1 The eigenvalue distribution function For an N × N matrix AN , the eigenvalue distribution function 1 (e.d.f.) F AN (x) is defined as F AN (x) = Number of eigenvalues of AN ≤ x . (1) N As defined, the e.d.f. is right continuous and possibly atomic i.e. with step discontinuities at discrete points. In practical terms, the derivative of (1), referred to as the (eigenvalue) level density, is simply the

The Classical Random Matrix Ensembles The Wigner Matrix (or Hermite Ensemble) The Wigner matrices [1, 2] are often known as the Hermite or Gaussian ensembles are well studied in physics and in the book by Mehta [3]. The term Wigner matrix does not require the entries be normal, though the term Gaussian ensemble and Hermite

1 Largest Eigenvalue Distributions In this section, the distributions of the largest eigenvalue of matrices in the β-ensembles are studied. His￾tograms are created first by simulation, then by solving the Painlev´e II nonlinear differential equation

Random Variables and Probability Densities We assume that the reader is familiar with the most basic of facts concerning continuous random variables or is willing to settle for the following sketchy description. Samples from a (univariate or multivariate) experiment can be histogrammed either in practice or as a thought experiment. Histogramming counts

Student replies - Prof Hastings assessmentValue of science delivered will be superior to robotics - maybe

Globalization trends – Longer distances between producers and consumers – Emerging markets, e.g. China, South America, Africa

– A current issue of national debate – Ties in directly with Part III of the book – Frequent topic in Aviation Week – Aligns with current student interests

3:05-3:10 Announcements and Introductions 3:10-3:55 LEV Ch 5 Discussion 3:55-4:05 Break 4:05-4:50 Av Week Article Discussion

A lean enterprise is an integrated entity that efficiently creates value for the multiple stakeholders by employing lean principles and practices.” Lean Enterprises

Learning Objectives ¾ Session Design (60-90 Awareness of the contrast min.) between “mass” and “lean” ¾ Two mindsets (7-10 min.) mindsets Appreciation of the historical context for lean thinking