Minors & Certificates
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 |
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| 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: Astrophysics Sequence: | Ìý Ìý |
| 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
Visit the Energy Engineering Minor WebsiteÌý
| 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 |
| 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
| 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.
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