From Abstract to Applied: A New Approach to Teaching Data Science Fundamentals
Most statistics textbooks follow the same tired formula: teach probability theory first, then move on to statistics. This traditional structure creates a disconnect that leaves students unmotivated by abstract concepts and struggling to connect theoretical foundations to practical applications. CDS Associate Professor of Mathematics and Data Science Carlos Fernandez-Granda decided to break from this convention in his new book “Probability and Statistics for Data Science,” published by Cambridge University Press.
The book emerged from a decade of teaching experience at CDS, where Fernandez-Granda noticed fundamental problems with conventional approaches. “Teaching probability first and then eventually statistics didn’t work. Students didn’t see the point when learning probabilistic concepts in the abstract. Then, by the time we got to statistics, they had forgotten most of them, and we had to review them anyway,” he said.
Instead of segregating the two subjects, Fernandez-Granda presents probability and statistics side by side throughout the text. This approach allows students to see immediate applications of probability concepts through statistical examples with real data, while understanding the theoretical foundations underlying data science methods. The book covers random variables, nonparametric and parametric models, causal inference, correlation, estimation of population parameters, hypothesis testing, principal component analysis, low-rank models, and both linear and nonlinear regression and classification methods.
The project began when Fernandez-Granda started teaching a course that originally covered probability, statistics, linear algebra, and optimization. He wrote his own notes because existing textbooks didn’t fit his vision. After the course was restructured to focus solely on probability and statistics, he continued developing the materials, adding videos during the COVID-19 pandemic to help the students learn the material asynchronously.
Real-world datasets anchor every concept in the 624-page text. The accompanying website features a free preprint, 102 Python notebooks using 23 different real-world datasets, 115 instructional videos, and solutions to 200 exercises. Throughout this material there is an emphasis on fundamental data science challenges such as overfitting, the curse of dimensionality, and causal inference.
Student feedback shaped the book’s evolution over years of classroom testing. “I am very grateful to the students in CDS, because over the years, their feedback has been at times tough, but on point,” Fernandez-Granda said. The emphasis on practical examples came directly from student requests: “They have always requested a lot of real world data sets, which motivated me, because it’s a lot of work to develop these examples. They also appreciated the videos, so I decided to continue recording them after the pandemic.”
The book targets multiple audiences. Advanced undergraduates can use it as a foundation, while master’s and PhD students will find the mathematical rigor they need. Industry practitioners seeking theoretical grounding for data science methods represent another key readership.
At CDS, the material spans a two-course sequence. The first seven chapters form the foundation course, while the remaining five chapters constitute the advanced follow-up. The website provides enough resources for self-directed learning, with video lectures, Python notebooks that can be run online in Google Colab, and comprehensive exercise solutions.
Fernandez-Granda hopes other institutions will adopt the text for their probability and statistics courses, particularly as data science programs seek materials that bridge theory and applications. The timing of the book’s release aligns with fall semester planning, as schools prepare curricula for September courses.
By Stephen Thomas
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