Mastering the Math Behind AI, Data Science

With a Ph.D. in mathematics and advanced studies spanning applied mathematics, bioinformatics, cell and molecular biology, physics and data science, Elinor Velasquez, Ph.D., brings a deeply interdisciplinary perspective to her online classroom.

Since joining us in 2021, Elinor has taught Introduction to Biostatistics and has added our linear algebra course to her roster. In this course, she connects foundational concepts such as matrices, vectors and eigenvalues to real-world applications in AI, data science and engineering. Describing her teaching style as “precise, patient and happy,” Elinor focuses on making advanced mathematics approachable for students from a wide range of academic and professional backgrounds.

Why do you enjoy teaching our students?

They are highly motivated, which makes teaching them highly rewarding and fun!

Typically, the physical location of my students varies widely: For example, I’ve had students located on at least three continents, studying in different time zones, so they are especially dedicated to the course.

I want to give them a satisfying experience so that their dedication is not wasted.

When I teach a particular linear algebra topic, I am mindful that the student may seriously apply what they are learning at their work or for scholarly pursuits. So I describe not just theoretical leanings, but also applications.

Tell me about the topics you discuss in your Linear Algebra course. How does your professional experience impact your teachings?

Linear algebra, calculus and statistics are much of the foundation for studies in computer science and various types of engineering, finance and economics, computational biology and biostatistics/public health. Learning about matrices, vectors and matrix equations are important for understanding and creating models, pursuing advanced coursework and applications in one’s actual or intended profession.

When I teach a particular linear algebra topic, I am mindful that the student may seriously apply what they are learning at their work or for scholarly pursuits. So I describe not just theoretical leanings, but also applications. For example, I discuss Markov models (Markov chains)—not just because it is in the textbook, but because this topic pops up everywhere.

I also discuss the basics such as least squares, determinants, singular-value decomposition and Gram-Schmidt, as well as contemporary topics like dimensionality reduction illustrated by principal component analysis, as well as applications of optimization illustrated by neural networks.

What are your expectations for your students?

Ask questions whenever something is unclear, or when a topic or homework problem sparks your curiosity and makes you want a deeper explanation—whether about the specific details or the bigger picture.

How do you support students during the class?

I provide ample time during class to address any concerns. I assign homework problems that are directly relevant to what we discuss in class. I always provide several examples to any theory being posed.

Outside of class, I encourage students to contact me, and I reply to them quickly so they feel heard. I provide explicit answers to questions: I make sure every question raised has an answer. I provide written feedback on their work rather than just assigning a score.

The goal is for each student to master the course material so they can apply it in other settings.

This diversity among the students makes for a lively class and requires me to make the material easily approachable and, most importantly, usable.

Many students feel intimidated by linear algebra. How do you make the material approachable for beginners or those returning to math after a break?

The course is self-contained. I don’t assume the students have taken a plethora of mathematics classes prior to enrolling in linear algebra. I may have a high school student taking the course in addition to their usual classes, as well as an advanced learner who needs the course to increase their knowledge base so they can confidently direct a team in solving a business challenge.

This diversity among the students makes for a lively class and requires me to make the material easily approachable and, most importantly, usable.

Linear algebra is foundational in fields like data science and AI. How do you bring those applications into your classroom?

I use data science and AI almost every day so it’s easy for me to come up with applications of linear algebra, especially in the sciences. Some applications—such as Markov models, Principal Component Analysis (PCA) and neural networks—I have adapted for the students to use.

What’s something students can do after your course that they couldn’t do before?

They are able to apply the concepts of linear algebra to model relevant scenarios at work or in school. For example, they can lead a team involved with deep learning because they now understand why a neural network behaves as it does. They can use this background knowledge to spark new models, like a transformer.

Be a lifelong learner and learn to adapt.

What sparked your own interest in linear algebra?

Physics is a subject that naturally lends itself to vectors and matrices. As a student, I thought classical mechanics was beautiful and was inspired to read an earlier edition of Gilbert Strang’s Linear Algebra (our course’s textbook) on my own.

What advice would you give to your student on how best to succeed in our current workforce?

Be a lifelong learner and learn to adapt.

Outside of work, where can we find you?

I love to visit Golden Gate Park in San Francisco. The park is enormous and stretches from the city to the beach, with beautiful flora throughout. It contains the Botanical Gardens, Conservatory of Flowers (a wood-and-glass greenhouse), several wonderful museums and a Japanese tea garden, plus other awesome features.

What is the one item in your office that is most representative of your personality?

The little green rubber duck that guards my desk.