Differential and integral calculus of multiple variables. Topics include partial differentiation; optimization of functions of several variables; line, area, volume, and surface integrals; vector functions and vector calculus; theorems of Green, Gauss, and Stokes; applications to selected problems in engineering and applied science.
Introduction to understanding and writing mathematical proofs. Emphasis on precise thinking and the presentation of mathematical results, both in oral and in written form. Intended for students who are considering majoring in mathematics but wish additional training. CC/GS: Partial Fulfillment of Science Requirement. BC: Fulfillment of General Education Requirement: Quantitative and Deductive Reasoning (QUA).
This course will explore drawing as an open-ended way of working and thinking that serves as a foundation for all other forms of visual art. The class is primarily a workshop, augmented by slides lectures and videos, homework assignments and field trips. Throughout the semester, students will discuss their work individually with the instructor and as a group. Starting with figure drawing and moving on to process work and mapping and diagrams, we will investigate drawing as a practice involving diverse forms of visual culture.
Prerequisites: a working knowledge of calculus.
Corequisites: a course in calculus-based general physics.
First term of a two-term calculus-based introduction to astronomy and astrophysics. Topics include the physics of stellar interiors, stellar atmospheres and spectral classifications, stellar energy generation and nucleosynthesis, supernovae, neutron stars, white dwarfs, and interacting binary stars.
Prerequisites: In Lecture MWF 11-11:50am & 12-12:50pm; Laboratory one afternoon M-F: 1:10-5pm / TH: 8:10-11:50am. Counts towards Lab Science Requirement.
Corequisites: CHEM BC2011 and CHEM BC2012
Atoms; elements and compounds; gases; solutions; equilibrium; acid-base, precipitation, and oxidation-reduction reactions; thermochemistry. Laboratory experience with both qualitative and quantitative techniques.
Introductory biology course for majors in biology or environmental biology, emphasizing the ecological and evolutionary context of modern biology.
Prerequisites: some calculus or the instructor's permission.
Intended as an enrichment to the mathemathics curriculum of the first years, this course introduces a variety of mathematical topics (such as three dimensional geometry, probability, number theory) that are often not discussed until later, and explains some current applications of mathematics in the sciences, technology and economics.
Corequisites: Calculus I or the equivalent.
Fundamental laws of mechanics. Kinematics, Newton's laws, work and energy, conservation laws, collisions, rotational motion, oscillations, gravitation.
Lecture and recitation. Islamic civilization and its characteristic intellectual, political, social, and cultural traditions up through 1800.
Interdisciplinary and thematic approach to the study of Africa, moving from pre-colonial through colonial and post-colonial periods to contemporary Africa. Focus will be on its history, societal relations, politics and the arts. The objective is to provide a critical survey of the history as well as the continuing debates in African Studies.
Introduces students to crucial theories of society, paying particular attention to classic social theory of the late 19th and 20th centuries. Traces a trajectory through writings essential for an understanding of the social: from Saussure, Durkheim, Mauss, Marx, Freud, and Weber, on to the structuralist ethnographic elaboration of Claude Levi-Strauss, the historiographic reflections on modernity of Michel Foucault, and contemporary modes of socio-cultural analysis. Explored are questions of signification at the heart of anthropological inquiry, and to the historical contexts informing these questions.
This course will focus on individual and collaborative projects designed to explore the fundamental principles of image making. Students acquire a working knowledge of concepts in contemporary art through class critiques, discussion, and individual meetings with the professor. Reading materials will provide historical and philosophical background to the class assignments. Class projects will range from traditional to experimental and multi-media. Image collections will be discussed in class with an awareness of contemporary image production.
Prerequisites: one year of college chemistry, or a strong high school chemistry background.
Lecture and recitation. Recommended as the introductory biology course for biology and related majors, and for premedical students. Fundamental principles of biochemistry, molecular biology, and genetics. Website:
http://www.columbia.edu/cu/biology/courses/c2005/index.html.
SPS, Barnard, and TC students may register for this course, but they must first obtain the written permission of the instructor, by filling out a paper Registration Adjustment Form (Add/Drop form). The form can be downloaded at the URL below, but must be signed by the instructor and returned to the office of the registrar. registrar.
http://registrar.columbia.edu/sites/default/files/content/reg-adjustment.pdf
Prerequisites: one year of college chemistry, or a strong high school chemistry background.
