Erich Prisner

Professor, Mathematics and Computing

Habilitation, Universität Hamburg, Germany
Ph.D. Universität Hamburg, Germany
Diploma (M.A.) Universität Hamburg, Germany

Office: Lowerre Academic Center, North Campus, Office 11
Phone: +41 91 986 36 55
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Profile:

The teaching and research experience of Professor Prisner includes the University of Louisville, the University of Maryland University College (Schwäbisch Gmünd), the Technical University of Cottbus (Germany), the Technical University of Berlin, and Franklin University Switzerland. Dr. Prisner has published extensively on intersection graphs and graph-theoretic operators, to include a book on graph dynamics. A recipient of numerous research awards and grants, he also has been particularly active in integrating information technology in his teaching.

2019-2020 Courses:

MAT 103	College Algebra	FALL 2019
The first part of this course reviews the basic concepts of algebra, real numbers, first-degree equations and inequalities, rational expressions, exponents and radicals, and polynomials, systems of equations and inequalities. The second part strongly emphasizes graphs and functions. The most important functions for applications are introduced, such as linear, quadratic, exponential, logarithmic, and rational functions.
MAT 115T	Measuring the Alps	FALL 2019
People live in three-dimensional space but are restricted to the earth surface which is usually locally flat, two-dimensional. But when entering the Alps, the third dimension of height becomes important when describing location or movement. This is also expressed by the fact that in the mountains a map is not too useful---rather a topographic map is needed. Starting with a description of the Alps or any mountains by topographic maps, or mathematically as functions with two independent variables, students will investigate how certain well-known features are reflected by the topography of the area . Examples are the location of mountain brooks, watersheds, movement of glaciers, avalanches, and rockfall. Students will also investigate the question of visibility in the mountains, whether and how it is possible to predict what can be seen from where. A further aspect is GPS technology. During the travel, the class will visit various places in the Swiss, Austrian, and Italian Alps, such as Davos, Innsbruck, Villnoess. Students will hike and measure, but will also discuss questions relevant to Alpine life, such as glaciers, avalanches or rockfall forecasts. If possible, the class will also visit places where such research is conducted. The course includes one mandatory weekend hike in September in addition to the ordinary travel in October. Hiking boots are required.
MAT 200	Calculus	FALL 2019
The course begins with a review of functions and their graphs, after which students are introduced to the concepts of differentiation and integration. Understanding is reinforced through extensive practical work, with a strong emphasis on applications in economics, statistics and management science.
MAT 109	Introduction to Game Theory	SPRING 2020
This course is an elementary introduction to Game Theory. It focuses on how to ana-lyze situations and make rational decisions based on the information gathered. Students will analyze parlor games, gambling, and real-world situations. As mathematical basis for the analysis, Probability Theory and some Algebra are needed, but will be developed in detail
MAT 200	Calculus	SPRING 2020
The course begins with a review of functions and their graphs, after which students are introduced to the concepts of differentiation and integration. Understanding is reinforced through extensive practical work, with a strong emphasis on applications in economics, statistics and management science.
MAT 307	Multivariable Calculus and Linear Algebra	SPRING 2020
The first half of the course gives an introduction into Linear Algebra. Vectors and vector spaces, analytical geometry, matrices and linear equations, and their rank, and also determinants are discussed. The second half of the course discusses the theory of partial and total derivatives for functions of several variables. Topics considered here are limits, partial derivatives, chain rule, gradients, and optimization with or without restrictions.
CPT 150	Intro Computer Programming	SUMMER 2020
This course offers an introduction to computer programming using some high level language. Students will learn how to formulate, represent, and solve problems using the computer. Emphasis will be on the features common to most of these languages. After introducing data structures, expressions, functions, control structures, input and output, the course will proceed to classes, events, user interface construction, documentation, and program testing. Both procedural and object-oriented programming paradigms will be discussed.
MAT 201	Introduction to Statistics	SUMMER 2020
This computer-based course presents the basic concepts in statistics: random variables, random sampling, frequency distributions, central tendency measures, variance and standard deviation, kurtosis and skewness, probability rules, Bayes theorem and posterior probability. Important statistical methods like contingency analysis, ANOVA, and correlation analysis are introduced and their algorithms are explained. The most important probability distributions are introduced: Binomial, Poisson, and Normal distribution, as well as the Chebyshev theorem for non-symmetrical distributions. Inferential statistics, sampling distributions and confidence intervals are briefly covered in order to introduce statistical model building and single linear regression and trend analysis. Students learn how to promote the scientific method, how to identify questions, collect evidence, discover and apply tools to interpret the data, and communicate results. EXCEL is used to enhance algorithmic learning. Selected SPSS or STATA examples are also provided.

Publications:

“Best Response Digraphs for Two Location Games on Graphs”, in: Contributions to Game Theory and Management. Vol. IV (Petrosyan, Leon A. et al. ed.), Collected papers of the 4th international conference game theory and management (GTM 2010), June 28-30, 2010, St. Petersburg, Russia, 378-388 (2011).

Radius versus diameter in co comparability and intersection graphs, Discrete Mathematics 163 (1997) 109-117.

Intersection multigraphs of uniform hypergraphs, Graphs and Comb. 14 (1998) 363-376.

Recognizing clique graphs of directed and rooted path graphs, (joint work with Jayme L. Szwarcfiter), Discrete Applied Mathematics 94 (1999) 321-328.

Generalized octahedra and cliques in intersection graphs of uniform hypergraphs, Discrete Mathematics 206 (1999) 187-195.

Recognizing k-path graphs, Discrete Appl. Mathematics 99 (2000) 169-182.

Bicliques in graphs I: Bounds on their number, Combinatorica 20 (2000) 109-117.

Source reversal and chip firing on graphs (joint work with E. Goles), Theoret. Comput. Sci. 233 (2000) 287-295.

A note on k-rotation graphs, Ars Combinatoria 55 (2000), 289-292.

Eccentricity-approximating trees in chordal graphs, Discrete Mathematics 220 (2000) 263-269.

Recognizing random intersection graphs, Discrete Math. 223 (2000) 263-274.

Eulerian iterated line graphs and digraphs, Discrete Math. 236 (2001) 315-323.

Additive tree spanners, (joint work with Dieter Kratsch, Hoàng-Oanh Le, Haiko Müller, Dorothea Wagner), SIAM J. Discrete Math. Fall 2003

The recognition problem for line bigraphs, Discrete Math. 268, No.1-3, 243-256 (2003).

Additive tree spanners, (joint work with D. Kratsch, Hoang-Oanh Le, H. Mueller, D. Wagner), SIAM J. Discrete Math. 17 (2003) 332-340;

Selected papers from the 1st international workshop on algorithms, combinatorics, and optimization in interconnnection networks (IWACOIN'99), co-guest editor (together with Roger Labahn and Art Liestman) of a special issue of Discrete Appl. Math. 137, (2004) 125-236;

k-Pseudosnakes in n-dimensional Hypercubes, Discrete Math. 17C (2004) 237-240.

AT-free graphs: Linear bounds for the oriented diameter, (joint work with Fedor Fomin, Martin Matamala, Ivan Rapaport), Discrete Appl. Math. 141 (2004) 135-148.