Department of Applied Mathematics
Keith Julien, Department Chair
UCB 526
1111 Engineering Drive, ECOT 225
Boulder, CO 80309
T: 303-492-4668
The Department of Applied Mathematics in the College of Arts and Sciences offers a Bachelor of Science degree in applied mathematics through the College of Engineering and Applied Science. The BS degree is designed to prepare graduates for exciting and diverse professional careers, and for graduate study in a wide variety of disciplines.
Courses at the undergraduate level provide training in a broad range of mathematical techniques and problem-solving strategies. These courses teach the concepts and methods central to applications of linear algebra, ordinary and partial differential equations, numerical analysis, probability, statistics and data science, complex variables and nonlinear dynamics. Since applied mathematicians often are involved in interdisciplinary work, the BS degree requires an in-depth knowledge of some area of science or engineering where mathematics is used. This knowledge prepares graduates to successfully communicate and cooperate with engineers and scientists. The BS degree also requires knowledge of a programming language and skill in using the computer.
For more information, visit the department's Prospective Students webpage.
Research Opportunities
The Department of Applied Math offers a broad range of undergraduate research opportunities funded by multiple agencies including the National Science Foundation. Working with faculty, applied math students have developed solutions to a variety of problems in fluids, dynamical systems, data analysis, networks, signal processing, math biology, math education and numerics. Students can do both theoretical and experimental work in the Dispersive Hydrodynamics Lab, gain practical experience in statistics and data science through LISA, the Laboratory for Interdisciplinary Statistical Analysis or work on individual research projects with departmental and affiliated faculty.
Students can gain professional exposure through the student chapter of the Society of Industrial and Applied Mathematics (SIAM) or through the Data Buffs, the student chapter of the American Statistical Association. Applied Math also has a local chapter of AWM, the Association for Women in Mathematics.
- Requirements
- Recommended Areas of Application
- I. Actuarial
- II. Aerospace Engineering Sciences
- III. Chemical Engineering
- IV. Civil, Environmental and Architectural Engineering
- V. Computational Biology and Bioinformatics
- VI. Computer Science
- VII. Creative Technology and Design
- VIII. Electrical, Computer & Energy Engineering
- IX. Engineering Physics/Physics
- X. Finance
- XI. Geographic Information Science (GIS)
- XII. Geological Sciences
- XIII. Mechanical Engineering
- XIV. Statistics and Data Science
- XV. Advisor Approved Option
Requirements
Required Courses and Credits
The BS degree in applied mathematics requires the satisfactory completion of a minimum of 128 credit hours as follows. All prerequisite courses must be passed with a C- or better.
Code | Title | Credit Hours |
---|---|---|
Calculus | ||
APPM 1350 | Calculus 1 for Engineers | 4 |
or APPM 1345 | Calculus 1 with Algebra, Part B | |
or MATH 1300 | Calculus 1 | |
APPM 1360 | Calculus 2 for Engineers | 4 |
or MATH 2300 | Calculus 2 | |
APPM 2350 | Calculus 3 for Engineers | 4 |
or MATH 2400 | Calculus 3 | |
Computing Experience | ||
APPM 1650 | Python for Math and Data Science Applications | 4 |
or ASEN 1320 | Aerospace Computing and Engineering Applications | |
or CSCI 1300 | Computer Science 1: Starting Computing | |
or CSCI 2275 | Programming and Data Structures | |
or CHEN 1310 | Introduction to Engineering Computing | |
or ECEN 1310 | Introduction to C Programming | |
Science Requirement | ||
PHYS 1110 | General Physics 1 | 4 |
or PHYS 1115 | General Physics 1 for Majors | |
PHYS 1120 | General Physics 2 | 4 |
or PHYS 1125 | General Physics 2 for Majors | |
PHYS 1140 | Experimental Physics 1 | 1 |
Select at least 4 additional credits of chemistry or biology (including 1 credit of laboratory science) from one of the following: | 4-8 | |
General Chemistry for Engineers 1 and Laboratory in General Chemistry 1 | ||
Accelerated Chemistry for Engineers and Engineering General Chemistry Lab | ||
