A Brief Quadrivium with Dr. Peter Ulrickson

Episode 12 of the The University of Dallas Classical Education Podcast podcast, hosted by The St. Ambrose Center for Catholic Liberal Education & Culture at the University of Dallas, titled "A Brief Quadrivium with Dr. Peter Ulrickson" was published on December 15, 2025 and runs 42 minutes.

December 15, 2025 ·42m · The University of Dallas Classical Education Podcast

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Summary

Summary In this episode, Shannon Valenzuela and Peter Ulrickson explore the significance of the Quadrivium in education and Dr. Ulrickson's unique presentation of teaching these arts in his books A Brief Quadrivium and the accompanying teacher's guide. They discuss the interconnectedness of mathematics and the arts and highlight the unique perspectives offered by each discipline. They explore the importance of modeling, proof, and observation and the role of rhetoric and logic in mathematics....

Episode Description

Summary

In this episode, Shannon Valenzuela and Peter Ulrickson explore the significance of the Quadrivium in education and Dr. Ulrickson's unique presentation of teaching these arts in his books A Brief Quadrivium and the accompanying teacher's guide. They discuss the interconnectedness of mathematics and the arts and highlight the unique perspectives offered by each discipline. They explore the importance of modeling, proof, and observation and the role of rhetoric and logic in mathematics. The conversation also addresses the sensory engagement in learning and the value of teaching mathematics classically.

Topics Covered:

The importance of proof and the power of modeling
The arts of the Quadrivium and their perspectives on cosmic order
The role of rhetoric and logic in the study of mathematics
Engaging the senses in the experience of learning mathematics
The transformation of students' perceptions of mathematics through an encounter with the Quadrivium

Today's Guest:

Peter Ulrickson is a professor of mathematics at the Catholic University of America. In addition to his work on the quadrivium, he publishes original research in various areas of modern mathematics. Professor Ulrickson received his Ph.D. from the University of Notre Dame.

For more information about the books: briefquadrivium.com

Timestamps:

00:00 Introduction
03:28 Introduction to A Brief Quadrivium
04:07 Exploring Music and Astronomy in the Quadrivium
10:01 Proof and Modeling in Mathematics
13:09 Developing the Sense for Order
20:45 Engaging the Senses in Mathematical Inquiry
26:51 The Ordering of the Quadrivial Arts
30:48 Exploring the Teacher's Guide

Resources Mentioned in Today's Episode:

Peter Ulrickson, A Brief Quadrivium (publisher, Amazon) and Teaching the Quadrivium (publisher, Amazon)

"The Quadrivium and the Stakes for Ordering the Mathematical Arts" by Lesley-Anne Dyer Williams

University of Dallas Links:

Classical Education Master’s Program at the University of Dallas: udallas.edu/classical-ed
St. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/

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