Applied Mathematics

APPM 1235 (4) Pre-Calculus for Engineers

Prepares students for the challenging content and pace of the calculus sequence required for all engineering majors. Covers algebra, trigonometry and selected topics in analytical geometry. Prepares students for the calculus courses offered for engineering students. Requires students to engage in rigorous work sessions as they review topics that they must be comfortable with to pursue engineering course work. Structured to accustom students to the pace and culture of learning encountered in engineering math courses. For more information about the math placement referred to in the "Enrollment Requirements", please contact your academic advisor. Formerly GEEN 1235.

Equivalent - Duplicate Degree Credit Not Granted: MATH 1021 or MATH 1150
Requisites: Requires an ALEKS math exam taken in 2016 or earlier, or placement into pre-calculus based on your admissions data and/or CU Boulder coursework.

APPM 1340 (4) Calculus 1 with Algebra, Part A

Studies selected topics in analytical geometry and calculus: rates of change of functions, limits, derivatives and their applications. This course and APPM 1345 together are equivalent to APPM 1350. The sequence of this course and APPM 1345 is specifically designed for students whose manipulative skills in the techniques of high school algebra and precalculus may be inadequate for APPM 1350. For more information about the math placement referred to in the "Enrollment Requirements", please contact your academic advisor.

Requisites: Requires prerequisite course of APPM 1235 or MATH 1021 or MATH 1150 or MATH 1160 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into pre-calculus based on your admissions data and/or CU Boulder coursework.
Additional Information: Arts Sci Gen Ed: Quantitative Reasoning Math

APPM 1345 (4) Calculus 1 with Algebra, Part B

Continuation of APPM 1340. Studies selected topics in calculus: derivatives and their applications, integration, differentiation and integration of transcendental functions. Algebraic and trigonometric topics are studied throughout, as needed.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1350 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 or MATH 1330
Requisites: Requires prerequisite course of APPM 1340 (minimum grade C-).

APPM 1350 (4) Calculus 1 for Engineers

Topics in analytical geometry and calculus including limits, rates of change of functions, derivatives and integrals of algebraic and transcendental functions, applications of differentiations and integration. Students who have already earned college credit for calculus 1 are eligible to enroll in this course if they want to solidify their knowledge base in calculus 1. For more information about the math placement referred to in the "Enrollment Requirements", contact your academic advisor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 1345 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 or MATH 1330
Requisites: Requires prerequisite course of APPM 1235 or MATH 1021 or MATH 1150 or MATH 1160 or MATH 1300 (minimum grade C-) or an ALEKS math exam taken in 2016 or earlier, or placement into calculus based on your admissions data and/or CU Boulder coursework.
Additional Information: GT Pathways: GT-MA1 - Mathematics
Arts Sci Core Curr: Quant Reasn Mathmat Skills
Arts Sci Gen Ed: Quantitative Reasoning Math

APPM 1360 (4) Calculus 2 for Engineers

Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series.

Equivalent - Duplicate Degree Credit Not Granted: MATH 2300
Requisites: Requires prerequisite course of APPM 1345 or APPM 1350 or MATH 1300 (minimum grade C-).

APPM 1390 (1) A Game for Calculus

Coaches students to implement study strategies geared specifically toward APPM Calculus in a structured, supportive, small group environment. Enrollment requires instructor approval.

Repeatable: Repeatable for up to 3.00 total credit hours.

APPM 2350 (4) Calculus 3 for Engineers

Covers multivariable calculus, vector analysis, and theorems of Gauss, Green, and Stokes.

Equivalent - Duplicate Degree Credit Not Granted: MATH 2400
Requisites: Requires prerequisite course of APPM 1360 or MATH 2300 (minimum grade C-).

APPM 2360 (4) Introduction to Differential Equations with Linear Algebra

Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations.

Equivalent - Duplicate Degree Credit Not Granted: both MATH 2130 and MATH 3430
Requisites: Requires prerequisite course of APPM 1360 or MATH 2300 (minimum grade C-).

APPM 2450 (1) Calculus 3 Computer Lab

Selected topics in analytic geometry and calculus with a focus on symbolic computation using Mathematica.