Lecture and recitation. Recommended as the introductory biology course for biology and related majors, and for premedical students. Fundamental principles of biochemistry, molecular biology, and genetics. Website:
http://www.columbia.edu/cu/biology/courses/c2005/index.html.
SPS, Barnard, and TC students may register for this course, but they must first obtain the written permission of the instructor, by filling out a paper Registration Adjustment Form (Add/Drop form). The form can be downloaded at the URL below, but must be signed by the instructor and returned to the office of the registrar. registrar.
http://registrar.columbia.edu/sites/default/files/content/reg-adjustment.pdf
This course will focus on individual and collaborative projects designed to explore the fundamental principles of image making. Students acquire a working knowledge of concepts in contemporary art through class critiques, discussion, and individual meetings with the professor. Reading materials will provide historical and philosophical background to the class assignments. Class projects will range from traditional to experimental and multi-media. Image collections will be discussed in class with an awareness of contemporary image production.
Prerequisites: MATH UN1201 or the equivalent.
Matrices, vector spaces, linear transformations, eigenvalues and eigenvectors, canonical forms, applications. (SC)
Corequisites: CHEM BC2001 and CHEM BC2011.
Required laboratory section for BC2001x General Chemistry.
All students enrolled in BC2001x must also be enrolled in one section of BC2012 and one section of BC2011 on the SAME day.
This course examines major developments and debates in the history of cinema between 1930 and 1960, from the consolidation of the classic Hollywood studio system in the early sound era to the articulation of emergent “new waves” and new critical discourses in the late 1950s. Our approach will be interdisciplinary in scope, albeit with an emphasis on social and cultural history – concerned not only with how movies have developed as a form of art and medium of entertainment, but also with cinema’s changing function as a social institution. FILM W2021
The topic of precarity is a growing field in the social sciences. The main purpose of this course is to explore the wide semantics and potentials of the term in relation to domains such as labour, law, ethics, technology, health, relationships, moods, shifts in opinion, in fashions or the durability of goods. Our interest in precarity is grounded in two interrelated key motives: the first addresses it as an object of study in its own right. Judging from recent unemployment rates of the industrialized west, the mass scale displacement of populations or the corrosion of security, there is enough reason to put precarity into context. Yet, we might also proceed by inquiring about its potentials as a methodology, one might even call it “a style of reasoning”. Given how much history relies on causation, sequence and linearity how to relate to precarity as a temporal structure in light of the complexities of the present? How does such multilateral present redefines the very conception of that present, of the historical and the now?
We will be relating to precarity not just as a condition of existence but also as an infrastructure with which to think societies across space and time. The course will focus on narratives, practices and structures that problematize and displace prima facie logics of the either/or. Instead, we want to highlight conjoined operations of the both/and which are changing the very nature of how we think norms, time and episteme. Taking a clue from the proliferation of forms of precarity, the course will be organized around specific themes. Within each two-week section, the first sessions will be a lecture and the remaining will combine lecture and discussion of the assigned items. As a whole, the course aims to sensitize students to the complexities and conditioning possibilities involved in the process of knowledge-making and to provide students with tools to better structure and critically access the information they receive and generate.
Prerequisites: (ECON UN1105)
The workshop prepares students to compete in the annual College Fed Challenge sponsored by the Federal Reserve. Topics covered include macroeconomic and financial conditions, monetary policy, financial stability and the Federal Reserve System.
By closely watching representative classics from countries including Italy, Poland, Russia and Argentina, we will study the distinctive trends and masters of this vibrant era. Special attention will be paid to the French New Wave (60s); the New German Cinema (70s); the reformulation of Hollywood studio filmmaking in the 70s (Altman, Cassavetes, Coppola), and the rise of the independent American cinema (80s). FILM W2031
Prerequisites: MATH UN1102 and MATH UN1201 or the equivalent.
Special differential equations of order one. Linear differential equations with constant and variable coefficients. Systems of such equations. Transform and series solution techniques. Emphasis on applications.
Prerequisites: A grade of 5 on the Chemistry Advanced Placement exam and an acceptable grade on the Department placement exam or an acceptable grade in CHEM UN1604.
