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 studies3.0 points
2-6. Five additional courses in American Studies with no distribution or seminar requirements. Students are encouraged to take seminars.
back to topMinor in Applied Mathematics
Prospective students should consult the first- and second-year requirements for applied mathematics majors to ensure that prerequisites for the appliedmathematics 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.back to top
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 points
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
E4112:
Laser physics 3.0 points
APPH E4300:
Applied electrodynamics 3.0 points
APPH E4301:
Introduction to plasma physics 3.0 points
Minor in Architecture
1-2. Two of the following courses:
ARCH V1020:
Introduction to architectural design and visual culture 3.0 points
AHIS C3001:
Introduction to architecture 3.0 points
ARCH V3117:
Perception of architecture 3.0 points
ARCH A4220:
Enclosures and environments, I 3.0 points
3-5. Three of the following courses:
ARCH A4221:
Enclosures and environments, II 3.0 points
ARCH A4125:
Building systems, I 3.0 points
ARCH A4610:
Building systems, II 3.0 points
ARCH A4627:
Materials and methods in architecture 3.0 points
ARCH A4629:
Architectural acoustics/architecture lighting 3.0 points
ARCH A4634:
Advanced curtain walls 3.0 points
ARCH A4684:
Sustainable design 3.0 points
ARCH A4151:
Foundations of urban economic analysis 3.0 points
ARCH A4208:
Quantitative techniques 3.0 points
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.
back to topMinor 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 Track3. 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 or 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 of the following courses:
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 of 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 of 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
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 two)
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
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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. Participation 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 Java3.0 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
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 of 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 of the following performance/ choreography courses:
DNCE BC 2555:
Ensemble repertory: modern
DNCE 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.
back to topMinor 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
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.back to top
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:
ECON W2257:
Global economy
ECON W2261:
Intro to accounting and finance
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 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 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
7. One of the following statistics courses (or sequence of courses):
STAT W1211:
Introduction to statistics
SIEO W3600:
Introduction to probability and statistics
SIEO W3658:
Probability
and
STAT W3659 or W4107:
Statistical inference
SIEO W4150:
Introduction to probability and statistics
• 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 ECON W2261: 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.
• 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.
back to top
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.back to top
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
back to top
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.
back to topMinor 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.
back to topMinor 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.
back to topMinor 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.
back to topMinor 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.
back to topMinor 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.back to top
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.
back to topMinor 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.back to top
Minor in Materials Science and Engineering
1. MSAE E3103: Elements of materials science 3.0 points
2-3. Two of the following courses:
MSAE E3111:
Thermodynamics, kinetic theory, and statistical mechanics 3.0 points
or
CHEN E3010:
Principles of chemical engineering thermodynamics 3.0 points
MSAE E3141:
Processing of metals and semiconductors 3.0 points
MSAE E3142:
Processing of ceramics and polymers 3.0 points
MSAE E4206: Electronic and magnetic properties of
solids 3.0 points
MSAE E4101: Structural analysis
of materials 3.0 points
4–6. Three of 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
EAEE E4900: Applied transport and chemical
rate phenomena 3.0 points
ELEN E3106: Solid-state
devices and materials 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
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
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.
back to topMinor in Music
1. MUSI V2318-V2319: Diatonic harmony and counterpoint 6.0 points
2. MUSI V1312-V1313: Introductory ear training 1.0 points
3. MUSI V2314: Ear training, I 1.0 points
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.
back to top
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.back to top
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.
back to topMinor in Political Science
1–2. Two of 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.
back to topMinor 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.
Minor in Religion
1–5. Five courses (total 15 points), one of which must
be at the 2000 level.
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.back to top
Minor in Statistics
1. STAT W1111 or W1211: Introduction to statistics3.0 points
2. STAT W2110: Introduction to applied statistics3.0 points
3. STAT W3000: Introduction to statistics: probability models 3.0 points or SIEO W4105: Probability 3.0 points
4. STAT W3659 or STAT W4107 3.0 points
5. STAT W4315: Linear regression models 3.0 points
6. One course from the following:
STAT W3701:
Advanced data analysis 3.0 points
STAT W4220: Analysis of categorical data 3.0 points
STAT W4325: Generalized linear models 3.0 points
STAT W4330: Regression and multilevel models
3.0 points
STAT W4437: Time series analysis 3.0 points
STAT W4415: Multivariate statistical inference
3.0 points
STAT W4543: Survival analysis 3.0 points
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