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Course Criteria
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3.00 Credits
Students, in consultation with a faculty advisor, individually design and plan a course of study or research not offered in the curriculum. Course work includes a reflective component, evaluation, and completion of an agreed-upon product. Sponsorship by a faculty member in the program/department, a course prospectus, and permission of the chair are required. Students may register for no more than one independent study during a Short Term. Normally offered every year. Staff.
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3.00 Credits
Mathematical models are increasingly important throughout the life sciences. This course provides an introduction to deterministic and statistical models in biology. Examples are chosen from a variety of biological and medical fields such as ecology, molecular evolution, and infectious disease. Computers are used extensively for modeling and for analyzing data. Prerequisite(s): Mathematics 105. Not open to students who have received credit for Biology/Mathematics 155. Not open to students who have received credit for BI/MA 155. Open to first-year students. Enrollment limited to 30. B. Shulman.
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3.00 Credits
Optimal control theory unifies numerous economic problems related to the creation and use of physical capital. This course introduces optimal control theory as a tool for dynamic optimization and applies that theory to a variety of classic economic problems involving capital. Among the economic problems examined are optimal use of a renewable resource, optimal use of a nonrenewable resource, and optimal economic growth when growth begets pollution. The course includes formally proving Pontryagin's maximum principle, which characterizes dynamic optima, in the special case context of common economic problems. Prerequisite(s): Mathematics 206 and one economics course. M. Murray.
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3.00 Credits
Techniques for analyzing data are described in ordinary English without emphasis on mathematical formulas. The course focuses on graphical and descriptive techniques for summarizing data, design of experiments, sampling, analyzing relationships, statistical models, and statistical inference. Applications are drawn from everyday life: drug testing, legal discrimination cases, and public opinion polling. Not open to students who have received credit for Biology 244, Economics 250 or 255, Environmental Studies 181, Mathematics 215 or 315, Psychology 218, or Sociology 305. Enrollment limited to 30. [Q] Normally offered every year. B. Shulman.
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3.00 Credits
While the word calculus originally meant any method of calculating, it has come to refer more specifically to the fundamental ideas of differentiation and integration that were first developed in the seventeenth century. The subject's early development was intimately connected with understanding rates of change within the context of the physical sciences. Nonetheless, it has proven to be widely applicable throughout the natural sciences and some social sciences, as well as crucial to the development of most modern technology. This course develops the key notions of derivatives and integrals and their interrelationship, as well as applications. An emphasis is placed on conceptual understanding and interpretation, as well as on calculational skills. Graphing calculators are used in the course. Students are required to attend approximately six additional 50-minute laboratory sessions at times to be arranged. Students must read the mathematics department calculus FAQs before registering ( http://abacus.bates.edu/acad/depts/math/faq.html). Enrollment limited to 25 per section. [Q] Normally offered every semester. A. Salerno, D. Haines, S. Ross, M. Greer.
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3.00 Credits
A continuation of Calculus I. Further techniques of integration, both symbolic and numerical, are studied. The course then treats applications of integration to problems drawn from fields such as physics, biology, chemistry, economics, and probability. Differential equations and their applications are also introduced, as well as approximation techniques and Taylor series. Graphing calculators are used in the course. Students are required to attend approximately six additional 50-minute laboratory sessions at times to be arranged. Recommended background: Math 105 or equivalent. Students must read the mathematics department calculus FAQs before registering ( http://abacus.bates.edu/acad/depts/math/faq.html). Enrollment limited to 25 per section. [Q] Normally offered every semester. D. Haines, Staff.
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3.00 Credits
Is mathematics composed of impenetrable formulas to be memorized, a series of insurmountable cliffs to be scaled Are there individuals who can think logically and creatively, but never "do math" In this course, students are asked to use their imagination to grapple with challenging mathematical concepts. The process enables them to master techniques of effective thinking, experience the joy of discovering new ideas, and feel the power of figuring out things on their own. Together they contemplate some of the greatest and most intriguing creations of human thought, from Pythagoras to the fourth dimension, from chaos to symmetry. Enrollment limited to 30. [Q] Normally offered every year. G. Coulombe.
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3.00 Credits
How could we count if we had no numbers The Incas used quipus as a sophisticated counting device to keep tally in the absence of a written number system. Mathematical ideas arise in many different cultural and historical contexts. Many of these ideas can be recast using contemporary Western mathematical theory. For example, Sona drawings of the Chokwe people of South Central Africa can be understood using graph theory. In this course students investigate selected cultural activities and practices (e.g., kin relations, symmetries in art, counting devices) as a way to explore contemporary mathematical topics (e.g., group theory, geometry, number systems). G. Coulombe.
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3.00 Credits
Vectors and matrices are introduced as devices for the solution of systems of linear equations with many variables. Although these objects can be viewed simply as algebraic tools, they are better understood by applying geometric insight from two and three dimensions. This leads to an understanding of higher dimensional spaces and to the abstract concept of a vector space. Other topics include orthogonality, linear transformations, determinants, and eigenvectors. This course should be particularly useful to students majoring in any of the natural sciences or economics. Prerequisite(s): Mathematics 105, 106, or 155. Open to first-year students. Enrollment limited to 25 per section. Normally offered every semester. S. Ross, P. Jayawant.
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3.00 Credits
This course extends the ideas of Calculus I and II to deal with functions of more than one variable. Because of the multidimensional setting, essential use is made of the language of linear algebra. While calculations make straightforward use of the techniques of single-variable calculus, more effort must be spent in developing a conceptual framework for understanding curves and surfaces in higher-dimensional spaces. Topics include partial derivatives, derivatives of vector-valued functions, vector fields, integration over regions in the plane and three-space, and integration on curves and surfaces. This course should be particularly useful to students majoring in any of the natural sciences or economics. Prerequisite(s): Mathematics 106 and 205. Open to first-year students. Normally offered every semester. Staff.
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