General Chemistry 1 and Laboratory in General Chemistry 1 | ||
General Biology 1 and General Biology 2 and General Biology Laboratory 1 and General Biology Laboratory 2 | ||
Introduction to Cellular and Molecular Biology and Principles of Genetics (and one 2-credit lab) 1 | ||
Introduction to Quantum Mechanics and Its Applications and Experimental Physics 2 | ||
Foundations of Modern Physics and Experimental Physics 2 | ||
APPM Courses | ||
APPM 2360 | Introduction to Differential Equations with Linear Algebra | 4 |
or MATH 2130 & MATH 3430 | Introduction to Linear Algebra for Non-Mathematics Majors and Ordinary Differential Equations | |
APPM 3310 | Matrix Methods and Applications | 3 |
APPM 4350 | Methods in Applied Mathematics: Fourier Series and Boundary Value Problems | 3 |
APPM 4360 | Methods in Applied Mathematics: Complex Variables and Applications | 3 |
APPM 4600 | Numerical Methods and Scientific Computing | 4 |
Select one of the following: | 3 | |
Undergraduate Applied Analysis 1 | ||
Analysis 1 | ||
Abstract Algebra 1 | ||
APPM or STAT Courses Numbered 4000 or Above | ||
A two-semester course sequence of applied mathematics or statistics courses numbered 4000 or above in addition to APPM 4350 and APPM 4360. For example: | 6-7 | |
Modeling in Applied Mathematics and Modeling in Mathematical Biology | ||
Undergraduate Applied Analysis 1 and Undergraduate Applied Analysis 2 | ||
Numerical Methods and Scientific Computing and Numerical Differential Equations | ||
Applied Probability and Introduction to Mathematical Statistics 2 | ||
Applied Probability and Markov Processes, Queues, and Monte Carlo Simulations 2 | ||
Markov Processes, Queues, and Monte Carlo Simulations and Introduction to Mathematical Statistics | ||
Statistical Methods and Application I and Statistical Methods and Applications II | ||
APPM or STAT Courses Numbered 3000 or Above | ||
A minimum of 25 credit hours in APPM and/or STAT courses numbered 3000 or above (including the required courses). 3 | 25 | |
Area of Application | ||
A minimum of 24 credit hours in engineering or approved courses with significant mathematical content in Arts & Sciences or Business (see "Recommended Options For Applied Math Majors") | 24 | |
General Bachelor's Degree Requirements | ||
Humanities & social sciences electives 4 | 15 | |
Writing 5 | 3 | |
Free Electives | ||
Free electives should be chosen to bring the total credit hours to a minimum of 128. | 6 | |
Total Credit Hours | 128-133 |
1 | Plus one MCDB lab course for 2 credits, chosen from MCDB 1161, MCDB 1171, MCDB 1181, or MCDB 2171. |
2 | APPM 3570 is the only 3000-level course that can be used to satisfy this requirement. |
3 | No more than 3 credit hours of APPM 4840 may count toward these 24. No more than 6 credit hours of independent study are allowed for credit toward the BS degree in applied mathematics. |
4 | Students may choose courses from the list of college-approved humanities and social sciences (HSS) electives. |
5 | Students may choose a course from the list of college-approved writing courses. |
Recommended Areas of Application
In order to fulfill their degree requirements, applied mathematics majors are required to take 24 credit hours in engineering or approved courses with significant mathematical content in A&S or business courses, with at least 6 credit hours in courses numbered 3000 or above, and at least 15 credit hours in courses numbered 2000 or above. Here are several possible options. It should be stressed that the listed courses and options are suggestions and not requirements. Students may formulate their own option to meet their educational and career goals. Final course selection should be made in consultation with an applied math advisor.
These 24 credit hours are in addition to those required credit hours listed in "Computing Experience" and "Science Requirement" (mentioned in the Requirements section). In general, ENES courses may not be used to fulfill this requirement, although they may be used as humanities and social sciences electives. Several possible pre-approved ENES course options are listed below.
I. Actuarial
BCOR 1025 is a prerequisite for BCOR 2203 and BCOR 2204. Students are advised to substitute an applied math prob/stats course for this prerequisite.
