University Catalog 2016-2017

University of Colorado Boulder
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Applied Mathematics

    The Department of Applied Mathematics in the College of Arts and Sciences offers a BS 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. The department also offers a five-year BS/MS, as well as an MS degree and a PhD degree through the Graduate School.

    The objectives of the Department of Applied Mathematics at CU-Boulder are summarized below:

    • provide undergraduate and graduate students with high-quality education and training in applied mathematics, and prepare them for careers in industry, laboratories and the academic professions;
    • offer and monitor degree programs leading to BS, MS and PhD degrees in applied mathematics;
    • nourish and maintain a professional environment in which excellence in teaching, learning, scholarship and creativity are of central importance; 
    • assure teaching and research expertise in a number of key areas of applied mathematics including the methodology of applied mathematics, computational mathematics and algorithms, industrial applications, mathematical biology, applied probability and statistics.

    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 and statistics, 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.

    Desired Outcomes

    The undergraduate degree in applied mathematics emphasizes knowledge and awareness of:

    • 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; and
    • numerical solutions of linear and nonlinear problems.

    In addition, students completing a degree in applied mathematics acquire:

    • an in-depth knowledge of an area of application (an engineering discipline or a natural science field or one of the quantitative areas of business and economics);
    • knowledge of problem-formulation, problem-solving and modeling techniques and strategies central to applications; and 
    • the ability to communicate analytic arguments clearly and concisely in oral and written forms.

    Course code for this program is APPM.

    Minor Programs

    The department offers a minor in applied mathematics that is available to all undergraduate students. A minor in applied mathematics indicates that a student has received in-depth training in mathematical techniques and computational methods well beyond the training usually received by science and engineering majors.

    The department also offers a minor in statistics was developed to provide in-depth training in statistical methods and techniques well beyond the training usually received by science and engineering majors. The ability to understand, visualize, and analyze data is becoming an increasingly important skill in many disparate fields. This minor offers undergraduate students from any major the opportunity to develop their statistical knowledge.

    Bachelor's Degree Program(s)

    Bachelor’s Degree in Applied Mathematics

    The BS degree in applied mathematics requires the satisfactory completion of a minimum of 128 credit hours as follows:

    • Three semesters of calculus (APPM 1350, 1360 and 2350) with a minimum grade of C- in each course.
    • Computing experience (CSCI 1300/1310/1320 or CHEN 1310 or ECEN 1310).
    • Science requirement: completion of PHYS 1110, 1120 and 1140. Completion of at least 5 additional credits of chemistry or biology (including 2 credits of laboratory science), chosen from one of the following: CHEM 1221 and CHEN 1211; CHEM 1351; EBIO 1210, 1220, 1230 and 1240; or MCDB 1150, 1151, 2150 and 2151.
    • Completion of the following required applied mathematics courses: APPM 2360; APPM 3310; APPM 4350 and 4360; APPM 4650; and APPM 4440 or MATH 3001 or 3140.
    • A two-semester course sequence of applied mathematics or mathematics courses numbered 4000 or above in addition to APPM 4350 and 4360 (for example, APPM 4380 and 4390, APPM 4440 and 4450, APPM 4570 and 4580, APPM 4560 and 4520, APPM 4650 and 4660, or APPM 3570 and either APPM 4520 or 4560). Note: APPM 3570 is the only 3000-level course that can be used to satisfy this requirement.
    • A minimum of 24 credit hours in applied mathematics or mathematics courses numbered 3000 or above (including the required courses). No more than 3 credits of APPM 4840 may count toward these 24. No more than 6 credits of independent study are allowed for credit toward the BS degree in applied mathematics.
    • A minimum of 24 credit hours in engineering courses (or approved courses with a significant mathematical content in arts and sciences or business) with at least 15 credit hours in courses numbered 2000 or above and at least 6 credit hours in courses numbered 3000 or above. These 24 credit hours are in addition to those required credit hours listed in numbers 2 and 3 (mentioned above). HUEN 3100, 3200, 4100 and 4200 may not be used to fulfill this requirement, although they may be used as social and humanistic electives. Several possible options are listed separately.
    • The general bachelor’s degree requirements of the College of Engineering and Applied Science require 18 credit hours of social science/humanities/writing electives. See details at www.colorado.edu/engineering/academics/policies/hss

    Recommended Options For Applied Math Majors

    In order to fulfill their degree requirements, Applied Mathematics majors are required to take 24 credits in engineering or approved courses with significant mathematical content in A&S or Business courses, with at least 6 credits in courses numbered 3000 or above and at least 15 credits 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.  Final course selection should be made in consultation with an Applied Math advisor.

