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Course Criteria
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3.00 Credits
This course studies geometric concepts in Euclidean and non-Euclidean geometries. Topics include isometries, arc lengths, curvature of curves and surfaces, and tessellations, especially frieze and wallpaper patterns. Prerequisite(s): Mathematics 206. P. Wong.
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3.00 Credits
The notion of "closeness" underlies many important mathematical concepts, such as limits and continuity. Topology is the careful study of what this notion means in abstract spaces, leading to a thorough understanding of continuous mappings and the properties of spaces that they preserve. Topics include metric spaces, topological spaces, continuity, compactness, and connectedness. Continued development of good mathematical writing and/or a presentation is a major component of this course. Prerequisite(s): Mathematics 206 and s21. [W2] S. Ross.
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3.00 Credits
Computational mathematics considers how computing can aid the study of mathematics. Computers may be used to perform numerical calculations involved in modeling, provide graphical understanding in analysis, or complete symbolic calculations in algebra. Mathematical study of computer algorithms can lead to more efficient algorithms and actual implementation of algorithms helps student deepen their understanding of mathematics while gaining appreciation for computers' capabilities as well as deficiencies. Normally offered every year.
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3.00 Credits
This course studies the best ways to perform calculations that have already been developed in other mathematics courses. For instance, if a computer is to be used to approximate the value of an integral, one must understand both how quickly an algorithm can produce a result and how trustworthy that result is. While students implement algorithms on computers, the focus of the course is the mathematics behind the algorithms. Topics may include interpolation techniques, approximation of functions, solving equations, differentiation and integration, solution of differential equations, iterative solutions of linear systems, and eigenvalues and eigenvectors. Prerequisite(s): Mathematics 106 and 205. Not open to students who have received credit for Mathematics 218. [Q] Staff.
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3.00 Credits
Finding a path with certain characteristics (such as the shortest path between two locations) is important in many applications such as communications networks, design of integrated circuits, and airline scheduling. Graph theory is the branch of mathematics that provides the framework to find these paths. Topics may include definitions and properties of graphs and trees, Euler and Hamiltonian circuits, shortest paths, minimal spanning trees, network flows, and graph coloring. Some of the class meetings are devoted to learning to program in Maple. Students implement one or more of the path algorithms in a computer program at the end of the semester. Prerequisite(s): Mathematics s21. Not open to students who have received credit for Mathematics 365D. Enrollment limited to 30. P. Jayawant.
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3.00 Credits
The computational and representational power of computers has had a great impact on mathematics. In this course students use the functional programming language Scheme to represent mathematical ideas and construct computational solutions to abstract mathematical problems. Topics may include: logic; orders of growth; representation of and arithmetic on number systems; testing integers for primality; representation of abstract structures such as sets, groups, and graphs; symbolic operations from calculus; algebra of polynomials, rational functions, and matrices; representation of geometric figures; random number generators; noncomputable problems; and representation of the infinite. Prerequisite(s): any two mathematics courses or Short Term courses. Not open to students who have received credit for Mathematics 365E. [W2] D. Haines.
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3.00 Credits
The study of long-term behaviors of feedback processes, dynamical systems is best understood from both theoretical and computational viewpoints, as each informs the other. Students explore attracting and repelling cycles and witness the complicated dynamics and chaos a simple quadratic function can exhibit. Real and complex functions are considered. Simultaneously, students learn sound computer science fundamentals by writing Visual Basic programs that illustrate the theory of dynamical systems. In particular, students plot both orbit and bifurcation diagrams, Julia sets, and the Mandelbrot set. The course explores both dynamical systems and computer science in depth, thus requiring four meetings per week. Prerequisite(s): Mathematics s21. Not open to students who have received credit for Mathematics 365F. Enrollment limited to 12. S. Ross.
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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 per semester. This course may not be used to fulfill requirements for the mathematics major or minor in mathematics. Normally offered every semester. Staff.
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3.00 Credits
Content varies from semester to semester. Possible topics include chaotic dynamical systems, number theory, mathematical logic, measure theory, algebraic topology, combinatorics, and graph theory.
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3.00 Credits
The theory of numbers is concerned with the properties of the integers, one of the most basic of mathematical sets. Seemingly naive questions of number theory stimulated much of the development of modern mathematics and still provide rich opportunities for investigation. Topics studied include classical ones such as primality, congruences, quadratic reciprocity, and Diophantine equations, as well as more recent applications to cryptography. Additional topics such as continued fractions, elliptical curves, or an introduction to analytic methods may be included. Prerequisite(s): Mathematics s21. Staff.
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