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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.
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.
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.
Advanced Writing. 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.
Internship Experiences recognize that learning can take place outside the classroom. Carroll College allows its students to participate in opportunities that relate to their area of study. This opportunity must relate directly a student's program of study in order to qualify for an internship. Close cooperation among Carroll and the participating organizations ensures an experience that contributes significantly to the student's overall growth and professional development. Juniors and seniors in any major area may participate with the approval of faculty internship advisor and/or department chair, Career Services, and a site supervisor. Students will receive academic credit and may or may not receive monetary compensation for an internship. A student may apply a maximum of 12 semester hours to degree requirements; academic departments will determine the number of credits that may count toward the major (most majors accept 6 hours total). Enrollment in the course must be during the same semester in which the experience takes place. Interested students should contact their academic advisor and Career Services prior to the start of an experience.
This course in the history of mathematics is intended to give students an insight into some of the great masterpieces of mathematics, as seen in their historical contexts. Developing an understanding of the individuals who were the creators of mathematics helps one better appreciate their creations.
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.
Special Topics courses include ad-hoc courses on various selected topics that are not part of the regular curriculum, however they may still fulfill certain curricular requirements. Special topics courses are offered at the discretion of each department and will be published as part of the semester course schedule - view available sections for more information. Questions about special topics classes can be directed to the instructor or department chair.
Advanced Writing. 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.