Tradeoffs in using Mathematica templates in an introductory numerical methods course

Shirley B. Pomeranz

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Conference: 2013 ASEE Annual Conference & Exposition
Location: Atlanta, Georgia
Publication Date: June 23, 2013
Start Date: June 23, 2013
End Date: June 26, 2013
ISSN: 2153-5965
Conference Session: Mathematics Division Technical Session 2
Tagged Division: Mathematics
Page Count: 19
Page Numbers: 23.1258.1 - 23.1258.19
DOI: 10.18260/1-2--22643
Permanent URL: https://peer.asee.org/22643
Download Count: 350

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Shirley B. Pomeranz University of Tulsa

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Shirley Pomeranz
Associate Professor
Mathematics Graduate Student Advisor
Department of Mathematics
The University of Tulsa

Research and Teaching Interests:
Boundary Element Method and Finite Element Method, Numerical Methods, Engineering Applications of
Mathematics, Applications of Mathematica, Women in Mathematics

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Abstract

Tradeoffs in using Mathematica templates in an introductory numerical methods courseThis paper presents tradeoffs involved in using Mathematica® templates to “level the playingfield” and facilitate teaching an introduction to numerical methods course. Given increases classsizes and decreases in budgets and facilities, the demands and needs of this course are evolving.The technology used the workplace is changing. Therefore, the rationale for using computeralgebra system (CAS) templates to teach numerical methods encompasses issues that havechanged due to today’s educational and employment environment.Experiences from 20 years of teaching numerical methods to science, engineering, andmathematics (SEM) students are used to validate the use of Mathematica programmingtemplates. The course is a survey course taught to science, engineering, computer science, andmathematics juniors, seniors, and beginning graduate students, and is offered by the Departmentof Mathematics in the College of Engineering and Natural Sciences. The Mathematicaassignments are used in two different ways: (1) to assist in understanding the numerical methodsstudied in the course, and (2) to increase expertise in the use of Mathematica to solve problemsencountered in the SEM disciplines and in the workplace. CAS such as Mathematica arebecoming more commonly used in engineering fields and the workplace. Therefore, for manystudents learning Mathematica, as opposed to some other programming language, makes sense.Further, many other SEM courses at our university use Mathematica.Mathematica templates are used to “jump-start” students with weaker Mathematica backgroundsso that these students can program early in the course, Due to the diverse student backgrounds,interests, and familiarity with Mathematica, it was determined that Mathematica programmingtemplates would be used to help students get started with the programming aspects of the course.There are transfer students, graduate students, and non-traditional students. These studentsgenerally are not familiar with the use of Mathematica. Therefore, the templates given tostudents consist of either a similar simpler solution notebook (program file) or a related problemnotebook with the main body of code missing. For example, sample code for initialization, anoutline, and output formatting might be given. The student then writes the main code for themethod. More advanced students have the option of rewriting the sample code.Student feedback with respect to the templates was solicited via several questionnaires.Advantages and disadvantages from a student’s perspective and from an instructor’s perspective.Various ways in which students put the templates to use and anecdotal student comments aregiven. Pedagogical problems that are solved and new pedagogical problems that arise arediscussed. Comparisons are made with similar studies for specific engineering courses done byother researchers. Samples of templates for topics such as fixed-point iteration, Newton’smethod, cubic splines, Runge-Kutta method, predictor-corrector method, and systems of ordinarydifferential equation-initial value problems are available by contacting the author.

Citation
Format

Pomeranz, S. B. (2013, June), Tradeoffs in using Mathematica templates in an introductory numerical methods course Paper presented at 2013 ASEE Annual Conference & Exposition, Atlanta, Georgia. 10.18260/1-2--22643

TY  - CPAPER
AB  -        Tradeoffs in using Mathematica templates in an introductory numerical                               methods courseThis paper presents tradeoffs involved in using Mathematica® templates to “level the playingfield” and facilitate teaching an introduction to numerical methods course. Given increases classsizes and decreases in budgets and facilities, the demands and needs of this course are evolving.The technology used the workplace is changing. Therefore, the rationale for using computeralgebra system (CAS) templates to teach numerical methods encompasses issues that havechanged due to today’s educational and employment environment.Experiences from 20 years of teaching numerical methods to science, engineering, andmathematics (SEM) students are used to validate the use of Mathematica programmingtemplates. The course is a survey course taught to science, engineering, computer science, andmathematics juniors, seniors, and beginning graduate students, and is offered by the Departmentof Mathematics in the College of Engineering and Natural Sciences. The Mathematicaassignments are used in two different ways: (1) to assist in understanding the numerical methodsstudied in the course, and (2) to increase expertise in the use of Mathematica to solve problemsencountered in the SEM disciplines and in the workplace. CAS such as Mathematica arebecoming more commonly used in engineering fields and the workplace. Therefore, for manystudents learning Mathematica, as opposed to some other programming language, makes sense.Further, many other SEM courses at our university use Mathematica.Mathematica templates are used to “jump-start” students with weaker Mathematica backgroundsso that these students can program early in the course, Due to the diverse student backgrounds,interests, and familiarity with Mathematica, it was determined that Mathematica programmingtemplates would be used to help students get started with the programming aspects of the course.There are transfer students, graduate students, and non-traditional students. These studentsgenerally are not familiar with the use of Mathematica. Therefore, the templates given tostudents consist of either a similar simpler solution notebook (program file) or a related problemnotebook with the main body of code missing. For example, sample code for initialization, anoutline, and output formatting might be given. The student then writes the main code for themethod. More advanced students have the option of rewriting the sample code.Student feedback with respect to the templates was solicited via several questionnaires.Advantages and disadvantages from a student’s perspective and from an instructor’s perspective.Various ways in which students put the templates to use and anecdotal student comments aregiven. Pedagogical problems that are solved and new pedagogical problems that arise arediscussed. Comparisons are made with similar studies for specific engineering courses done byother researchers. Samples of templates for topics such as fixed-point iteration, Newton’smethod, cubic splines, Runge-Kutta method, predictor-corrector method, and systems of ordinarydifferential equation-initial value problems are available by contacting the author.
AU  - Shirley B. Pomeranz
CY  - Atlanta, Georgia
DA  - 2013/06/23
PB  - ASEE Conferences
TI  - Tradeoffs in using Mathematica templates in an introductory numerical methods course
UR  - https://peer.asee.org/22643
DO  - 10.18260/1-2--22643
ER  -