2008 - 2009 SEAS Bulletin
Bulletin

Undergraduate Minors

Undergraduate minors are designed to allow engineering and applied science students to study, to a limited extent, a discipline other than their major. Besides engineering minors offered by SEAS departments, new liberal arts minors are available.

A minor requires at least 15 points of credit, and no more than one course can be taken outside of Columbia or met through AP or IB credit. This includes courses taken through study abroad. In SEAS departments with more than one major program, a minor in the second program may be permitted, if approved by the department.

No substitutions or changes of any kind from the approved minors are permitted (see lists below). No appeal for changes will be granted. Please note that the same courses may not be used to satisfy the requirements of more than one minor. No courses taken for pass/fail may be counted for a minor. Minimum GPA for the minor is 2.0. Departments outside SEAS have no responsibility for nonengineering minors offered by SEAS.

For a student to receive credit for a course taken while studying abroad, the department offering the minor must approve the course in writing, ahead of the student’s study abroad.

Students must expect a course load that is heavier than usual. In addition, unforeseen course scheduling changes, problems, and conflicts may occur. The School cannot guarantee a satisfactory completion of the minor.

Minor in American Studies

Minimum: 18 points.

1. AMST W101: Introduction to American studies (3.0 points )

2-6. Five additional courses in American Studies with no distribution or seminar requirements. Students are encouraged to take seminars.

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Minor in Applied Mathematics

Prospective students should consult the first- and second-year requirements for applied mathematics majors to ensure that prerequisites for the applied mathematics minor are satisfied in the first two years.

Course work counting toward the applied mathematics minor may not include advanced placement credits. Any substitutions for the courses listed below require the approval of the applied mathematics program adviser.

1. APMA E3101: Linear algebra (3.0 points)
or
MATH V2010: Linear algebra (3.0 points)

2. APMA E3102: Partial differential equations (3.0 points)
or
MATH V3028: Partial differential equations (3.0 points)

3-5. Any three of the following courses:

APMA E4300: Introduction to numerical methods (3.0 points)
APMA E4204: Functions of a complex variable (3.0 points)
APMA E4101: Introduction to: dynamical systems (3.0 points)
MATH V2500: Analysis and optimization (3.0 points)
SIEO W4105: Probability (3.0 points)
STAT W4107: Statistical inference (3.0 points)

or any other course designated APMA, MATH, STAT, IEOR, or COMS that is approved by the applied mathematics program adviser.

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Minor in Applied Physics

Prospective students should consult the first- and second-year requirements for applied physics majors to ensure that prerequisites for the applied physics minor are satisfied in the first two years.

Course work counting toward the applied physics minor may not include advanced placement credits.

1. APPH E4901: Seminar: problems in applied physics (1.0 point)

2. PHYS W3003: Mechanics (3.0 points)

3. APPH E3100: Introduction to quantum mechanics (3.0 points)

4. APPH E3300: Applied electromagnetism (3.0 points)

5. MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3.0 points)

6. Two of the following courses:

APPH E4010: Introduction to nuclear science (3.0 points)
APPH E4100: Quantum physics of matter (3.0 points )
APPH E4110: Modern optics (3.0 points)
APPH E4112: Laser physics (3.0 points)
APPH E4300: Applied electrodynamics (3.0 points)
APPH E4301: Introduction to plasma physics (3.0 points)

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Minor in Architecture

1. Studio course (choose one from the following):
ARCH V1020: Introduction to architectural design and visual culture (4.0 points)
ARCH V3101: Arch representation: abstraction (4.0 points)
ARCH V3103: Arch representation: perception (4.0 points)

2–4. History/theory courses (see Note below)

5. Elective course (must be either an approved second design studio or an additional history/theory course)

Note: A list of the approved history/theory courses is available at the departmental office each semester.

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Minor in Art History

1-7. Seven courses in art history, covering four of the following areas: (a) ancient Mediterranean, (b) medieval Europe, (c) Renaissance and baroque, (d) 18th, 19th, and 20th century, and (e) non-Western.

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Minor in Biomedical Engineering

The Biomedical Engineering program offers a minor in one of three tracks: (I) cellular engineering, (II) biomechanics, and (III) biomedical imaging. Students who wish to get a minor in biomedical engineering should take the core BME requirements, as well as select courses from one of the three tracks, described below. Participation in the minor is
subject to the approval of the major program adviser.

