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Lyles, Danielle Jeanette Instructor

Positions

Research Areas research areas

Research

research overview

  • Her research involves building mathematical models to represent biological systems. The model terms are derived based on data. The goal is to understand what features of the system are important and how they interact. In particular, she has studied systems where both predictable (deterministic) and random (stochastic) processes are crucial to the observed behavior. Thus, she included both types of quantities, resulting in hybrid deterministic-stochastic mathematical models. One key accomplishment in her thesis work was creating an algorithm to solve the hybrid model numerically on the computer. The most interesting aspect of these hybrid models is how the interplay between predictable and random processes affects the behavior of the model and its implication for the system under study – a key theme of her work. Her current interests involve machine learning and the interplay between dynamical modeling and machine learning models.

Teaching

courses taught

  • APPM 1350 - Calculus 1 for Engineers
    Primary Instructor - Fall 2018
    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. Degree credit not granted for this course and APPM 1345 or ECON 1088 or MATH 1081 or MATH 1300 or MATH 1310 or MATH 1330.
  • APPM 1360 - Calculus 2 for Engineers
    Primary Instructor - Summer 2018 / Summer 2019 / Fall 2019
    Continuation of APPM 1350. Focuses on applications of the definite integral, methods of integration, improper integrals, Taylor's theorem, and infinite series. Degree credit not granted for this course and MATH 2300.
  • APPM 2360 - Introduction to Differential Equations with Linear Algebra
    Primary Instructor - Spring 2018 / Spring 2019
    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 4120 - Introduction to Operations Research
    Primary Instructor - Spring 2019
    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. Same as APPM 5120 and MATH 4120 and MATH 5120.
  • APPM 4380 - Modeling in Applied Mathematics
    Primary Instructor - Fall 2018
    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. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 5380.
  • APPM 4390 - Modeling in Mathematical Biology
    Primary Instructor - Spring 2018
    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. Same as APPM 5390.
  • APPM 5120 - Introduction to Operations Research
    Primary Instructor - Spring 2019
    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. Department enforced prerequisite: APPM 2130 or MATH 2135 or MATH 2135. Same as APPM 4120 and MATH 4120 and MATH 5120.
  • APPM 5380 - Modeling in Applied Mathematics
    Primary Instructor - Fall 2018
    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. Department enforced prerequisites: APPM 2350 or MATH 2400 and APPM 2360. Recommended prerequisites: APPM 3310 and APPM 4350 and APPM 4650. Same as APPM 4380.
  • APPM 5390 - Modeling in Mathematical Biology
    Primary Instructor - Spring 2018
    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. Department enforced prerequisites: APPM 2360 and APPM 3310 or MATH 2130 or MATH 2135 or instructor consent required. Same as APPM 4390.
  • MATH 4120 - Introduction to Operations Research
    Primary Instructor - Spring 2019
    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. Same as MATH 5120 and APPM 4120 and APPM 5120.
  • MATH 5120 - Introduction to Operations Research
    Primary Instructor - Spring 2019
    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. Department enforced prerequisite: MATH 2130 or MATH 2135 or APPM 3310. Instructor consent required for undergraduates. Same as MATH 4120 and APPM 4120 and APPM 5120.

Background

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