Dual degree plan prerequisite coursework

by Dr. Eugeniy E. Mikhailov

Foreword

The W&M liaisons do their best to make the following list of prerequisites up-to-date and matching Columbia requirements. However, you are advised to check the original source of requirements yourself. If you spot an error please let us know.

Please, have a look at the list of the Frequently Asked Questions.

Disclaimer

William & Mary is accredited by the Southern Association of Colleges and Schools Commission on Colleges to award baccalaureate, master’s, educational specialist, and doctoral degrees. Columbia University is not accredited by SACS Commission on Colleges and the accreditation of William & Mary does not extend to or include Columbia University or its students. Further, although William & Mary agrees to accept certain course work from Columbia University to be applied toward an award from William & Mary, that course work may not be accepted by other colleges or universities in transfer, even if it appears on a transcript from William & Mary. The decision to accept course work in transfer from any institution is made by the institution considering the acceptance of credits or course work.

General requirements

Foundation Courses Required of All Majors

Mathematics

Physics

Chemistry

Lab Requirement

Computer Science

Humanities and Social Sciences

Major-Specific Coursework

Notes

Courses marked with a * may be taken either before or during enrollment at Columbia.

Applied Mathematics or Applied Physics

Mathematics

  • Columbia: Ordinary Differential Equations (MATH UN2030)
    • W&M: Ordinary Differential Equations (MATH 302)

Physics

Chemistry/Biology (one of the following; labs not required)

  • Columbia: General Chemistry I (CHEM UN1403)
  • Columbia: Environmental Biology I: Elements to Organisms (EEEB UN2001)
    • W&M: Introduction to Molecules, Cells, Development (BIOL 225) discontinued since 2018 and replaced with Introduction to Biology (BIOL 203)
  • Columbia: Introduction to Biology I: Biochemistry, Genetics and Molecular Biology (BIOL UN2005)
    • W&M: Introduction to Organisms, Ecology, Evolution (BIOL 220) discontinued since 2018 and replaced with Introduction to Biology (BIOL 204)

Biomedical Engineering

Mathematics

  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101)

Physics

  • Columbia: Introduction to Classical and Quantum Waves (PHYS UN1403)

Chemistry

  • Columbia: General Chemistry II (CHEM UN1404)
    • W&M: Inorganic and General Chemistry II (CHEM 305 discontinued since 2017) or General Chemistry II for Life Sciences (CHEM 308) discontinued since 2017) or General Chemistry II and Introduction to Inorganic Chemistry (CHEM 208) or Advanced Freshman Chemistry (CHEM 205)
  • Columbia: General Chemistry Lab (CHEM UN1500)
    • W&M: General Chemistry I Laboratory (CHEM 103L)

Computer Science

  • Columbia: Introduction to Computing for Engineers and Applied Scientists in Python (ENGI E1006)
    • W&M: Computational problem solving (CSCI 141) or Practical Computing for Scientists (PHYS 256)

Additional

  • Columbia: Introduction to Biology I: Biochemistry, Genetics and Molecular Biology (BIOL UN2005)
    • W&M: Introduction to Organisms, Ecology, Evolution (BIOL 220) discontinued since 2018 and replaced with Introduction to Biology (BIOL 204)
  • Columbia: Introduction to Biology II: Cell Biology, Development and Physiology (BIOL UN2006)
    • W&M: Introduction to Molecules, Cells, Development (BIOL 225) discontinued since 2018 and replaced with Introduction to Biology (BIOL 203)
  • Columbia: Introduction to Electrical Engineering (ELEN E1201)*.

Chemical Engineering

Mathematics (choose one)

  • Columbia: Ordinary Differential Equations (MATH UN2030)
    • W&M: Ordinary Differential Equations (MATH 302)
  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101). Students must take both an ODE course and a Linear Algebra course.

