Mathematics at New College is challenging and exciting. Working closely with faculty mentors, you will have the opportunity to actively participate in your own education, and by your senior year you will be taking advanced coursework more typically found at the master's level rather than undergraduate.
Did you know that New College’s mascot is the Null Set, the mathematical concept written as { }? That’s our notsosubtle way of noting that New College is not a bigtime athletics school. But it also connotes what we do value: a rigorous, liberal arts education within small, closeknit departments such as Mathematics.
Our Math faculty hold degrees from M.I.T., Stanford, CalBerkeley, University of Warwick and other prestigious schools and have a wide variety of expertise, from knot theory and mathematical biology to distributed computing and networking. Our classes are intense, as you might expect from one of the nation’s top liberal arts colleges, but you will also enjoy plenty of time to talk one on one with faculty, who are expert teachers and mentors as well as researchers.
Our core program for students electing an Area of Concentration (AOC) in Mathematics includes three semesters of calculus, linear algebra, differential equations, two semesters of modern abstract algebra, and two semesters of real analysis and complex analysis. In addition, students are encouraged to take courses in topology, discrete mathematics, graph theory and number theory as well as computer science and the other sciences. Finally, students are applauded for forays into other liberal arts courses in the humanities and social sciences. There is a great deal of flexibility involving coursework for advanced students. Past advanced courses, tutorials and independent study projects have included algebraic geometry, algebraic topology, combinatorial optimization, differential geometry, differential topology, foundations of mathematics, Fourier analysis, functional analysis, Galois theory, representation theory of finite groups, group theory, mathematical biology, measure theory, model theory, partial differential equations, probability, projective geometry and topics in mathematical physics. In addition to standard coursework, many students in Pure Mathematics, Applied Math, Computational Science and Bioinformatics at New College pursue summer research and internships through a variety of local, regional and national organizations. The quality of our math programs has resulted in a number of students receiving prestigious National Science Foundation (NSF) REU grants in recent years. Students have also completed internships with Lovelace Respiratory Research Institute, one of the country’s leading biomedical research organizations. Others have participated in internships with a host of other local and regional business partners associated with New College. This combination of academic rigor, advanced coursework at the undergraduate level and personal mentoring from skilled faculty is one reason New College students in Mathematics have been so successful in garnering elite scholarships and awards in recent years. For example, since 2001, four New College students in Mathematics have received prestigious Barry M. Goldwater Scholarships, given out annually to the nation’s top undergraduates majoring in math, science and engineering. It is also the reason so many of our graduates go on to the nation’s leading graduate programs and pursue their Ph.D.’s in Mathematics. Among the graduate schools attended by New College graduates in Mathematics are CalBerkeley, Caltech, University of Cambridge (UK), Columbia and Johns Hopkins, to name just a few. 
Our core program for students electing an Area of Concentration (AOC) in Mathematics includes three semesters of calculus, linear algebra, differential equations, two semesters of modern abstract algebra, and two semesters of real analysis and complex analysis. In addition, students are encouraged to take courses in topology, discrete mathematics, graph theory and number theory as well as computer science and the other sciences. Beyond these core components, there is a great deal of flexibility involving coursework for advanced students. Past advanced courses, tutorials and independent study projects have included algebraic geometry, algebraic topology, combinatorial optimization, differential geometry, differential topology, foundations of mathematics, Fourier analysis, functional analysis, Galois theory, representation theory of finite groups, group theory, mathematical biology, measure theory, model theory, partial differential equations, probability, projective geometry and topics in mathematical physics. For detailed requirements, check out our General Catalog and the Mathematics Academic Learning Compact. Here’s a list of recent course offerings in Mathematics: Patterns Puzzles, Proofs, and Paradoxes Calculus I Calculus II Calculus III Calculus with Theory I Calculus with Theory II Discrete Math Introduction to Number Theory with Applications to Cryptography Graph Theory Graphs, Networks and Algorithms Linear Algebra Computational Ordinary Differential Equations Probability Discrete Dynamical Modeling Mathematical Modeling I Introduction to Numerical Methods Mathematical Biology Advanced Linear Algebra Algebraic Graph Theory Abstract Algebra I Abstract Algebra II Real Analysis I Real Analysis II Complex Analysis Partial Differential Equations Computational Fluid Mechanics Computational Partial Differential Equations Differential Geometry Topology Topics in Algebra Topics in Analysis Topics in Geometry and Topology Topics in Number Theory and Cryptography Science on the Computer Mathematics Seminar Tutorials in Mathematics For a complete list of courses, click here. 


