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A Face in the Crowd: A Contextualized, Integrated, Intro to Linear Algebra

The module “A Face in the Crowd” is the opening module in the 12-credit, 3-semester QEA sequence. The module introduces the major ideas in linear algebra with a focus on intuition building and application in an effort to build deep understanding. The module is organized around the engineering challenging of building a facial recognition system. Rather than purely focus on the technical components of this challenge, students read about the societal issues surrounding the technology (e.g., algorithmic bias). Along the way students also see applications of linear algebra applied to different domains (e.g., neuroscience).

The full course “textbook” can be found using this link AFaceInTheCrowdSpring2020.pdf. Source files for this website and the assignments themselves can be found at


Key Features of QEA

QEA is a highly interdisciplinary, integrated course for teaching technical content. 


Computational Platform

Students use MATLAB as a programming environment during this module. Use the button below to see sample code and other supporting materials. 


Module Overview

The module introduces fundamental ideas in linear algebra through a deep dive into creating a facial recognition system. 


Supporting Documentation & Code

These resources provide some of the sample code we give in an easy to download and view format along with a guide to setting up your own photo booth so one can collect a dataset of images for facial recognition from a class.

Sample MATLAB Code

Teaching Team Documentation


Big Picture Framing and Linear Algebra Basics

The module begins with a day 1 activity that frames the big ideas of facial recognition (both in terms of technical concepts and societal implications). Students then build their understanding of the basic entities of linear algebra and how to operate on them.


Eigenthings and Applications of Linear Algebra

Next, students build on the basic properties of matrices and vectors and learn key concepts of Eigenvalues and Eigenvectors. Our presentation of these important concepts is heavy on visualization and intuition-building. We also provide several applications of these concepts to help students understand the power and utility of the math they are learning.


Matrix Decomposition with Applications in a Project

Students learn about several algorithms for matrix decomposition: Eigen Value Decomposition, Singular Value Decomposition, and Principal Components Analysis. The module culminates with a substantial project in which students build algorithms for facial recognition and processing while seriously considering the implications of their work for potential users and society in general.

Other Documents on QEA

S. Govindasamy, R.J. Christianson, J. Geddes, C. Lee, S. Michalka, P. Ruvolo, M.H. Somerville, A.C. Strong:

A Contextualized, Experiential Learning Approach to Quantitative Engineering Analysis, FIE 2018.