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Course Criteria
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3.00 Credits
This course introduces differential equations and analytical, numerical, and graphical techniques for their analysis. First and second order differential equations and linear systems are studied. Applications are selected from areas such as biology, chemistry, economics, ecology, and physics. Students use computers extensively to calculate and visualize results. Prerequisite: Mathematics 126 or 128 and 220. Offered both semesters.
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3.00 Credits
Discrete (noncontinuous) mathematics has become increasingly important as more phenomena are investigated, represented and solved using computers (essentially, discrete machines). Students explore finite graphs, recurrence relations, and combinatorial optimization using problem solving techniques and algorithm design strategies. Prerequisite: Mathematics 120 or 121, or permission of the instructor. Offered alternate years.
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3.00 Credits
This course provides students with a transition from calculus and linear algebra to more advanced courses in theoretical mathematics. The unique feature of this course is that it is taught with a cultural context in Budapest, Hungary. This course not only supplies a bridge from beginning to advanced mathematics, but also allows participants to encounter an important worldwide center of mathematics.
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3.00 Credits
This course introduces students to the mathematics of complex systems, as applied to problems from biology. Topics include discrete and continuous models of single species and multiple species populations, age structure of populations, disease spread, evolution and game theory, and competition. Prerequisite: Mathematics 126 or 128, and Mathematics 220. Offered Spring Semester only.
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3.00 Credits
This course introduces number theory -- the study of patterns and relationships satisfied by natural numbers. Topics include prime numbers, congruences, primitive roots, quadratic residues, and the design and breaking of codes. Prerequisite: Mathematics 220 or permission of instructor.
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3.00 Credits
Modern mathematics is characterized by the interaction of theoretical and computational techniques. In this course, students study topics from pure and applied mathematics with the aid of computation. Symbolic, graphical, and numerical computational techniques are introduced. Students develop computational skills sufficient to investigate mathematical questions independently. No previous programming experience is required.
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3.00 Credits
Students encounter the theory of calculus and develop tools for communicating mathematical ideas with technical accuracy and sophistication. The goal is mastery of the concepts (e.g., limit, continuity, derivatives, and integrals) necessary to verify such important results as the Fundamental Theorem of Calculus, the continuity of the uniform limit of continuous functions, and the Bolzano-Weierstrass Theorem. Prerequisite: Mathematics 126 or 128. Offered both semesters.
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3.00 Credits
Algebra is concerned with sets of objects and operations on these sets. In an axiomatic or abstract treatment one assumes basic properties and then deduces many other properties. Using this method we study structures known as groups, rings, and fields. Prerequisite: Mathematics 220. Offered both semesters.
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3.00 Credits
This course introduces the mathematics of randomness and games of chance. Topics include combinatorial analysis, elementary probability measures, conditional probability, random variables, special distributions, expectations, generating functions, and limit theorems. Prerequisite: Mathematics 126 or 128. Offered both semesters.
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3.00 Credits
Students are introduced to modeling and mathematical optimization techniques (e.g., linear programming, network flows, discrete optimization, constrained and unconstrained nonlinear programming, queuing theory). The course emphasizes applications, but prior computer experience is not assumed. Prerequisites: Mathematics 126 or 128 and 220. Recommended: Mathematics 226 and/or 262. Offered Spring Semester only.
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