The College of Engineering and Applied ScienceÌýhas numerous minor and certificate optionsÌýfor engineering students. You can find out about all of your options by visiting the .

You may also be interested in minors and certificates offered outside of the College of Engineering and Applied Science such asÌýApplied Math, Astrophysics, Economics, World Languages, and more. You can find information about all available minors at CU Boulder through our .Ìý

How to Structure Your Classes

Considering a minor or certificate but wondering how it might impact your course schedule? Most minor and certificate classes can also be used to fulfill requirements of your mechanical engineering degree.ÌýThe charts below outline how to best structure your classes to overlap with your major for the most common minor, certificate, and option programs. Use the web links above each chart to view the official, current requirements for each program.

Please note: some minor programs require an application/ prerequisites/ minimum GPA.ÌýPlease contact your academic advisor with questions regarding minors/certificates and their potential impact onÌýyour degree plan.Ìý

Minors

Visit the Applied Math Minor websiteÌý

Applied Math Minor Requirements ME Equivalent

APPM 2350ÌýCalculus 3 for Engineers
or MATH 2400 Calculus 3

Calculus 3

APPM 2360ÌýDiff Eq w/Linear Algebra

APPM 2360

APPM 3310ÌýMatrix Methods

One area of emphasis (see below)

Choose One Emphasis:

General Emphasis

Choose two of the following three courses

APPM 4600 Numerical Methods and Scientific Computing MCEN 3030
APPM 4350 Fourier Series & Boundary Value Problems General Technical Elective
APPM 4360 Complex Variable and ApplicationsÌý General Technical Elective

²¹²Ô»åÌý

One upper-division APPM or STAT Course (3000/4000 Level) General Technical Elective

Scientific Computation Emphasis

APPM 3050ÌýScientific Computing Matlab
or APPM 3650ÌýAlgorithms and Data Structures in Python

General Technical Elective
APPM 4600 Numerical Methods and Scientific Computing MCEN 3030
APPM 4610 Numerical Differential Equations General Technical Elective

Probability & Statistics Emphasis

APPM 3570 Applied Probability General Technical Elective

and one of the following sequences

STAT 4000ÌýStatistical Methods and Applications I
& STAT 4010ÌýStatistical Methods and Applications II

General Technical Elective
General Technical Elective

APPM 4560ÌýMarkov Processes, Queues, and Monte Carlo Simulations
&ÌýSTAT 4520ÌýIntro to Mathematical Statistics

General Technical Elective
General Technical Elective

Visit the Astronomy Minor websiteÌý

Astronomy Minor Requirements (6 courses min.) ME Equivalent

Elementary ASTR Coursework (max of 3)

Recommended: ASTR 2000ÌýAncient Astronomies

Lower-DivisionÌýHumanities/Social Sciences Elective

Advanced ASTR Coursework: 2 courses from one upper-level course sequence--

Planetary Sequence:
ASTR 3720 Planets and Their Atmospheres
ASTR 3750 Planets, Moons, & Rings

Astrophysics Sequence:
ASTR 3730 Stellar & Interstellar
ASTR 3830 Galactic & Extragalactic

Ìý

Ìý

ÌýorÌýGeneral Technical Elective
General Technical Elective

General Technical Elective
General Technical Elective

1 upper-level course from their pre-approved list

General Technical Elective

Visit the Biomedical Minor website

Biomedical Minor Requirements ME Equivalent

BMEN 2000: Biomed Gateway

Cannot apply towards any major requirements

Biomed Elective

Biomed Elective (must be 3000+)

General Technical Elective

Biomed ElectiveÌý(must be 3000+)

General Technical Elective

Biomed ElectiveÌý(must be 3000+)

ME Technical Elective

Biomed ElectiveÌý(must be 3000+)

ME Technical Elective

Business Minor Requirements ME Equivalent

BUSM 2010 & 2011: Marketing & Management

Free Elective

BUSM 2020 & 2021: Finance & Accounting

Free Elective

Track Elective

General Technical Elective

BUSM 4010: Business Plan Development

General Technical Elective

Visit the Computer Science Minor website

Computer Science Minor Requirements

ME Equivalent

CSCI 1300/ ECEN 1310/ ASEN 1320ÌýComputer Science 1

MCEN 1030

CSCI 2270ÌýData Structures

Free Elective

CSCI 2824ÌýDiscrete Structures (Optional but recommended)

Both CSCI 3104 (Algorithms) and CSCI 3155 (Principles of Programming Languages) require a discrete mathematics course as a prerequisite. Students who want to take either of these courses as their Core option will need to plan to take an approved discrete mathematics prerequisite courseÌýin addition toÌýthe course requirements for the minor.Ìý

