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Restrepo, Juan G Associate Professor

Positions

Research Areas research areas

Research

research overview

  • 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 network-coupled oscillators and excitable systems such as neurons, and cardiac cells coupled in tissue. The analysis of network-coupled 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

Publications

selected publications

Teaching

courses taught

  • 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, 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.
  • 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 8000 - Colloquium in Applied Mathematics
    Primary Instructor - Fall 2021
    Introduces graduate students to the major research foci of the Department of Applied Mathematics.
  • 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.

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