{"title":"Analysis of algorithms as a teaching experience","authors":"D. Merlini","doi":"10.5206/mt.v3i2.15664","DOIUrl":"https://doi.org/10.5206/mt.v3i2.15664","url":null,"abstract":"Teaching analysis of algorithms to students in Computer Science degrees, using the approach popularized by Knuth in his series of books ``The Art of Computer Programming\" and later by Sedgewick and Flajolet in the book ``An Introduction to the Analysis of Algorithms\", is not a simple task since, in general, these students are more interested in the implementation of an algorithm than in the corresponding theoretical aspects. This approach concentrates on precisely characterizing the performance of algorithms by determining their best, worst and average case performance using a methodology based on symbolic tools such as recurrence relations and generating functions.The most difficult aspect is to understand the average case since this corresponds to studying the algorithm as its possible inputs vary: this represents the most important goal since generally students have no difficulty in understanding the best and worst cases, corresponding to particular input configurations.A compromise that has been successful over the years consists in teaching students the analytical aspects of the problem and then organize a simulation of the algorithm with a system of symbolic computation in order to precisely check the theoretical results.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124860935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Special Functions in Problem Solving Environments: A personal view","authors":"Robert Corless","doi":"10.5206/mt.v3i2.15927","DOIUrl":"https://doi.org/10.5206/mt.v3i2.15927","url":null,"abstract":"This paper discusses some of the philosophical and historical underpinnings of the talk “The Mathieu Functions: Computational and Historical Perspectives” given at the Maple Conference 2022. I also comment on the role Problem Solving Environments (PSEs) play in curating the computational knowledge of the 19th century, which is so necessary for us to think of special functions as answers rather than questions.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130319903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"What's New in Maple 2022: Formal Power Series","authors":"J. Gerhard","doi":"10.5206/mt.v3i1.15944","DOIUrl":"https://doi.org/10.5206/mt.v3i1.15944","url":null,"abstract":"\u0000The convert/FormalPowerSeries functionality was completely rewritten for Maple 2022. It is based on Dr. Bertrand Teguia Tabuguia's PhD thesis, Power Series Representations of Hypergeometric Type and Non-Holonomic Functions in Computer Algebra, under the supervision of Prof. Wolfram Koepf at University of Kassel, Germany, May 2020.\u0000","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131380508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jaehee Post, Tracy H. Howell, Katrina Palmer, William C. Bauldry, Michael J. Bossé
{"title":"Graphing the Remainder","authors":"Jaehee Post, Tracy H. Howell, Katrina Palmer, William C. Bauldry, Michael J. Bossé","doi":"10.5206/mt.v3i1.14322","DOIUrl":"https://doi.org/10.5206/mt.v3i1.14322","url":null,"abstract":"Employing the Remainder Theorem, analytic and graphical tools, and dynamic applets, this paper investigates when the graphs of rational functions intersect horizontal, oblique, and curved asymptotes. Additionally, we consider how the respective remainder function perturbs the asymptotic function to producethe rational function. Dynamic applets assist in the development of the ideas herein. Finally, this paper endswith a significant number of student investigations.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117016627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"About this issue","authors":"Robert Corless","doi":"10.5206/mt.v3i1.15951","DOIUrl":"https://doi.org/10.5206/mt.v3i1.15951","url":null,"abstract":"Welcome to the third issue of Maple Transactions. For a variety of global reasons, this issue's production was slow enough that by the time the original contributions were ready, a whole new batch of contributions were also ready. So this is basically a \"double issue\". We have two Featured Contributions: \"How to Hunt Wild Constants\" which surveys the software for guessing what a floating-point constant might really be; and another on \"Arbitrary precision computation of the gamma function\" which surveys the state-of-the-art for computation of that remarkable function. We have our first video presentation hosted on Western's Institutional Repository instead of YouTube, for better international access. We have contributions on mathematical research and on educational research, and on educational practice. We have a nice educational paper on how to program in Maple. And, since it's kind of a double issue, I have written two columns for the Editor's corner. I hope you will enjoy them, but more than that I am certain that you will find a lot of interesting material in this issue.