Το MuPAD είναι ένα πλήρες υπολογιστικό σύστημα σχεδιασμένο για μια ευρεία κλίμακα χρηστών. Η γλώσσα ΜuPAD έχει σύνταξη παρόμοια με της Pascal και επιτρέπει συναρτησιακό και αντικειμενοστραφή προγραμματισμό. Το πρώτο μέρος της εργασίας λειτουργεί ως πρακτικός οδηγός εκμάθησης των βασικότερων συναρτήσεων και εντολών του λογισμικού. Για το σκοπό αυτό παρατίθενται πλήθος παραδειγμάτων λειτουργίας των παραπάνω συναρτήσεων από εφαρμογές τους σε διαφορετικά πεδία των Μαθηματικών, όπως: Γραμμική Άλγεβρα, αναλυτική Γεωμετρία, Απειροστικό λογισμό, Στατιστική κασι Πιθανότητες. ιδιαίτερη έμφαση δίνεται στις εντολές που αφορολυν στη σχεδίαση δισδιάστατων και τρισδιάστατων γραφικών. Στο δεύτερο μέρος της εργασίας γίνεται αξιοποίηση του λογισμικού στη διδασκαλία συναρτήσεων πολλών μεταβλητών και των παραγώγων τους. Ο κώδικας σχεδίασης των γραφικών παρατίθεται στο παράρτημα της εργασίας. / MuPAD is a full-fledged computer algebra system with a rich set of extensive mathematics capabilities for symbolic and numeric computation. The MuPAD language haw a Pascal-like syntax and allows functional and object-oriented programming. In the first chapter my intention is facilitating a fast and simle approach to the computer algebra system myPAD. each section in this volume begin with a table listing the MuPAD commands and instructions on how to utilize MuPAD functions. I place special emphasis on the capability of MuPAD to produce graphical output. In the second chapter I have used MuPAD for teaching multivariable functions and their derivatives. The code wich produces graphical output is given in the end of this booklet.

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In this thesis we study the number of periodic points of congruential monomial dynamical system. By concept of index calculus we are able to calculate the number of solutions for congruential equations. We give formula for the number of r-periodic points over prime power. Then we discuss about calculating the total number of periodic points and cycles of length r for prime power.

The use of technology has become increasingly popular in mathematics education. Instructors have implemented technology into classroom lessons, as well as various applications outside of the classroom. This thesis outlines technology developed for use in a first-year calculus classroom and investigates the relationship between the use of weekly formative online Maple T.A. quizzes and student performance on the final exam. The data analysis of the online quizzes focuses on two years of a five-year study. Linear regression techniques are employed to investigate the relationship between final exam grades and both how a student interacts with and performs on the online quizzes. A set of interactive class notes and a library of computer demonstrations designed to be used in and out of a calculus classroom are presented. The demonstrations are coded in Maple and designed to give geometric understanding to challenging calculus concepts.

Even though lambda calculus (λ-calculus) and combinatory logic (CL) appear to be equivalent, they are not. As yet we do not have a reduction in CL which corresponds to β-reduction in λ-calculus. There are three proposals but they all have few problems one of which is the lack of a complete characterization of CL-terms corresponding to λ-terms in β-normal form. Finding such a characterization for any of the three proposals appears to require a lot of examples which are tedious and time consuming to develop by hand. For this reason, a computer program to do reductions and abstractions of CL-terms would be useful. This thesis is about an attempt to write such a program. The program that we have does not yet work for the three proposals but it works for βη-strong reduction. Coding this program turned out to be much harder than anticipated. Dr. Robin Cockett developed a semantic translation which helped in coding the program but his semantic translation needs to be extended to all three proposals to obtain the program originally desired and that needs a lot of research. / v, 96 leaves ; 29 cm

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In this thesis, we design and implement an analysis tool for a language called kiltera which is a timed extension of pi-calculus. kiltera allows the modeling of concurrent, mobile, real-time and distributed systems. Our analyzer takes a kiltera model as input and performs analyses such as detection of deadlock states, stable states etc. To improve performance, the analyzer uses some transformation techniques to simplify the input kiltera model without changing its behavior. We provide a detailed description of the design and implementation of the analyzer and discuss some performance optimizations. Finally, we present some case studies to illustrate the capabilities of our analyzer. / Thesis (Master, Computing) -- Queen's University, 2010-09-29 12:02:41.361

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