Explores a variety of models and optimization techniques for the solution of airline schedule planning problems. Schedule design, fleet assignment, aircraft maintenance routing, crew scheduling, robust planning, passenger mix, integrated schedule planning, and other topics. Solution techniques involving decomposition, e.g., Lagrangian relaxation, column generation and partitioning, and state-of-the-art applications of these techniques to airline problems. Explores a variety of models and optimization techniques for the solution of airline schedule planning and operations problems. Schedule design, fleet assignment, aircraft maintenance routing, crew scheduling, passenger mix, and other topics are covered. Recent models and algorithms addressing issues of model integration, robustness, and operations recovery are introduced. Modeling and solution techniques designed specifically for large-scale problems, and state-of-the-art applications of these techniques to airline problems are detailed.

I use this activity to build understanding with equivalent fractions.Students model equivalent fractions with fraction bar models and number lines.  In both types of models students need to focus on partitioning or ceating equal parts.  They also need to make sure their models are properly labeled.Naming the multiplier or divisor allows students to practice with simplifying or unsimplifying fractions.

This is an advanced interdisciplinary introduction to applied parallel computing on modern supercomputers. It has a hands-on emphasis on understanding the realities and myths of what is possible on the world's fastest machines. We will make prominent use of the Julia Language software project.

Big Ideas: A fraction describes the division of wholes into equal shares. Equal shares have the same area or amount, but do not have to be the same shape.
This lesson builds on students' work with partitioning circles and rectangles into two, three, and four equal shares. This task uses a scenario in which students share a birthday cake. Students will be presented with kids who each want to share their cake differently and asked to justify which kids are sharing equally. Students will be building their foundational knowledge of fractions by representing, labeling, and justifying equal shares. The mathematical concepts in this lesson build toward students' future work with naming fractions, comparing fractions, and equivalent fractions.
Vocabulary: fraction, equal shares, halves, thirds, fourths, sixths, eighths

I use this activity to help students develop a deeper understanding for unit fractions.