    I. Aerospace Engineering Sciences 

    • ASEN 2001 Intro to Statics, Structures, and Materials—4
    • ASEN 2002 Intro to Thermodynamics and Aerodynamics—4
    • ASEN 2003 Intro to Dynamics and Systems—5
    • ASEN 2004 Aerospace Vehicle Design and Performance—5
    • ASEN 2012 Experimental and Computational Methods in AES—2
    • Take at least 6 credits of ASEN courses at the 3000-level or above. 

    Advising Note: Students wishing to enroll in ASEN courses must register through an Aerospace advisor. 

    II. Chemical Engineering Option

    • CHEN 1211 Gen. Chemistry for Eng.—3 & CHEM 1221 Eng. Gen. Chem Lab—2

    Recommended courses (total of 23 credits):

    • CHEN 2120 Material & Energy Balances—3
    • CHEN 3200 Fluid Mechanics—3
    • CHEN 3210 Heat Transfer—3
    • CHEN 3220 Separations and Mass Transfer—3
    • CHEN 3320 Thermodynamics—3
    • CHEM 4521 Physical Chemistry for Engineers—3
    • CHEN 4330 Reaction Kinetics—3
    • CHEM 3311 Organic Chemistry 1—4

    Students choosing this option must take CHEN 1310 as part of their Applied Math major. CHEN 1310 is a prerequisite for CHEN 2120.

    III. Computer Science Option

    Required Course (total of 4 credits):

    • CSCI 2270 Data Structures—4 (Note: CSCI 1300 is a prerequisite)

    Additional courses to bring the total number of credits to 24; at least two of these must be at the 3000 level.  Possible choices include:

    • CSCI 3104 Algorithms—4*
    • CSCI 3155 Principles of Programming Languages—4
    • CSCI 3287 (Database and Information Systems—3
    • CSCI 3753 (Operating Systems—4
    • Additional CSCI courses to bring the total number of credits to at least 24

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

    * CSCI 3104 has APPM 3170 or CSCI 2824 as a prerequisite.

    IV. Technology, Arts & Media Option

    Required Courses

    • ATLS 2000 Meaning of Info Tech.—3*
    • ATLS 3010 Digital Media 1—3
    • CSCI 2270 Data Structures—4 (Note: CSCI 1300 is a prerequisite for CSCI 2270)
    • CSCI 3104 Algorithms—4
    • CSCI 4229 Computer Graphics—3
    • CSCI 4448 Object Orientated Analysis and Design—3 

     * This course may be used to satisfy EITHER 3 credits of H&SS requirement or the Applied Math area of emphasis, but not both 

    Recommended additional courses to bring the total to at least 24 credits:

    • Advisor approved technical electives to complete the ATLAS/TAM Certificate in Digital Media
    • CSCI 3202 (Intro to Artificial Intelligence—3
    • CSCI 4202 (Artificial Intelligence 2—3
    • Students are advised to take APPM 3570, 4560, and 4660 as part of their Applied Math coursework.

    Advising Note: More information on the ATLAS/TAM Certificate in Digital Media, as well as the ATLS Minor in Technology, Arts & Media may be found at http://tam.colorado.edu

    V. Electrical & Computer Engineering Option

    The Department of Electrical and Computer Engineering offers two separate minor programs.

    A. Students interested in this option should consult with an advisor as several areas are available (computer engineering, electrical engineering, signals and systems, and electrical renewable energy systems.) A minimum of 24 credits is required.

