Columbia University and Whitworth University
The Fu Foundation School of Engineering and Applied Science
PRE – COMBINED PLAN CURRICULUM GUIDE
For fall 2012 admission
The equivalents of the following Columbia courses are required. Please see the SEAS Bulletin for course and program
descriptions: http://www.engineering.columbia.edu/bulletin/. Students must complete the Combined Plan program in
four (4) consecutive semesters. Please e-mail combinedplan@columbia.edu with questions regarding course
equivalencies. If your institution does not offer a required course listed in this guide, please speak with your liaison
about other ways to fulfill the requirement.
FOUNDATION COURSES REQUIRED OF ALL MAJORS:
i.
MATHEMATICS
□
ii.
PHYSICS
□
□
iii.
The full sequence of Calculus I, II, III, IV (V1101, V1102, V1201, V1202).
Whitworth course equivalents MA 171 Calculus I, MA 172 Calculus II, MA 273 Calculus III
Mechanics and Thermodynamics (C1401)
Whitworth course equivalents PS 151 General Physics I
Electricity, Magnetism, and Optics (C1402)
Whitworth course equivalent PS 153 General Physics II
CHEMISTRY
□
General Chemistry I (C1403)
Whitworth course equivalent CH 161 General Chemistry I
Please see individual programs below for details. Some programs require an additional second semester of General
Chemistry (C1404) or have possible substitutions.
iv.
LAB REQUIREMENT
Whitworth course equivalent PS 151L, PS153L or CH 161L
Either one-semester physics lab or one-semester chemistry lab is generally required. Please see individual programs below
for more details.
v.
COMPUTER SCIENCE
□
Introduction to computer science and programming in C++, JAVA, or MATLAB (W1003,
W1004, W1005, W1007 or W1009)
Whitworth course equivalent CS171 Computer Science I
Some majors require a specific programming language (see requirements for majors below).
vi.
HUMANITIES AND SOCIAL SCIENCES
□
Twenty-seven- (27) -point nontechnical requirement is satisfied by the course work taken for the
bachelor’s degree awarded by the home institution. Among those courses the students must
include:
○
Principles of Economics (ECON W1105)
Whitworth course equivalent EC 210 Principles of Microeconomics
○
English Composition (ENGL C1010 University Writing).
Whitworth course equivalent EL 110 Writing I or EL 210 Writing II
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
1
REQUIRED FOR MAJORS IN:
(Notes in italics clarify requirements.)
APPLIED MATHEMATICS or APPLIED PHYSICS
MATHEMATICS
□
Ordinary Differential Equations (E1210)
Whitworth course equivalent MA 281 Differential Equations
PHYSICS
□
□
Classical and Quantum Waves (C1403)
Physics Lab (C1493/4)
Whitworth course equivalent PS 251W General Physics III and PS 251L
CHEMISTRY / BIOLOGY (choose one course listed below. Chemistry/Biology labs not required.)
□
□
□
General Chemistry I (C1403)
Whitworth course equivalent CH 161General Chemistry I
Environmental Biology: Molecules to Cells (EEEB W2001)
Whitworth course equivalent BI 140: General Biology I, Genes, Cells, Evolution
Introduction to Molecular and Cellular Biology (C2005)
Whitworth course equivalent BI 140: General Biology I, Genes, Cells, Evolution
BIOMEDICAL ENGINEERING
ALL TRACKS
MATHEMATICS
□
Introduction to applied mathematics – Ordinary Differential Equations and Linear Algebra
(APMA E2101). Students who take an ODE course must also take a Linear Algebra course.
