教育

• Ph.D., 亚利桑那大学, 数学
• B.A., Bethany Lutheran College, 数学
• B.A., Bethany Lutheran College, Theatre

Background

上大学前, I was very interested in the humanities, and my plans were to double major in English and theatre. 就读文科院校的一个令人惊奇的事情是，在大学的第一年，你可以在广泛的领域学习课程, and this can sometimes spark interests that you never knew you had! A Gen-Ed math class (Calculus I) opened up my eyes to a whole new world. I found the inherent challenge of learning math to be very stimulating, 爱上了理解一个新思想或第一次瞥见数学景观的新部分所带来的美和惊奇感(顺便说一句), I also love hiking in physical landscapes).

When in 2019 my husband and I both accepted calls to serve WLC, God called us here all the way from France. We met during graduate school in Tucson, 亚利桑那州, and then enjoyed a three-year stint near Paris during Jeff’s postdoc. 我们通过沉浸式学习语言，我终于遇到了一些数学“祖先”，他们住在巴黎地区. In addition to my vocations as math professor and wife, I’m very blessed to be a mom. Our family loves traveling and adventuring together, as well as practicing hospitality when we’re at home. 我们是圣. Marcus Lutheran Church in Milwaukee.

I love 教学 at WLC for a number of reasons. 学院的部分使命和愿景是保持对圣经的忠诚，同时通过文科培养学生的仆人式领导, 这些东西 真的 informs what we do on a day-to-day basis! 我也喜欢在一个足够小的机构任教，这样我就可以在他们大学生涯的几个阶段教同样的学生, and to mentor them throughout their time with us. 在这种规模的项目中，有很多机会了解学生，并为他们量身定制教育. 在类, 我试着把项目结合起来，让学生有机会在很长一段时间内思考一个想法, take ownership of the problem and their solution, balance individual with collaborative work, and communicate effectively what they’ve come to understand. 这些都是需要练习的技能，将帮助学生为大学毕业后的下一次冒险做好准备, 不管是研究生院, 教学, 或者从事商业事业, 行业, 或政府. Beyond classes and growing out of my relationships with students in that context, 我真的很喜欢把他们与外界的机会联系起来，比如会议和暑期研究项目.

教学

• MAT 117 – Elementary Statistics
• MAT 221 -微积分1
• MAT 222 -微积分II
• MAT 224 – Ordinary Differential Equations
• MAT 230 – Discrete 数学
• MAT 421 -实分析1
• MAT 423 -复杂分析 

研究兴趣

数学定理证明首先引起我兴趣的是创造性思维和严谨思维的结合，这是需要的:尝试几种方法直到一种方法有效的创造力, 严谨的思维，适当地使用逻辑和数学结构，并评估我的论点的正确性. 证明定理的实际工作包括这两种思维方式的循环:辨明问题和适当的起点, think about different possible approaches and try one, 评估第一种方法是否正确，是否朝着预期的结果取得进展, 然后接受自我反馈，重复这个过程，直到出现一个正确而漂亮的证明. As time went on and I learned the basics in a few fields of mathematics, 另一个引起我兴趣的想法是数学中两个或两个以上看似不同的领域的交集.

As an undergraduate student, I had the opportunity to do two reSearch projects. The first one was in the intersection of abstract algebra and computational methods. 我和一组同伴一起编写计算机程序，实现已经发展起来的理论，将所有具有特定属性的群体分类. (In our abstract algebra course, MAT 431, you’ll learn what groups are!) My other reSearch project was in the intersection of linear algebra and real analysis, an intersection which is important enough that it is a field of math in its own right, 叫做功能分析(你可以在研究生院选修功能分析的课程)!). 在这个项目中, 我们学习了一种几何，其中“点”是称为“算子”的对象(它们本身是函数的推广). To gain intuition about our problem, we played with finite-dimensional versions of operators, which are just matrices (you’ll learn all about matrices in our linear algebra course, 垫333). Once we had an intuitive idea of how the operators behaved under certain mappings, 然后，我们推广并证明了从分析技术的结果(你会得到分析领域的介绍), 我的专业, MAT 421). 长话短说, the courses in a math major train students in the fundamental ideas, 技术, 严谨的思考为解决有趣的问题提供了很多可能性!