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115821430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Blends have decent numerical properties","authors":"Robert M Corless","doi":"10.5206/mt.v3i1.15890","DOIUrl":"https://doi.org/10.5206/mt.v3i1.15890","url":null,"abstract":"A \"blend\" is a two-point Hermite interpolational polynomial, typically of quite high degree. This note shows that implementing them in a double Horner evaluation scheme has good backward error, and also shows that the Lebesgue constant for a balanced blend or nearly balanced blend on the interval [0,1] is bounded by 2, independently of the grade or degree of the approximation. On [-1,1], which is a more natural interval for comparison, it is of course unbounded, but grows only like 2√(m/π) where 2m+1 is the grade of approximation. I also show that the quadrature schemes for balanced blends amplify errors only by O( ln(m) ).","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126627698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algorithmic study of the algebraic parameter estimation problem for a class of perturbations","authors":"Maya Chartouny, T. Cluzeau, A. Quadrat","doi":"10.5206/mt.v2i2.14467","DOIUrl":"https://doi.org/10.5206/mt.v2i2.14467","url":null,"abstract":"We consider the algebraic parameter estimation problem for a class of standard perturbations. We assume that the measurement z(t) of a solution x(t) of a linear ordinary differential equation -- whose coefficients depend on a set θ := {θ₁, ..., θᵣ} of unknown constant parameters -- is affected by a perturbation γ(t) whose structure is supposed to be known (e.g., an unknown bias, an unknown ramp), i.e., z(t)=x(t, θ)+γ(t). We investigate the problem of obtaining closed-form expressions for the parameters θᵢ's in terms of iterative indefinite integrals or convolutions of z. The different results are illustrated by explicit examples computed using the NonA package -- developed in Maple -- in which we have implemented our main contributions.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116657908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Online Tutoring with Maple Learn","authors":"Paul Staadecker","doi":"10.5206/mt.v3i1.14780","DOIUrl":"https://doi.org/10.5206/mt.v3i1.14780","url":null,"abstract":"Maple Learn is one of Maplesoft’s educational products. Here, I discuss my use of it in online mathematics tutoring. I share my tutoring setup, compare it with other possible setups, and discuss the pros and cons of Maple Learn for tutoring. I conclude that Maple Learn allows tutors to write and format math easily while talking to students, unlike other products. It does not allow multiple users to work on the same document simultaneously. Overall, I recommend the product to tutors.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128676904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"How to program with formulas in Maple","authors":"M. Monagan","doi":"10.5206/mt.v3i1.15169","DOIUrl":"https://doi.org/10.5206/mt.v3i1.15169","url":null,"abstract":"Maple's main strength is its ability to compute with mathematical formulasand not just with numbers. It can multiply and factor, differentiate and integrate, and simplify formulas. In this article, using differentiation as an example, I explain how to program with formulas in Maple. The key is the data representation that Maple uses for a formula and the operations Maple provides for operating on formulas. I will also discuss Automatic Differentiation as an alternative which differentiates programs.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131968349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Devilish Tricks for Sequence Acceleration","authors":"Robert M Corless","doi":"10.5206/mt.v3i1.14777","DOIUrl":"https://doi.org/10.5206/mt.v3i1.14777","url":null,"abstract":"The two most famous quotes about divergent series are Abel's \"Divergent series are the invention of the devil, and it is shameful to base on them any demonstration whatsoever,\" and Heaviside's \"This series is divergent, therefore we may be able to do something with it.\" Today a lot more is known about divergent series than in either's day, so we can say now that, on balance, Heaviside wins, and we now have plenty of license to use divergent series. This article talks about some \"well-known\" methods (that is, well-known to experts) to do so, and in particular talks about some of the devilishly good features of evalf/Sum, long one of my favourite tools in Maple. But Abel had a point, too, and we'll see some \"shameful\" things, which will give the reader some necessary caution to go along with their license.","PeriodicalId":355724,"journal":{"name":"Maple Transactions","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123878919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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