Iordan Ganev (Class of 2010)

photo of Iordan Ganev

  • senior Mathematics and Statistics major
  • co-major in Environmental Science
  • 2009 Recipient Astronaut Foundation Scholarship
  • member of Astronomy Club and Pi Mu Epsilon (national mathematics honorary)
  • plans to attend International Congress of Mathematics meeting in Hyderabad, India (August 2010)

International Experiences

Archeological Dig in Israel

Iordan Ganev accepting Astronaut Foundation Scholarship from Al Worden

"During my first semester at Miami, I took an honors class in comparative religion. The professor is an archeologist who takes students to digs in Israel every summer. I've been interested in ancient civilizations for a very long time and, in 2007, I signed on to a dig at Tel Halif with my religion professor.

"Throughout that summer, I glimpsed how people's lives from thousands of years ago intersected with modern life in a kibbutz and the cosmopolitan bustle of Jerusalem. Our work involved digging, sketching, labeling artifacts, taking elevations, cleaning pottery, and attending lectures. We also traveled to prominent archeological sites throughout Israel. Members of the dig formed a diverse group, and I developed connections with people from around the world. A major part of this learning experience was communication of ideas among members of the dig."

Study Abroad in London

"I spent my junior year at Royal Holloway, University of London. I took classes in mathematics and biology and conducted a research project in group theory with a professor at Royal Holloway. We investigated Hölder's formula for the number of groups of a square-free order. I used a number of books and papers as resources, including Hölder's original paper.

"My final report presents a complete derivation of Hölder's formula that differs from the original proof and from more recent explanations: It employs modern structural concepts and at the same time assumes familiarity with only undergraduate group theory. I presented my project at the Binghamton University Graduate Conference in Algebra and Topology and am preparing this manuscript for publication in an undergraduate mathematics research journal. While working on this project, I came across several open questions and developed ideas for future research.

"At Royal Holloway, I joined a hiking club and traveled around the UK and Europe with friends who were as eager as I was to explore natural wonders. We went caving in Yorkshire, hiking in the Lake District (in January without proper equipment—it was scary but loads of fun!), and hiking in the French Alps."

Research Opportunities

Iordan Ganev with Al Worden, CAS deans, and his faculty mentors

Behavioral Ecology of Prairie Voles

"One of my objectives at Miami was to learn how mathematics and statistics can be applied to the natural sciences. I expressed this interest to a zoology professor and began working in her lab in my first semester. As an undergraduate research assistant, I analyzed how capture patterns of adult prairie voles (Microtus ochrogaster) reflect their social organization. In particular, I focused on what information can be inferred when two or more adult voles are caught in the same trap—i.e., multiple capture.

"This sort of study had never been done before with prairie voles. I determined the most prevalent categories of multiple capture and used statistical software to analyze the average relatedness of individuals caught together. Prairie voles are considered to be socially monogamous, and our results support this conclusion since male-female multiple captures were most prevalent. However, the high percentage of females caught with males outside their social unit suggests that prairie voles may not be sexually monogamous.

"I presented the results in a poster session at the Miami Undergraduate Research Forum and was first author of a publication in the Journal of Mammalogy. I wrote the statistical methods, results, and discussion sections of the paper."

Statistical Models in Ecology

"During my sophomore year, I completed an independent study of mixed models in ecology, which culminated in a 10-week research project. This interdisciplinary interaction was the ideal environment for me to learn about theoretical statistical tools and their practical implementation in ecology.

"I became proficient in the computing languages R and WinBUGS and read a number of statistical studies that developed foundations for mixed models, as well as biological studies that applied these statistical tools. I simulated specific kinds of hierarchical data sets in order to compare classical and Bayesian methods for estimating the random effects in mixed models in situations where usual assumptions are not satisfied. In addition, I was interested in developing more precise statistical tools that would yield insight in those aberrant scenarios.

"On a certain level, these two research projects (prairie voles and statistics in ecology) felt like the fulfillment of a childhood dream: I was unraveling some of nature's deepest mysteries. At the same time, such interdisciplinary endeavors allowed me to combine my passion for mathematics with an interest in ecology."

Group Theory

"While mathematics is a powerful tool in the study of the natural world, I am also fascinated with its theoretical and logical structures. During my sophomore year, this fascination led to a research project in group theory, a branch of theoretical mathematics. While working on a homework assignment for one of my favorite courses, Abstract Algebra, I realized that a problem could be extended in order to reach a more general result. My professor encouraged me to pursue the problem further.

"Based on the prime-power factorization of the order of a group, I found a formula for the order dimension of the group, that is, the maximum number of nonidentity elements that can be contained in a proper subgroup. A group is said to have property # if it has a subgroup whose order dimension is maximum. I characterized property # and proved general results for several families of groups.

"As far as I am aware, the notions of 'order dimension' and 'property #' have not been addressed before in group theory literature. My paper was published in the Rose-Hulman Undergraduate Mathematics Journal and I have presented this research several times."

[January 2010]