Students develop expertise in applied mathematics, and supplement math courses with courses in other fields. Biology, chemistry, computer science, and engineering are integrated with mathematic theory. Majors go on to attend graduate schools like MIT, Notre Dame, and Carnegie Mellon, and have successful careers in business, science, government, engineering and education. Carroll teams have placed as "Outstanding" (the top 1%) three times in the international Interdisciplinary Contest in Modeling in the past nine years.
Quantitative Analysis. An extension of MA 201 into geometry, measurement, set theory, and statistics. The course focuses on both mathematical content and methods for teaching geometry and statistics. There is a particular focus on visual models and children's mathematical thinking at the elementary school level.
This is a one-credit, pass/fail, seminar-style course. There will be three main segments: select a faculty director for either an honors thesis or a senior project and write a research proposal, write a resume and research job opportunities, and write a graduate school essay and research graduate school opportunities. The overall goal of this course is to prepare students for their senior year and beyond. This course should be taken in the spring of the year before intended graduation (typically in the spring of the junior year).
This course is an introduction to numerical methods and MATLAB programming. We focus not just on how numerical methods work, but when they are appropriate, where they fail, and how to interpret their results. Specific topics vary by instructor but will be chosen from roundoff and truncation errors, root-finding methods, numerical methods for linear algebra, least squares regression methods, interpolation, numerical integration and differentiation, and numerical algorithms for solving ordinary and partial differential equations. Students will learn to write functions in MATLAB using looping and control statements. This is a writing intensive course and students will complete several coding and writing intensive projects throughout the semester.
A comprehensive study of elementary functions to prepare students for a college course in calculus. Topics include a review of intermediate algebra including the solution of equations and inequalities, and an in-depth look at functions, inverse functions, their graphs, symmetries, asymptotes, intercepts, and transformations. Linear, polynomial, rational, radical, exponential, logarithmic, and trigonometric functions are studied, and graphing calculators are used extensively.
Advanced Differential Equations and Linear Algebra. This is the second course (after MA 141) in a two course sequence in differential equations and linear algebra. In this course, we focus on both systems of differential equations, with special attention given to modeling, linearization, and equilibrium analysis; as well as the mathematical language of systems-linear algebra, especially transformations, orthogonality, vector spaces, inner product spaces and the eigenvalue/eigenvector problem. We will motivate the material through applications such as population models, structural, and electrical systems, and linear algebra applications such as 3-D imaging, Markov processes, and Leslie matrices. Technology will again play a major role in this course, as we will have frequent computer demonstrations in class and weekly computer labs to explore the quantitative aspects of these topics. Students will have the opportunity to explore topics beyond the textbook on group projects throughout the semester.
This course is an introduction to difference equations, differential equations, and linear algebra. Specific topics include analytical and numerical solutions to difference equations and first-order linear differential equations, phase line analysis, stability of equilibrium, matrix equations and eigenvalues. We emphasize how this mathematics can be used on many real-world problems such as how to predict the spread of a disease, how a home mortgage works, and how to understand the growth of animal populations. We use computers and calculators extensively, meeting in the computer lab once each week. We also focus on learning how to explain mathematics verbally and in writing.
Cultural Diversity. This three-credit course will look at the role that energy plays in our modern world. Students will learn about the physics of energy so that they can calculate the energy content of a variety of systems, such as: gasoline, other fossil fuels, nuclear, solar, wind, bio mass and so on. Applications of the energy schemes in our lives will then be explored. We will discuss the global use and needs of energy and the environmental problems that have resulted from energy development and how we can improve our community and the world. Three hours of lecture and field trips per week.
This course covers the calculus of functions of a single complex variable. We will follow the traditional development of calculus of a single real variable, but we will discover the beauty that naturally arises when allowing the domains and ranges of functions to be subsets of the complex numbers. The topics covered are: complex numbers, limits, differentiation, Cauchy-Riemann equations, harmonic functions, elementary functions, conformal mapping, contour integrals, Cauchy integral representation, power series, and residues. Attention will be given to theoretical, computational, geometric, and applied problems. As such, students will be expected to prove theorems and to use a variety of tools to solve problems.
Why does calculus work? In this course, we study real numbers, sequences, and functions, in order to develop the logical foundations for calculus. What does it mean to say that a function has a particular limit? What does it mean for a function to be continuous? We learn to create the mathematical proofs that make up the logical structure behind the limits, derivatives, infinite series, and integrals of calculus.