Students are required to take APPM 35703, STAT 45202 and STAT 45402,5 for the actuarial option. Students are strongly advised to take STAT 3400, STAT 44005 and APPM 4560.5 Additional courses that may be useful include ACCT 3220 or ACCT 3230. BCOR, FNCE and ACCT courses listed are only available for students enrolled in the Actuarial and Quantitative Finance Certificate Program.
Code | Title | Credit Hours |
---|---|---|
BCOR 2203 | Principles of Accounting I (prerequisites for this course are waived for Actuarial Certificate students) | 1.5 |
BCOR 2204 | Principles of Financial Management | 1.5 |
ECON 2010 | Principles of Microeconomics 1 | 4 |
ECON 2020 | Principles of Macroeconomics 1 | 4 |
ECON 3070 | Intermediate Microeconomic Theory 2,4 | 4 |
ECON 4070 | Topics in Microeconomics | 3 |
FNCE 3010 | Corporate Finance 2,4 | 3 |
Some (or all) of the following courses should be taken: | 3-9 | |
Investment and Portfolio Management | ||
Derivative Securities | ||
Introduction to Econometrics | ||
Total Credit Hours | 24-30 |
1 | ECON 2010 and ECON 2020 may not count toward the 24 credit hours of the option requirement; however, they can be used to meet the 18-credit-hour social science/humanities requirement of the College of Engineering. |
2 | These courses satisfy the Society of Actuaries requirement that students take certain college courses to earn the Validation by Education Experiences (VEE) credit, provided a grade of B- or better is obtained. These courses are also required for students completing the Actuarial Certificate Program. VEE credit is granted for BCOR 2203, BCOR 2204 and FNCE 3010. |
3 | The first actuarial examination, Exam P/1, can be taken after completing this course. |
4 | The second actuarial examination, Exam FM/2, can be taken after completing these courses, as well as a self-study in interest theory. |
5 | The third and fourth actuarial exams, Statistics for Risk Modeling and Fundamentals of Actuarial Mathematics, require several statistics courses and independent study. Students should consult the website for the Society of Actuaries for details. |
II. Aerospace Engineering Sciences
Students who pursue this option are usually double majors. Students who wish to enroll in ASEN courses without being a double major should see their applied mathematics advisor for next steps.
III. Chemical Engineering
Students choosing this option must take CHEN 1310 as part of their applied math major. CHEN 1310 is a prerequisite for CHEN 2120.
Code | Title | Credit Hours |
---|---|---|
CHEN 1211 & CHEM 1221 | Accelerated Chemistry for Engineers and Engineering General Chemistry Lab | 5 |
Recommended courses: | 20 | |
Chemical Engineering Material and Energy Balances | ||
Chemical Engineering Fluid Mechanics | ||
Chemical Engineering Heat and Mass Transfer | ||
Chemical Engineering Separations | ||
Chemical Engineering Thermodynamics | ||
Physical Chemistry for Engineers | ||
Kinetics and Reactor Design | ||
Organic Chemistry 1 | ||
Total Credit Hours | 25 |
IV. Civil, Environmental and Architectural Engineering
Students wishing to enroll in CVEN courses that are restricted to majors only must do so through the departmental course request form.
Code | Title | Credit Hours |
---|---|---|
Recommended Basic Courses | ||
CVEN 2121 | Analytical Mechanics 1 | 3 |
AREN 2110 | Thermodynamics | 3 |
CVEN 3161 | Mechanics of Materials 1 | 3 |
CVEN 3313 | Theoretical Fluid Mechanics | 3 |
or AREN 2120 | Fluid Mechanics and Heat Transfer | |
Additional Courses | ||
Select two courses from any one of the following groups plus additional courses to bring the total credit hours to 24: | 12 | |
Group A | ||
Fundamentals of Environmental Engineering | ||
Engineering Hydrology | ||
Group B | ||
Structural Analysis | ||
Geotechnical Engineering 1 | ||
Steel Design | ||
Reinforced Concrete Design | ||
Group C | ||
Building Materials and Systems | ||
Energy Efficient Buildings | ||
Illumination I | ||
Total Credit Hours | 24 |
V. Computational Biology and Bioinformatics
The following concentration of selected courses from computer science, biology and chemistry provide the foundation for work in mathematical biology, computational biology and/or bioinformatics.
