REU Site: California State University, Fresno Research Experiences in Mathematics

该加州州立大学，弗雷斯诺夏季REU将在2016年至2018年的夏天为24名学生。该计划的目标是：（1）让本科生参与数学研究;（2）增加代表性不足和少数民族学生参与此类研究，并鼓励他们考虑就读研究生院;（3）为研究机会有限的机构的学生提供体验数学研究的机会。学生将对当前感兴趣的研究问题进行配对，通常是建立在该计划过去参与者完成的工作基础上。每年，一位资深教师导师将与一位初级导师配对，监督学生的研究，以扩大指导和合作的影响。该计划将继续为参与者提供一个支持和欢迎的环境，在这个环境中，学生面临着学术和专业成长的挑战。为此，该计划将提供有关提高写作和口语技能、研究方法和学术界一般属性的研讨会。该周期的研究领域将是纽结理论、复分析、解析数论、统计学、有限几何和组合学以及应用数学。更明确地说，参与者将学习结和链接不变量，整个函数的零点分布，多项式族的精确零轨迹，其生成函数是合理的，波动建模，有限几何中的最小支配集和阻塞集，以及计算算法的数值实现。学生将每周进行一次演讲，并将完成三个最终产品：一个抛光20分钟的谈话，一个专业的海报，和一篇文章质量的研究报告。主讲嘉宾将就旨在拓宽学生数学视野的主题进行讲座，并将参与科学话语的计划参与者，鼓励学生深入研究他们的研究课题，并验证他们迄今为止的努力。弗雷斯诺州REU将继续参与NSF REU计划范围内的努力，让代表性不足的少数民族学生参与研究，并向所有学生通报他们在学术界和其他领域的就业机会。学生将离开该计划已经深入研究了数学的一个小区域，提高了他们的口头和书面技能，结交了新朋友和联系，并准备作为本科生，研究生或行业专业人士进一步挑战。

The California State University, Fresno summer REU will serve 24 students during the summers of 2016-2018. The objectives of the program are: (1) to involve and engage undergraduate students in research in mathematics; (2) to increase the involvement of underrepresented and minority students in such research and to encourage them to consider attending graduate school; and (3) to afford students from institutions with limited research opportunities the chance to experience mathematics research. Students will work in pairs on research problems of current interest, often building on work completed by past participants of the program. Each year, a senior faculty mentor will pair up with a junior mentor in supervising student research, so as to broaden the impact of mentoring and collaboration. The program will continue to provide its participants with a supportive and welcoming environment, in which students are challenged to grow academically as well as professionally. To this end the program will provide workshops on improving writing and speaking skills, research methods, and general attributes of academia.The research areas for this cycle will be knot theory, complex analysis, analytic number theory, statistics, finite geometry and combinatorics, and applied mathematics. More explicitly, participants will study knot and link invariants, the distribution of zeros of entire functions, exact zero loci of polynomial families whose generating function is rational, volatility modeling, minimal dominating sets and blocking sets in finite geometries, and numerical implementations of computing algorithms. Students will give weekly presentations, and will complete three final products: a polished 20 minute talk, a professional poster, and an article quality research report. Guest speakers will give lectures on topics intended to broaden students' mathematical horizons, and will engage program participants in scientific discourse, both encouraging students to delve deeper into their research topic, and validating their efforts to date. The Fresno State REU will continue to participate in the NSF REU program-wide effort to involve underrepresented minority students in research and to inform all students about career opportunities available to them both in academia and otherwise. Students will leave the program having studied a small area of mathematics deeply, having improved their oral and written skills, having made new friends and connections, and ready to be further challenged as an undergraduate student, graduate student, or industry professional.