This course deals with the physical and cognitive description of language sound structure. It covers speech production, the analysis of acoustic recordings, and the principles by which syllable structure, stress, and sequential constraints govern the possible forms of words. Fundamentals of experimental design and data analysis will be introduced through laboratory exercises.
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The goals of this course are to introduce students to the fundamental principles of theoretical syntax, to place them in a position to pursue more advanced study in syntax, and to provide a foundation for their own research. Students will learn the analytical methods used in syntactic research: how to analyze syntactic data, how to formulate plausible hypotheses to explain the data, and how to compare and evaluate hypotheses. Thus, the main focus of the course is on learning how to do syntax, and secondarily on learning a particular theory of syntax. No textbook will be used, and there will be minimal reading assignments; instead, the course will proceed on the basis of class discussion and weekly written assignments. Although the primary source of linguistic data will be English, examples will also be drawn from other languages both in class and on the assignments.
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This course examines the internal structure of words and productive processes for creating new words. It surveys different types of word formation processes (such as inflection and derivation, nonconcatenative systems, and compounding). We will explore phonological, syntactic, and semantic constraints on these processes, and develop formal representations revealing how properties of complex words relate to properties of their component parts. We will also discuss how insights from the generative literature may be integrated with insights from the psycholinguistic literature on morphological processing.
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This course is an introduction to the basic concepts and methods of semantics and pragmatics. We will explore different aspects of meaning (word meaning, sentence meaning, truth conditions, speech acts) and inference types (entailment, presupposition, implicature), become familiar with the analytical tools used to investigate these phenomena, and discuss major theoretical approaches to the study of linguistic meaning. This course is a prerequisite for higher-level courses in semantics and pragmatics, and is recommended to students specializing in other areas of linguistics as a comprehensive overview of linguistic meaning.
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Recent popular works by prominent scientists and intellectuals have renewed interest in atheism, broadly construed as the absence of belief in deities. In this seminar we will evaluate, compare and contrast four significant contributions in this direction by mathematician John Allen Paulos, biologist Richard Dawkins, neuroscientist Sam Harris and journalist Christopher Hitchens.
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Finite Mathematics: Primarily for the behavioral sciences. Topics chosen from elementary linear algebra and its applications, finite probability, and elementary statistics.
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Differential calculus in one variable. Review of trigonometric, exponential, logarithmic and inverse functions. Limits, continuity, derivative of a function, product, quotient and chain rule, mean value theorems, Newton's method, linear approximation and differentials, optimization problems. Enrollment is by permission only. This course is intended for students with little or no calculus background. Math 212, 213, and 214 cover the same materials as Math 220 and 224.
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Definition of a function, trigonometric, exponential, logarithmic and inverse functions, graphs, limits, continuity, derivative of a function, product, quotient and chain rule, implicit differentiation, linear approximation and differentials, related rates, mean value theorems, curve plotting, optimization problems, Newton's method and anti-derivatives.
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Integral Calculus in one variable. Some review of 220-0 (mainly in the Fall Quarter for incoming freshmen). Definite integrals and the Fundamental Theorem of Calculus. Techniques of integration including integration by parts, trigonometric integrals, trigonometric substitutions, partial fractions, numerical integration and improper integrals. Applications of integration: computation of volumes, arc length, average value of functions, the mean value theorem for integration, work and probability. Sequences and Series: the integral and comparison tests, power series, ratio test, introduction to Taylor's formula and Taylor series and using series to solve differential equations.
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Vectors, dot and cross products, equations of lines and planes, polar, cylindrical, and spherical coordinates, differentiation of vector functions, velocity and acceleration, arc length, parametric surfaces, functions of several variables, partial derivatives, tangent plane and linear approximations, chain rule for partial derivatives, directional derivative and gradient, max-min problems for functions of several variables, Lagrange multipliers.
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Multiple Integration and Vector Calculus. Cylindrical and spherical coordinate systems, double and triple integrals, line and surface integrals. Change of variables in multiple integrals; gradient, divergence, and curl. Theorems of Green, Gauss, and Stokes.
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Basic concepts of linear algebra. Solutions of systems of linear equations; vectors and matrices; subspaces, linear independence, and bases; determinants; eigenvalues and eigenvectors; other topics and applications as time permits.
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Multivariable differential calculus, multiple integration and vector calculus.
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Linear Algebra
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An introduction to linear algebra covering computations and applications, but giving primary emphasis to theory. Topics covered in this course include vector spaces, linear independence, dimension, determinants, eigenvalues and eigenvectors. This material provides the foundation for the vector calculus material in Math 290-2 and Math 290-3.
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Introduction to fundamental mathematical ideas  such as sets, functions, equivalence relations, and cardinal numbers  and basic techniques of writing proofs.
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Discrete probability spaces, random variables, expected value, combinatorial problems. Special distributions, independence, and conditional probability. Weak law and central limit theorem (CLT).
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Rigorous analysis in Euclidean space and on metric spaces. Metric space topology, properties of Euclidean spaces, limits and continuity, differentiation and integration, sequences and series, the inverse and implicit function theorems. Lebesgue integration with applications. 321-1,2 differ from 320-1,2 in two respects: they cover more topics in more depth, and aim at intensive development of students ability to analyze and create mathematical proofs. Faster than 320, and at a higher level of abstraction.
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Groups and their structure; elementary ring theory; polynomial rings.
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An introduction to basic group theory: definition of a group; examples; subgroups; normal subgroups and quotient groups; homomorphisms and automorphisms; Cayley's theorem; permutation groups; Sylow's theorem: direct products; finite abelian groups. Groups and their structure, elementary ring theory; polynomial rings. 331 differs from 330 in two respects: it covers more topics in more depth, and aims at intensive development of students ability to analyze and create mathematical proofs.
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A one-quarter introduction to partial differential equations and their solution by the methods of Fourier analysis. Topics include the solution of boundary and initial-value problems for the heat equation, the wave equation and Laplace's equation in both rectangular, cylindrical and spherical coordinates. Special attention will be paid to questions of convergence and asymptotic behavior of the series solutions. Use of the Fourier integral permits an overview of the series solutions obtained.
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Ordinary differential equations and partial differential equations with applications to mathematical modeling.
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Fourier series and boundary value problems.
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Probability theory and its social science applications.
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Introduction to classical and schemetheoretic methods of algebraic geometry. Algebraic vector bundles, sheaf cohomology, the Riemann-Roch theorem for curves, and intersection theory.
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