Whitworth course equivalent MA 281 Differential Equations
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS
□
Classical and Quantum Waves (C1403)
Whitworth course equivalent PS 251W General Physics III
CHEMISTRY
□
□
□
General Chemistry II (C1404)
Whitworth course equivalent CH 181 General Chemistry II
General Chemistry Lab (C1500)
Whitworth course equivalent CH 181L General Chemistry II Lab
Organic Chemistry I (C3443)
Whitworth course equivalent CH 271 Organic Chemistry I
ELECTRICAL ENGINEERING
□
Introduction to Electrical Engineering (ELEN E1201) [may be taken the summer before entering or
while at Columbia]
Whitworth course equivalent PS 373 Electronics
ELECTRICAL MECHANICS
□
Mechanics (ENME E3105) [may be taken the summer before entering or while at Columbia]
Whitworth course equivalent EN 351 Mechanics: Dynamics
COMPUTER SCIENCE
Introduction to Computer Science and Programming in MATLAB (COMS W1005) preferred
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
2
CHEMICAL ENGINEERING
MATHEMATICS (choose one course listed below)
□ Ordinary Differential Equations (E1210)
Whitworth course equivalent MA 281 Differential Equations
□
Introduction to applied mathematics – Ordinary Differential Equations & Linear Algebra
(APMA E2101).
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
CHEMISTRY
□
General Chemistry II (C1404)
Whitworth course equivalent CH 181 General Chemistry II
□
General Chemistry Lab (C1500)
Whitworth course equivalent CH 181L General Chemistry II Lab
□
Organic Chemistry I (C3443)
Whitworth course equivalent CH 271 Organic Chemistry I
□
Organic Chemistry Lab (C3543)
Whitworth course equivalent CH 271L Organic Chemistry I Lab
CIVIL ENGINEERING
MATHEMATICS
□
Introduction to applied mathematics – Ordinary Differential Equations & Linear Algebra
(APMA E2101). Students who take an ODE course must also take a Linear Algebra course.
Whitworth course equivalent MA 281 Differential Equations
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
□
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
ENGINEERING MECHANICS
□
Mechanics (ENME E3105) [may be taken the summer before entering or while at Columbia]
Whitworth course equivalent EN 351 Mechanics: Dynamics
COMPUTER SCIENCE
Introduction to Computer Science and Programming in MATLAB (COMS W1005) preferred
COMPUTER ENGINEERING
MATHEMATICS
□
Introduction to applied mathematics – Ordinary Differential Equations & Linear Algebra
(APMA E2101). Students who take an ODE course must also take a Linear Algebra course.
Whitworth course equivalent MA 281 Differential Equations
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
□
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
3
COMPUTER SCIENCE (Computer Programming in JAVA is required.)
□
Discrete Mathematics (COMS W3203)
Whitworth course equivalent MA 278 Discrete Math and CS 372 JAVA Applications Development
ELECTRICAL ENGINEERING
□
Introduction to Electrical Engineering (ELEN E1201) [may be taken the summer before entering or
while at Columbia]
Whitworth course equivalent PS 373 Electronics
COMPUTER SCIENCE
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
COMPUTER SCIENCE (Computer Programming in JAVA is required.)
□
□
□
Whitworth course equivalent CS 372 JAVA Applications Development
Data Structures and Algorithms (COMS W3137)
Whitworth course equivalent CS 273 Data Structures
Discrete Mathematics (COMS W3203)
Whitworth course equivalent MA 278 Discrete Math
Scientific Computation (COMS W3210)
Whitworth course equivalent MA 350 Numerical Analysis
EARTH AND ENVIRONMENTAL ENGINEERING
MATHEMATICS
□
Introduction to applied mathematics – Ordinary Differential Equations & Linear Algebra
(APMA E2101). Students who take an ODE course must also take a Linear Algebra course.
Whitworth course equivalent MA 281 Differential Equations
Whitworth course equivalent MA 330 Linear Algebra
CHEMISTRY
□
□
General Chemistry II (C1404)
Whitworth course equivalent CH 181 General Chemistry II
General Chemistry Lab (C1500)
Whitworth course equivalent CH 181L General Chemistry II Lab
OTHER SCIENCE ELECTIVE (choose one course listed below)
□
Organic Chemistry (CHEM C3443)
Whitworth course equivalent CH 271 Organic Chemistry I
□
Classical & Quantum Waves (PHYS C1403)
Whitworth course equivalent PS 251W General Physics III
□
Introduction to Molecular and Cellular Biology (BIOL C2005)
Whitworth course equivalent BI 140: General Biology I, Genes, Cells, Evolution
EARTH AND ENVIRONMENTAL SCIENCES (choose one course listed below)
No Whitworth course equivalents
□
Advanced General Geology (EESC W4001) [may be taken while at Columbia]
□
The Climate System (EESC V2100) [may be taken while at Columbia]
□
The Solid Earth System (EESC V2200) [may be taken while at Columbia]
EARTH AND ENVIRONMENTAL ENGINEERING
No Whitworth course equivalents
□
Alternate Energy Resources (EAEE E2002) [may be taken at Columbia]
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
4
ELECTRICAL ENGINEERING
MATHEMATICS
□
Introduction to applied mathematics – Ordinary Differential Equations & Linear Algebra
(APMA E2101). Students who take an ODE course must also take a Linear Algebra course.