Free Elective

CSCI 2400ÌýComputer Systems
or ECEN 4593 Computer Organization

Free Elective
orÌýGeneral Technical Elective

One Core Option:
CSCI 3104 Algorithms
CSCI 3155 Principles of Programming Languages
CSCI 3753 Design and Analysis of Operating Systems

General Technical Elective
General Technical Elective
General Technical Elective

Computer Science Elective:
MCEN 3030 orÌýCSCI 3656

MCEN 3030

Computer Science Elective

General Technical Elective

Visit theÌýCreative Technology and Design Minor website

CDT Minor Requirements ME Equivalent

ATLS 1100 Design Foundations

Free Elective

ATLS 1300 Computation Foundations
(CSCI 1200, CSCI 1300, INFO 1701 also accepted)

MCEN 1030 or Free Elective
ATLS 2000 The Meaning of Information Technology Lower-DivisionÌýHumanities/Social Sciences Elective

ATLS 2100ÌýImage

Free Elective

ATLS 2200ÌýWeb

Free Elective

ATLS 2300ÌýText

Free Elective

Upper-Division Focus Elective or Critical Perspectives in Technology Elective (MCEN 3017 and MCEN 4026 qualify)

MCEN 3017 or MCEN 4026

Electrical Engineering Minor Requirements ME Equivalent

MCEN 3017 Circuits & Electronics
Substitutes as ECEN 2250 for EE minors

MCEN 3017

ECEN 2260ÌýCircuits as SystemsÌý

*

ECEN 2270ÌýElectronics Design LabÌý

*

Electrical Engineering Elective

General Technical Elective

Electrical Engineering Elective

General Technical Elective

Electrical Engineering Elective

Free Elective

* ECEN 2260 and ECEN 2270 combined will satisfy ME's Math/Science Foundation requirement.Ìý

Ìý

Energy Engineering Minor Requirements ME Equivalent

Fundamentals-based course:
MCEN 3032 Thermodynamics 2

MCEN 3032

Energy policy/environment-based course:
ENVS 3621 Energy Policy and Society, or
ENVS/PHYS 3070 Energy and the Environment, or
MCEN 4032 Sustainable Energy

Humanities/Social Sciences Elective, or
General Technical Elective, or
ME Technical Elective

Energy Elective

ME Technical Elective, or
General Technical Elective, or

Energy Elective

ME Technical Elective, or
General Technical Elective, or

Energy Elective:ÌýMCEN 3022 Heat Transfer

MCEN 3022

Energy Elective:ÌýMCEN 3017 Circuits and Electronics

MCEN 3017

Ìý

Visit the Engineering Management Minor website

Engineering Management Minor Requirements ME Equivalent

EMEN 4030ÌýProject Management

General Technical Elective

EMEN 4100ÌýEngineering Economics

General Technical Elective

EMEN Elective
MCEN 3047ÌýData/Measurements

MCEN 3047

EMEN Elective

Free Elective

EMEN Elective

Free Elective

Vist the Engineering Entrepreneurship Minor website

Engineering Entrepeneurship Minor Requirements ME Equivalent

EMEN 4820ÌýEntrepreneurial Product Development

General Technical Elective

EMEN 4800ÌýTechnology Ventures and Marketing

General Technical Elective

Engineering EntrepreneurshipÌýElective
MCEN 4045 Senior Design 1 (if ESI section), or
MCEN 4238 Design for Community

MCEN 4045, orÌý
ME Technical ElectiveÌý

Engineering EntrepreneurshipÌýElective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

Engineering EntrepreneurshipÌýElective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

Visit the Global Engineering Minor website

Global Engineering Minor Requirements ME Equivalent

ENES 2360/3360ÌýGlobal State of Mind

Humanities/Social Sciences ElectiveÌý

Language Coursework

Humanities/Social Sciences ElectiveÌý

Regional, Global, and Technical Perspective Course

Humanities/Social Sciences ElectiveÌýor Free Elective

Regional, Global, and Technical Perspective CourseÌý(3000+ level)

Humanities/Social Sciences ElectiveÌýor Free Elective

Regional, Global, and Technical Perspective CourseÌý(3000+ level)

Humanities/Social Sciences ElectiveÌýor Free Elective

Regional, Global, and Technical Perspective CourseÌý(3000+ level)

Humanities/Social Sciences ElectiveÌýor Free Elective

Global ExperienceÌý

n/a

Visit the LeadershipÌýMinor website

Leadership Minor Requirements ME Equivalent

LEAD 1000ÌýBecome a Leader

Free elective

Leadership Foundaions Elective

Humanities/Social Sciences ElectiveÌýor Free Elective

Leadership Application Elective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

