Aaron’s Scholarly Stuff
Basically a long laundry list of projects I have worked on. Some are still incomplete, others have been abandoned. The most recent material is at the top with earlier material farther down. They are ordered based on when I last worked on the project (not by completion date). Common abbreviations are CWU (Central Washington University), PUNC (Purdue University North Central) and UW (University of Wisconsin-Madison).
Many of these items have additional information available in PDF format. This is indicated by the PDF icon to the left of the item's name.
Some of these items have additional information available in HTML format. This is indicated by the HTML icon to the left of the item's name.
Documents
Calculus | |
Type: book
Status: currently in development
| |
| A calculus text I am working on. It incorporates my work with function and limit. | |
 | College Algebra Project: Unifying Representation of Function |
Type: grant
Last Modified: 15 November 2004
Status: unfunded by CWU Graduate Office
| |
| Based on a number of previous works, this grant proposes further development of a unifying representation for the function concept. | |
| College Algebra Project: Unifying Representation of Function |
Type: grant
Last Modified: 3 November 2004
Status: submitted to FIPSE
| |
| Based on a number of previous works, this grant proposes further development of a unifying representation for the function concept. | |
| Documenting Your Code with doxygen |
Type: paper
Last Modified: 1 March 2004
Status: published in MacTech
| |
| A short article describing how to use command line UNIX tools in Mac OS X development. It focuses on the doxygen command line tool for documenting code. | |
| An Alternative Representation of Function |
Type: paper
Last Modified: 3 December 2003
Status: unpublished by CMJ and PRIMUS, led to grant submission
| |
| An early paper describing using arrows to represent functions and providing techniques for doing traditionally algebraic manipulations in a more conceptual manner. Reviewers suggested that data needed to be collected (something I am now doing). | |
| ILAPs at CWU |
Type: grant
Last Modified: 15 December 2003
Status: partially funded by NSF
| |
| A $75,000 project to develop Interdisciplinary Lively Application Projects at CWU. | |
| Strengthen Student Conception of Function |
Type: grant
Last Modified: 30 November 2003
Status: unfunded by CCHE, led to grant submission
| |
| A grant designed to increase student understanding of the function concept in calculus courses using computer programming and arrow diagrams (see Another Representation of Function). | |
| Hairy Parabola |
Type: paper
Last Modified: 1 November 2003
Status: published in The College Math Journal
| |
| A short Classroom Capsule describing how the standard calculus technique used to find maxima and minima can lead to incorrect results when applied to non-continuous situations. | |
ILAPs at CWU | |
Type: grant
Last Modified: 4 December 2002
Status: unfunded by NSF, resubmitted in 2003
| |
| A proposal to develop Interactive Lively Application Projects at CWU. The grant was resubmitted with suggested changes in 2004 and the resubmitted grant was partially funded. | |
| Strengthening Student Conception of Function |
Type: grant
Last Modified: 30 November 2002
Status: unfunded by CCHE, resubmitted in 2003
| |
| A grant designed to create materials to increase student understanding of the concept of function through computer programming and arrow diagrams. | |
| Learning Linear Algebra with ISETL |
Type: book
Last Modified: 31 July 2002
Status: distributed on Internet
| |
| A textbook written with members of RUMEC designed using APOS theory. The book is designed for a course introducing students to abstract mathematics and linear algebra. The course does significant work with finite fields and the ISETL programming language. | |
| Strengthening Student Conception of Function |
Type: grant
Last Modified: 6 June 2002
Status: unfunded by NSF, led to grant submission
| |
| A CCLI-EMD grant proposal designed to allow the development of calculus materials focusing on the function concept. | |
| Unusual Application of Snell's Law |
Type: paper
Last Modified: 30 May 2002
Status: unpublished
| |
| This paper presented an application of Snell's Law to max-min problems which do not involve light travelling through different media. | |
| Web Course Development (CWU) |
Type: grant
Last Modified: 19 October 2001
Status: funded
| |
| A small grant to support some of my web development projects related to teaching at CWU. In particular, the grant paid for the purchase of a new digital camera for photographing my whiteboards. | |
| PowerPlant Workshop 5 |
Type: paper
Last Modified: 1 August 2001
Status: published in MacTech
| |
| The last article in a series of five articles. This article describes how to work with dialogs using the PowerPlant C++ application framework by Metrowerks. | |
| PowerPlant Workshop 4 |
Type: paper
Last Modified: 1 July 2001
Status: published in MacTech
| |
| The fourth article in a series of five articles. This article describes how to work with files using the PowerPlant C++ application framework by Metrowerks. | |
| PowerPlant Workshop 3 |
Type: paper
Last Modified: 1 June 2001
Status: published in MacTech
| |
| The third article in a series of five articles. This article describes how to work with windows using the PowerPlant C++ application framework by Metrowerks. | |
| PowerPlant Workshop 2 |
Type: paper
Last Modified: 1 May 2001
Status: published in MacTech
| |
| The second in a series of five articles. This article describes how to work with the debugging features of the PowerPlant C++ application framework by Metrowerks. | |
| PowerPlant Workshop 1 |
Type: paper
Last Modified: 1 April 2001
Status: published in MacTech
| |
| The first in a series of five articles. This article describes how to start projects using the PowerPlant C++ application framework by Metrowerks. | |
