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.
This is the second of a two-semester, six-credit calculus sequence. In this course we study topics in integral calculus, emphasizing how we can use calculus to understand real-world problems such as fluid pumping and lifting, how rain catchers are used in city drain systems, and how a compound bow fires an arrow. Specific topics include optimization, related rates, antiderivatives, definite integrals, the fundamental theorems of calculus, integration by substitution, integration by parts, applications of integration, and an introduction to differential equations. We use technology extensively, and we also focus on learning how to explain mathematics orally and in writing. The sequence MA 121-MA 122 is considered to be equivalent to MA 131.
Independent study is open to junior and senior students only. At the time of application, a student must have earned a 3.0 cumulative grade point average. A student may register for no more than three (3) semester hours of independent study in any one term. In all cases, registration for independent study must be approved by the appropriate department chairperson and the Vice President for Academic Affairs.
The senior thesis is designed to encourage creative thinking and to stimulate individual research. A student may undertake a thesis in an area in which s/he has the necessary background. Ordinarily a thesis topic is chosen in the student's major or minor. It is also possible to choose an interdisciplinary topic. Interested students should decide upon a thesis topic as early as possible in the junior year so that adequate attention may be given to the project. In order to be eligible to apply to write a thesis, a student must have achieved a cumulative grade point average of at least 3.25 based upon all courses attempted at Carroll College. The thesis committee consists of a director and two readers. The thesis director is a full-time Carroll College faculty member from the student's major discipline or approved by the department chair of the student's major. At least one reader must be from outside the student's major. The thesis director and the appropriate department chair must approve all readers. The thesis committee should assist and mentor the student during the entire project. For any projects involving human participants, each student and his or her director must follow the guidelines published by the Institutional Review Board (IRB). Students must submit a copy of their IRB approval letter with their thesis application. As part of the IRB approval process, each student and his or her director must also complete training by the National Cancer Institute Protection of Human Participants. The thesis is typically to be completed for three (3) credits in the discipline that best matches the content of the thesis. Departments with a designated thesis research/writing course may award credits differently with approval of the Curriculum Committee. If the thesis credits exceed the full-time tuition credit limit for students, the charge for additional credits will be waived. Applications and further information are available in the Registrar's Office.
In this course, each student will complete an independent research project in mathematics under the direction of a faculty member who will serve as the project director. The student and the project director will work together to select a topic that is of interest to the student, and at the end of the project the student will complete a written report and an illustrated presentation of the work involved.
A course primarily for prospective elementary teachers, designed to build a background in number and operations with a particular focus on visual models for whole numbers, fractions, and early algebraic reasoning. The course focuses on both mathematical content and methods for teaching number and operations. There is a particular focus on current curriculum and children's mathematical thinking at the elementary school level.
Quantitative Analysis. Introductory college mathematics course in finite difference equations and linear algebra. Topics include sequences, differences, linear and nonlinear difference equations, systems of difference equations, numerical solutions of linear and nonlinear equations, and analytical techniques for solving linear systems using linear algebra. Applications from many fields are studied and the role of mathematical modeling is a central focus. Formal computer labs are a part of the course each week, with spreadsheets being the primary software employed. This course satisfies a Carroll College Core Curriculum for all students and the mathematics requirement for business majors.
This course covers the traditional topics from abstract algebra, including groups, rings, integral domains, fields, and homomorphic and isomorphic relationships, as well as standard topics from geometry, including axiomatic systems in both Euclidean and Non-Euclidean geometrics and transformational geometry with vectors and matrices. The focus for the class is the contemporary applications of the concepts presented, together with the weaving together of geometric and algebraic themes. Linear algebra is the integrating theme.
Quantitative Analysis. The basic concepts used in statistics such as measures of central tendency, variation, and probability distributions, and statistical inference are stressed. Applications are made in the social, communication, health, biological, and physical sciences. This course does not count toward a major or minor in mathematics, nor does it count toward the math requirement for biology majors.
This course is a project-based exploration of topics in optimization and simulation. Topics vary by instructor but typically include linear, integer, binary, and nonlinear programming, stochastic processes, some network optimization, and the Analytic Hierarchy Process. We explore the modeling, algorithmic and heuristic solution approaches to, and sensitivity analysis of problems such as the simplex method, scheduling problems, resource allocation problems, the Knapsack problem, Traveling Salesman problem, and ranking problems. Computers and technology will again play an important role as we investigate both the implementation and the theoretical basis of solution techniques. This course will bring together topics from single and multivariable calculus, linear algebra, and probability.
Modern Applications of Discrete Mathematics. A look at some applications of discrete mathematics that emphasize such unifying themes as mathematical reasoning, proof, algorithmic thinking, modeling, combinatorial analysis, graph theory, and the use of technology. Possible topics include proof techniques, cryptography, primes and factoring, computer passwords, networking problems, shortest paths, scheduling problems, building circuits, and modeling computation.