Core BME Requirements

1. BIOL C2005: Introduction to molecular and cellular biology (4.0 points)

2. BMEN E4001: Quantitative physiology, I (3.0 points)
or
BMEN E4002: Quantitative physiology, II (3.0 points)

I. Cell and Tissue Engineering Track
3. CHEN E3010: Chemical engineering thermodynamics (4.0 points)

4. BMEN E4501: Tissue engineering, I (3.0 points)

5. BMEN E4502: Tissue engineering, II (3.0 points)

6. One of the following courses:

BMEN E3320: Fluid biomechanics (3.0 points)
BMEN E4570: Science and engineering of body fluids, I (3.0 points)
BMEN E4580: Science and engineering of body fluids, II (3.0 points)
ECBM E3060: Introduction to genomic information (3.0 points)
CHEN E3110: Transport phenomena, I (4.0 points )
CHEN E4700: Principles of genomic technologies (3.0 points)
MSAE E3103: Elements of materials science (3.0 points )


II. Biomechanics Track
3. BMEN E4300: Solid biomechanics (3.0 points)

4. BMEN E3320: Fluid biomechanics (3.0 points )

5-6. Two from the following course groups:

ENME E3113: Mechanics of solids (3.0 points)
ENME E3161: Fluid mechanics (4.0 points)
or
MECE E3100: Introduction to mechanics of fluids (3.0 points)
MECE E3301: Thermodynamics (3.0 points)
or
MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3.0 points)

III. Biomedical Imaging Track
3. BMEN E4894: Biomedical imaging (3.0 points)

4-5. Two from the following courses:
BMEN E4430: Principles of magnetic resonance imaging (3.0 points )
BMEN E4400: Wavelet applications in biomedical image and signal processing (3.0 points)
BMEN E4898: Phototonics (3.0 points )
BMEN E4410: Ultrasound in diagnostic imaging (3.0 points)
BMEN E4420: Biomedical signal processing and signal modeling (3.0 points)

6. One from the following courses:
ELEN E3801: Signals and systems (3.0 points )
ELEN E4810: Digital signal processing (3.0 points)
ELEN E4830: Digital image processing (3.0 points )

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Minor in Chemical Engineering

Of the six courses required, at least three must have the CHEN, CHEE, or CHAP designator:

1. CHEN E3100: Material and energy balances (4.0 points)

2. CHEN E3010: Principles of chemical engineering thermodynamics (4.0 points)
or
MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3.0 points)
or
MECE E3301: Thermodynamics (3.0 points)

3. CHEN E3110: Transport phenomena, I (4.0 points) or one of the following:

EAEE E4900: Applied transport and chemical rate phenomena (3.0 points)
MECE E3100: Introduction to mechanics of fluids (3.0 points )
ENME E3161: Fluid mechanics (4.0 points)

4. CHEN E4230: Reactor design and control (4.0 points)

5-6. Two courses from the following:
Any 3000-level or higher BMCH, CHEN, CHAP, or CHEE course
APMA E3101: Applied mathematics, I (3.0 points)
APMA E3102: Applied mathematics, II (3.0 points)
BMEN E3320: Fluid biomechanics (3.0 points )
BMEN E4001: Quantitative physiology, I (3.0 points)
BMEN E4002: Quantitative physiology, II (3.0 points)
ELEN E3201: Circuit analysis (3.5 points )
ELEN E3301: Electronic circuits (3.0 points)
SIEO W3600: Introduction to probability and statistics (4.0 points)
IEOR W4105: Probability (3.0 points )
IEOR W4106: Stochastic models (3.0 points)
MSAE E3103: Elements of materials science (3.0 points)
MSAE E3142: Processing of ceramics and polymers (3.0 points)

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Minor in Civil Engineering

1. CIEN E3121: Structural analysis (3.0 points)
or
ENME E3161: Fluid mechanics (4.0 points )
or
MECE E3100: Introduction to mechanics of fluids (3.0 points)