Corequisites: CHEM UN1507
Premedical students may take
CHEM UN2045
,
CHEM UN2046
,
CHEM UN1507
and
CHEM UN2545
to meet the minimum requirements for admission to medical school. This course covers the same material as
CHEM UN2443-CHEM UN2444
, but is intended for students who have learned the principles of general chemistry in high school OR have completed
CHEM UN1604
in their first year at Columbia. First year students enrolled in
CHEM UN2045-CHEM UN2046
are expected to enroll concurrently in
CHEM UN1507
. Although
CHEM UN2045
and
CHEM UN2046
are separate courses, students are expected to take both terms sequentially. A recitation section is required. Please check the Directory of Classes for details and also speak with the TA for the course.
Prerequisites: BIOL BC1500, BIOL BC1501, BIOL BC1502, BIOL BC1503 or the equivalent. This course is a pre-requisite for most 3000-level courses.
Mendelian and molecular genetics of both eukaryotes and prokaryotes, with an emphasis on human genetics. Topics include segregation, recombination and linkage maps, cytogenetics, gene structure and function, mutation, molecular aspects of gene expression and regulation, genetic components of cancer, and genome studies.
Prerequisites: First-year chemistry and physics or equivalent.
This course serves as an introduction to the chemical engineering profession. Students are exposed to concepts used in the analysis of chemical engineering problems. Rigorous analysis of material and energy balances on open and closed systems is emphasized. An introduction to important processes in the chemical and biochemical industries is provided.
Introduction to design for a sustainable planet. Scientific understanding of the challenges. Innovative technologies for water, energy, food, materials provision. Multi-scale modeling and conceptual framework for understanding environmental, resource, human, ecological and economic impacts and design performance evaluation. Focus on the linkages between planetary, regional and urban water, energy, mineral, food, climate, economic and ecological cycles. Solution strategies for developed and developing country settings.
Prerequisites: high school algebra. Recommended preparation: high school chemistry and physics; and one semester of college science.
Origin and development of the atmosphere and oceans, formation of winds, storms and ocean currents, reasons for changes through geologic time. Recent influence of human activity: the ozone hole, global warming, water pollution. Laboratory exploration of topics through demonstrations, experimentation, computer data analysis, and modeling. Students majoring in Earth and Environmental Sciences should plan to take EESC W2100 before their senior year to avoid conflicts with Senior Seminar.
Prerequisites: The department's permission required through writing sample. Please go to 609 Kent for submission schedule and registration guidelines or see http://www.arts.columbia.edu/writing/undergraduate.
Intermediate workshops are for students with some experience with creative writing, and whose prior work merits admission to the class (as judged by the professor). Intermediate workshops present a higher creative standard than beginning workshops, and increased expectations to produce finished work. By the end of the semester, each student will have produced at least seventy pages of original fiction. Students are additionally expected to write extensive critiques of the work of their peers.
Prerequisites: AKAD UN1101 and AKAD UN1102 or the instructor's permission.
Readings in Akkadian literature.
Prerequisites: BCRS UN1102 or the equivalent.
Readings in Serbian/Croatian/Bosnian literature in the original, with emphasis depending upon the needs of individual students.
Prerequisites: BENG UN1101 and BENG UN1102 or the instructor's permission.
Further develops a student's knowledge of Bengali, a major language of northeast India and Bangladesh.
Prerequisites: (CANT W1101 and CANT UN1102)
CANT W1101-W1102
or the instructor's permission.
This course further continues the study of the Cantonese language. Emphasis is on linguistic rules to enable students to communicate with more competence. The lessons will not only focus on language, but also incorporate discussions on history, current events, literature, popular culture, and native values. Includes field trips to Chinatown and other Cantonese-speaking neighborhoods.
Note:
This course is part of the language exchange program with New York University (NYU). Classes will be held at NYU.
Prerequisites: CZCH UN1102 or the equivalent
Rapid review of grammar. Readings in contemporary fiction and nonfiction, depending upon the interests of individual students.
Prerequisites: DTCH UN1101-UN1102 or the equivalent.
Continued practice in the four skills (aural comprehension, reading, speaking, and writing); review and refinement of basic grammar; vocabulary building. Readings in Dutch literature.
Prerequisites:
FILI W1101-W1102
or the instructor's permission.
