In the 2009-2010 academic year, the Mathematics Department will begin offering 3 one-credit courses. The courses will each meet once per week and, as noted, carry one credit. These courses will not count as electives for the purpose of the mathematics electives for a mathematics major or minor. Neither will they count as courses for the 38-course requirement for graduation from Boston College. Rather, these should be seen as enrichment courses for mathematics majors or interested students in other disciplines.
| MT370 Applications of Abstract Algebra (Fall 2009: 1) |
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Prerequisite: MT 310 This course is open to all majors who have had MT 310. The immediate goal is to present some topics that extend and apply the subject matter of 310. At the same time, students may gain a deeper understanding of groups and rings that they only imperfectly understood the first time around. A secondary goal is for students to appreciate that the abstract concepts learned in 310 can have relevance to the outside world; for example, cryptography as applied to modern communications, or concepts from algebra and number theory that may be taught in the high school classroon. |
| MT371 Proof and Truth in Mathematics (Fall 2009: 1) |
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Prerequisite: MT 216 Can mathematical truths be deduced from a set of first principles or axioms? The wide use of axioms in mathematics shows that many can, but what can be proven falls short of all mathematical truths and even of all truths in the theory of numbers. This course will explore what is known about the limitations of the axiomatic method and computation as they relate to the discovery of mathematical truth, and will include Godel's incompleteness theorems. |
| MT372 Introduction to Mathematical Problem Solving with Mathematica (Fall 2009: 1) |
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Prerequisite: MT 210 or MT 305. May be taken concurrently. The purpose of this course is to give a directed introduction to Mathematica (Wolfram Research, Inc.), to allow students to apply this powerful tool in such courses as mathematical modeling, ordinary and partial differential equations, dynamical systems, probability theory, and mathematical statistics. Topics include computer algebra, 2D/3D graphics, and the calculus and simulation capabilities of Mathematica. |
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MT373 Numbers, Notations, and Recreations (Spring 2010: 1) |
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Prerequisite: MT 216. This one-credit course applies the introductory abstract mathematics of MT 216 to parts of the secondary mathematics curriculum, in particular topics related to numbers systems and notations, and recreational math problems in these areas. Many examples which are directly useful in secondary mathematics will be included, and we will use ideas from MT 216 to explain and generalize them. Specific topics include applications of modular arithmetic; decimal notation (and other bases) for integers, rationals, and reals; complex numbers; Fibonacci numbers and similar sequences; binomial coefficients and their applications. |
| MT374 Pedagogical Lab associated with MT 320 (Spring 2010: 1) |
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Prerequisite: MT 320. May be taken concurrently. This one-credit course is designed for our current or previous MT 320 (Introduction to Analysis) students that are interested in teaching high school mathematics. The pedagogical lab will emphasize how to apply those abstract theories from MT 320 to the teaching of high school pre-calculus and calculus. We will also discuss various issues involved in the teaching of these courses, such as reformed curriculums, common misconceptions, and mistakes in the understanding of these materials. |