2. ENME E3105: Mechanics (4.0 points)

3. ENME E3113: Mechanics of solids (3.0 points)

4-6. Electives (any three)
CIEN E1201: Design of buildings, bridges, and spacecraft (3.0 points)
ENME E3161: Fluid mechanics (4.0 points )
ENME E3114: Experimental mechanics of materials (4.0 points)
MECE E3414: Advanced strength of materials (3.0 points )
CIEN E4332: Finite element analysis, I (3.0 points )
CIEN E3125: Structural design (3.0 points )
CIEN E4241: Geotechnical engineering fundamentals (3.0 points)
CIEE E3250: Hydrosystems engineering (3.0 points )
CIEE E4163: Environmental engineering: wastewater (3.0 points)
CIEN E3129: Project management for construction (3.0 points )
CIEN E4131: Principles of construction techniques (3.0 points)

Note: At least three of the courses must be courses that are not required in the student's major.
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Minor in Computer Science

Students who pass the Computer Science Advanced Placement Exam, either A or AB, with a 4 or 5 will receive 3 points and exemption from COMS W1004. An additional elective is to be recommended but not required. Parti-cipation in the minor is subject to the approval of the major program adviser. For further information, please see the QuickGuide at www.cs.columbia. edu/education/undergrad/seasguide.


1. COMS W1004: Introduction to computer science and programming in Java (3.0 points)

2. COMS W1007: Object-oriented programming and design (3.0 points)
or
COMS W1009: Introduction to computer science (honors) (3.0 points)

3. COMS W3133: Data structures in C (3.0 points)
or
COMS W3134: Data structures in Java (3.0 points )
or
COMS W3137: Data structures and algorithms (4.0 points)
or
COMS W3139: Data structures and algorithms (honors) (4.0 points)

4. COMS W3157: Advanced programming (4.0 points)

5. COMS W3203: Discrete mathematics (3.0 points)

6. COMS W3261: Computer science theory (3.0 points)

7. CSEE W3827: Fundamentals of computer systems (3.0 points)
or
a 4000-level COMS technical elective

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Minor in Dance

The SEAS dance minor consists of five 3-point courses. Please note that no performance/choreography courses below count toward the nontech requirement for SEAS students

1–2. Two from the following history/criticism courses:
DNCE BC 2565/2566: History of dance, I and/or II
DNCE BC2570: Dance in New York City
DNCE BC 3000: From the page to the dance stage
DNCE BC 3570: Latin American and Caribbean dance: identities in motion
DNCE BC 3577: Performing the political
DNCE BC 3574: Seminar on contemporary choreographers and their works
DNCE BC 3576: Dance criticism
DNCE BC 3578: Traditions of African-American dance

3–4. Two from the following performance/choreography courses:
DNCE BC 2555: Ensemble repertory: modernDNCE BC 3571: Solo repertory
DNCE BC 2563: Dance composition: form
DNCE BC 2564: Dance composition: content
DNCE BC 3565: Group forms: advanced dance composition
DNCE BC 2567: Music for dance
DNCE BC 2557: Evolution of classic Spanish dance
DNCE BC 2580: Tap as an American art form
DNCE BC 3590: Rehearsal and performance in dance

5. One elective.

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Minor in Earth and Environmental Engineering

1-3. Three courses from the following:
EAEE E3101: Earth resource production systems (3.0 points )
EAEE E3103: Energy, minerals and materials systems (3.0 points)
EAEE E3255: Environmental control and pollution reduction systems (3.0 points)
EAEE E4003: Introduction to aquatic chemistry (3.0 points )
EAEE E4004: Physical processing and recovery of solids (3.0 points)
EAEE E4006: Field methods for environmental engineering (3.0 points)
EAEE E4001: Industrial ecology of earth resources (3.0 points )
EAEE E4160: Solids and hazardous waste management (3.0 points)
EAEE E4257: Environmental data analysis and modeling (3.0 points)
EAEE E4361: Economics of Earth resource industries (3.0 points )
EAEE E4150: Air pollution prevention and control (3.0 points )
EAEE E4200: Production of inorganic materials (3.0 points )
EAEE E4009: GIS for resource, environment and infrastructure management (3.0 points)