我的研究生工作是分析组合学的交叉点(用分析技术解决问题的计数)。, discrete dynamical systems (systems which change at regular intervals of time), and integrable systems (systems which have a conserved quantity, 比如能量守恒). 我的贡献是用一种不同的方式来看待某些结果(解决某个计数问题的优雅公式), 最初是由物理学家利用量子力学的路径积分公式推测出来的)，并展示了这些结果背后的深层数学结构，起初看起来只是“棘手”. 寻找一种有用的方法来思考这个问题的创造性过程包括计算机模拟工作来可视化时间动力学. 严格的证明, once I understood what was going on, 包括微积分II的学生可以理解的概念(你们将在MAT 222中学习)，以及我为了写证明而必须学习的椭圆函数的性质!

我目前对更广泛地理解某些系统的离散动力学感兴趣, including the one from my graduate work. 一群高级WLC学生帮助我开始使用计算机可视化研究这些系统. 在早期阶段, 我们在看电脑生成的系统图片，比较当我们改变函数的定义域时会发生什么, “turn on” a part of the system which depends on its history, 等等....... 

Another developing interest of mine is in applied mathematics. The subject on its own is beautiful, but as the physicist Eugene Wigner famously commented, 数学在解释自然科学的结构方面也“不合理地有效”, and even making empirical predictions or pointing the way to future advances. 数学建模是利用数学中的各种工具解释“现实世界”中的结构的过程. 创造性思维和严谨思维的结合对于应用数学和定理证明一样是必要的:定义问题, determining assumptions that simplify the problem just enough, figuring out a mathematical structure that captures the essential parts of the problem, solving that mathematical problem, 将数学解决方案转换回原始问题域是数学建模的每个步骤，它结合了两种思维模式. 

学术作品

出版物 

布朗,T., N. M. Ercolani. 2020. Integrable Mappings from a Unified Perspective. Integrable Systems and Algebraic Geometry I, Cambridge University Press: London Mathematical Society Lecture Note Series, 卷. 458.

林德伯格,T., N. Fieldsteel T. 伦敦,H. Tran H. Xu. 2013. Classification of Groups with Strong Symmetric Genus Up To Twenty-Five. 休斯顿数学杂志. 39(1): 51-60.

林德伯格,T., D. Ethier,. Luttman. 2010. Polynomial Identification in Uniform and Operator Algebras. 泛函分析年鉴. 1(1): 105-122.

选定的演讲 

“Integrable Mappings from a Unified Perspective.” AMS-MAA Joint 数学 Meetings, AMS Special Session in Combinatorial Structures and Integrable Systems, 丹佛, CO; January 15, 2020.

“An Integrable Dynamical Systems Approach for Solving Recursive Map Enumeration Problems.海报展示. 组合与相互作用，国际数学中心，马赛，法国. 2017年1月10日.

“Dynamics of Discrete Painlevé-I Through Elliptic Functions.分析、动力学和应用研讨会，亚利桑那大学数学系. 2016年3月8日.

 “Combinatorial Hamiltonian Dynamics.” AMS-MAA Joint 数学 Meetings, AMS Special Session in Integrable Systems, Painleve方程, 和随机矩阵, 西雅图, WA; January 6, 2016.

 “Scaling Limits of Random Walks in Random Environments.“亚利桑那大学数学系数学物理与概率研讨会”. 2015年3月25日.

“The Connection Between Map Enumeration and Matrix Integrals.” Current Ideas in the Mathematical Sciences Recruitment Workshop, 数学系, 亚利桑那大学. 2014年3月10日.

服务 

• 教务委员会
• National Science Foundation Reviewer
• Conference Organizer SIMIODE EXPO 2022

专业的会员

• Mathematical Association of America
• Project NExT Fellow (Brown 2020 cohort)