Requisites: Requires a corequisite course of APPM 2350.
Grading Basis: Pass/Fail

APPM 2460 (1) Differential Equations Computer Lab

Selected topics in differential equations and linear algebra with a focus on symbolic computation using MATLAB.

Requisites: Requires enrollment in a corequisite course of APPM 2360.
Grading Basis: Pass/Fail

APPM 2720 (1-3) Open Topics in Lower Division Applied Mathematics

Provides a vehicle for the development and presentation of new topics that are accessible to lower division Applied Mathematics students. These topics have the potential to be incorporated into the core APPM curriculum.

Repeatable: Repeatable for up to 6.00 total credit hours. Allows multiple enrollment in term.
Requisites: Requires prerequisite course of APPM 1350 or MATH 1300 (minimum grade C-).
Grading Basis: Letter Grade

APPM 2750 (4) Java: Training, Mathematical Algorithms, and Mobile Apps

Preparatory course for Java programming. Provides necessary background for Java language: basic object-oriented concepts, analysis, and design. Learn to create Java applets, applications and mobile apps, create graphic context, and identify the key features of Java foundation classes as well as other Java-related technology. Material is taught in the context of mathematical algorithms from calculus. Department enforced requisite, knowledge of a programming language.

Requisites: Requires prerequisite course of APPM 1350 or MATH 1300 (minimum grade C-).

APPM 3010 (3) Chaos in Dynamical Systems

Introduces undergraduate students to chaotic dynamical systems. Topics include smooth and discrete dynamical systems, bifurcation theory, chaotic attractors, fractals, Lyapunov exponents, synchronization and networks of dynamical systems. Applications to engineering, biology and physics will be discussed.

Requisites: Requires prerequisite course of APPM 2360 or MATH 3430 (minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 3050 (3) Scientific Computing in Matlab

Topics covered include: approximations in computing, computer arithmetic, interpolation, matrix computations, nonlinear equations, optimization, and initial-value problems with emphasis on the computational cost, efficiency, and accuracy of algorithms. The problem sets are application-oriented with examples taken from orbital mechanics, physics, genetics, and fluid dynamics.

Requisites: Requires prerequisite course of APPM 2360 or MATH 3430 (minimum grade C-).

APPM 3170 (3) Discrete Applied Mathematics

Introduces students to ideas and techniques from discrete mathematics that are widely used in science and engineering. Mathematical definitions and proofs are emphasized. Topics include formal logic notation, proof methods; set theory, relations; induction, well-ordering; algorithms, growth of functions and complexity; integer congruences; basic and advanced counting techniques, recurrences and elementary graph theory. Other selected topics may also be covered.

Requisites: Requires a prerequisite of APPM 1360 or MATH 2300 (all minimum grade C-).

APPM 3310 (3) Matrix Methods and Applications

Introduces linear algebra and matrices with an emphasis on applications, including methods to solve systems of linear algebraic and linear ordinary differential equations. Discusses vector space concepts, decomposition theorems, and eigenvalue problems.

Equivalent - Duplicate Degree Credit Not Granted: MATH 2130 and MATH 2135
Requisites: Requires prerequisite course of APPM 2350 or APPM 2360 or MATH 2400 (minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 3350 (3) Advanced Engineering Calculus

Extends the treatment of engineering mathematics beyond the topics covered in Calculus 3 and differential equations. Topics include non-dimensionalization, elementary asymptotics and perturbation theory, Reynold's transport theorem and extensions of Leibnitz's rule, as applied to continuum conservation equations, Hamiltonian formulations, Legendre and Laplace transforms, special functions and their orthogonality properties.

Requisites: Requires prerequisite course of APPM 2350 or MATH 2400 and APPM 2360 (all minimum grade C-).

APPM 3570 (3) Applied Probability

Studies axioms, counting formulas, conditional probability, independence, random variables, continuous and discrete distribution, expectation, joint distributions, moment generating functions, law of large numbers and the central limit theorem.