4-6. Three courses from the following (other environmentally related courses may also be approved):
ECIA W4100: Management and development of water systems (3.0 points )
CIEN E3141: Soil mechanics (3.0 points )
CIEE E3250: Hydrosystems engineering (3.0 points)
MECE E4211: Energy: sources and conversion (3.0 points)
CIEN E4250: Waste containment design and practice (3.0 points)
CIEE E4252: Environmental engineering (3.0 points )
CIEE E4260: Urban ecology studios (3.0 points )
CHEE E4252: Intro to surface and colloid chemistry (3.0 points)
CIEE E4257: Groundwater contaminant transport and remediation (3.0 points)
CIEE E4163: Environmental engineering: wastewater (3.0 points )
CHEN E4410: Environmental control technology (3.0 points )
CHEN E3010: Principles of chemical engineering thermodynamics (3.0 points)
CHEN E3110: Transport phenomena, I (4.0 points )
SIEO W3600: Introduction to probability and statistics (4.0 points)

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Minor in East Asian Studies

1–5. Any two of the survey courses on Chinese, Japanese, or Korean civilization (ASCE V2359, V2361, V2363), plus three elective courses dealing with East Asia. The elective courses may be taken in departments outside of East Asian Languages and Cultures. The minor does not include a language requirement. However, one semester of an East Asian language class may be used to fulfill one of the three electives, as long as at least two semesters of that language have been taken. Placement exams may not be used in place of these courses.

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Minor in Economics

1. ECON W1105: Principles of economics

2. ECON W3211: Intermediate microeconomics

3. ECON W3213: Intermediate macroeconomics

4. ECON W3412: Introduction to econometrics

Note: W1105 is a prerequisite for W3211, W3213, and W3412. Students must have completed Calculus I before taking W3213, Calculus III before taking W3211, and one of the introductory statistics courses (see list) before taking W3412.

5-6. Two electives from the following:

5–6. Two electives from the following:
ECON W2257: Global economy
BUSI W3003: Corporate finance
or
ECON W4280: Corporate finance
ECON V3025: Financial economics
ECON V3265: Economics of money and banking
ECON W4020: Economics of uncertainty and information
ECON W4080: Globalization, incomes and inequality
ECON W4211: Advanced microeconomics
ECON W4213: Advanced macroeconomics
ECON W4228: Urban economics
ECON G4235: Historical foundations of modern economics
ECON W4251: Industrial organization
ECON G4301: Economic growth and development
ECON W4321: Economic development
ECON W4329: Economics of sustainable development
ECON W4345: World economic problems
ECON W4370: Political economy
ECON W4400: Labor economics
ECON W4412: Advanced econometrics
ECON W4415: Game theory
ECON W4438: Economics of race in the United States
ECON W4457: Industrial organization of art, entertainment and communications
ECON W4465: Public economics
ECON W4480: Gender and applied economics
ECON W4490: Economics of the Internet
ECON W4500: International trade
ECON W4505: International monetary theory and policy
ECON W4615: Law and economics
ECON W4625: Economics of the environment
ECON W4750: Globalization and its risks

Note: Electives may be taken only after the completion of both ECON W3211 and W3213, with the exception of ENGI E2261 and ECON W2257, which may be taken after completion of ECON W1105. Some of the elective courses listed above have additional prerequisites. Courses may be taken only after the completion of all prerequisites. Please see the Columbia College bulletin for course descriptions and complete lists of prerequisites.

7. One from the following statistics courses (or sequence of courses):
STAT W1211: Introduction to statistics
SIEO W3600: Introduction to probability and statistics
IEOR W3658: Probability
and
STAT W3659 or W4107: Statistical inference
SIEO W4150: Introduction to probability and statistics

Notes:

  • The statistics course must be finished before taking ECON W3412, and it is recommended that students take ECON W3412 in the semester following the statistics course.
  • Generally speaking, course work done as part of the economics minor counts toward fulfilling the School's nontechnical requirements. However, ECON W3412: Introduction to econometrics and ENGI E2261: Introduction to accounting and finance, which may be used as courses in the minor program, may not be applied toward satisfaction of the nontechnical course requirements; refer to the nontechnical section on pages 10-12 of this bulletin for further details.
  • Students with AP credit for economics and an exemption for ECON W1105 may use the credit toward the minor
  • Transfer or study abroad credits may not be applied to fulfill the requirements of the economics minor.
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Minor in Electrical Engineering

1. ELEN E1201: Introduction to electrical engineering (3.5 points) (May be replaced by a similar course or roughly equivalent experience)

2. ELEN E3201: Circuit analysis (3.5 points)

3. CSEE W3827: Fundamentals of computer systems (3.0 points)

4. ELEN E3081 and ELEN E3082: Electrical engineering labs (2.0 points)

5. ELEN E3801: Signals and systems (3.5 points)

6. ELEN E3106: Solid-state devices and materials (3.5 points)
or
ELEN E3401: Electromagnetics (4.0 points)

Note: Not available to computer engineering majors.

