目前的研究活动

用几何图形推理 - It has long been assumed in mathematical communities that diagrams can be properly used only as aids to human intuition which have no place in formal proofs, reducing 图表给数学世界的二等公民.  我的研究目的是 show that diagrams can be used rigorously and fruitfully in formal mathematics, and, indeed, that the formal proofs that one gets using diagrams are more understandable and correspond better to  normal informal proofs (of the kind that one finds in Euclid's 元素(例如)比传统的语言形式证明.

• 在我的书中可以找到我工作中最完整的图表版本 欧几里得和他在20世纪的对手: Diagrams in the Logic of Euclidean Geometry,可用 在这里 来自芝加哥大学出版社.  这本书也可以在大多数网上书店买到. 本书的pdf预印本可在此下载: euclid20thcenturyrivalsmiller.pdf.
• A beta version of my computer program CDEG: Computerized Diagrammatic Euclidean Geometry, 这本书中所描述的，是可用的吗 在这里.
• "The Philosophical and Pedagogical Implications of a Computerized Diagrammatic System 欧几里得几何" briefly describes CDEG and some of its philosophical and pedagogical implications.  它出现在MAA笔记卷中 数学哲学在本科数学教学中的应用, © 2017年美国数学协会.  这整个卷目前都是可用的 为MAA会员免费提供电子书.
• “CDEG:计算机图解几何2.“0”是一篇皇冠app安卓下载安装这台计算机的简短论文 系统，我以海报的形式在 图2012 会议.  本文的预印本可在此下载: cdeg_diag2012_poster.pdf.  可在此下载海报的powerpoint文件: D2012Poster.ppt.  该论文的扩展(未发表)版本可在此处下载: cdeg_diag2012.pdf.
• 我的书的扩展摘要在 图2006 会议 at Stanford University and appeared the Springer-Verlag Lecture Notes in AI系列卷4045  图解表示与推理， Barker-Plummer, Cox和Swoboda主编.，©2006施普林格出版社.  你可以下载 在这里: extabstract.pdf.
• “论妈妈的欧盟的不一致性”是一篇发表在 《皇冠app官方版下载》 (2012) 53: 27-52 在这里. 本文的预印本可在此下载: onmummaseundjfl.pdf.  John Mumma's Eu is another diagramatic formal system for giving proofs in Euclidean 几何 which is similar to my formal system FG, but has several key differences 事实证明，这使得他的体系不健全、不一致. 本文将解释 这些问题与他的正式体系有关.
• The most technical results about the computational complexity of using diagrams in Euclidean 几何 can be found in my article "Computational Complexity of Diagram Satisfaction in Euclidean Geometry," Journal of Complexity 22 (2006) 250-274, which 是可用的 在这里.  本文的预印本可在此下载: complexity_case_analysis_diagrams.pdf.
• "A Brief Proof of the Full Completeness of Shin's Venn Diagram Proof System" was published in the Journal of Philosophical Logic (2006) 35: 289-291, and 是可用的 在这里. 本文的预印本可在此下载: compactvenn.pdf.
• 2001年康奈尔大学博士学位.D. 论文是 欧几里得几何的图解形式系统.  你可在此下载pdf格式的报告:  论文.pdf.  除了描述我的正式系统 FG for giving diagrammatic proofs in Euclidean Geometry, it contains: a short history 图表，逻辑和几何，从公元前1700年.C. up to the present;  examples of how 使用较弱的子系统 FG to determine the logical structure of 几何; discussion of the unique role of lemmas in diagrammatic proofs in 几何;  sample transcripts from CDEG，计算机系统实现 FG; proofs that the question of whether or not a given diagram is satisfiable (that is, whether or not it represents a physically realizable situation) is decidable, but is NP-hard, and t在这里fore not solvable in a reasonable amount of time;  a discussion of  earlier work by Isabel Luengo developing a different diagrammatic formal system for 几何, and an explaination of why her system in unsound; and a general discussion 为什么一个正式的系统 FG 是有用的.
• This is a three page non-technical 概述 of some of my work, in pdf format: 概述.pdf.  它发表在 Springer-Verlag Lecture Notes in AI Series volume 图的理论与应用， Anderson, Cheng和Haarslev编.，©2000斯普林格出版社. 这是“案例”论文 欧几里得几何学中的分析”，在本综述中提到: caseanal.pdf.

