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

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.

Calculus
APPM 1350Calculus 1 for Engineers4
or APPM 1345 Calculus 1 with Algebra, Part B
or MATH 1300 Calculus 1
APPM 1360Calculus 2 for Engineers4
or MATH 2300 Calculus 2
APPM 2350Calculus 3 for Engineers4
or MATH 2400 Calculus 3
Computing Experience
APPM 1650Python for Mathematical and Statistical Applications4
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 C Programming for ECE
Science Requirement
PHYS 1110General Physics 14
or PHYS 1115 General Physics 1 for Majors
PHYS 1120General Physics 24
or PHYS 1125 General Physics 2 for Majors
PHYS 1140Experimental Physics 11
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 2360Introduction to Differential Equations with Linear Algebra4
or MATH 2130
MATH 3430
Introduction to Linear Algebra for Non-Mathematics Majors
and Ordinary Differential Equations
APPM 3310Matrix Methods and Applications3
APPM 4350Methods in Applied Mathematics: Fourier Series and Boundary Value Problems3
APPM 4360Methods in Applied Mathematics: Complex Variables and Applications3
APPM 4600Numerical Methods and Scientific Computing 24
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 3
Applied Probability
and Markov Processes, Queues, and Monte Carlo Simulations 3
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). 425
Area of Emphasis
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 515
Writing 63
Free Electives
Free electives should be chosen to bring the total credit hours to a minimum of 128.6
Total Credit Hours128-133

Recommended Options

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 35703STAT 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.

BCOR 2203Principles of Accounting I (prerequisites for this course are waived for Actuarial Certificate students)1.5
BCOR 2204Principles of Financial Management1.5
ECON 2010Principles of Microeconomics 14
ECON 2020Principles of Macroeconomics 14
ECON 3070Intermediate Microeconomic Theory 2,44
ECON 3080Intermediate Macroeconomic Theory 2,43
ECON 4070Topics in Microeconomics3
FNCE 3010Corporate Finance 2,43
Some (or all) of the following courses should be taken:3-9
Investment and Portfolio Management
Derivative Securities
Introduction to Econometrics
Total Credit Hours27-33

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.

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
Chemical Engineering Reaction Kinetics
Organic Chemistry 1
Total Credit Hours25

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

Recommended Basic Courses
CVEN 2121Analytical Mechanics 13
AREN 2110Thermodynamics3
CVEN 3161Mechanics of Materials 13
CVEN 3313Theoretical Fluid Mechanics3
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 Hours24

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 3570STAT 4520STAT 4540 and APPM 4390 as part of their applied math coursework. Other recommended courses include CSCI 3287.

CSCI 2270Computer Science 2: Data Structures4
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 3104Algorithms4
CSCI 4314Dynamic Models in Biology3
Total Credit Hours29

VI. Computer Science

Students completing the computer science option should have a minor in computer science. Check with the Computer Science Department.

Required Course
CSCI 2270Computer Science 2: Data Structures4
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 Hours24

VII. Creative Technology and Design

Students are advised to take APPM 3570APPM 4560 and APPM 4610 as part of their applied math coursework.

Students may wish to consider the creative technology and design minor.

Required Courses
ATLS 2000The Meaning of Information Technology 13
ATLS 2100Image3
ATLS 2200Web3
ATLS 2300Text3
ATLS 1300Computational Foundations 14
CSCI 2270Computer Science 2: Data Structures4
CSCI 3104Algorithms4
CSCI 4229Computer Graphics3
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 Hours31

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 choosing this option are advised to take APPM 3570. MATH 3140 may also be useful for students interested in theoretical physics.

Students completing the physics option should have a minor in physics. Check with the Physics Department.

Recommended Courses 1
PHYS 2130Introduction to Quantum Mechanics and Its Applications3
or PHYS 2170 Foundations of Modern Physics
PHYS 2150Experimental Physics 21
PHYS 2210Classical Mechanics and Mathematical Methods 13
PHYS 3210Classical Mechanics and Mathematical Methods 23
PHYS 3220Quantum Mechanics 13
PHYS 3310Principles of Electricity and Magnetism 13
PHYS 3320Principles of Electricity and Magnetism 23
PHYS 3330Electronics for the Physical Sciences2-3
or PHYS 4230 Thermodynamics and Statistical Mechanics
Additional physics courses to total at least 24 credits.2-3
Total Credit Hours24

X. Finance

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 3570 and STAT 4520 as part of the major's required 24 credits at 3000 level or above for the finance option. Students are advised to take APPM 4560 and STAT 4540 if time permits.

Students wishing to take College of Business courses cannot register until the first day of classes. Alternatively, students can 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.

Recommended Basic Courses14-16
Principles of Accounting I
Principles of Financial Management
Corporate Finance
Principles of Microeconomics
and Principles of Macroeconomics
and Intermediate Microeconomic Theory
and Intermediate Macroeconomic Theory 1
Introduction to Econometrics
Additional Courses
Select a minimum of two of the following courses in order to meet the 24-credit requirement of the option. All of them must be taken to complete the requirements of the Quantitative Finance Certificate Program:8-10
Corporate Financial Reporting 1
Investment and Portfolio Management
Derivative Securities
Topics in Finance
Financial Markets and Institutions
Total Credit Hours24

Additional courses that may be taken as time permits:

ACCT 3230Corporate Financial Reporting 23
FNCE 4000Financial Institutions Management3
FNCE 4050Capital Investment Analysis3
FNCE 4060Special Topics in Finance1-6

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.

GEOG 3023Statistics and Geographic Data4
CSCI 2270Computer Science 2: Data Structures4
GEOG 3053Geographic Information Science: Mapping4
GEOG 4103Geographic Information Science: Spatial Analytics4
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 Hours24

XII. Geological Sciences

Students completing the geological sciences option should have a minor in geology. Check with the Geological Sciences Department.

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 1030Introduction to Geology Laboratory 11
Additional Courses
Additional courses to bring the total number of credits to 24; at least two of these must be at the 3000 level17
Introduction to Field Geology
Introduction to Mineralogy
Statistics and Geographic Data
Structural Geology
Paleobiology
Sedimentology and Stratigraphy
Remote Sensing of the Environment
Principles of Geomorphology
Total Credit Hours24

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

Recommended Courses
MCEN 2023Statics and Structures3
MCEN 2043Dynamics3
MCEN 2063Mechanics of Solids3
MCEN 3012Thermodynamics3
MCEN 3021Fluid Mechanics3
MCEN 3022Heat Transfer3
MCEN 3025Component Design3
MCEN 4043System Dynamics3
Total Credit Hours24

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 and 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.

Recommended Four-Year Plan of Study

Students must complete 128 hours for graduation.

Plan of Study Grid
Year One
Fall SemesterCredit 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 Mathematical and Statistical Applications 4
Humanities or Social Sciences Elective 1 3
 Credit Hours16
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 Hours17
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 Hours15
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 Hours17
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 Hours15
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 Hours16
Year Four
Fall Semester
APPM 4600 Numerical Methods and Scientific Computing 3 4
APPM 4XXX 3
Technical Electives (Area of Emphasis) 6
Free Electives 3
 Credit Hours16
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 Hours16
 Total Credit Hours128

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 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.