Peter Zizler

On wide sense stationary processes over finite non-abelian groups

Let X be a real-valued wide sense stationary process over a finite non-abelian group G. We provide results on optimal orthogonal decomposition of X into real-valued mutually orthogonal components and using this decomposition we develop a test for correlation of X over the group G. Applications of these results to the analysis of variance of the carry-over effects in the cross-over designs in clinical studies are given. Our focus will be on groups , and .

Ranking in Professional Sports: An Application of Linear Algebra for Computer Science Students

Linear algebra is one of the required mathematics courses for students majoring in computer science. With the small class sizes at our institution, we have the opportunity to use teaching strategies often reserved for senior level courses at larger universities. In this paper the authors discuss their experience with an innovative project schema that is designed for students in an elementary linear algebra course, and how it fullfills the requirements from the report to ACM [11].

Sequences and Series

This chapter deals with sequences, series, and products of real numbers, and the fundamental concept of convergence of these entities. We shall treat, too, approximation of real numbers by rational numbers, and we shall introduce the Euler number e.

Basics on Descriptive Statistics

Probability is a part of measure theory. This short section tries to describe what is called Discrete Probability Theory or, sometimes, “Descriptive Statistics.”

Real Numbers: The Basics

In this chapter we introduce the system of real numbers and study the basic structural properties of this space. We will meet among others the following three principles: The concept of compactness, the principle of the supremum, and the Baire Category method.

Excursion to Functional Analysis

In modern analysis, most of the problems in science and engineering have solutions in infinite-dimensional spaces of functions, where closed bounded sets are usually not compact, the measure theory is of limited use, linear operators may not have eigenvalues even in the complex case, or even reasonable continuous functions do not attain their extrema on closed bounded sets, just to mention some difficulties. Thus we encounter there problems additional to those we handled in the first chapters of this text. Functional analysis helps in solving these problems by providing additional powerful tools that work in general contexts, allowing in this way to treat a large variety of situations looking at them from a unifying point of view.