Applied Mathematics at New College is both challenging and exciting. Working closely with faculty, you will have the chance not only to learn advanced mathematical methods but also to individually tailor your academic program to match your unique interests and needs. And well before graduation, you will be able to work on advanced material that students often encounter only in master's programs, thus giving you an advantage when it comes to graduate school and future employment.
Compared to other Areas of Concentration (AOCs) at New College, Applied Mathematics is relatively new. While this dynamic and fast-growing field once had a heavy emphasis on physics, today at New College and around the world it combines the use of advanced mathematical methods in seeking answers to complex problems in the biological sciences, engineering and industry.
As an Applied Mathematics AOC student at New College, you’ll have the opportunity to work side by side with faculty who work in broad areas of applied and pure mathematics including game theory, algorithms, bioinformatics, combinatorics, partial differential equations, fluid dynamics, mathematical biology and scientific computing. You’ll also have the opportunity to take mathematics courses that are not typically taught at the undergraduate level, such as Mathematical Modeling and Systems Biology. These courses better prepare our students for graduate studies, an area in which we have excellent placement success. They also provide a unique opportunity for those who want to pursue jobs in highly demanded fields such as computational biology, bioinformatics and systems biology.
For instance, one of New College’s professors in Applied Mathematics conducts research on mathematical modeling of biological systems with a focus on regulatory biochemical networks. He collaborates with faculty at other universities to create models and shares his findings and research opportunities with his students. These are the sort of opportunities you will not find available at other leading liberal arts colleges.
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. New College also opens doors for students to network and pursue research and internships off campus. Since 2007, our faculty and students have been working with Lovelace Respiratory Research Institute (LRRI), one of the country’s leading biomedical research organizations, to establish a joint bioinformatics partnership to provide faculty and students research opportunities in a wide assortment of emerging fields within the discipline. The quality of our math programs has resulted in a number of students receiving prestigious National Science Foundation (NSF) REU grants in recent years. Others have participated in internships with a host of other local and regional business partners associated with New College.
Although young, our Applied Math AOC has seen impressive results when it comes to graduate school and career success. Students from the program have gone on to attend master’s and Ph.D. programs at some of the nation’s top graduate schools, including Princeton, Stanford, UC-Berkeley and the University of Chicago. From there, they have become college professors, math teachers, financial analysts, research assistants, and a host of other careers where they can use their advanced math and analytical skills.
Many New College students pursue an Applied Mathematics AOC all on its own, while others combine the major with studies in Biology, Physics and other concentrations in what we call a “slash” degree. Your faculty advisor can assist you in determining which path is best for your special interests and goals.
The (minimal) course work for a slash degree in Applied Mathematics includes the following:
A course in Programming is also recommended.
In addition to the coursework listed above, the (minimal) course work for a stand-alone major in Applied Mathematics includes the following:
• A course in programming
• Advanced Linear Algebra
• Partial Differential Equations
A course in Complex Analysis is also highly recommended.
Other requirements for the major include:
• A two-semester introductory sequence (or two semesters of more advanced material) in either Biology, Chemistry or Physics
• Three semesters of Math Seminar
• A senior thesis involving Applied Mathematics
For detailed requirements, check out our General Catalog.
Here’s a list of recent course offerings in Applied Mathematics:
Calculus is a means for calculating the rate of change of a quantity which varies with time and the total accumulation of the quantity whose rate of change varies with time. Although calculus is only about three centuries old, calculus ideas are the basis for most modern applications of mathematics, especially those underlying our technology. The development of the calculus is one of the great intellectual achievements of Western civilization. A balance will be struck between presenting calculus as a collection of techniques for computation, and as a handful of difficult but very powerful concepts. Wherever possible, we will motivate the ideas as ways of answering questions about real world problems. Prerequisites: Complete the math placement exam.
This course takes up where Calculus I leaves off. The topics covered include integration techniques, sequences, series, Taylor series, complex numbers, areas and volumes. This course is recommended for students pursuing interests in the physical sciences, applied mathematics and economics. Prerequisite: Calculus I and instructor’s permission.
This class is a continuation of Calculus I and II. We will cover the calculus in n-dimensional Euclidean space. The topics covered during the course of the semester include the fundamental constructions of the calculus of multivariable functions (vector fields, gradients, line integrals, surface integrals etc) and the associated fundamental results (Green’s Theorems, Gauss’ Theorem, Stokes’ Theorem, etc). The course will focus on application and computation and will include an introduction to differential equations. Prerequisite: Calculus II.
This course is an introduction to the theory of vector spaces and linear transformations and to their representation by means of matrices. The topics that will be covered are: matrices and linear systems of equations, algebra of matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, matrix diagonalization, and inner product spaces. Prerequisites: Calculus or the consent of instructor.
Mathematical Modeling I
Mathematical modeling plays a central role in understanding of complex systems that are changing in time. Such systems are called dynamical systems. This course is designed to introduce students to the elements of dynamical systems. Both continuous and discrete systems will be covered. In the course of the term, students will come to understand how mathematical models are formulated, and how their short and long term behaviors can be uncovered through a combination of analysis and computer simulation. Qualitative, quantitative and graphical techniques will be used to analyze and understand mathematical models and to compare theoretical predictions with available data. Mathematical concepts of steady states, cycles and chaos will be introduced. Examples will be given from physics, biology, chemistry and economics. Prerequisites: Calculus and differential equations (or the approval of instructor).
