# 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 5-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 Program

The department also 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.

### 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 or GEEN 1300 or APPM 2750 or ECEN 1030).
- 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 engineering.colorado.edu/hss.

**Some Recommended Options for Applied Math Majors**

### Aerospace Engineering Sciences Option

**Recommended Courses and Semester Credit Hours **

- ASEN 2001 Aero 1: Introduction to Statics, Structures, and Materials—4
- ASEN 2002 Aero 2: Introduction to Thermodynamics and Aerodynamics—4
- ASEN 2003 Aero 3: Introduction to Dynamics and Systems—5
- ASEN 2004 Aero 4: Introduction to Vehicle Design and Performance—5
- At least two more ASEN courses at the 3000 level or above

*Advising Note: Students seeking to enroll in ASEN courses must register through an aerospace advisor.*

### Chemical Engineering Option

Recommended courses (total of 25 credit hours):

- CHEN 2120 Material and Energy Balance—3
- CHEN 3210 Heat Transfer—3
- CHEN 3220 Mass Transfer—3
- CHEN 3311 Organic Chemistry 1—4
- CHEN 3320 Thermodynamics—3
- CHEN 4330 Reaction Kinetics—3
- CHEM 3200 Fluids—3
- CHEM 4511 Physical Chemistry—3

### Computer Science Option

Required course:

- CSCI 2270 Data Structures (prereq. CSCI 1300)—4

Additional courses to bring the total number of credits to at least 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 Systems—3
- CSCI 3753 Systems—4

*Advising Note: Students completing the computer science option should have a minor in computer science. Check with the computer science department.*

### Electrical and Computer Engineering Option

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 credit hours is required.

### Engineering Physics Option

Recommended courses after first-year physics (22 or 23 credit hours):

- PHYS 2150 Experimental Physics—1
- PHYS 2170 Foundations of Modern Physics—3
- PHYS 2210 Classical Mechanics and Math Methods 1—3
- PHYS 3210 Classical Mechanics and Math Methods 2—3
- PHYS 3220 Quantum Mechanics and Atomic Physics—3
- PHYS 3310 Principles of Electricity and Magnetism 1—3
- PHYS 3320 Principles of Electricity and Magnetism 2—3

Plus either of the following:

- PHYS 3330 Junior Laboratory—2
- PHYS 4230 Thermodynamics and Statistical Mechanics—3

*Note: Additional courses are required to bring the total number of physics credits to 24.*

Also recommended:

- APPM 3570 Applied Probability—3
- MATH 3140 Abstract Algebra 1—3

*Advising Note: Students completing the physics option should have a minor in physics. Check with the physics department.*

### Mechanical Engineering Option

Recommended courses (total of 24 credit hours):

- 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

Also recommended:

- APPM 4570 Statistical Methods—3

### Civil, Environmental, and Architectural Engineering Option

Recommended basic courses (total of 12 credit hours):

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

Students also take a minimum of two courses from any one of the following groups, plus additional CVEN or AREN courses to bring total to 24 credit hours:

- a) AREN 2406 Introduction to Building Construction—3

AREN 3010 Mechanical Systems for Building—3

AREN 3540 Illumination 1—3 - b) CVEN 3414 Introduction to Environmental Engineering—3

CVEN 4333 Engineering Hydrology—3 - c) CVEN 3525 Structural Engineering 1—3

CVEN 3708 Geotechnical Engineering 1—3

CVEN 4555/4545 Reinforced Concrete Design/Steel Design—3

### Actuarial Option

Recommended basic courses (19 credit hours):

- BCOR 2000 Accounting and Financial Analysis 1—4
- BCOR 2200 Accounting and Financial Analysis 2 (formerly 2100) (Note 1)—3
- FNCE 3010 Corporate Finance—3
- ECON 3070 Intermediate Microeconomics Theory (Note 2)—3
- ECON 3080 Intermediate Macroeconomics Theory (Note 2)—3
- ECON 4070 Topics in Microeconomics—3

Some of the following courses should also be taken:

- ECON 4818 Introduction to Econometrics—3
- FNCE 4030 Investment and Portfolio Management—3
- FNCE 4040 Derivative Securities—3

*Curriculum Notes*

###### 1. BCOR 1020 Business Statistics is a prerequisite for BCOR 2200 (formerly 2100). Students are advised to substitute an applied math probability/statistics course for this prerequisite.

###### 2. ECON 2010 and 2020 (prerequisites for ECON 3070 and 3080) should be taken in either the first or second year. They do not count toward the 24 credits of the option requirement, but they can count toward the 18-credit humanities/social science requirement of the College of Engineering and Applied Science.

###### 3. Students are advised, but not required, to take as many of the following courses as possible as part of their applied math requirement: APPM 3570, 4520, 4540, and 4560.

###### 4. To assure admittance into Leeds School of Business courses, students should apply to the Actuarial Studies and Quantitative Finance Certificate Program.

### Finance Option

#### Recommended basic courses (14–16 credit hours):

- BCOR 2000 Accounting and Financial Analysis 1—4
- BCOR 2200 Accounting and Financial Analysis 2 (formerly 2100) (Note 1)—3
- ECON 3070 Intermediate Microeconomics Theory (Note 2)—3
- ECON 3080 Intermediate Macroeconomics Theory (Note 2)—3
- FNCE 3010 Corporate Finance—3

Plus at least two of the following courses to meet the 24 credit-hour requirement of the option:

- FNCE 4000 Financial Institutions Management—3
- FNCE 4030 Investment and Portfolio Management—3
- FNCE 4040 Derivative Securities—3
- FNCE 4050 Capital Investment Analysis—3
- FNCE 4060 Special Topics in Finance—variable credit
- FNCE 4070 Financial Markets and Institutions—3

##### Curriculum Notes

###### 1. BCOR 1020 Business Statistics is a prerequisite for BCOR 2200 (formerly 2100). Students are advised to substitute an applied math probability/statistics course for this prerequisite.

###### 2. ECON 2010 and 2020 (prerequisites for ECON 3070 and 3080) should be taken in either the first or second year. They do not count toward the 24 credits of the option requirement, but they can count toward the 18-credit humanities/social science requirement of the College of Engineering and Applied Science.

###### 3. To assure admittance into Leeds School of Business courses, students should apply to the Actuarial Studies and Quantitative Finance Certificate Program.

### 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 and Semester Credit Hours**

- CSCI 2270 Data Structures (Note: CSCI 1300 is a prerequisite for CSCI 2270.)—4
- CHEM 331 and 3321 Organic Chemistry 1 and Lab—5
- CSCI 4314 Algorithms for Molecular Biology—3
- MCDB 1150 and 1151 Introduction to Cellular and Molecular Biology and Lab—4
- MCDB 2150 and 2151 Principles of Genetics and Lab—4
- MCDB 3120 and 3140 Cell Biology and Lab—5
- MCDB 3500 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 course work. Other recommended courses include CSCI 3104 Algorithms and CSCI 3287 Database and Information Systems.*

Other areas of academic focus are also possible. Check with the applied mathematics office or more information.

### 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 3.400 or higher, a minimum GPA of 3.400 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.

### 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.