Physics

Chemistry

  • Columbia: General Chemistry II (CHEM UN1404)
    • W&M: Inorganic and General Chemistry II (CHEM 305 discontinued since 2017) or General Chemistry II for Life Sciences (CHEM 308) discontinued since 2017) or General Chemistry II and Introduction to Inorganic Chemistry (CHEM 208) or Advanced Freshman Chemistry (CHEM 205)
  • Columbia: General Chemistry Lab (CHEM UN1500)
    • W&M: General Chemistry I Laboratory (CHEM 103L)
  • Columbia: Organic Chemistry I (CHEM UN2443)
  • Columbia: Organic Chemistry Lab (CHEM UN2943)*
    • W&M: Organic Chemistry Laboratory I (CHEM 206L)
  • Columbia: Introduction to Computing for Engineers and Applied Scientists in Python (ENGI E1006)
    • W&M: Computational problem solving (CSCI 141) or Practical Computing for Scientists (PHYS 256)

Civil Engineering

Mathematics

  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101). Students must take both an ODE course and a Linear Algebra course.

Computer Science

  • Columbia: Introduction to Computer Science and Programming in MATLAB (COMS W1005). The department strongly recommends MATLAB over other languages, though it will accept any language.
    • W&M: Computational problem solving (CSCI 141) or Practical Computing for Scientists (PHYS 256)

Additional

  • Columbia: Earth: Origin, Evolution, Processes Future (EESC UN1011)
    • W&M: The Dynamic Earth: Physical Geology (GEOL 101)
  • Columbia: Mechanics (ENME E3105)*
    • W&M: Classical Mechanics of Particles and Waves I (PHYS 208)

Computer Engineering

Mathematics

  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101). Students must take both an ODE course and a Linear Algebra course.

Computer Science

  • Columbia: Discrete Mathematics (COMS W3203)
    • W&M: Discrete Structures of Computer Science (CSCI 243) (recomended) or Foundations of Mathematics (MATH 214)
  • Columbia: Introduction to Computer Science and Programming in Java (COMS W1004) or Honors Introduction to Computer Science in Java (COMS W1007)
    • W&M: Computational problem solving (CSCI 141) or Practical Computing for Scientists (PHYS 256)

Additional

Computer Science

Computer Science

  • Columbia: Discrete Mathematics (COMS W3203)
    • W&M: Discrete Structures of Computer Science (CSCI 243) (recomended) or Foundations of Mathematics (MATH 214)
  • Columbia: Introduction to Computer Science and Programming in Java (COMS W1004) or Honors Introduction to Computer Science in Java (COMS W1007)
    • W&M: Computational problem solving (CSCI 141) or Practical Computing for Scientists (PHYS 256)
  • Columbia: Data Structures in Java (COMS W3134) or Data Structures and Algorithms (COMS W3137)

Earth and Environmental Engineering

Mathematics

  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101). Students must take both an ODE course and a Linear Algebra course.
  • Columbia: Introduction to Probability and Statistics (CIEO W3600)* The course must have calculus, including multivariable integration, as a prerequisite.

Chemistry

  • Columbia: General Chemistry II (CHEM UN1404)
    • W&M: Inorganic and General Chemistry II (CHEM 305 discontinued since 2017) or General Chemistry II for Life Sciences (CHEM 308) discontinued since 2017) or General Chemistry II and Introduction to Inorganic Chemistry (CHEM 208) or Advanced Freshman Chemistry (CHEM 205)
  • Columbia: General Chemistry Lab (CHEM UN1500)
    • W&M: General Chemistry I Laboratory (CHEM 103L)

Additional

  • Columbia: A Better Planet by Design (EAEE E2100)*
    • W&M: No equivalent

Additional (choose one)

  • Columbia: Earth’s Environmental Systems: The Climate System (EESC UN2100)*
    • W&M: Earth’s Environmental Systems: Physical Geography (GEOL 110)
  • Columbia: Earth’s Environmental Systems: The Solid Earth System (EESC UN2200)*
    • W&M: The Dynamic Earth: Physical Geology (GEOL 101)

Additional Elective (choose one)

  • Columbia: Organic Chemistry I (CHEM UN2443)
  • Columbia: Introduction to Classical and Quantum Waves (PHYS UN1403)
  • Columbia: Introductory Biology I: Biochemistry, Genetics and Molecular Biology (BIOL UN2005)
    • W&M: Introduction to Organisms, Ecology, Evolution (BIOL 220) discontinued since 2018 and replaced with Introduction to Biology (BIOL 204)

Electrical Engineering

Mathematics

  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101). Students must take both an ODE course and a Linear Algebra course.

