactions. Department of Mathematical Logic and Applications, Faculty of Mathematics and Computer Science, Sofia University, Bulgaria. Diploma Thesis. November 1998. [bib] |
| 78. | Contributions to Symbolic q-Hypergeometric Summation. RISC, J. Kepler University Linz. PhD Thesis. 1997. [pdf] [bib] |
| 79. | Parametric Robust Stability by Quantifier Elimination. RISC, Johannes Kepler University Linz. PhD Thesis. 1997. [bib] |
| 80. | Implementierung von Automaten-Algorithmen mit Hilfe von binären Entscheidungsdiagrammen. Lehrstuhl für Künstliche Intelligenz (Informatik VIII), Friedrich Alexander Universität Erlangen-Nürnberg. Diploma Thesis. 1997. (Engl. translation: Implementation of Algorithms for Automatons with Binary Decision Diagrams - BDD). Diploma Thesis. [ps] [pdf] [bib] |
| 81. | Computer Generated Proofs of Binomial Multi-Sum Identities. RISC, J. Kepler University. Diploma Thesis. May 1997. [ps] [bib] |
| 82. | Lagrange Inversion. RISC, J. Kepler University Linz. Diploma Thesis. 1997. [pdf] [ps] [ps] [bib] |
| 83. | Symbolic Pattern Solving in Algebraic Structures. RISC, Johannes Kepler University Linz. PhD Thesis. 1997. [bib] |
| 84. | Fibered Structures and Applications to Automated Proving in Certain Classes of Finitely-Valued Logics. RISC, Johannes Kepler University Linz. PhD Thesis. 1997. [bib] |
| 85. | Algorithmic Manipulations and Transformations of Univariate Holonomic Functions and Sequences. RISC, J. Kepler University. Diploma Thesis. August 1996. [ps] [pdf] [bib] |
| 86. | Fast Planning of a Good Path for a Manipulator Using Potential Fields on a Non-Uniform Grid in C-space. RISC, Johannes Kepler University Linz. PhD Thesis. 1996. [bib] |
| 87. | A Hybrid Symbolic-Numerical Approach in Computer Aided Geometric Design (CAGD) and Visualization. RISC, Johannes Kepler University Linz. PhD Thesis. 1996. [bib] |
| 88. | On Combinatorial Identities: Symbolic Summation and Umbral Calculus. RISC, J. Kepler University Linz. PhD Thesis. 1996. [ps] [pdf] [bib] |
| 89. | A Subresultant Theory for Linear Differential, Linear Difference and Ore Polynomials. RISC, Johannes Kepler University Linz. PhD Thesis. 1996. [pdf] [bib] |
| 90. | A Mathematica q-Analogue of Zeilberger's Algorithm for Proving q-Hypergeometric Identities. RISC, J. Kepler University Linz. Diploma Thesis. 1995. [pdf] [bib] |
| 91. | Gröbner Bases Computation and Gaussian Elimination. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 92. | Invariant Theory of Finite Groups and Applications. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 93. | Rational Parametrization of Algebraic Surfaces. Symbolic Solution of an Equation in three Variables. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 94. | A Categorical Framework and Calculus for Critical-Pair Completion. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 95. | Castle â Design and Implementation of a Symbolic Computation Language with Emphasis on Polymorphism and Efficiency. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 96. | Contributions to Symbolic Summation. RISC, J. Kepler University. Diploma Thesis. December 1995. [ps] [pdf] [bib] |
| 97. | Faster Algorithms for Reconstructing Rationals, Computing Polynomial GCDs, and Factoring Polynomials. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 98. | Algebraic and Geometric Approach to Parametrization of Rational Curves. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 99. | Interval Methods for Bounding the Range of Polynomials and Solving Systems of Nonlinear Equations. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 100. | Decidability Results for Categorical Notions Related to Monads by Rewriting Techniques. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 101. | Parallel Functional Programming for Computer Algebra. RISC, Johannes Kepler University Linz. PhD Thesis. 1995. [bib] |
| 102. | Computer-assisted Studies in Algebraic Combinatorics. RISC, J. Kepler University Linz. PhD Thesis. 1994. [pdf] [ps] [bib] |
