CSUMS: Theory, techniques, and research in computational mathematics

Li0703532 这个CSUMS项目将William and Mary的数学、计算机科学和应用科学系的教师联系起来，在本科课程中创建计算数学部分。 项目人员修改大一和大二的课程，更加强调计算问题，从而为本科生准备特殊的高年级课程，并最终参与本科生的研究。 学生做研究项目的理论和实际问题，从数值线性代数，量子计算，优化，动力系统，和药物生物学。 通常情况下，该项目的学生在大三和接下来的夏天开始做研究，并在大四通过仔细监督的荣誉继续他们的工作。 此外，学年活动包括特殊的计算数学研讨会和访客，加上一个年度研讨会，学生在其中展示他们的发现。 重要的科学发现被提交给专业期刊发表，并在学术会议上发表。 此外，学生们还讨论了他们在当地高中、弗吉尼亚州州长科学和数学学校以及地区两年制大学的成果和经验。 这样的外展演示应该吸引更大，更多样化的年轻学生进入计算数学的进一步研究，并给予研究生在该计划的额外实践中沟通数学给他人。 为了拓宽学生的视野，并鼓励思想交流，有访问其他机构和研究机构在美国和国外。 建立了一个网站，以促进与其他研究小组和计算数学程序的交流。 在现代计算机和信息技术的基础上，是一个跨学科的领域，称为计算数学。该项目结合了数学、计算机科学和应用科学系教师的技能和知识，在本科课程中创建了一个新的计算组件。 它为学生准备参加计算理论和实践方面的本科研究项目，并在William和玛丽的计算数学课程与国内外类似课程之间建立联系。 本课程的成功经验吸引学生进一步学习计算几何学并在该领域就业。 该项目教师的不同研究背景相互作用，打破了阻碍学生和教师进步的智力划分。 在该计划中开发的新思想通过我们的学生和他们的教师导师的会议演讲和出版物传播。 除了与高中和社区大学的课程联系外，他们还吸引了更大、更多样化的大学预科学生进入这里和其他地方的计算数学课程。 该项目得到了MPS数学科学部、MPS多学科活动办公室和EHR本科教育部的支持。

Li0703532 This CSUMS project links faculty from the departments ofmathematics, computer science, and applied science at William andMary to create a computational mathematics component in theundergraduate program. Project personnel modify freshman andsophomore courses to place greater emphasis on computationalissues, thereby preparing undergraduates for special upperdivision courses and eventual participation in undergraduateresearch. Students do research projects on theoretical andpractical problems from numerical linear algebra, quantumcomputing, optimization, dynamical systems, and mathematicalbiology. Typically, students in the program start doing researchin their junior year and the following summer, and continue theirwork during their senior year through carefully supervised honorstheses. In addition, academic year activities include specialcomputational mathematics seminars and visitors, plus an annualworkshop in which students present their discoveries. Importantscientific findings are submitted for publication in professionaljournals and presented at scholarly conferences. In addition,students discuss their results and experiences in local highschools, in the Virginia Governor's School for Science andMathematics, and in regional two-year colleges. Such outreachpresentations should attract a larger and more diverse populationof younger students into further study of computationalmathematics, and give research students in the program additionalpractice in communicating mathematics to others. To broaden theperspective of the students in the program, and to encourage theinterchange of ideas, there are visits to other institutions andresearch agencies in the U.S. and abroad. A website is set upto facilitate communication with other research groups andcomputational mathematics programs. At the base of modern computer and information technology isan interdisciplinary field called computational mathematics. This project unites the skills and knowledge of faculty from thedepartments of mathematics, computer science, and applied scienceto create a new computational component within the undergraduatecurriculum. It prepares students to participate in undergraduateresearch projects in the theoretical and practical aspects ofcomputation, and it builds linkages between the computationalmathematics programs at William and Mary and similar programsnationally and abroad. Successful experiences in this programattract students to further study in computational mathematicsand to careers in the field. The diverse research backgrounds ofthe program's faculty interact to break down the intellectualcompartmentalization that stands in the way of progress for bothour students and our faculty. The new ideas developed in theprogram are disseminated through conference talks and scholarlypublication by our students and their faculty mentors. Throughoutreach to high school and community college programs, theyattract a larger and more diverse group of pre-college studentsinto computational mathematics programs here and elsewhere. Theproject is supported by the MPS Division of MathematicalSciences, the MPS Office of Multidisciplinary Activities, and theEHR Division of Undergraduate Education.