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Minor in Engineering Mechanics

1. ENME E3105: Mechanics (4.0 points)

2. ENME E3113: Mechanics of solids (3.0 points)

3. ENME E3161: Fluid mechanics (4.0 points)
or
MECE E3100: Mechanics of fluids (3.0 points)

4-6. Electives (any two):
ENME E3106: Dynamics and vibrations (3.0 points)
ENME E3114: Experimental mechanics of materials (4.0 points)
or
MECE E3414: Advanced strength of materials (3.0 points )
CIEN E3121: Structural analysis (3.0 points )
ENME E4202: Advanced mechanics (3.0 points)
ENME E4113: Advanced mechanics of solids (3.0 points
ENME E4114: Mechanics of fracture and fatigue (3.0 points)
ENME E4214: Theory of plates and shells (3.0 points)
ENME E4215: Theory of vibrations (3.0 points)
MECE E3301: Thermodynamics (3.0 points)

Note: At least three of the courses must be courses that are not required in the student's major.
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Minor in English and Comparative Literature

1–5. Any five courses in the English Department with no distribution requirement. No speech courses, only one writing course as above and excluding ENGL C1010, may be taken; total 15 points.

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Minor in French

1-2. FREN W3333: Major literary works to 1800 (3.0 points)
and
FREN W3334: Major literary works since 1800 (3.0 points)

3-5. Three additional courses in French beyond satisfaction of the language requirement, including one course in French cultural studies.

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Minor in French and Francophone Studies

Required: 15 points beyond second-year French.

1-2. FREN W3420: Introduction to French and francophone studies, I (3.0 points)
and
FREN W3421: Introduction to French and francophone studies, II (3.0 points)

3-5. Three additional courses in French beyond satisfaction of the language requirement, including one course in French cultural studies and one in francophone literature.

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Minor in German

Required: 15 points beyond second-year German.

1. GERM V3001 or V3002: Advanced German, I or II (3.0 points)

2. GERM W3333: Introduction to German literature (3.0 points)

3-4. Any two of the period survey courses in German literature and culture, GERM W3442, W3443, W3444, W3445; at least one of these must focus on pre-20th-century culture.

5. One course taken from any 3000/4000 level German or CompLit-German courses taught in German or English.

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Minor in Greek or Latin

1-4. A minimum of 13 points in the chosen language at the 1200-level or higher.

5. 3 points in ancient history of the appropriate civilization.

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Minor in Hispanic Studies

1. SPAN W3300: Advanced language through content (3.0 points)

2. SPAN W3330: Introduction to Hispanic cultures (3.0 points)

3. SPAN W3349: Hispanic cultures, I: Islamic Spain through the colonial period (3.0 points)

4. SPAN W3350: Hispanic cultures, II: Enlightenment to the present (3.0 points)

5. One additional 3000- or 4000-level elective course in the Department of Spanish and Portuguese

Note: Please see the director of undergraduate studies in the Department of Spanish and Portuguese for more information and to declare the minor.
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Minor in History

1-5. Minimum 15 points in the History Department with no distribution or seminar requirements. Transfer or study-abroad credits may not be applied.

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Minor in Industrial Engineering

1. SIEO W3600: Introduction to probability and statistics (4.0 points)

2. IEOR E3608: Introduction to mathematical programming (4.0 points)

3. IEOR E3402: Production-inventory planning and control (3.0 points)

4. IEOR E4003: Industrial economics (3.0 points)

5-6. Electives: Two IEOR courses of interest and approved by a faculty adviser.