| 103. | RISC-CLP(Tree) A Constraint Logic Programming System with Parametric Domain. RISC, Johannes Kepler University Linz. PhD Thesis. 1994. [bib] |
| 104. | Systolic Multiprecision Arithmetics. RISC, Johannes Kepler University Linz. PhD Thesis. 1994. [bib] |
| 105. | Symbolic Computation with Algebraic Sets. RISC, Johannes Kepler University Linz. PhD Thesis. 1993. [bib] |
| 106. | Algorithmen zur Summation rationaler Funktionen. University of Erlangen-Nürnberg. Diploma Thesis. 1992. [pdf] [ps] [bib] |
| 107. | Gröbner Bases: A Characterization by Syzygy Completeness and an Implementation. University of Linz, RISC Institute. Diploma Thesis. January 1992. [ps] [bib] |
| 108. | Real-Time Dynamic Collision Checking Integrated into Graphic Manufacturing Simulation. RISC, Johannes Kepler University Linz. PhD Thesis. 1991. [bib] |
| 109. | Three Contributions to Elimination Theory. RISC, Johannes Kepler University Linz. PhD Thesis. 1991. [bib] |
| 110. | Resonant Interactions of Rossby waves in Bounded Domains [in Russian]. P.P.Shirshov Institute for Oceanology, USSR Academy of Sciences, Moscow. PhD Thesis. December 1990. [bib] |
| 111. | A Verification System for Total Correctness of the Parallel L-Language. RISC, Johannes Kepler University Linz. PhD Thesis. 1989. [bib] |
| 112. | Decomposing and Parametrizing the Solution Set of an Algebraic System. RISC, Johannes Kepler University Linz. PhD Thesis. 1989. [bib] |
| 113. | Algorithmic Problems: Primary Decompostion and Beyond. RISC, Johannes Kepler University Linz. PhD Thesis. 1989. [bib] |
| 114. | Algebraic Approaches to Automated Geometry Theorem Proving. RISC, Johannes Kepler University Linz. PhD Thesis. 1988. [bib] |
| 115. | Multiprocessor List Memory Management. RISC, Johannes Kepler University Linz. PhD Thesis. 1988. [bib] |
| 116. | A Medley of Solutions to the Robot Collision Problem in two and three Dimensions. RISC, Johannes Kepler University Linz. PhD Thesis. 1988. [bib] |
| 117. | The Church-Rosser Property in Computer Algebra and Special Theorem Proving. RISC, Johannes Kepler University Linz. PhD Thesis. 1984. [bib] |
| 118. | PL/ADT: Ein System zur Verwendung algebraisch spezifizierter abstrakter Datentypen in PL/I. RISC, Johannes Kepler University Linz. PhD Thesis. 1980. [bib] |
| 119. | Kreativität und Universalität. RISC, Johannes Kepler University Linz. PhD Thesis. 1980. [bib] |
| 120. | Contributions to the Systematics of Creativity Concepts. RISC, Johannes Kepler University Linz. PhD Thesis. 1980. [bib] |
| 121. | Universalitaet und Reduzierbarkeit von partiell rekursiven Funktionen, Automaten und deren Numerierungen. RISC, Johannes Kepler University Linz. PhD Thesis. 1978. [bib] |
| 122. | Ueber die Vernetzung berechnbarer Funktionen. RISC, Johannes Kepler University Linz. PhD Thesis. 1976. [bib] |
| 123. | Implementierung einer Metasprache zur Definition von auf symbolischen Daten operierenden Interpretern und ihr Einsatz in der Programmverifikation. RISC, Johannes Kepler University Linz. PhD Thesis. 1976. [bib] |
| 124. | Ein Algol 60 Interpreter. RISC, Johannes Kepler University Linz. PhD Thesis. 1975. [bib] |
| 125. | Eine Metasprache zur Definition von Programmiersprachen und ihre Implementierung. RISC, Johannes Kepler University Linz. PhD Thesis. 1974. [bib] |
| 126. | Blum'sche Komplexitätsmasse in der verallgemeinerten Rekursionstheorie von Moschovakis. RISC, Johannes Kepler University Linz. PhD Thesis. 1974. [bib] |
| 127. | Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalen Polynomideal (An Algorithm for Finding the Basis Elements in the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal). Mathematical Institute, University of Innsbruck, Austria. PhD Thesis. 1965. English translation in J. of Symbolic Computation, Special Issue on Logic, Mathematics, and Computer Science: Interactions. Vol. 41, Number 3-4, Pages 475-511, 2006. [pdf] [bib] |