Students selecting this option are advised to take APPM 3570, STAT 4520, STAT 4540 and APPM 4390 as part of their applied math coursework. Other recommended courses include CSCI 3287.
Code | Title | Credit Hours |
---|---|---|
CSCI 2270 | Computer Science 2: Data Structures | 4 |
CHEM 3311 & CHEM 3321 | Organic Chemistry 1 and Laboratory in Organic Chemistry 1 | 5 |
MCDB 1150 & MCDB 1152 | Introduction to Cellular and Molecular Biology and Problem Solving Co-Seminar for Introduction to Molecular and Cellular Biology | 4 |
MCDB 2150 & MCDB 2152 | Principles of Genetics and Problem Solving Co-Seminars for Genetics | 4 |
MCDB 3135 & MCDB 3140 | Molecular Biology and Cell Biology Laboratory | 5 |
CSCI 3104 | Algorithms | 4 |
CSCI 4314 | Dynamic Models in Biology | 3 |
Total Credit Hours | 29 |
VI. Computer Science
Students completing the computer science option should have a minor in computer science. Check with the Computer Science Department.
Code | Title | Credit Hours |
---|---|---|
Required Course | ||
CSCI 2270 | Computer Science 2: Data Structures | 4 |
Additional Courses | ||
At least two of these must be at the 3000 level. Possible choices include: | 20 | |
Computer Systems | ||
Algorithms | ||
Principles of Programming Languages | ||
Design and Analysis of Database Systems | ||
Software Development Methods and Tools | ||
Design and Analysis of Operating Systems | ||
Additional CSCI courses to bring the total number of credit hours to at least 24 | ||
Total Credit Hours | 24 |
VII. Creative Technology and Design
Students are advised to take APPM 3570, APPM 4560 and APPM 4610 as part of their applied math coursework.
Students may wish to consider the creative technology and design minor.
Code | Title | Credit Hours |
---|---|---|
Required Courses | ||
ATLS 2000 | The Meaning of Information Technology 1 | 3 |
ATLS 2100 | Image | 3 |
ATLS 2200 | Web | 3 |
ATLS 2300 | Text | 3 |
ATLS 1300 | Computational Foundations 1 | 4 |
CSCI 2270 | Computer Science 2: Data Structures | 4 |
CSCI 3104 | Algorithms | 4 |
CSCI 4229 | Computer Graphics | 3 |
Additional Courses | ||
Recommended additional courses to bring the total to at least 24 credit hours: | 4 | |
Advisor-approved technical electives to complete the ATLAS/TAM Certificate in Digital Media | ||
Introduction to Artificial Intelligence | ||
Object-Oriented Analysis and Design | ||
Total Credit Hours | 31 |
1 | This course may be used to satisfy either 3 credit hours of H&SS requirement or the applied math area of application, but not both. |
VIII. Electrical, Computer & Energy Engineering
Students interested in this option should consult with an advisor in the Department of Electrical and Computer Engineering as several areas are available (computer engineering, electrical engineering, quantum computing and signals, and systems) and can lead to one of that department's minors. A minimum of 24 credits is required.
IX. Engineering Physics/Physics
Students completing the physics option should have a minor in physics. Check with the Physics Department.
Code | Title | Credit Hours |
---|---|---|
Recommended courses after first-year Physics: 1 | ||
PHYS 2130 | Introduction to Quantum Mechanics and Its Applications | 3 |
or PHYS 2170 | Foundations of Modern Physics | |
PHYS 2150 | Experimental Physics 2 | 1 |
PHYS 2210 | Classical Mechanics and Mathematical Methods 1 | 3 |
PHYS 3210 | Classical Mechanics and Mathematical Methods 2 | 3 |
PHYS 3220 | Quantum Mechanics 1 | 3 |
PHYS 3310 | Principles of Electricity and Magnetism 1 | 3 |
PHYS 3320 | Principles of Electricity and Magnetism 2 | 3 |
PHYS 3330 | Electronics for the Physical Sciences | 2 |
or PHYS 4230 | Thermodynamics and Statistical Mechanics | |
Additional Physics courses to total at least 24 credits | 3 | |
Total Credit Hours | 24 |
1 | Students choosing this option are advised to take APPM 3570 (Applied Probability – 3 cr.). MATH 3140 (Abstract Algebra 1 – 3 cr.) may also be useful for students interested in theoretical physics. |
X. Finance
Students wishing to take College of Business courses must apply for admittance to the Actuarial Studies and Quantitative Finance Certificate Program. Students accepted into this program receive preferential treatment with respect to other non-business students when registering for business courses. For more information, please see your applied math advisor.
