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Mathematica ist ein hervorragendes Programm um mathematische Berechnungen – auch sehr komplexe – auf relativ einfache Art und Weise durchführen zu lassen. Dieses Skript soll eine wirklich kurze Einführung in Mathematica geben und als Nachschlagewerk einiger gängiger Anwendungen von Mathematica dienen. Dabei wird folgende Grobgliederung verwendet: - Grundlagen: Graphische Oberfläche, einfache Berechnungen, Formeleingabe - Bedienung: Vorstellung einiger Kommandos und Einblick in die Funktionsweise - Praxis: Beispielhafte Berechnung einiger Abitur- und Übungsaufgaben
The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS. Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first three chapters can be dealt within the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 4, 5 and 6 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. Chapter 7 (case study) deals with a practical case and demonstrates the presented methods. It is possible to use this chapter independent in a seminar or practical training course, if the concepts of time series analysis are already well understood. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific parts are highlighted. This book is an open source project under the GNU Free Documentation License.
The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS. Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first three chapters can be dealt within the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 4, 5 and 6 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. Chapter 7 (case study) deals with a practical case and demonstrates the presented methods. It is possible to use this chapter independent in a seminar or practical training course, if the concepts of time series analysis are already well understood. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific parts are highlighted. This book is an open source project under the GNU Free Documentation License.
Mathematica ist ein hervorragendes Programm um mathematische Berechnungen – auch sehr komplexe – auf relativ einfache Art und Weise durchführen zu lassen. Dieses Skript soll eine wirklich kurze Einführung in Mathematica geben und als Nachschlagewerk einiger gängiger Anwendungen von Mathematica dienen. Dabei wird folgende Grobgliederung verwendet: - Grundlagen: Graphische Oberfläche, einfache Berechnungen, Formeleingabe - Bedienung: Vorstellung einiger Kommandos und Einblick in die Funktionsweise - Praxis: Beispielhafte Berechnung einiger Abitur- und Übungsaufgaben
Bei vielen Fragestellungen, in denen sich eine Grundgesamtheit in verschiedene Klassen unterteilt, ist weniger die relative Klassengröße als vielmehr die Anzahl der Klassen von Bedeutung. So interessiert sich beispielsweise der Biologe dafür, wie viele Spezien einer Gattung es gibt, der Numismatiker dafür, wie viele Münzen oder Münzprägestätten es in einer Epoche gab, der Informatiker dafür, wie viele unterschiedlichen Einträge es in einer sehr großen Datenbank gibt, der Programmierer dafür, wie viele Fehler eine Software enthält oder der Germanist dafür, wie groß der Wortschatz eines Autors war oder ist. Dieser Artenreichtum ist die einfachste und intuitivste Art und Weise eine Population oder Grundgesamtheit zu charakterisieren. Jedoch kann nur in Kollektiven, in denen die Gesamtanzahl der Bestandteile bekannt und relativ klein ist, die Anzahl der verschiedenen Spezien durch Erfassung aller bestimmt werden. In allen anderen Fällen ist es notwendig die Spezienanzahl durch Schätzungen zu bestimmen.