探究性数学的教与学 Most of my teaching is done using inquiry-based methods, and I have had several publications 以及这个领域的演讲.

• "Teaching Inquiry to High School Teachers Through the Use of Mathematics Action 研究 项目" describes the use of mathematics Action 研究 项目 (ARPs) as a capstone experience 为在职中学教师开设的硕士课程. 它认为，这些项目 have had the effect of encouraging teachers to decide to try more inquiry-based teaching methods in their own classrooms, and at the same time, have given them the knowledge 以及成功做到这一点的工具. 它发表在 博智金融 《皇冠app安卓下载安装》特刊，目前可在网上免费获得. 一个预印本 本文的版本可以下载 在这里.
• "写作教学和校对" describes a 一年级 Writing Seminar that I developed and taught in the math department at Cornell University as part of Cornell's Writing Across the Curriculum program.  它出现在MAA笔记卷中 Beyond Lecture: Resources and Pedagogical Techniques for Enhancing the Teaching of 课程中的写作校对, © 2016年美国数学协会.  这整个卷目前都是可用的 为MAA会员免费提供电子书.
• "A Mentoring Program for Inquiry-Based Teaching in a College Geometry Class," written with Nathan Wakefield, describes our experiences in implementing an intensive year-long mentoring program for training a novice instructor (Nathan) in using inquiry-based 教学方法.  这篇论文于2014年发表在 国际数学、科学与技术教育杂志 2(4), 266-272.
• "数学建模" is a set of notes for a project-based mathematical modeling class for in-service 我在皇冠app官方版下载学习和教学的中学老师 MathTLC 格兰特.  它们已发表在 数学探究性学习杂志.
• "R . H . Bing平面拓扑学课程笔记" is a set of notes for an inquiry-based, Moore method plane topology class originally 作者:r.h. Bing.  我编辑了这些笔记，并添加了一些皇冠app安卓下载安装如何教学的讨论 从他们. 它们已发表在 数学探究性学习杂志. 
• Multiply-Modified Moore/Miller Methods: The Many Faces of Inquiry-Based Learning in 我的课 是皇冠app安卓下载安装我的教学如何随着时间的推移而发展的演讲吗.  这个演讲是在 第14届R的遗产. L. 2011年6月在华盛顿举行的摩尔会议上.
• "现代几何II" is a set of annotated course notes for my inquiry-based 现代几何II class 这篇文章发表在 数学探究性学习杂志. These are notes for a second semester class that explores Euclidean and non-Euclidean geometries from multiple perspectives, with an emphasis on developing problem solving, communication, and logical reasoning skills, directed primarily at pre-service secondary 数学教师. 非欧几里得几何包括出租车几何、双曲几何和球面几何 几何. 这是一门以探究为基础的课程，学生们大部分时间都花在这门课上 在课堂上小组解决问题，然后把它们写下来. 这些材料意味着 与书相伴 经历了几何 (亨德森 & Taimina, 2005).
• "现代几何I" is a set of annotated course notes for my inquiry-based 现代几何I class 这篇文章发表在 数学探究性学习杂志.  These are notes for a class that explores Euclidean and non-Euclidean geometries from multiple perspectives, with an emphasis on developing problem solving, communication, and logical reasoning skills, directed primarily at pre-service secondary 数学教师 还有专门教数学的职前小学教师. 这是一个基于查询的类 in which students spend most of their time in class working on problems in groups 然后把它们写下来. 材料是松散地基于前几个 书中的章节 经历了几何 (亨德森 & Taimina, 2005).
• "Visualization on Cones and Pool Tables Using Geometer's Sketchpad" describes several activities that I have developed for use in an undergraduate modern 几何 course K-12职前教师.  发表于 博智金融,卷. 十六,没有. 3(2006年9月)，页. 第257 - 274页，并可在此下载: 博智金融.pdf.  (不幸的是，它是一个非常大的文件.)这篇论文也包含在指导员中 我上面提到的现代几何的版本.

其他的研究:

• 广义棒球曲线:三种对称性，你入选了!, written with Dean Allison and Ricardo Diaz, was published in the online MAA journal 位点.  棒球的缝线勾勒出的曲线有许多对称性.  这篇文章 explores the class of closed spherical curves with the same symmetries, which we call 广义棒球曲线.