Leadership in Context Elective

Humanities/Social Sciences ElectiveÌýor Free Elective

LEAD 4000ÌýCapstone

Free Elective

Visit the Math Minor website

Math Minor Requirements ME Equivalent

MATH 1300 Calculus 1, or
APPM 1350 Calculus 1 for Engineers

APPM 1350

MATH 2300 Calculus 2, or
APPM 1360 Calculus 2 for EngineersÌý

APPM 1360

MATH 2400 Calculus 3, or
APPM 2350 Calculus 3 for EngineersÌý

APPM 2350

MATH 2001 Intro to Discrete Math, or
MATH 2002 Number Systems: An Intro to Higher Math

Free Elective

MATH 2130 Intro to Linear Algebra

APPM 2360 &Ìý*

MATH Elective (3000+ level)
MATH 3430 Differential Equations

APPM 2360 &Ìý*

MATH Elective (3000+ level) General Technical Elective
MATH Elective (4000+ level) General Technical Elective

* MATH 2130 & MATH 3430 combined will satisfy both APPM 2360 & ME's Math/Science Foundation requirement.Ìý

Visit the Music Minor website

Music Minor Requirements ME Equivalent

MUEL 1081ÌýBasic Music Theory*

Free Elective

EMUS 1xx7 or 3xx7ÌýMusic Ensemble**

Humanities/Social Sciences ElectiveÌýor Free Elective

Creating Music Electives

Free Elective

Creating Music Electives

Free Elective

Thinking Music ElectivesÌý

Humanities/Social Sciences ElectiveÌýor Free Elective

Thinking Music ElectivesÌý

Humanities/Social Sciences ElectiveÌýor Free Elective

Creative/Thinking Music Electives

Humanities/Social Sciences ElectiveÌýor Free Elective

* Students with appropriate background and instructor approval may substitute MUSC 1101 and MUSC 1121 for MUEL 1081. Ìý

** Ensembles requiring no audition include Golden Buffalo Marching Band (auditions for drumline and color guard only), Concert Band, Festival Chorus, Japanese Ensemble, Latin American Ensemble, African Ensemble, Gamelan Ensemble, and World Vocal Ensemble. Ensembles requiring an audition include Wind Symphony, Symphonic Band, University Singers, University Choir, Women’s Chorus, Jazz ensembles (Big Bands 1-3 and combos 1-7), Symphony Orchestra, and Campus Orchestra. ÌýÌý

Physics Minor Requirements ME Equivalent

PHYS 1110ÌýPhysics 1

PHYS 1110

PHYS 1120ÌýPhysics 2

PHYS 1120

PHYS 1140ÌýExperimental Physics 1

PHYS 1140

PHYS 2130 Intro to Quantum Mechanics, or
PHYS 2170 Foundations of Modern Physics

PHYS 2150ÌýExperimental Physics 2

Free Elective

PHYS 2210: Classical Mechanics

Free Elective

Physics Elective

General Technical Elective

Physics Elective

General Technical Elective

Physics Elective

Free Elective

Space Minor Requirements ME Equivalent

ASEN 1969 Pathway to Space

Free Elective

Space Elective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

Space Elective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

Space Elective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

Space Elective

Humanities/Social Sciences ElectiveÌýor
General Technical ElectiveÌýor
Free Elective

*There are a lot of options for each elective, that could count for a variety of requirements. Please check with your Advisor for details.

Ìý

Certificates

Visit theÌýEngineering, Ethics, & Society Certificate website

Engineering, Ethics, & Society Certificate Requirements ME Equivalent

Great Books Seminar course

Humanities/Social Sciences Elective

STEM & H&SS Intersection course

Humanities/Social Sciences Elective

Additional Herbst or EHON (Engineering Honors) course

Humanities/Social Sciences ElectiveÌýor Free Elective

Course in Humanities or Social Science from the College of Arts & Sciences linked to EES (Engineering, Ethics & Society) themes*

Humanities/Social Sciences ElectiveÌýor Free Elective

*Students must confer with the EES Certificate Director to determine the suitability of a particular course.ÌýÌý

Visit theÌýSocial InnovationÌýCertificate website

Social Innovation Certificate Requirements ME Equivalent

SOCY 4160ÌýDesigning Social Innovations

Humanities/Social Sciences ElectiveÌý

SOCY 4161ÌýExecuting Social Innovations*

Humanities/Social Sciences ElectiveÌý

Social Innovation ElectiveÌý

Humanities/Social Sciences ElectiveÌýor General Technical Elective

Social Innovation ElectiveÌý

Humanities/Social Sciences ElectiveÌýor General Technical Elective

Social Innovation Elective
MCEN 4045 Senior Design 1 (ESI Section)

MCEN 4045
Social Innovation Elective
MCEN 4085 Senior Design 2 (ESI Section)
MCEN 4085

Ìý