Emphasis is placed on the linguistic rules to enable students to communicate with more competence. The lessons will not only focus on language but also will use a holistic approach and incorporate discussions on history, current events, literature, pop culture, and native values.
Note:
This course is part of the language exchange program with New York University (NYU). Classes will be held at NYU.
Prerequisites: FINN UN1101-UN1102 or the instructor's permission.
Continued practice in aural comprehension, reading, speaking, and writing; review and refinement of grammatical structures; vocabulary building. Readings include Finnish fiction and nonfiction.
Prerequisites: two terms of college French or two years of secondary school French. Equivalent to
FREN UN2101
.
$15.00= Language Resource Fee, $15.00 = Materials Fee
Equivalent to
French UN2101
. Prepares students for advanced French language and cultures, focusing on developing correct usage through explanations and practice. Gaining a deeper understanding of the French language through readings of poems and short stories, students practice a variety of communication tasks, as they are engaged in ever more complex forms of discourse. Daily assignments, quizzes, laboratory work, and screening of video materials.
Prerequisites: GERM UN1102 or the equivalent.
Complete grammar review through regular exercises. Wide range of texts are used for close and rapid reading and writing exercises. Practice in conversation aims at enlarging the vocabulary necessary for daily communication.
Prerequisites:
GREK UN1101- GREK UN1102
or the equivalent.
Selections from Attic prose.
Prerequisites: GRKM UN1101 and GRKM UN1102 or the equivalent.
Corequisites: GRKM UN2111
This course is designed for students who are already familiar with the basic grammar and syntax of modern Greek language and can communicate at an elementary level. Using films, newspapers, and popular songs, students engage the finer points of Greek grammar and syntax and enrich their vocabulary. Emphasis is given to writing, whether in the form of film and book reviews or essays on particular topics taken from a selection of second year textbooks.
Prerequisites:
HNGR UN1101-UN1102
or the equivalent.
Further develops a student's knowledge of the Hungarian language. With the instructor's permission the second term of this course may be taken without the first. Students with a schedule conflict should consult the instructor about the possibility of adjusting hours.
Prerequisites:
INDO W1101-W1102
or the instructor's permission.
This course further develops a student's knowledge of Bahasa Indonesia, a major language of Indonesia and South East Asia.
Prerequisites:
IRSH W1101-W1102
or the instructor's permission.
For the more advanced student of Irish, this course focuses on improving conversational fluency and on expanding vocabulary through reading complex literature in Irish, and writing in the Irish language, further encouraging students to strengthen their pronunciation and command of spoken Irish.
Prerequisites:
ITAL UN1102
or the equivalent. If you did not take Elementary Italian at Columbia in the semester preceding the current one, you must take the placement test, offered by the Italian Department at the beginning of each semester.
A review of grammar, intensive reading, composition, and practice in conversation. Exploration of literary and cultural material. Lab: hours to be arranged.
Prerequisites:
LATN UN1101-UN1102
, or
LATN UN1121
, or the equivalent.
Selections from Catullus and from Cicero or Caesar.
Prerequisites:
QUCH W1101-W1102
or the instructor's permission.
Quechua is the most important and most widely-distributed indigenous language in South America, with over 10 million speakers living from the high mountains to the tropical lowlands in Colombia, Ecuador, Peru, Bolivia, Chile, and Argentina. Those who speak it call the language runa simi or runa shimi, "human speech." It was the principal language of the Inca empire and the key language of cultural interaction during the colonial era. Quechua has remained central to indigenous peoples' efforts to preserve their cultural autonomy. It has gained greater force in recent years, during which indigenous movements have swept Quechua speakers into national politics, where they have succeeded in transforming constitutions to recognize cultural diversity, making Quechua an official language of state, and successfully promoting schooling in the language. Students who satisfactorily complete Elementary Quechua I and II will be well-prepared for intensive summer study at one of many summer study abroad programs in Ecuador, Peru, and Bolivia that will put them in closer contact with the indigenous world.
Prerequisites: RUSS UN1102 or the equivalent.
Drill practice in small groups. Reading, composition, and grammar review."Off-sequence"
Prerequisites:
SWHL W1101-W1102
or the instructor's permission.
A review of the essentials of Swahili grammar; detailed analysis of Swahili texts; practice in conversation. No P/D/F or R credit is allowed for this class.