Note: In addition to the required courses, students majoring in operations research or engineering and management systems minoring in industrial engineering must take three industrial engineering courses that are not used to satisfy the requirements of their major.
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Minor in Materials Science and Engineering

1. MSAE E3103: Elements of materials science (3.0 points)

2-3. Two from the following courses:
MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3.0 points)
MSAE E3141: Processing of metals and semiconductors (3.0 points )
MSAE E3142: Processing of ceramics and polymers (3.0 points)
MSAE E4090:Nanotechnology (3.0 points)
MSAE E4101: Structural analysis of materials (3.0 points)
MSAE E4206: Electronic and magnetic properties of solids (3.0 points)
MSAE E4215: Mechanical behavior of materials (3.0 points)
MSAE E4250: Ceramics and composites (3.0 points)

4–6. Three from the following courses (other materials-related courses may be acceptable):
APPH E4100: Quantum physics of matter (3.0 points)
CHEE E4050: Industrial and environmental electrochemistry (3.0 points)
CHEE E4252: Introduction to surface and colloid chemistry (3.0 points)
CHEE E4530: Corrosion of metals (3.0 points)
CHEE E4620: Introduction to polymer science (3.0 points)
CHEN E4630: Polymer laboratory (3.0 points)
CHEM C3443-C3444: Organic chemistry (3.5 points)
ELEN E4411: Fundamentals of photonics (3.0 points)
ELEN E4301: Introduction to semiconductor devices (3.0 points)
ELEN E4944: Principles of device microfabrication (3.0 points)
ENME E4113: Advanced mechanics of solids (3.0 points)
ENME E4114: Mechanics of fracture and fatigue (3.0 points)
MECE E4608: Manufacturing processes (3.0 points)
MECE E4701: Introductory biomechanics (3.0 points)

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Minor in Mechanical Engineering

1–4. Any four courses from the following (equivalent substitution courses require the approval of the mechanical engineering program adviser):
MECE E3100: Introduction to mechanics of fluids (3.0 points)
or one of the following:

ENME E3161: Fluid mechanics (4.0 points)
CHEN E3110: Transport phenomena, I (4.0 points)
EAEE E4900: Applied transport and chemical rate phenomena (3.0 points)
ENME E3105: Mechanics (4.0 points)

MECE E3301: Thermodynamics (3.0 points)
or one of the following:

CHEN E3010: Principles of chemical engineering thermodynamics (4.0 points)
MSAE E3111: Thermodynamics, kinetic theory, and statistical mechanics (3.0 points)


ENME E3113: Mechanics of solids (3.0 points)
MECE E3408: Computer graphics and design (3.0 points)
MECE E3311: Heat transfer (3.0 points)
MECE E4608: Manufacturing processes (3.0 points)
MECE E3409: Computer-aided design (3.0 points)
EEME E3601: Classical control systems (3.0 points)

5–6. Electives: Two additional mechanical engineering courses from either the above list or the following (not all courses in this list are given every year):
MECE E3401: Mechanics of machines (3.0 points)
MECE E4058: Mechatronics and embedded microcomputer control (3.0 points)
MECE E4100: Mechanics of fluids (3.0 points)
MECE E4211: Energy: sources and conversion (3.0 points)
MECE E4212: Microelectromechanical systems (3.0 points)
MECE E4302: Advanced thermodynamics (3.0 points)
MECE E4404: Lubrication theory and design (3.0 points)
MECE E4501: Geometrical modeling (3.0 points)
MECE E4502: Computational geometry for CAD/CAM (3.0 points)
EEME E4601: Digital control systems (3.0 points)
MECE E4602: Introduction to robotics (3.0 points)
MECE E4604: Product design for manufacturability (3.0 points)
MECE E4609: Computer-aided manufacturing (3.0 points)
MECE E4610: Advanced manufacturing processes (3.0 points)

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Minor in Middle East and Asian Languages and Cultures

1–5. Five courses, to be chosen with the approval of the MEALAC Director of Undergraduate Studies; no elementary or intermediate language courses may be taken.

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Minor in Music

1. MUSI V2318-V2319: Diatonic harmony and counterpoint (6.0 points)

2. MUSI V1312-V1313: Introductory ear training (1.0 point)

3. MUSI V2314: Ear training, I (1.0 point)

4. One course from the following:
MUSI V3128: History of Western music I: Middle Ages to baroque (3.0 points)
MUSI V3129: History of Western music II: classical to 20th century (3.0 points)

5–6. Any two electives at the 3000- or 4000- level. See also the SEAS-approved nontechnical electives in music (page 15).

