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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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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Linear algebra is foundational to academic mathematics. Its constructions and ideas are ubiquitous throughout pure and applied mathematics. It is both an algebraic discipline and a geometric discipline - it solves systems of equations and builds algebra structure, but it also studies vectors and transformations of euclidean space. This course introduces the rich landscape of ideas and tool of linear algebra, starting with vectors and linear equations and building up to eigenvalues and modelling through linear dynamical systems.

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Single variable calculus introduced the main ideas of derivatives and integrals of functions. However, many of the most important functions, both for the delight of pure mathematics and the utility of applied mathematics, involve more than one variable. This course shows the remarkable and surprisingly ways that the basic tools of derivatives and integrals extend into multivariable situations. It develops the integral and differential calculus of parametric space curves, scalar fields and vector fields.

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The differential equation is perhaps the most useful and important tool that mathematical models use to describe the world. By understanding the relationship between a function and its rate of change, the dynamics of complicated and fluctuating systems can be captured in a remarkably unique and powerful way. This course seeks to build a solid foundation of conceptual understanding and solution techniques for ordinary DEs, including second order linear equations and solutions by Taylor series and Laplace transforms. It also includes a brief introduction to partial DEs via and heat equation and solution by Fourier series.

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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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Abstract algebra seeks to understand the structure of abstract objects in mathematics: constructions that generalize the familiar structure of numbers, vectors, matrices and functions. To that end, mathematicians have devised many different schemes and systems of abstract rules and worked to understand the implications of these rules systems. This course introduces and investigates the three core algebraic structures: groups, rings and fields.

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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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The richness and complexity of biological systems presents a fascinating and unique challenge to mathematicians seeking to build models describing these systems. In this survey of mathematical biology, techniques from linear algebra, differential equations and difference equations are used to try to accurately capture the complex dynamics of single populations, interacting populations, infectious diseases, and population genetics. A mix of exact solutions, approximate solutions, and qualitative analysis are employed to gain insight into each biological system.

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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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