1 \documentclass[a4paper, 12pt]{scrartcl}
3 \usepackage[english,german]{babel}
4 \usepackage[T1]{fontenc}
5 \usepackage[latin1]{inputenc}
12 \usepackage{isabellesym}
14 \bibliographystyle{alpha}
16 \def\isac{${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
17 \def\sisac{\footnotesize${\cal I}\mkern-2mu{\cal S}\mkern-5mu{\cal AC}$}
23 \bf Interactive Course Material for Signal Processing based on Isabelle/\isac\\~\\
25 \sisac-Team of the Institute for Software Technology,\\~\\
26 in Cooperation with the Institute of Signal Processing and Speech Communication\\~\\
27 Graz University of Technology\\
33 \author{Jan Simon Rocnik\\{\tt jan.rocnik@student.tugraz.at}}
42 \section{Introduction}
46 motivation from \textbf{practice of mathematics learning} ... STEOP
48 \textbf{mathematics applied} in signal processing (SP)
50 mathematics mechanized in Computer Theorem Provers \textbf{(CTP)} ... (almost) traditional mathematical notation (predicate calculus) for axioms, definitions, lemmas, theorems. Recent developments provide also proofs in a humand readable format TODO
52 This thesis tries to \textbf{connect these two worlds} ... this trial is one of the first; others see related work
54 \subsection{Mechanization of Mathematics}
58 hughe theories of mathematics
60 still a hugh gap between these theories and ``real applications'' e.g. in SP
62 ? academic engineering starts from physics (experimentation, measurement) and then proceeds to mathematical modelling --- mechanized math starts from mathematical models and (hopefully !) proceeds to match physics.
64 CTP Isabelle ... survey of knowledge, links to knowledge
69 adds an ``application'' axis (formal specifications of problems) and an ``algorithmic'' axis to the ``deductive'' axis of knowledge ... 3-dimensional universe of mathematics.
71 \subsection{Goals of the Thesis}
75 \subsection{Milestones for the Project}
76 Die Planung des Projekts teilt sich in folgende Iterationen:
78 \item \textbf{Sammeln von Informationen über Themengebiete und deren Realisierbarkeit } (29.06. -- 27.07.)
79 identify problems relevant for certain SP lectures
81 estimate chances to realized them within the scope of this thesis
83 order for implementing the problems negotiated with lecturers
86 \item \textbf{1. Präsentation - Auswählen der realisierbaren Themengebiete} (27.07.)
87 \item \textbf{Ausarbeiten der Aufgaben in \isac} (01.09. -- 11.11.)
88 \item \textbf{Dokumentation der Aufgaben} (14.11. -- 02.12.)
89 \item \textbf{Ausarbeitung in Latex, Bakkarbeit} (05.12. -- todo)
90 \item \textbf{2. Präsentation - Abschluss der Arbeit} (todo)
93 \subsection{Structure of the Thesis}
97 \section{Mechanization of Mathematics for SP Problems}
100 \subsection{Relevant Knowledge available in Isabelle}
103 \paragraph{example FFT}, describe in detail !!!!
105 ? different meaning: FFT in Maple
107 gap between what is available and what is required (@)!
109 traditional notation ?
111 \subsection{Relevant Knowledge available in \isac}
114 specifications (``application axis'') and methods (``algorithmic axis'')
116 partial fractions, cancellation of multivariate rational terms, ...
118 \subsection{Survey: Available Knowledge and Selected Problems}
121 estimate gap (@) for each problem (tables)
123 conclusion: following order for implementing the problems ...
125 \subsection{Formalization of missing knowledge in Isabelle}
128 axiomatization ... where ... and
130 \subsection{Notes on Problems with Traditional Notation}
135 f x = why not f(x) ?!?!
139 terms are not full simplified in traditional notations, in isac we have to simplify them complete to check weather results are compatible or not. in e.g. the solutions of an second order linear equation is an rational in isac but in tradition we keep fractions as long as possible and as long as they are 'beautiful' (1/8, 5/16,...)
141 \section{Implementation of Certain SP Problems}
144 \subsection{Formal Specification of Problems}
147 \subsection{Methods Solving the Problems}
150 \subsection{Integration of Subproblems available in \isac}
153 \subsection{Examples and Multimedia Content}
157 \section{Related Work and Open Questions}
160 See ``introduction'': This thesis tries to connect these two worlds ... this trial is one of the first; others see related work
164 \section{Beschreibung der Meilensteine}\label{ms-desc}
166 \section{Bericht zum Projektverlauf}
168 \section{Abschliesende Bemerkungen}
179 \section{Demobeispiel}
181 %\input{./Inverse_Z_Transform/document/Inverse_Z_Transform.tex}
189 \section{Stundenliste}
191 \subsection*{Voraussetzungen zum Arbeitsbeginn schaffen}
192 \begin{tabular}[t]{lll}
193 {\bf Datum} & {\bf Stunden} & {\bf Beschreibung} \\
194 10.02.2011 & 2:00 & Besprechung der Problemstellung \\
197 \section{Calculations}