This course aims to accomplish two things. The first is to introduce three broad traditions of normative thinking about social issues from around the globe: a Confucian tradition, one based in Islamic legal traditions, and one derived from European liberalism. The second is to address three current areas of normative debate: about global economic inequality, about gender justice and human rights. We shall explore these first-order questions against the background of the three broad traditions. Our aim will be to understand some of differences of approach that shape the global conversation about these issues that concern people around the world.
Considers questions such as the following: Can I have knowledge of anything outside my own mind?for example, physical objects or other minds? Or is the skeptic’s attack on my commonplace claims to know unanswerable? What is knowledge, and how does it differ from belief?
Lecture and laboratory course that provides students with broad exposure to current questions and experimental approaches in cellular neuroscience. Lectures and laboratories are organized into three areas: cell structure aLecture and laboratory course that provides students with broad exposure to current questions and experimental approaches in cellular neuroscience. Lectures and laboratories are organized into three areas: cell structure and organization of the vertebrate central nervous system, mechanisms underlying neural signaling and plasticity, and control of cell form and its developmental determinants. Laboratory instruction in anatomical, physiological, and biochemical methods for investigating the biology of nerve cells.
Lecture and laboratory course that provides students with broad exposure to current questions and experimental approaches in cellular neuroscience. Lectures and laboratories are organized into three areas: cell structure and organization of the vertebrate central nervous system, mechanisms underlying neural signaling and plasticity, and control of cell form and its developmental determinants. Laboratory instruction in anatomical, physiological, and biochemical methods for investigating the biology of nerve cells.
Explores the underlying principles and inner workings of the tonal system, a system that has guided all of Western music from the years 1600 to 1900. It includes a discussion of historical background and evolution. Focuses on concepts and notation of key, scale, tonality, and rhythm. Related skills in sight-singing, dictation, and keyboard harmony are stressed in the recitation sections.
Students study principles of tonal music composition including 18th and 19th century harmonic, formal, and contrapuntal practices. Exercises in four-part voice-leading and species counterpoint are supplemented by analyses of music from around the world and from a variety of genres, including concert and popular music. Weekly lab sections are devoted to skills in musicianship and are required throughout the sequence.
Historical-political background of the Middle East and its contemporary social and political problems, including the impact of the West; religious and liberal reactions; conflict of nationalisms (Arab, Iranian, Turkish, and Zionist); and revolutionary socialism. Specific social, political, and economic problems?using a few selected countries for comparison and analysis?including the role of the military, the intelligentsia, the religious classes, the legitimization of power, urban-rural cleavages, bureaucracy, and political parties.
Designed to further develop fluency in oral and written communication. In addition to the class, small-group activities, and language and computer lab sessions, students are given an individual assignment to work with native speakers from the community and report on their findings. The reading assignments are designed to broaden understanding of content used for oral presentations.
Continues where Elementary Urdu leaves off. The students are introduced to literary texts. Along with specific language tasks, criticism and analysis now form part of the curriculum. Dictation, memorizing poetry, comprehension, and engaging in longer sessions of conversation form an important part of this course. By the end of this course, students should have achieved some fluency in reading literary texts, writing short essays, and carrying on a conversation.
Builds on the skills acquired in Elementary Arabic I and II, with increased emphasis on writing and reading from modern sources, in addition to aural/oral proficiency.
Brief review of multivariate calculus: partial derivatives, chain rule, Riemann integral, change of variables, line integrals. Lagrange multipliers. Inverse and implicit function theorems and their applications. Introduction to calculus on manifolds: definition and examples of manifolds, tangent vectors and vector fields, differential forms, exterior derivative, line integrals and integration of forms. Gauss’ and Stokes’ theorems on manifolds.
The scope of this honors class will include the usual MATH-UA 123 syllabus; however this class will move faster, covering additional topics and going deeper. Functions of several variables. Vectors in the plane and space. Partial derivatives with applications, especially Lagrange multipliers. Double and triple integrals. Spherical and cylindrical coordinates. Surface and line integrals. Divergence, gradient, and curl. Theorem of Gauss and Stokes.
Prerequisites: a grade of C or better in Honors Analysis I (MATH-UA 328), or a grade of A in Analysis (MATH-UA 325) and permission of instructor. Continuation of Honors Analysis I (MATH-UA 328). Topics include: metric spaces, differentiation of functions of several real variables, the implicit and inverse function theorems, Riemann integral on R^n, Lebesgue measure on R^n, the Lebesgue integral.
Prerequisites: a grade of C or better in Honors Algebra I (MATH-UA 348), or a grade of A in Algebra (MATH-UA 343) and permission of instructor. Principal ideal domains, polynomial rings in several variables, unique factorization domains. Fields, finite extensions, constructions with ruler and compass, Galois theory, solvability by radicals.
Prerequisite: A grade of C or higher in Calculus III (MATH-UA 123) or Math for Economics III (MATH-UA 213) (for economics majors). Recommended: Mathematical Physics (PHYS-UA 106). Fluid dynamics is the branch of physics that can describe the flow of blood in the human body, the flight of an insect, or the motions of weather systems. Key concepts include: the formalism of continuum mechanics; the conservation of mass, energy, and momentum in a fluid; the Euler and Navier-Stokes equations; and viscosity and vorticity. These concepts are applied to such classic problems in fluid dynamics as potential flow around a cylinder, the propagation of sound and gravity waves, and the onset of instability in shear flow.
Further topics in vector calculus. Vector spaces, matrix analysis. Linear and nonlinear programming with applications to game theory. This course will provide economics students who have taken MATH-UA 211 Mathematics for Economics I and MATH-UA 212 Mathematics for Economics II with the tools to take higher-level mathematics courses.
Introduction to abstract algebraic structures, including groups, rings, and fields. Sets and relations. Congruences and unique factorization of integers. Groups, permutation groups, homomorphisms and quotient groups. Rings and quotient rings, Euclidean rings, polynomial rings. Fields, finite extensions.