Whitworth course equivalent MA 281 Differential Equations
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS
□
□
Classical and Quantum Waves (C1403)
Whitworth course equivalent PS 251W General Physics III
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
COMPUTER SCIENCE
Computer Programming in JAVA (W1007) is recommended.
ELECTRICAL ENGINEERING
□
Introduction to Electrical Engineering (ELEN E1201) [may be taken the summer before entering or
while at Columbia]
Whitworth course equivalent PS 373 Electronics
IEOR: ENGINEERING MANAGEMENT SYSTEMS
MATHEMATICS (choose one course listed below)
□
Linear Algebra (MATH V2010 or APAM E3101)
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
COMPUTER SCIENCE (choose one set of courses listed below)
□
□
□
□
Computer Programming in C (W1003)
Whitworth course equivalent CS171 Computer Science I
Data Structures in C (W3133)
Whitworth course equivalent CS 273 Data Structures
-orComputer Programming in JAVA (W1007)
Whitworth course equivalent CS 372 JAVA Applications Development
Data Structures in JAVA (W3134)
The Department strongly recommends JAVA over C.
ECONOMICS
□
Introduction to Accounting and Finance (E2261)
Whitworth course equivalent BU 230 Financial Accounting
PROBABILITY AND STATISTICS
□
Introduction to Probability and Statistics (W3600)
Please note that the course must have calculus as a pre-requisite. The Department strongly suggests taking two
separate courses: one in Probability and one in Statistics.
Whitworth course equivalent MA 357 Mathematical Statistics I
IEOR: FINANCIAL ENGINEERING
Students cannot apply directly to IEOR: Financial Engineering because this concentration in
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
5
Operations Research requires an application after one semester of study at Columbia. Students
interested in this concentration must adhere to the following pre-requisite requirements:
MATHEMATICS (choose one course listed below)
□
Linear Algebra (MATH V2010 or APAM E3101)
Whitworth course equivalent MA 330 Linear Algebra
□
Ordinary Differential Equations (MATH V1210)
Whitworth course equivalent MA 281 Differential Equations
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
□
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
COMPUTER SCIENCE (choose one set of courses below)
□
Computer Programming in C (W1003)
Whitworth course equivalent CS 171 Computer Science I
□
Data Structures in C (W3133)
Whitworth course equivalent CS 273 Data Structures
-or□
Computer Programming in JAVA (W1007)
Whitworth course equivalent CS 372 JAVA Applications Development
□
Data Structures in JAVA (W3134)
The Department strongly recommends JAVA over C.
ECONOMICS
□
Introduction to Accounting and Finance (E2261)
Whitworth course equivalent BU 230 Financial Accounting
PROBABILITY AND STATISTICS
□
□
Probability (IEOR E3658)
Whitworth course equivalent MA 357 Mathematical Statistics I
Statistical Inference (W3659)
Whitworth course equivalent MA 358W Mathematical Statistics II
Please note that the course must have calculus as a pre-requisite.
IEOR: INDUSTRIAL ENGINEERING
MATHEMATICS (choose one course listed below)
□
Linear Algebra (MATH V2010 or APAM E3101)
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
□
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
COMPUTER SCIENCE (choose one set of courses below)
□
Computer Programming in C (W1003)
Whitworth course equivalent CS 171 Computer Science I
□
Data Structures in C (W3133)
Whitworth course equivalent CS 273 Data Structures
-or□
Computer Programming in JAVA (W1007)
Whitworth course equivalent CS 372 JAVA Applications Development
□
Data Structures in JAVA (W3134)
The Department strongly recommends JAVA over C.
