Minors & Certificates
The College of Engineering and Applied Science has numerous minor and certificate options for 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 as Applied Math, Astrophysics, Economics, World Languages, and more. You can find information about all available minors at ÃÛÌÇÖ±²¥ Boulder through our .
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. The 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. Please contact your academic advisor with questions regarding minors/certificates and their potential impact on your degree plan.
Minors
Visit the Applied Math Minor website
| Applied Math Minor Requirements | ME Equivalent |
|---|---|
| APPM 2350 Calculus 3 for Engineers or MATH 2400 Calculus 3 | Calculus 3 |
| APPM 2360 Diff Eq w/Linear Algebra | APPM 2360 |
| APPM 3310 Matrix 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 Applications | General Technical Elective |
and
| One upper-division APPM or STAT Course (3000/4000 Level) | General Technical Elective |
Scientific Computation Emphasis
| APPM 3050 Scientific Computing Matlab or APPM 3650 Algorithms 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 4000 Statistical Methods and Applications I & STAT 4010 Statistical Methods and Applications II | General Technical Elective General Technical Elective |
| APPM 4560 Markov Processes, Queues, and Monte Carlo Simulations & STAT 4520 Intro to Mathematical Statistics | General Technical Elective General Technical Elective |
Visit the Astronomy Minor website
| Astronomy Minor Requirements (6 courses min.) | ME Equivalent |
|---|---|
Elementary ASTR Coursework (max of 3) Recommended: ASTR 2000 Ancient Astronomies | Lower-Division Humanities/Social Sciences Elective |
Advanced ASTR Coursework: 2 courses from one upper-level course sequence-- Planetary Sequence: Astrophysics Sequence: |
|
| 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 Elective (must be 3000+) | General Technical Elective |
| Biomed Elective (must be 3000+) | ME Technical Elective |
| Biomed Elective (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 1320 Computer Science 1 | MCEN 1030 |
| CSCI 2270 Data Structures | Free Elective |
CSCI 2824 Discrete 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 course in addition to the course requirements for the minor. | Free Elective |
| CSCI 2400 Computer Systems or ECEN 4593 Computer Organization | Free Elective or General 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 or CSCI 3656 | MCEN 3030 |
| Computer Science Elective | General Technical Elective |
Visit the Creative 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-Division Humanities/Social Sciences Elective |
| ATLS 2100 Image | Free Elective |
| ATLS 2200 Web | Free Elective |
| ATLS 2300 Text | 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 2260 Circuits as Systems | * |
| ECEN 2270 Electronics Design Lab | * |
| 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.
Visit the Energy Engineering Minor Website
| 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: MCEN 3022 Heat Transfer | MCEN 3022 |
| Energy Elective: MCEN 3017 Circuits and Electronics | MCEN 3017 |
Visit the Engineering Management Minor website
| Engineering Management Minor Requirements | ME Equivalent |
|---|---|
| EMEN 4030 Project Management | General Technical Elective |
| EMEN 4100 Engineering Economics | General Technical Elective |
| EMEN Elective MCEN 3047 Data/Measurements | MCEN 3047 |
| EMEN Elective | Free Elective |
| EMEN Elective | Free Elective |
Vist the Engineering Entrepreneurship Minor website
| Engineering Entrepeneurship Minor Requirements | ME Equivalent |
|---|---|
| EMEN 4820 Entrepreneurial Product Development | General Technical Elective |
| EMEN 4800 Technology Ventures and Marketing | General Technical Elective |
| Engineering Entrepreneurship Elective MCEN 4045 Senior Design 1 (if ESI section), or MCEN 4238 Design for Community | MCEN 4045, or ME Technical Elective |
| Engineering Entrepreneurship Elective | Humanities/Social Sciences Elective or General Technical Elective or Free Elective |
| Engineering Entrepreneurship Elective | Humanities/Social Sciences Elective or General Technical Elective or Free Elective |
Visit the Global Engineering Minor website
| Global Engineering Minor Requirements | ME Equivalent |
|---|---|
| ENES 2360/3360 Global State of Mind | Humanities/Social Sciences Elective |
| Language Coursework | Humanities/Social Sciences Elective |
| Regional, Global, and Technical Perspective Course | Humanities/Social Sciences Elective or Free Elective |
| Regional, Global, and Technical Perspective Course (3000+ level) | Humanities/Social Sciences Elective or Free Elective |
| Regional, Global, and Technical Perspective Course (3000+ level) | Humanities/Social Sciences Elective or Free Elective |
| Regional, Global, and Technical Perspective Course (3000+ level) | Humanities/Social Sciences Elective or Free Elective |
| Global Experience | n/a |
Visit the Leadership Minor website
| Leadership Minor Requirements | ME Equivalent |
|---|---|
| LEAD 1000 Become a Leader | Free elective |
| Leadership Foundaions Elective | Humanities/Social Sciences Elective or Free Elective |
| Leadership Application Elective | Humanities/Social Sciences Elective or General Technical Elective or Free Elective |
| Leadership in Context Elective | Humanities/Social Sciences Elective or Free Elective |
| LEAD 4000 Capstone | 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 Engineers | APPM 1360 |
| MATH 2400 Calculus 3, or APPM 2350 Calculus 3 for Engineers | 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 & * |
| MATH Elective (3000+ level) MATH 3430 Differential Equations | APPM 2360 & * |
| 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.
| Music Minor Requirements | ME Equivalent |
|---|---|
| MUEL 1081 Basic Music Theory* | Free Elective |
| EMUS 1xx7 or 3xx7 Music Ensemble** | Humanities/Social Sciences Elective or Free Elective |
| Creating Music Electives | Free Elective |
| Creating Music Electives | Free Elective |
| Thinking Music Electives | Humanities/Social Sciences Elective or Free Elective |
| Thinking Music Electives | Humanities/Social Sciences Elective or Free Elective |
| Creative/Thinking Music Electives | Humanities/Social Sciences Elective or Free Elective |
* Students with appropriate background and instructor approval may substitute MUSC 1101 and MUSC 1121 for MUEL 1081.
** 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.
| Physics Minor Requirements | ME Equivalent |
|---|---|
| PHYS 1110 Physics 1 | PHYS 1110 |
| PHYS 1120 Physics 2 | PHYS 1120 |
| PHYS 1140 Experimental Physics 1 | PHYS 1140 |
| PHYS 2130 Intro to Quantum Mechanics, or PHYS 2170 Foundations of Modern Physics | |
| PHYS 2150 Experimental 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 Elective or General Technical Elective or Free Elective |
| Space Elective | Humanities/Social Sciences Elective or General Technical Elective or Free Elective |
| Space Elective | Humanities/Social Sciences Elective or General Technical Elective or Free Elective |
| Space Elective | Humanities/Social Sciences Elective or General Technical Elective or 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.