Introduction to Numerical Methods
This is a survey course of the basic numerical methods which are used to solve practical scientific problems. Important concepts such as accuracy, stability, and efficiency and convergence are discussed. The course provides an introduction to MATLAB, an interactive program for numerical linear algebra. Objectives of the course: Develop numerical methods for approximately solving problems from continuous mathematics on the computer. Examine the accuracy, stability, and failure modes of these methods. Implement these methods in a computer language MATLAB. Prerequisites: Calculus and Differential Equations.
Ordinary Differential Equations
Familiarity with the material covered in a first course in differential equations is essential for those interested in advanced work in pure and applied mathematics. Topics covered during the semester include; first order equations, second order linear equations, series solutions, Laplace transform, systems of first order linear equations, qualitative properties of nonlinear equations, boundary value problems and Sturm-Liouville theory. Prerequisites: Calculus II.
Introduction to Programming in Python
This course is an interdisciplinary introduction to Programming in Python. It satisfies LAC curriculum requirements. The course introduces students to the most important programming concepts such as algorithms, sequences, selections, loops, functions, methods, numeric and string types, file processing, collections, classes and object-oriented programming, and recursion. This course serves as an informal prerequisite for many science classes which require programming. Students enrolled in this course MUST also attend the mandatory workshop. Prerequisites: The course is at the introductory – freshman level. It has no prerequisites and no prior programming experience is assumed. However, it requires a large time commitment and the ability to work with computers for extended periods of time.
Advanced Linear Algebra
Linear algebra is a critical mathematical tool in all of the sciences. Therefore, an in-depth knowledge of linear algebra is useful not only to mathematicians, but also to any scientist using mathematics. Topics to be covered include a review of basic linear algebra, the Moore-Penrose Pseudoinverse, singular value decompositions, generalizations of matrix equations, projections and inner products, least squares problems, Jordan canonical form, linear differential equations and the matrix exponential, and difference equations. Prerequisite: Linear Algebra or permission of the instructor.
Partial Differential Equations
This course is designed to prepare students for advanced work in geometry and mathematical physics by developing the knowledge of partial differential equations common to both topics. Topics covered during the semester include: Laplace equations, wave equations, heat equations, Hamilton-Jacobi equations, Fourier theory, and the theory of distributions. Prerequisites: Calculus III and Ordinary Differential Equations.
The course will consist of two parts. In the first part, we will begin by studying discrete spaces and simple games of chance. We will introduce and study the basic notions of probability including random variables, distribution, expectation, and variance. We will study continuous distributions as they relate to approximations of various discrete objects. In the second part of the course we will use our knowledge of simple games of chance to construct discrete models of simple physical systems. The models and the ideas behind their construction have found applications in many different areas (Physics, Chemistry, Biology, Economics, etc.). Time permitting; we will study several such examples in detail. Prerequisite: Calculus.
Complex numbers were introduced in the study of the roots of polynomial equations and have found applications in nearly every branch of modern mathematics. This course will develop the notion of a function of a complex variable and the corresponding calculus. The theorems and applications to be discussed are some of the most beautiful results of modern mathematics. Topics for the course include analytic functions, complex integration and the Cauchy integral formula, series representations, residues, the Dirichlet problem, and conformal mappings. Prerequisites: Real Analysis I or permission of instructor.
For a complete list of courses, click here.
William P. Thurston (1946-2012) was a world-renowned 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.
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, UC-Berkeley, UC-Davis and Cornell.
“Before Thurston, no one would have looked at a knot, and asked what the volume of the space outside it was,” O’Shea said. “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.”
New College is proud of the many Applied Mathematics graduates who have contributed to the field. Here’s a sampling of some of our graduates:
Sample of Graduate Schools Attended by NCF Students in Applied 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 thesis projects in Applied Mathematics:
“Mathematical Modeling of Pacific Pink Salmon (Oncorhynchus Gorbuscha) Population Dynamics” by Tania Harrison
“Guerrilla Clusters for Science: The Application of Genetic Algorithms to Spectroscopy” by Noah Henry Anderson
“Identifying Melanoma Using Computer Vision and an Artificial Neural Network” by Hannah Rivers
“Mathmatical Modeling and Optimal Experimental Design in Systems Biology” by Jonathan Statz
“Dancing Under the Moonlight: A Mathematecal Modeling Approach to Foraging Octracod” by John Correa
“Agricultural Modeling: Predicting the effects of genetic coefficients on maize yield in waterlimiting environments” by Anne Amelia Farrell
“Emprical Estimation of Asian Import Demand Functions: An Implication of Thirlwall’s Law for Developing Nations” by Preston Bebas
“Spatial Analysis of Octopus Dens and Predation” by Elizabeth Alene Hamman
“Local Algebraic Invariant Statistics for a Heuristic to Compare Phylogenetic Trees” by Ian Haywood
“Variations on a Theme: Brachistochrones Revisited” by Mark Kot
The Jane Bancroft Cook Library at New College is home to a broad assortment of books, scholarly journals, national and international databases, and other print and electronic media related to Applied Mathematics and is available to students throughout the year.
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The Mathematics program at New College of Florida has built a strong sense of community, including the following on and off-campus resources and opportunities for students:
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 upper-level 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 other 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 Sudoku 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 math-related 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 co-sponsored by New College and local high schools.