Equivalent - Duplicate Degree Credit Not Granted: ECEN 3810 or MATH 4510 STAT 3100
Requisites: Requires a prerequisite or corequisite course of APPM 2350 or MATH 2400 (prereq minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4120 (3) Introduction to Operations Research

Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5120 and MATH 4120 and MATH 5120
Requisites: Requires a prerequisite course of APPM 3310 or MATH 3130 or MATH 3135 (minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4350 (3) Methods in Applied Mathematics: Fourier Series and Boundary Value Problems

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution of these equations via separation of variables, with Fourier series, Fourier integrals, and more general eigenfunction expansions.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5350
Requisites: Requires prerequisite courses of APPM 2350 or MATH 2400 and APPM 2360 (all minimum grade C-) and a prerequisite or corequisite course of APPM 3310 or MATH 3130 or MATH 3135 (prereq minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4360 (3) Methods in Applied Mathematics: Complex Variables and Applications

Introduces methods of complex variables, contour integration and theory of residues. Applications include solving partial differential equations by transform methods, Fourier and Laplace transforms and Reimann-Hilbert boundary-value problems, conformal mapping to ideal fluid flow and/or electrostatics.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5360
Requisites: Requires prerequisite courses of APPM 2350 or MATH 2400 and APPM 2360 (all minimum grade C-) and a prerequisite or corequisite course of APPM 3310 or MATH 3130 or MATH 3135 (prereq minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4380 (3) Modeling in Applied Mathematics

An exposition of a variety of mathematical models arising in the physical and biological sciences. Students' modeling projects are presented in class. Topics may include: GPS navigation, medical imaging, ocean waves, and computerized facial recognition.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5380
Requisites: Requires prerequisite courses of APPM 2350 or MATH 2400 and APPM 2360 (all minimum grade C-).
Recommended: Prerequisites APPM 3310 and APPM 4350 and APPM 4650.
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4390 (3) Modeling in Mathematical Biology

Investigates how complex systems in biology can be studied using applied mathematics. Examines several case studies which include topics from microbiology, enzyme reaction kinetics, neuroscience, ecology, epidemiology, physiology and bioengineering.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5390
Requisites: Requires prerequisite courses of APPM 2360 and APPM 3310 or MATH 3130 or MATH 3135 (all minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4440 (3) Undergraduate Applied Analysis 1

Provides a rigorous treatment of topics covered in Calculus 1 and 2. Topics include convergent sequences; continuous functions; differentiable functions; Darboux sums, Riemann sums, and integration; Taylor and power series and sequences of functions.

Requisites: Requires prerequisite courses of APPM 2350 or MATH 2400 and APPM 2360 (all minimum grade C-) and a prerequisite or corequisite course of APPM 3310 or MATH 3130 or MATH 3135 (prereq minimum grade C-).

APPM 4450 (3) Undergraduate Applied Analysis 2

Continuation of APPM 4440. Study of multidimensional analysis including n-dimensional Euclidean space, continuity and uniform continuity of functions of several variables, differentiation, linear and nonlinear approximation, inverse function and implicit function theorems, and a short introduction to metric spaces.

Requisites: Requires prerequisite course of APPM 4440 or MATH 3001 (minimum grade C-).

APPM 4500 (3) Statistical Collaboration

Educates and trains students to become effective interdisciplinary collaborators by developing the communication and collaboration skills necessary to apply technical statistics and data science skills to help domain experts answer research questions. Topics include structuring effective meetings and projects; communicating statistics to non-statisticians; using peer feedback, self-reflection and video analysis to improve collaboration skills; creating reproducible statistical workflows; working ethically.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5500
Requisites: Requires a prerequisite course of APPM 4520 (minimum grade C-).
Grading Basis: Letter Grade
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4505 (2) Advanced Statistical Collaboration

Educates and trains students to become advanced interdisciplinary collaborators by developing and refining the communication, collaboration and technical statistics and data science skills necessary to collaborate with domain experts to answer research questions. Students work on multiple projects. Discussions center on technical skills necessary to solve research problems and video analysis to improve communication and collaboration skills.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5505
Requisites: Requires prerequisite course of APPM 4500 or APPM 5500 (minimum grade C-).
Grading Basis: Letter Grade
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4510 (3) Data Assimilation in High Dimensional Dynamical Systems

Develops and analyzes approximate methods of solving the Bayesian inverse problem for high-dimensional dynamical systems. After briefly reviewing mathematical foundations in probability and statistics, the course covers the Kalman filter, particle filters, variational methods and ensemble Kalman filters. The emphasis is on mathematical formulation and analysis of methods.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5510, STAT 4250 and STAT 5250
Requisites: Requires prerequisite courses of APPM 3310 and APPM 3570 or STAT 3100 or MATH 4510 (all minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4530 (3) Stochastic Analysis for Finance

Studies mathematical theories and techniques for modeling financial markets. Specific topics include the binomial model, risk neutral pricing, stochastic calculus, connection to partial differential equations and stochastic control theory.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5530, STAT 4230 and STAT 5230
Requisites: Requires prerequisite courses of APPM 3310 and APPM 3570, or STAT 3100, or MATH 4510 (all minimum grade C-).

