Prof. Juan G. Restrepo's research focuses on the analysis of emergent complex behavior in systems of interconnected units. This analysis often can be performed using techniques of nonlinear dynamics. Important examples of such systems are collections of networkcoupled oscillators and excitable systems such as neurons, and cardiac cells coupled in tissue. The analysis of networkcoupled systems requires developing an understanding of quantitative aspects of the structure of the coupling network. Accordingly, Prof. Restrepo is also studying how some characteristics of network structure can be quantified in order to understand their effect on these complex processes. Prof. Restrepo's research on cardiac dynamics spans ionic models for individual cells to the spatiotemporal dynamics of many coupled cells in tissue.
keywords
Nonlinear dynamics of networked and complex systems
APPM 2360  Introduction to Differential Equations with Linear Algebra
Primary Instructor

Spring 2018 / Spring 2021
Introduces ordinary differential equations, systems of linear equations, matrices, determinants, vector spaces, linear transformations, and systems of linear differential equations. Credit not granted for this course and both MATH 2130 and MATH 3430.
APPM 3010  Chaos in Dynamical Systems
Primary Instructor

Fall 2018 / Fall 2020
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.
APPM 3170  Discrete Applied Mathematics
Primary Instructor

Fall 2020
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, wellordering; 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.
APPM 3570  Applied Probability
Primary Instructor

Spring 2019 / Spring 2020
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. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as STAT 3100.
APPM 4720  Open Topics in Applied Mathematics
Primary Instructor

Fall 2019
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. May be repeated up to 15 total credit hours. Same as APPM 5720.
APPM 5320  Introduction to Dynamics on Networks
Primary Instructor

Fall 2021
Introduces modern approaches to model and analyze dynamical processes on complex networks. Many dynamical processes such as epidemic propagation, opinion formation, synchronization, and cascading processes take place on complex social or technological networks. This course will introduce the tools to understand the interplay between network structure and the outcome of these dynamical processes. Previously offered as a special topics course. Same as APPM 4320.
APPM 5720  Open Topics in Applied Mathematics
Primary Instructor

Fall 2019
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. May be repeated up to 6 total credit hours. Same as APPM 4720.
APPM 8100  Seminar in Dynamical Systems
Primary Instructor

Spring 2018 / Fall 2018 / Spring 2020 / Spring 2021
Introduces advanced topics and research in dynamical systems.
STAT 3100  Applied Probability
Primary Instructor

Spring 2019 / Spring 2020
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. Degree credit not granted for this course and ECEN 3810 or MATH 4510. Same as APPM 3570.