    B. Student choosing this option should plan on taking CSCI 1300 and CSCI 2270.

    Advising Note:  Students interested in the ECE Option should contact the ECE department and visit http://www.colorado.edu/engineering/academics/degrees-minors-certificates/minors

    VI. Engineering Physics / Physics Option

    Recommended courses after first-year Physics (23 or 24 credits):

    • PHYS 2130 or 2170 Foundations of Modern Physics—3        
    • PHYS 2150 Experimental Physics—1
    • PHYS 2210 Classical Mechanics and Mathematical Methods 1—3
    • PHYS 3210 Classical Mechanics and Mathematical Methods 2—3
    • PHYS 3220 Quantum Mechanics & Atomic Physics 1—3
    • PHYS 3310 Principles of Electricity & Magnetism 1—3
    • PHYS 3320 Principles of Electricity & Magnetism 2—3
    • PHYS 3330 Electronics for the Physical Sciences—2 OR
    • PHYS 4230 (Thermodynamics & Statistical Mechanics – 3 cr.)
    • Additional physics courses to total at least 24 credits.

    Students choosing this option are advised to take APPM 3570 (Applied Probability – 3 cr.) AND MATH 3140 (Abstract Algebra 1 – 3 cr.) as part of their Applied Math major.

    Advising Note:  Students completing the Physics Option should have a minor in Physics.  Check with the Physics Department.

    VII. Mechanical Engineering Option

    Recommended courses:

    • MCEN 2023 Statics & Structures—3
    • MCEN 2063 Mechanics of Solids—3
    • MCEN 3012 Thermodynamics—3
    • MCEN 3021 Fluid Mech.—3
    • MCEN 3022 Heat Transfer—3
    • MCEN 3025 Component Design—3
    • MCEN 2043 Dynamics—3
    • MCEN 4043 System Dynamics—3

    Students choosing this option are advised to take APPM 4570 (Statistical Methods – 3 cr.) or APPM 3570 (Applied Probability) and APPM 4520 (Introduction to Math Statistics) as part of their Applied Math major.

    VIII. Civil, Environmental and Architectural Engineering Option

    Recommended basic courses (total of 12 credits):

    • CVEN 2121 Analytical Mechanics 1—3
    • AREN 2110 Thermodynamics—3
    • CVEN 3161 Mechanics of Materials 1—3
    • CVEN 3313 Theoretical Fluid Mechanics—3

    Students also take 2 courses from any one of the following groups plus additional courses to bring the total credits to 24:

    • CVEN 3414 Fundamentals of Environmental Eng.—3
    • CVEN 4333 Engineering Hydrology—3
    • CVEN 3525 Structural Analysis 1—3
    • CVEN 3708 Geotechnical Engineering 1—3
    • CVEN 4545/4555 Steel Design/ Reinforced Concrete Design—3
    • AREN 2406 Introduction to Building Construction—3
    • AREN 3010 Mechanical Systems for Buildings—3
    • AREN 3540 Illumination 1—3

    Students wishing to enroll in CVEN courses that are restricted to majors only must do so through the CVEN advisor.

    IX. Actuarial Option

    BCOR 1025, Data Analysis in Business, is a prerequisite for BCOR 2200 and BCOR 2002.  Students are advised to substitute an Applied Math prob/stats course for this prerequisite.

    The following courses should be taken:

    • BCOR 2002 Principles of Accounting and Finance—3
    • ECON 2010* Principles of Microeconomics—4 
    • ECON 2020* Principles of Macroeconomics—4
    • ECON 3070+Intermediate Microeconomic Theory—3
    • ECON 3080+Intermediate Macroeconomic Theory—3
    • ECON 4070 Topics in Microeconomics—3
    • FNCE 3010+Corporate Finance—3

    * ECON 2010 and 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.

    + The Society of Actuaries requires students to take certain college courses that will earn the Validation by Educational Experiences (VEE) credit. Courses marked with a + satisfy this requirement, 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 both BCOR 220 and FNCE 3010. We will apply for VEE credit for BCOR 2002 and FNCE 3010, but this has not yet been granted.