An Alternative Motivation of Limit | |
Type: talk
Last Modified: 5 January 2001
Status: presented at AMS-MAA Joint Meeting
| |
| This talk presented an alternative motivation of the limit concept for students in freshman calculus. It is based on work done as part of the ARUME grant received in 2000. | |
Taking Variables Seriously | |
Type: talk
Last Modified: 5 January 2001
Status: presented at AMS-MAA Joint Meeting
| |
| This talk presented course materials developed for the Developmental Algebra courses at Purdue University North Central. The material focuses on spending time developing the concept of variable as a fixed but unknown quantity and reading algebraic expressions and equations. | |
Matrices: Tool or Topic | |
Type: talk
Last Modified: 5 January 2001
Status: presented at AMS-MAA Joint Meeting
| |
| This talk discussed how matrices are perceived by students taking an introductory linear algebra course. In particular, it contrasted the view that matrices are a tool for solving linear equations against the view that matrices form an interesting mathematical structure to be studied for their own sake. | |
| Number Systems for Linear Algebra |
Type: course material
Last Modified: 30 August 2000
Status: incorporated in LLAWI
| |
| An early version of the chapter on algebraic structures that evolved into the first chapter of Learning Linear Algebra with ISETL. | |
| Variables |
Type: course material
Last Modified: 30 August 2000
Status: used at PUNC
| |
| Course material designed to introduce developmental mathematics students to the concept of variable in the sense of a fixed (but unknown) quantity. This was introduced and used by all Developmental Mathematics Courses at PUNC from 2000-2002. I am unsure, but believe that they are still using some version of it on the campus today. | |
Using Flex and Bison | |
Type: paper
Last Modified: 1 July 2000
Status: published in MacTech
| |
| An article which describe the use of code generators flex and bison using the Metrowerks' Codewarrior Integrated Environment. A copy of the article can be found on the MacTech website (I'm trying to dig up the pdf version to post as well). | |
| Motivation of the Limit Concept |
Type: grant
Last Modified: 1 June 2000
Status: funded by MAA, led to grant submission
| |
| A $1,400 mini-grant from the MAA for research into undergraduate mathematics. This grant focused on an alternative motivation for the limit concept. It led to work on the concept of function. | |
| Knot Polynomials |
Type: talk
Last Modified: 1 February 2000
Status: presented at CWU
| |
| A talk given at Central Washington University during my interview process there. If focused on the development of knot polynomials to prove that the trefoil is not achiral. | |
 | Voting Theory |
Type: talk
Last Modified: 1 February 2000
Status: presented at Purdue University North Central
| |
| A talk given at Purdue University North Central during my interview process there. It focused on well-known voting paradoxes and Arrow's Theorem. | |
| An Alternative Definition for Limit |
Type: paper
Last Modified: 1 January 2000
Status: unpublished, led to grant submission
| |
| A paper presenting an alternative definition for limit that can be used in freshman calculus. The paper includes proofs that the given definition is equivalent to the standard epsilon-delta definition. | |
| Finding Tangent Lines with Algebra |
Type: course material
Last Modified: 30 August 1999
Status: used at PUNC
| |
| Maple lab for freshman calculus courses. Uses Maple to allow students to determine tangent lines of conics as the unique line intersecting the conic in exactly one point. | |
| Developmental Mathematics Report |
Type: report
Last Modified: 30 August 1999
Status: presented to the PUNC Math/Physics Section, led to course material
| |
| Longitudinal study of student accomplishment in developmental algebra and subsequent mathematics courses. As a result of the study, a committee was formed and the developmental algebra course sequence was restructured and new material was developed. | |
| Threaded ACGIs in PowerPlant |
Type: paper
Last Modified: 1 July 1999
Status: published in MacTech
| |
|
An article which describes the use of the Monsterworks' Framework (written by myself) to build threaded asynchronous common gateway interface (acgi) applications based on Metrowerks' PowerPlant application framework. This can also be found online at the MacTech website. This framework was originally designed for Mac OS 9. It has since been updated to not rely on PowerPlant and to run natively on Mac OS X. | |
Internet Security and You | |
Type: talk
Last Modified: 17 June 1999
Status: presented to PUNC Faculty Training
| |
| Short training session describing how to protect yourself while online. | |
| Using the Internet to Augment Classroom Teaching |
Type: poster
Last Modified: 11 March 1999
Status: presented at Purdue University's Teaching, Learning and Technology Workshop
| |
| Poster presentation describing the tools used to present Purdue University North Central's distance learning statistics course. | |
| Building Knowledge |
Type: essay
Last Modified: 1 January 1999
Status:
| |
| Short teaching philosophy statement. You can find more such statements in Why Computers Cannot Teach and Web of Knowledge. | |
| Why Computers Cannot Teach |
Type: essay
Last Modified: 20 November 1998
Status:
| |
| Short teaching philosophy statement. You can find more such statements in Building Knowledge and Web of Knowledge. | |
| PGP & SLS |
Type: talk
Last Modified: 1 November 1998
Status: presented to PUNC Internet Club
| |
| Introduction to the mathematics of RSA encryption algorithms and how they are used to implement Pretty Good Privacy and Secure Socket Layer. | |
| Weaving a Course Based Web |
Type: paper
Last Modified: 18 October 1998
Status: published in Enhancements: How Using Technology Changes What Faculty Do.