Students doing the Finance Option are required to take APPM 3570 and STAT 4520 as part of the major's required 24 upper-division credits. Students are advised to take APPM 4560 and STAT 4540 if time permits.
Code | Title | Credit Hours |
---|---|---|
The Following courses should be taken as part of the 24 credits required in the option: | ||
BCOR 2203 | Principles of Accounting I | 1.5 |
BCOR 2204 | Principles of Financial Management | 1.5 |
FNCE 3010 | Corporate Finance | 3 |
ECON 2010 | Principles of Microeconomics 1 | 4 |
ECON 2020 | Principles of Macroeconomics 1 | 4 |
ECON 3070 | Intermediate Microeconomic Theory | 4 |
ECON 4818 | Introduction to Econometrics | 3 |
A minimum of two of the following courses must be taken in order to meet the 24 credit requirements of the option. All of them must be taken to complete the requirements of the Quantitative Finance Program | 6 | |
Corporate Financial Reporting 1 | ||
Investment and Portfolio Management | ||
Derivative Securities | ||
Topics in Finance | ||
Financial Markets and Institutions | ||
Additional courses that may be taken as time permits | ||
Corporate Financial Reporting 2 | ||
Financial Institutions Management | ||
Capital Investment Analysis | ||
Special Topics in Finance | ||
Total Credit Hours | 27 |
1 | ECON 2010, ECON 2020 may not count toward the 24 credits of the option requirement; however, they can be used to meet the 18-credit social science/humanities requirement of the College of Engineering. |
Additional courses that may be taken as time permits:
Code | Title | Credit Hours |
---|---|---|
ACCT 3230 | Corporate Financial Reporting 2 | 3 |
FNCE 4000 | Financial Institutions Management | 3 |
FNCE 4050 | Capital Investment Analysis | 3 |
FNCE 4060 | Special Topics in Finance | 1-6 |
XI. Geographic Information Science (GIS)
Students completing the geographic information science option should qualify to receive a certificate in GIS and computational science. Check with the faculty contacts for the GIS Certificate Program.
Code | Title | Credit Hours |
---|---|---|
GEOG 3023 | Statistics and Geographic Data | 4 |
CSCI 2270 | Computer Science 2: Data Structures | 4 |
GEOG 3053 | Geographic Information Science: Mapping | 4 |
GEOG 4103 | Geographic Information Science: Spatial Analytics | 4 |
Additional Courses | ||
Additional courses to bring the total number of credits to 24. Possible choices include: | 8 | |
Advanced Quantitative Methods for Spatial Data | ||
Geographic Information Science: Spatial Programming | ||
Geographic Information Science: Space Time Analytics | ||
Geographic Information Science: Project Management | ||
GIS for Geologists | ||
Total Credit Hours | 24 |
XII. Geological Sciences
Students completing the geological sciences option should have a minor in geology. Check with the Geological Sciences Department.
Code | Title | Credit Hours |
---|---|---|
Required Courses | ||
One of the following introductory sequences: | 6 | |
Exploring Earth and Dodos, Dinos, and Deinococcus: The History of a Habitable Planet | ||
Geology of Colorado and Exploring Earth | ||
Global Change: An Earth Science Perspective and Exploring Earth | ||
Required Lab Course: | ||
GEOL 1030 | Introduction to Geology Laboratory 1 | 1 |
Additional Courses | ||
Additional courses to bring the total number of credits to 24; at least two of these must be at the 3000 level | 17 | |
Introduction to Field Geology | ||
Introduction to Mineralogy | ||
Statistics and Geographic Data | ||
Structural Geology | ||
Paleobiology | ||
Sedimentology and Stratigraphy | ||
Remote Sensing of the Environment | ||
Earth Surface Processes | ||
Total Credit Hours | 24 |
XIII. Mechanical Engineering
Students choosing this option are advised to take STAT 4000 or APPM 3570 and STAT 4520 as part of their applied math major.