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
6
ECONOMICS
□
Introduction to Accounting and Finance (E2261)
Whitworth course equivalent BU 230 Financial Accounting
PROBABILITY AND STATISTICS
□
Introduction to Probability and Statistics (W3600)
Please note that the course must have calculus as a pre-requisite. The Department strongly suggests taking two
separate courses: one in Probability and one in Statistics.
Whitworth course equivalent MA 357 Mathematical Statistics I
IEOR: OPERATIONS RESEARCH
MATHEMATICS
□
Linear Algebra (MATH V2010 or APAM E3101)
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
□
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
COMPUTER SCIENCE (choose one set of courses below)
□
Computer Programming in C (W1003)
Whitworth course equivalent CS 171 Computer Science I
□
Data Structures in C (W3133)
Whitworth course equivalent CS 273 Data Structures
-or□
Computer Programming in JAVA (W1007)
Whitworth course equivalent CS 372 JAVA Applications Development
□
Data Structures in JAVA (W3134)
The Department strongly recommends JAVA over C.
ECONOMICS
□
Introduction to Accounting and Finance (E2261)
Whitworth course equivalent BU 230 Financial Accounting
PROBABILITY AND STATISTICS
□
Introduction to Probability and Statistics (W3600)
Please note that the course must have calculus as a pre-requisite. The Department strongly suggests taking two
separate courses: one in Probability and one in Statistics.
Whitworth course equivalent MA 357 Mathematical Statistics I
ENGINEERING MECHANICS
MATHEMATICS
□
Ordinary Differential Equations (E1210)
Whitworth course equivalent MA 281 Differential Equations
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
ENGINEERING MECHANICS
□
Mechanics (ENME E3105) [may be taken the summer before entering or while at Columbia]
Whitworth course equivalent EN 351 Mechanics: Dynamics
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
7
MATERIALS SCIENCE AND ENGINEERING
MATHEMATICS
□
Ordinary Differential Equations (E1210)
Whitworth course equivalent MA 281 Differential Equations
PHYSICS
□
□
Classical and Quantum Waves (C1403)
Whitworth course equivalent PS 251W General Physics III
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
CHEMISTRY
□
□
General Chemistry II (C1404)
Whitworth course equivalent CH 181 General Chemistry II
General Chemistry Lab (C1500)
Whitworth course equivalent CH 181L General Chemistry II Lab
MECHANICAL ENGINEERING
MATHEMATICS
□
Introduction to applied mathematics – Ordinary Differential Equations & Linear Algebra
(APMA E2101). Students who take an ODE course must also take a Linear Algebra course.
Whitworth course equivalent MA 281 Differential Equations
Whitworth course equivalent MA 330 Linear Algebra
PHYSICS/BIOLOGY (choose one course listed below)
□
□
□
Classical and Quantum Waves (PHYS C1403)
Whitworth course equivalent PS 251W General Physics III
Environmental Biology: Molecules to Cells (EEEB W2001)
Whitworth course equivalent BI 140: General Biology I, Genes, Cells, Evolution
Introduction to Molecular and Cellular Biology (C2005)
Whitworth course equivalent BI 140: General Biology I, Genes, Cells, Evolution
PHYSICS/CHEMISTRY LAB (choose one course listed below)
□
□
Physics Lab (C1493/4)
Whitworth course equivalent PS 151L, PS 153L or PS 251L
General Chemistry Lab (C1500)
Whitworth course equivalent CH 161L or CH 181L
ENGINEERING MECHANICS
□
Mechanics (ENME E3105) [may be taken while at Columbia]
Whitworth course equivalent EN 351 Mechanics: Dynamics
ELECTRICAL ENGINEERING
□
Intro. to Electrical Engineering (ELEN E1201) or equivalent [may be taken while at Columbia]
Whitworth course equivalent PS 373 Electronics
Pre- Combined Plan Curriculum Guide (For fall 2011 admission)
8