Professor of Mathematics; Director of Data Science Program
(941) 4874375  mcdonald@ncf.edu
Associate Professor of Mathematics; Soo Bong Chae Chair
(941) 4874214  nyildirim@ncf.edu
William P. Thurston (19462012) was a worldrenowned mathematician and member of New College’s charter class, who revolutionized the study of topology in two and three dimensions, showing interplay between analysis, topology and geometry. For that, he won the Fields Medal at just 37 years of age. The medal is mathematics’ highest honor, often equated to the Nobel Prize. “Bill Thurston so transformed our knowledge of low dimensional topology and geometry that it is now impossible to imagine the field before him,” said New College President and mathematician Donal O’Shea. “Before Thurston, no one would have looked at a knot, and asked what the volume of the space outside it was. No one would have looked at the universe, and asked how to carve it up into pieces each with a natural geometry — in fact, no one would have known what exactly a natural geometry is. At New College, we are proud to have provided the space for the fecundity of his imagination to ripen.” Graduating from New College in 1967, Thurston wrote his senior thesis on “A Constructive Foundation for Topology.” He earned a doctorate from the University of California, Berkeley, and taught at MIT, Princeton, Berkeley, UC Davis and Cornell. New College is proud of the many Mathematics graduates who have contributed to the field. Here’s a sampling of some of our graduates: • Richard Canary is a Professor of Mathematics at University of Michigan, specializing in geometry and topology. • Damian Beil is an Associate Professor of Technology and Operations at University of Michigan. • Mike Carlisle is an Assistant Professor of Mathematics at CUNY. • Aaron Hillegrass is the founder and chief learning officer at Big Nerd Ranch, a technology company that trains developers on mobile technology and consults brands like Procter & Gamble, AT&T, Microsoft, Google, GE, Delta and Boeing. Hillegrass is also the author of iOS Programming: The Big Nerd Ranch Guide and Cocoa Programming for Mac OS X. • Nate Chandler is a software engineer at Big Nerd Ranch. • Meike Niederhausen is a Professor of Mathematics at the University of Portland. • Michael CatalanoJohnson is an Assistant Professor of Mathematics at Swarthmore College. • Donald Goldberg is Dean of Mathematical Sciences at El Camino College. • Allan Jaworski is a chief architect with Lockheed Martin Mission Systems. • Amie Bowles received her M.S. in mathematics from the University of Texas, Austin, and is currently a math professor at Northwest Florida State College. • William Kaufmann is a vice president with Goldman Sachs. • William Navidi is an Associate Professor of Biostatics at USC. • Ziva Myers gradauted from New College in 2011 and is currently attending graduate school in mathematics at Bryn Mawr. • Indra Shotland graduated from New College in 2010 and is currently attending graduate school in mathematics at Michigan State University. • Cody Gunton graduated from New College in 2012 and is currently attending graduate school in mathematics at University of Arizona. Sample of Graduate Schools Attended by NCF Students in Mathematics


Each academic experience builds toward your senior thesis project. It’s required for graduation, and our students tell us that while it’s demanding, it’s also one of the most rewarding experiences of their lives. Here are some recent thesis projects in Mathematics:
“A BostConnes System for Qp” by Cody Gunton “Fan Blowup of Analytic Surgery Spaces” by Brian Stanwyck “Reidemeister Torsion and the Classification of ThreeDimentional Lens Spaces” by Katherine Raoux “Sudoku Scheming: Am Algebraic Combinatorial Approach to Discovering Properties of Sudoku Graphs using Association Schemes” by Ziva Myer “Dynamics of an Analogue of the Quadratic Family on Su (2)” by John Anthony Emanuello “Hyperbolic Structures On Weave Complements” by Indra Shottland “Local Algebraic Invariant Statistics for a Heuristic to Compare Phylogenetic Trees” by Ian Haywood “A Natural Isomorphism from the Ordered Homology to the Oriented Homology of an Injective Set” by Nathaniel Chandler “OneDimensional Cellular Automata: Pascal’s Triangle and an Extension of Rule 90 for a NonAbelian Group” by Erin Craig “The Gröbner Annihilator Graph of a Ring” by Trevor McGuire “An Evolutionary Model for the Stable Marriage Problem” by Sarah Rose Karr “Fun with Elliptic Curves” by Lisa Bromberg “Cyclic Covering Spaces of Knot Complements” by Mark Flanagan “Red Tide and Mathematical Modeling” by Lance Price “Compiling Imperative and Functional Languages” by Jeremy W. Sherman “Outer Approximation of the