| |
| An article describing how to use the Internet to augment a standard classroom environment. | |
Web Interactivity | |
Type: talk
Last Modified: 1 October 1998
Status: presented to PUNC Internet Club
| |
| Introduction to various means of providing interactive web pages. Focused on Java, JavaScript, Flash and CGI programming. | |
| Factoring Polynomials |
Type: course material
Last Modified: 1 August 1998
Status: used at PUNC
| |
| Short course material packet developed as an introduction to factoring polynomials. | |
| Functions |
Type: course material
Last Modified: 1 August 1998
Status: used at PUNC
| |
| Short course material packet developed as an introduction to the concept of function. | |
Statistics Distance Learning | |
Type: grant
Last Modified: 15 May 1998
Status: funded by IHETS, led to presentation and article
| |
| A $12,000 grant from Indiana Higher Education Telecommunications Systems for distance learning couse development. Resulted in Purdue University North Central's frist distance learning course. The course was developed utilizing Java, JavaScript, PDF and C/C++ cgi programming. | |
| Graphing Rational Functions |
Type: course material
Last Modified: 30 August 1997
Status: used at PUNC
| |
| Short course material packet developed as an introduction to the graphing of rational functions. | |
| Calculus Notation |
Type: course material
Last Modified: 30 August 1997
Status: used at PUNC
| |
| Short course material packet developed as an introduction to the various notations used in calculus. | |
| Lusternik-Schnirelmann Category and Simplicial Sets (abstract) |
Type: paper
Last Modified: 30 June 1997
Status: doctoral dissertation
| |
| Abstract for my doctoral dissertation. See the Complete Dissertaion for more details. | |
| Lusternik-Schnirelmann Category and Simplicial Sets (overview) |
Type: paper
Last Modified: 30 June 1997
Status: doctoral dissertation
| |
| "Non-technical" overview of my doctoral dissertation. See the Complete Dissertaion for more details. | |
| Lusternik-Schnirelmann Category and Simplicial Sets (complete) |
Type: paper
Last Modified: 30 June 1997
Status: doctoral disseration
| |
| A complete version of my doctoral dissertation. The goal of the dissertation was to develop a theory of Lusternik-Schnirelmann Category for simplicial sets. The hope is that such a theory would provide a method for computing the Lusternik-Schnirelmann Category of a topological space. | |
| The Web of Knowledge |
Type: essay
Last Modified: 30 August 1996
Status:
| |
| An introduction to my teaching philosophy. It presents some of my opinions about constructivism (although I didn't know the term when I wrote it), as well as some thoughts about the order in which material in subjects should be taught. | |
| Lusternik-Schnirelmann Category and Simplicial Sets |
Type: talk
Last Modified: 5 January 1996
Status: presented at AMS-MAA Joint Meeting
| |
| A preliminary report of my doctoral work on Lusternik-Schnirelmann Category. A complete description of this can be found in Lusternik-Schnirelmann Category and Simplicial Sets | |
| How and When to Teach Why |
Type: talk
Last Modified: 30 August 1995
Status: presented at UW Teaching Workshop
| |
| Very primitive discussion of teaching philosophy. This work focused on developing the basic skills of college freshman prior to trying to show them the big picture. | |
| Graphing |
Type: course material
Last Modified: 30 August 1994
Status: used at UW
| |
| Material used to teach students how to graph trigonometric functions. The material makes use of tables in a way which is adapted in later work (see Another Representation of Function). | |
Topological Surfaces | |
Type: talk
Last Modified: 15 October 1991
Status: presented at Wisconsin Academy of Science, Arts and Letters
| |
| Short talk presented to a non-mathematical audience about how you can use the loops to distinguish between a plane, a sphere and a torus. | |
Tychonoff's Theorem and the Axiom of Choice | |
Type: talk
Last Modified: 17 March 1989
Status: presented at Pomona College
| |
| Short talk presented presenting a proof that Tychonoff's Theorem (that the arbitrary product of compact topological spaces is compact) is equivalent to the Axiom of Choice. This was presented as part of the requirements to receive honors in mathematics. | |
Optimization of a Connectivity Function in a Neural Network Model | |
Type: report
Last Modified: 12 August 1988
Status: presented as part of PEW Fellowship
| |
| As part of the requirements for the Pew Foundations Undergraduate Research Fellowship, I presented this report discussing the use of homotopy continuation methods to optimize a neural network for image recognition. |
Contact page: <http://www.monsterworks.com/>
Contact address: <mailto:montgoaa@cwu.edu>