Physics

  • Columbia: Introduction to Classical and Quantum Waves (PHYS UN1403)

Computer Science

  • Columbia: Sufficient knowledge of computer programming is needed in order to take Data Structures in Java (COMS W3134) or Data Structures and Algorithms (COMS W3137) at Columbia.
    • W&M: see prerequisites for Data Structures (CSCI 241)

Additional

Engineering Mechanics

Mathematics

  • Columbia: Ordinary Differential Equations (MATH UN2030)
    • W&M: Ordinary Differential Equations (MATH 302)

Additional

  • Columbia: Mechanics (ENME E3105)*
    • W&M: Classical Mechanics of Particles and Waves I (PHYS 208)

IEOR: Industrial Engineering, Engineering Management Systems or Operations Research

Mathematics

  • Columbia: Ordinary Differential Equations (MATH UN2030) This course must be taken prior to Columbia for any student with interests in the Financial Engineering major. Students cannot apply to this major until they are already enrolled at Columbia (after the first semester in Columbia Engineering).
    • W&M: Ordinary Differential Equations (MATH 302)
  • Columbia: Linear Algebra (MATH UN2010) or Applied Mathematics I: Linear Algebra (APMA E3101)
  • Columbia: Probability for Engineers (IEOR E3658) or Probability Theory (STAT GU4203)
  • Columbia: Applied Statistical Models in Operations Research (IEOR E4307) or Statistical Inference (STAT GU4204)
    • W&M: Mathematical Statistics (MATH 452)

Computer Science (choose one language pair)

The department strongly recommends JAVA over C/C++ with Python.

  • Columbia: Introduction to Computing for Engineers and Applied Scientists in Python (ENGI E1006) or Introduction to Computer Programming in Java (COMS W1004)
    • W&M: Computational problem solving (CSCI 141) or Practical Computing for Scientists (PHYS 256)
  • Columbia: Essential Data Structures in C/C++ (COMS W3136) or Data Structures in JAVA (COMS W3134)

Economics

  • Columbia: Introduction to Accounting and Finance (IEOR E2261)*, This course must be taken prior to Columbia for any student with interests in the Financial Engineering major. Students cannot apply to this major until they are already enrolled at Columbia (after the first semester in Columbia Engineering).
    • W&M: Principles of Accounting (BUAD 203)

Materials Science and Engineering

Mathematics

  • Columbia: Ordinary Differential Equations (MATH UN2030)
    • W&M: Ordinary Differential Equations (MATH 302)

Physics

  • Columbia: Introduction to Classical and Quantum Waves (PHYS UN1403)

Chemistry (choose one of the following two)

  • Columbia: General Chemistry I (CHEM UN1403)
  • Columbia: General Chemistry II (CHEM UN1404)
    • W&M: Inorganic and General Chemistry II (CHEM 305 discontinued since 2017) or General Chemistry II for Life Sciences (CHEM 308) discontinued since 2017) or General Chemistry II and Introduction to Inorganic Chemistry (CHEM 208) or Advanced Freshman Chemistry (CHEM 205)

Mechanical Engineering

Mathematics

  • Columbia: Introduction to Applied Mathematics: Ordinary Differential Equations and Linear Algebra (APMA E2101) Students must take both an ODE course and a Linear Algebra course.

Computer Science

  • Columbia: Foundations of Data Science ORCA E2500
    • W&M: Programming for Data Science (DATA 141) or Computational Problem Solving in Data Science (CSCI 140)

Additional

Physics/Biology (choose one)

  • Columbia: Introduction to Classical and Quantum Waves (PHYS UN1403)
  • Columbia: Environmental Biology I: Elements to Organisms (EEEB UN2001)
    • W&M: Introduction to Molecules, Cells, Development (BIOL 225) discontinued since 2018 and replaced with Introduction to Biology (BIOL 203)
  • Columbia: Introductory Biology I: Biochemistry, Genetics and Molecular Biology (BIOL UN2005)
    • W&M: Introduction to Organisms, Ecology, Evolution (BIOL 220) discontinued since 2018 and replaced with Introduction to Biology (BIOL 204)