Notes:

  • Students must successfully place out of MUSI V1002: Fundamentals of Western music (3.0 points).
  • Steps 4 and 5 must be completed to fulfill the nontechnical elective requirement for graduation.
  • Students are strongly encouraged to take HUMA W1123: Masterpieces of Western music (3.0 points) from the list of nontechnical electives.
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Minor in Operations Research

1. IEOR E3106: Stochastic models (3.0 points)

2. SIEO W3600: Introduction to probability and statistics (4.0 points)

3. IEOR E3608: Introduction to mathematical programming (4.0 points)

4. IEOR E4404: Simulation (3.0 points)

5–6. Electives: Two IEOR courses of interest and approved by a faculty adviser. IEOR E3402: Production-inventory planning and control (3.0 points) is strongly recommended.

Note: In addition to the required courses, students majoring in industrial engineering or engineering management systems must take three operations research courses that are not used to satisfy the requirements of their major.
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Minor in Philosophy

1–5. Any five courses in the Philosophy Department with no distribution requirement; total 15 points. See also the list of exceptions on page 17.

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Minor in Political Science

1–2. Two from the following courses:
W1201: Introduction to American government and politics (3.0 points)
W1501: Comparative politics: an introduction (3.0 points)
W1601: Introduction to international politics (3.0 points)

3–5. Any three courses in the Political Science Department with no distribution requirement; total 9 points.

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Minor in Psychology

Five courses required, including PSYC W1001 and courses in at least two of the three groups listed below (for example, you could select two courses from Group I and two from Group III along with the required W1001); total 15 points (minimum).

1. PSYC W1001: The science of psychology

2–5. Any four courses from, at a minimum, two of the three groups below:

I. PERCEPTION AND COGNITION
Courses numbered in the 2200s, 3200s, or 4200s. Also PSYC W1420, W1480, or W1490.

II. PSYCHOBIOLOGY AND NEUROSCIENCE
PSYC W1010: Mind, brain, and behavior (3.0 points)
Courses numbered in the 2400s, 3400s, or 4400s. Also PSYC W1440 or W4155.

III. SOCIAL, PERSONALITY, AND ABNORMAL
Courses numbered in the 2600s, 3600s, or 4600s. Also PSYC W1450 or W1455.

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Minor in Religion

1–5. Five courses (total 15 points), one of which must be at the 2000 level.

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Minor in Sociology

1. SOCI V1202: Sociological imagination (3.0 points)

2. SOCI V1205: Evaluation of evidence (3.0 points)

3. SOCI V3100: Classical social theory (3.0 points)

4–5. Any two 3000- or 4000-level courses offered by the Department of Sociology; total 6 points.

Note: The year’s array of elective courses can be found online in the Columbia College or General Studies bulletin.
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Minor in Statistics

1. STAT W1111 or W1211: Introduction to statistics (3.0 points)

2. STAT W2110: Introduction to applied statistics (3.0 points)

3. STAT W3105: Introduction to probability (3.0 points)
or
STAT W4105: Probability (3.0 points)

4. STAT W3107or STAT W4107 (3.0 points)

5. STAT W4315: Linear regression models (3.0 points)

6. One of any other 4000-level courses, excluding STAT W4105, W4107, and W3109.

Note: Well-prepared students may substitute W4201 (to be taken after W4315) for W1111 (or W1211) and V2010.

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Minor in Technological Entrepreneurship

 Minimum: 15 points

1-3. Required courses:
ENGI E2261: Introduction to accounting and finance (3.0 points)
BUSI W3020: Introduction to marketing and marketing management (3.0 points)
IEOR E4998: Mnaging technological innovation and entrepreneurship (3.0 points)

4-5. Electives (either two courses from list A or one course from list A and one from list B):

 A. Engineering electives (at least one)
CHEN E4020: Protection of industrial and business property (3.0 points)
CIEN E4136: Entrepreneurship in civil engineering and construction (3.0 points)
COMS W4444: Programming and problem solving (3.0 points)
BMEN E3998: Projects in biomedical engineering (3.0 points)
IEOR E4550: Entrepreneurial business creation for engineers (3.0 points)
ISME E4310: The manufacturing enterprise (3.0 points)


Either SCNC W3010: Science, technology, and society (3.0 points)
or
URBS V3310: Science and technology in urban environments (3.0 points)
(but not both)

B. Other electives (no more than one)
ECON W4280: Corporate finance (3.0 points)
BUSI W3010: Managing human behavior in the organization (3.0 points)
IEOR W4308: Industrial budgeting and finance control (3.0 points)

 

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