Course List

Mathematics is a language that numerically describes and shapes our world. The course introduces analytic geometry; functions, limits, derivatives, and applications; integration and applications. A major goal is to understand the behaviour of functions as mathematical models in the natural sciences, including population dynamics in biology and Newtonian mechanics in physics.

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Mathematics is a language that numerically describes and shapes our world. The course presents Transcendental and hyperbolic functions; methods of integration; sequences, series and applications. The course deepens the understand of functions as mathematical models in the natural sciences, specifically focusing on probably models for statistics and the use of infinite series in the algorithms of computing science.

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Mathematics is a language that numerically describes and shapes our world. The course is an introduction to linear algebra including solving linear equations, matrix algebra, determinants, vector spaces and linear transformations. A major goal is to introduce the use and importance of linear algebra models in the natural sciences, including Leslie matrices in biology and stochastic models in statistics.

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This course provides a study of foundational mathematical concepts and properties in the elementary and junior high curriculum. The course emphasizes conceptual understanding, reasoning, explaining why algorithms work, and problem solving. Topics include number systems, operations, fractional numbers, proportional reasoning, and aspects of geometry.

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This course explores the mathematical reasoning embedded in concepts encountered in the upper elementary and junior high curriculum. The course emphasizes conceptual understanding, reasoning, explaining why algorithms work, and problem solving. The content follows sequentially from Math 281. Topics include proportional reasoning, number theory, algebraic reasoning and aspects of geometry and probability.

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Series, power series and applications. Plane curves, polar coordinates and three dimensional analytic geometry. Partial differentiation and Lagrange multipliers.

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Multiple integrals, integrals in rectangular and polar coordinates. Introduction to vector calculus and Gauss', Green's and Stoke's theorems. Introduction to first- and second-order linear differential equations with applications.

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An introduction to formal logical reasoning and mathematical theory in computing science. Topics include: fundamental logic, set theory, induction, relations and functions, graphs, the principle of inclusion and exclusion, generating functions and recurrence.

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A course on a topic or field of special interest to a member of the mathematics faculty and offered on a non-recurring basis.

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An introduction to numerical computation. Topics include computer arithmetic, root approximation, interpolation, numerical integration, applications to differential equations, and error analysis.

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An introduction into advanced topics in the theory of computation. Topics include: models of computers including finite automata and Turing machines, computability, computational complexity, basics of formal languages.

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First, second, and higher order ordinary differential equations; power series methods of solution; Laplace transforms; linear systems of equations; numerical methods of solution. Applications to the physical sciences will be emphasized.

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An introduction to complex analysis. The course will cover properties of the complex plane, differentiation and integration with complex variables, Cauchy's Theorem, Taylor series, Laurent series, poles and residues.

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This course introduces the mathematical algorithms that are used in cryptography. This includes historic cryptography such as the Caesar and Vigenere ciphers, and the German enigma machine. The majority of the course will focus on modern, public key cryptography: the Diffie-Hellman key exchange, RSA, and elliptic curve cryptography. Students will also learn the mathematics used in these algorithms, which includes modular arithmetic, Euler's phi function, introductory information on elliptic curves, and the definitions of groups, rings and fields. The lab component explores prime detection and factorization algorithms, and the implementation of ciphers.

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An opportunity to do advanced study of a special topic of particular interest to a student. Students work with a member of the mathematics faculty. Students must apply in advance to a member of the mathematics faculty.

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