APPM 4560 (3) Markov Processes, Queues, and Monte Carlo Simulations

Brief review of conditional probability and expectation followed by a study of Markov chains, both discrete and continuous time, including Poisson point processes. Queuing theory, terminology and single queue systems are studied with some introduction to networks of queues. Uses Monte Carlo simulation of random variables throughout the semester to gain insight into the processes under study.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5560 and STAT 4100
Requisites: Requires prerequisite courses of APPM 3570 or STAT 3100 or MATH 4510 (all minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4565 (3) Random Graphs

Introduces mathematical techniques, including generating functions, the first- and second-moment method and Chernoff bounds to study the most fundamental properties of the Erdos-Renyl model and other celebrated random graph models such as preferential attachment, fixed degree distribution, and stochastic block models.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5565
Requisites: Requires prerequisite APPM 3570 or MATH 4510 (both minimum grade C).
Grading Basis: Letter Grade

APPM 4570 (3) Statistical Methods

Covers basic statistical concepts with accompanying introduction to the R programming language. Topics include discrete and continuous probability laws, random variables, expectation and variance, central limit theorem, testing hypothesis and confidence intervals, linear regression analysis, simulations for validation of statistical methods and applications of methods in R.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5570
Requisites: Requires prerequisite course of APPM 1360 or MATH 2300 (minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4590 (3) Statistical Modeling

Introduces methods, theory and applications of statistical models, from linear models (simple and multiple linear regression), to hierarchical linear models. Topics such as estimation, residual diagnostics, goodness of fit, transformations, and various strategies for variable selection and model comparison will be discussed in depth. Examples and exercises will be demonstrated using statistical software.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5590
Requisites: Requires prerequisite course of APPM 4520 or APPM 4570 or MATH 4520 (minimum grade C-).
Additional Information: Arts Sci Gen Ed: Distribution-Natural Sciences

APPM 4650 (3) Intermediate Numerical Analysis 1

Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced prerequisite: knowledge of a programming language.

Equivalent - Duplicate Degree Credit Not Granted: MATH 4650
Requisites: Requires a prerequisite course of MATH 3430 or APPM 2360 and APPM 3310 (minimum grade C-).

APPM 4660 (3) Intermediate Numerical Analysis 2

Continuation of APPM 4650. Examines numerical solution of initial-value problems and two-point boundary-value problems for ordinary differential equations. Also looks at numerical methods for solving partial differential equations. Department enforced prerequisite: knowledge of a programming language.

Equivalent - Duplicate Degree Credit Not Granted: MATH 4660
Requisites: Requires prerequisite course of APPM 4650 or MATH 4650 (minimum grade C-).

APPM 4720 (1-3) Open Topics in Applied Mathematics

Provides a vehicle for the development and presentation of new topics that may be incorporated into the core courses in applied mathematics. Department enforced prerequisite: variable, depending on the topic, see instructor.

Equivalent - Duplicate Degree Credit Not Granted: APPM 5720
Repeatable: Repeatable for up to 15.00 total credit hours. Allows multiple enrollment in term.

APPM 4840 (1-3) Reading and Research in Applied Mathematics

Introduces undergraduate students to the research foci of the Department of Applied Mathematics. Department enforced prerequisite: variable depending on the topic.

Repeatable: Repeatable for up to 9.00 total credit hours.

APPM 4950 (1-3) Seminar in Applied Mathematics

Introduces undergraduate students to the research foci of the program in applied mathematics. It is also designed to be a capstone experience for the program's majors. Department enforced prerequisite: variable depending on the topic.

Repeatable: Repeatable for up to 6.00 total credit hours. Allows multiple enrollment in term.