A Brief Quadrivium with Dr. Peter Ulrickson episode artwork

EPISODE · Dec 15, 2025 · 42 MIN

A Brief Quadrivium with Dr. Peter Ulrickson

from The University of Dallas Classical Education Podcast

SummaryIn 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 modelingThe arts of the Quadrivium and their perspectives on cosmic orderThe role of rhetoric and logic in the study of mathematicsEngaging the senses in the experience of learning mathematicsThe transformation of students' perceptions of mathematics through an encounter with the QuadriviumToday'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.comTimestamps:00:00 Introduction03:28 Introduction to A Brief Quadrivium04:07 Exploring Music and Astronomy in the Quadrivium10:01 Proof and Modeling in Mathematics13:09 Developing the Sense for Order20:45 Engaging the Senses in Mathematical Inquiry26:51 The Ordering of the Quadrivial Arts30:48 Exploring the Teacher's GuideResources 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 WilliamsUniversity of Dallas Links:Classical Education Master’s Program at the University of Dallas: udallas.edu/classical-edSt. Ambrose Center Professional Development for Teachers and Administrators: https://k12classical.udallas.edu/Support the showIf you enjoyed the show, please leave a rating and review — it helps others find us!

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....

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A Brief Quadrivium with Dr. Peter Ulrickson

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SummaryIn 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...

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