Students wishing to enroll in MCEN courses that are restricted to majors only must do so through the departmental course request form.
Code | Title | Credit Hours |
---|---|---|
Recommended Courses | ||
MCEN 2023 | Statics and Structures | 3 |
MCEN 2043 | Dynamics | 3 |
MCEN 2063 | Mechanics of Solids | 3 |
MCEN 3012 | Thermodynamics | 3 |
MCEN 3021 | Fluid Mechanics | 3 |
MCEN 3022 | Heat Transfer | 3 |
MCEN 3025 | Component Design | 3 |
MCEN 4043 | System Dynamics | 3 |
Total Credit Hours | 24 |
XIV. Statistics and Data Science
Students will take the courses in statistics for the APPM Statistics Minor plus additional coursework chosen from Computer Science, College of Media, Communication and Information, Technology, Arts and Media or another relevant area as approved by the advisor.
Students choosing this option must complete STAT 2600 as part of the statistics minor; APPM 1650 and
APPM 3650 are strongly recommended.
Students completing the statistics & data science option may qualify for an applied mathematics minor in statistics and should check with their advisor for confirmation. Students may earn a BS in applied mathematics and a minor in statistics. The 12 upper-division statistics credits required for the minor may not be counted toward the 25 credits of upper-division math courses for the bachelor's degree.
XV. Advisor Approved Option
Students may formulate their own option to meet their educational and career goals. In order to fulfill their degree requirements, applied mathematics majors are required to take 24 credit hours in engineering or advisor-approved courses with significant mathematical content in A&S or business courses, with at least 6 credit hours in courses numbered 3000 or above and at least 15 credit hours in courses numbered 2000 or above. These 24 credit hours are in addition to those required credit hours listed in "Computing Experience" and "Science Requirement" (mentioned in the Requirements section). In general, ENES courses may not be used to fulfill this requirement, although they may be used as humanities and social sciences electives.
Final course selection should be made in consultation with an applied math advisor.
Recommended Four-Year Plan of Study
Students must complete 128 hours for graduation.
Year One | ||
---|---|---|
Fall Semester | Credit Hours | |
APPM 1350 | Calculus 1 for Engineers | 4 |
CHEN 1201 | General Chemistry for Engineers 1 | 4 |
CHEM 1114 | Laboratory in General Chemistry 1 | 1 |
APPM 1650 | Python for Math and Data Science Applications | 4 |
COEN 1830 | Special Topics (First-Year Engineering Seminar) | 1 |
Humanities or Social Sciences Elective 1 | 2 | |
Credit Hours | 16 | |
Spring Semester | ||
APPM 1360 | Calculus 2 for Engineers | 4 |
PHYS 1110 | General Physics 1 | 4 |
Free Electives | 3 | |
Tech Elective (Area of Emphasis) | 3 | |
Humanities or Social Sciences Elective 1 | 3 | |
Credit Hours | 17 | |
Year Two | ||
Fall Semester | ||
APPM 2350 | Calculus 3 for Engineers | 4 |
PHYS 1120 | General Physics 2 | 4 |
PHYS 1140 | Experimental Physics 1 | 1 |
APPM 3170 | Discrete Applied Mathematics | 3 |
Humanities or Social Sciences Elective 1 | 3 | |
Credit Hours | 15 | |
Spring Semester | ||
APPM 2360 | Introduction to Differential Equations with Linear Algebra | 4 |
APPM 2460 | Differential Equations Computer Lab (Recommended, but not required) | 1 |
APPM 3310 | Matrix Methods and Applications | 3 |
Technical Electives (Area of Emphasis) | 3 | |
Free Electives | 3 | |
Humanities or Social Sciences Elective 1 | 3 | |
Credit Hours | 17 | |
Year Three | ||
Fall Semester | ||
APPM 4350 | Methods in Applied Mathematics: Fourier Series and Boundary Value Problems | 3 |
APPM 4440 | Undergraduate Applied Analysis 1 | 3 |
Technical Electives (Area of Emphasis) | 6 | |
College-approved writing course 2 | 3 | |
Credit Hours | 15 | |
Spring Semester | ||
APPM 3XXX | 3 | |
APPM 4360 | Methods in Applied Mathematics: Complex Variables and Applications | 3 |
Technical Electives (Area of Emphasis) | 3 | |
Free Electives | 4 | |
Humanities or Social Sciences Elective 1 | 3 | |
Credit Hours | 16 | |
Year Four | ||