Spectrum of a Fractal Laplacian” by Stacey Goff “Mixture Model of Mutagenetic Trees and Application in Evolutionary Biology” by Guangming Lang “The Stable Matching Problem*: Graphs and Competition a Preference Oriented Exploration of the Stable Matching Problem” by David Tanner “Optimizing Covertimes with Constraints” by Ryan Compton “Impact of Redundant Data on Evolution of Neural Networks” by Joshua Burroughs “Faithfulness Properties of the Burau Representation” by Caleb Hussey “Structural Comparison of Executables with Graph Isomorphisms” by Rolf Rolles “Adventures and Misadventures in Riemannian Geometry: Curvature Comparisons for Surfaces of Revolution” by Jake Silverstein “A Centralizer, Algebra Approach to Computing the Chromatic Polynomial” by Alexander Wires “From Homotopy to Homology through Pictures” by Eliza A. Khuner “Artificial Neural Network Approach to Eye Color Forecasting” by Kalin Ranov “Optimal Behavior of Contrite TitforTat Under Infinitesimal Rate of Error” by Timothy Teravainen “The Nonrelativistic Limit of Fermionic Operators with Lorentz Violation” by Homer F. Wolfe “Double Bubbles in Spaces of Constant Curvature” by Joseph A. Corneli “Using Homotopy Groups to Detect Topological Defects with Applications to a LoentzViolating Theory” by Selena Lee “Differential Geometry of Manifolds, the GaussBonnet Theorem, and Polygonal Approximations” by Amie Bowles “Designs and Codes in Odd Graphs” by Michael Cenzer “Stock Option Pricing: From Binomial to BlackScholes and (Slightly) Beyond” byMichael Carlisle “Mycroft: An Automated Predicate Logic Theorem Prover” by Austin Eliazar “On Integer Flows in Cayley Graphs: Excursions in Tutte’s 3edgecoloring Conjecture” by Scott Moser “Average Exit Time Moments of Geometric Graphs with Boundary” by Robert Meyers “Modeling Microtubule Dynamics” by Jake Byrnes “Percolation on a Random Tree” by Douglas Wahl “Optimal Transitional Labelings of Graphs: A Polarization Approach” by Andrea Saunders “Coping with a Curvy Cosmos: General Relativity, the LIGO Project, and Combinatorics” by Gilliss Dyer


The Mathematics program at New College of Florida has built a strong sense of community. Our Math Reading Room provides a place for faculty and students to gather and do mathematics together. This large seminar/study room is used for an active schedule of seminars, presentations, workshops, problem sessions, tutoring and discussions. The Math Reading Room is equipped with a computer that supports many different types of software (Mathematica, Maple, Illustrator and others) and provides Internet access. Beginning and advanced laboratories are equipped with a variety of microcomputers with additional workspace for upperlevel students. Recent additions in the areas of Computational Science and Applied Mathematics complement the theoretical areas of algebra, geometry, topology, analysis and theoretical computer science, allowing the faculty to offer a variety of courses and tutorials to challenge students with different backgrounds. The Quantitative Resource Center (QRC) is dedicated to aiding the New College community in working with quantitative matters. The QRC staff provide individual and small group peer tutoring for students needing assistance with various quantitative methods such as basic mathematics and statistics, SAS, SPSS, Excel and others applications. The Mathematics Seminar has been a longstanding tradition — an open forum for students of all levels interested in mathematics. The purpose of the seminar is to cover interesting or advanced topics in mathematics. Students may present talks about their research or an internship or tutorial experience. The seminar helps students learn how to research literature and use databases to explore topics as diverse as the mathematics of Soduko to the Google Matrix and more. Community Service — Each spring our students offer a free Math Clinic at Sarasota’s downtown Selby Public Library. Tutoring is available to all ages on the second level of the library at 1331 First Street, Sarasota, Florida. Students offer free math lessons and advice to people of all ages in Sarasota and Manatee counties to help them sharpen their math skills. The program is particularly popular among area middle school and high school students who need help with algebra, geometry and calculus. The Math Clinic was created by New College Professor of Mathematics Eirini Poimenidou in the late 1990s. The clinic is open to anyone with mathrelated questions, seeking to overcome a math phobia, looking to return to school but in need of a math refresher, or interested in discussing mathematical topics with fellow enthusiasts. You can also get involved in Math Day cosponsored by New College and local high schools. 