    Some (or all) of the following courses should be taken:

    • FNCE 3030 (Investment and Portfolio Management—3
    • FNCE 4040 (Derivative Securities—3
    • ECON 4818 (Intro to Econometrics—3

     Students are required to take APPM 3570, APPM 4520+, and APPM 4540+for the Actuarial Option. Students are strongly advised to take APPM 4560.

    Additional courses that may be useful include ACCT 3220, 3230, and BCOR 3000. These courses can be taken only if space is available on the first day of the semester.

    X. Finance Option

    BCOR 1025, Data Analysis in Business, is a prerequisite for BCOR 2200 and BCOR 2002. Students are advised to substitute an Applied Math prob/stats course for this prerequisite.

    Recommended basic courses (14 - 16 credit hours):

    • BCOR 2002 Principles of Accounting and Finance—3
    • FNCE 3010 Corporate Finance—3
    • ECON 2010**, 2020**, 3070 and 3080.
    • ECON 4818 (Econometrics)—3

    ** ECON 2010, 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.

    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 Certificate Program:

    • ACCT 3220 Corporate Financial Reporting 1—3
    • FNCE 3030 Investment and Portfolio Management—3
    • FNCE 4040 Derivative Securities—3
    • FNCE 4820 Topics in Finance: Mathematical Finance—3
    • FNCE 4070 Financial Markets and Institutions—3

    Students are required to take APPM 3570 and APPM 4520 for the Finance Option. Students are advised to   take APPM 4560 and APPM 4540 if time permits.

    Additional courses that may be taken as time permits:

                ACCT 3230 Corporate Financial Reporting 2—3

                FNCE 4000 Financial Institutions Management—3

                FNCE 4020 Applied Business Finance—3

                FNCE 4050 Capital Investment Analysis—3

                FNCE 4060 Special Topics in Finance—variable

    Advising note: Students wishing to take College of Business courses cannot register until the first day of classes. However, students can register for BCOR/FNCE courses in summer sessions. 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 and visit http://www.colorado.edu/asqf/.

    XI. Computational Biology and Bioinformatics Option

    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.

    Required courses

    • CSCI 2270 Data Structures—4 (Note: CSCI 1300 is a prerequisite for CSCI 2270)
    • CHEM 3311 & 3321 Organic Chemistry 1 and Lab—5)
    • MCDB 1150 & 1151 Introduction to Cellular and Molecular Biology and Lab—4
    • MCDB 2150 & 2151 Principles of Genetics and Lab—4
    • MCDB 3135 & 3140 Molecular Cell Biology 1 and Lab—5
    • CSCI 4314 Algorithms for Molecular Biology—3

    Advising Note:  Students selecting this option are advised to take APPM 3570, 4520, 4540, and 4390 as part of their Applied Math coursework. Other recommended courses include CSCI 3104 (Algorithms) and CSCI 3287 (Database and Information Systems).

    Concurrent Bachelor's/Master's Program

    Concurrent BS/MS Degree in Applied Mathematics

    The concurrent BS/MS program in applied mathematics enables well-qualified and motivated students to experience graduate-level course work earlier in their education and to obtain an MS degree in a reduced time period. Applied math majors may apply for this program during their junior year. Minimum requirements for admission include completion of at least two APPM courses numbered 3000 or higher, an overall GPA of 3.40 or higher, a minimum GPA of 3.40 in APPM and MATH courses and two letters of recommendation from APPM faculty. Students interested in this program are encouraged to consult with an applied mathematics faculty advisor early in their undergraduate career. 

    Graduate Degree Program(s)

    Graduate Study in Applied Mathematics

    The Department of Applied Mathematics offers MS and PhD programs through the College of Arts and Sciences.

    Dual Degree Programs

    Double Major with Civil Engineering

    As an exceptional opportunity for talented students who are interested in analytical and computational methods related to civil engineering and general engineering science, the applied mathematics and civil engineering departments offer a streamlined track by which a student can earn a baccalaureate degree from both programs with a minimum of 15 extra credit hours. Consult faculty advisors in applied mathematics and civil engineering for information and admission.