Fall Semester | ||
APPM 4600 | Numerical Methods and Scientific Computing | 4 |
APPM 4XXX | 3 | |
Technical Electives (Area of Emphasis) | 6 | |
Free Electives | 3 | |
Credit Hours | 16 | |
Spring Semester | ||
APPM 4610 | Numerical Differential Equations (or other course to complete senior sequence) | 3 |
APPM 4XXX | 3 | |
Technical Electives (Area of Emphasis) | 3 | |
Free Electives | 7 | |
Credit Hours | 16 | |
Total Credit Hours | 128 |
1 | Students may choose courses from the list of college-approved humanities and social sciences (HSS) electives. |
2 | Students may choose a course from the list of college-approved writing courses. |
Learning Outcomes
Content Knowledge
Students completing the undergraduate degree in Applied Mathematics will be broadly knowledgeable in a number of mathematical areas including:
- Differential and integral calculus in one and several variables.
- Vector spaces and matrix algebra.
- Ordinary and partial differential equations.
- At least one programming language.
- At least one application software package in either mathematics or statistics.
- Methods of complex variables as used in applications.
- Numerical solutions of linear and nonlinear problems.
- An in-depth knowledge of an area of application (statistics, an engineering discipline, a natural science field, or one of the quantitative areas of business and economics).
Student Outcomes
Upon graduation, students will:
- Acquire foundational knowledge in calculus, ordinary and partial differential equations, vector spaces and matrix methods, analysis, numerical analysis, complex variables, and probability and statistics.
- Develop proficiency in at least one programming language.
- Acquire an in-depth knowledge of an area of application (statistics, an engineering or natural science field, or one of the quantitative areas of finance and economics).
- Acquire problem-solving and modeling skills that allow them to formulate a real-world problem in a mathematical setting and implement a numerical solution.
- The ability to clearly and concisely, in oral and in written forms, communicate analytic arguments.
Bachelor's–Accelerated Master's Degree Program(s)
The bachelor's–accelerated master's (BAM) degree program options offer currently enrolled CU Boulder undergraduate students the opportunity to receive a bachelor's and master's degree in a shorter period of time. Students receive the bachelor's degree first but begin taking graduate coursework as undergraduates (typically in their senior year).
Because some courses are allowed to double count for both the bachelor's and the master's degrees, students receive a master's degree in less time and at a lower cost than if they were to enroll in a stand-alone master's degree program after completion of their baccalaureate degree. In addition, staying at CU Boulder to pursue a bachelor's–accelerated master's program enables students to continue working with their established faculty mentors.
BS and MS in Applied Mathematics
Admissions Requirements
In order to gain admission to the BAM program named above, a student must meet the following criteria:
- Have a cumulative GPA of 3.40 or higher.
- Have a minimum GPA of 3.40 in APPM and MATH courses.
- Have at least junior class standing.
- Completion of all MAPS requirements and no deficiencies remaining (students admitted to CU Boulder prior to Summer 2023 only).
- Satisfactory completion of at least two APPM courses numbered 3000 or higher.
- Two letters of recommendation from CU Boulder Department of Applied Mathematics faculty.
Program Requirements
Students may take up to and including 12 graduate credit hours while in the undergraduate program which can later be used toward the master’s degree. However, only six credits may be double counted toward the bachelor’s degree and the master’s degree. Students must apply to graduate with the bachelor’s degree, and apply to continue with the master’s degree, early in the semester in which the undergraduate requirements will be completed.
Please see the Applied Mathematics/Applied Mathematics BAM degree program webpage for more information.