Schmid College, Chapman University Courses

Weyl and the Transcendental Phenomenological Roots of Gauge Invariance

1 rating

Explore Hermann Weyl's contributions to gauge invariance and its philosophical foundations in transcendental phenomenology through Stanford professor Thomas Ryckman's insightful lecture.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Is Philosophy Useful for Mathematics, and/or Vice Versa?

1 rating

Explore the interplay between philosophy and mathematics, examining their mutual influence and potential benefits in academic discourse and research.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Mathematics and Society Reunited: Social Aspects of Brouwer's Intuitionism

1 rating

Explore Brouwer's intuitionism through a social lens, examining its connections to society and language. Uncover how social factors shaped intuitionism and its philosophical implications.

• YouTube
• 1 hour 33 minutes
• Self-Paced
• Free Video

On the Utility of Philosophy in Quantum Mechanics

1 rating

Explore the intersection of philosophy and quantum mechanics with insights from Matthew Leifer, delving into their mutual influence and practical applications.

• YouTube
• 1 hour 18 minutes
• Self-Paced
• Free Video

Making AI Systems Trustworthy Through Intuitive Design and Human Interaction

Explore key technical approaches for building trustworthy AI systems, focusing on intuitiveness, interaction, explainability, and human domain knowledge integration for more reliable and transparent artificial intelligence.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

How to Benefit from Uncertainty: An Introduction to Paraconsistent Bayesian Update

Explore how paraconsistent and paracomplete logics enhance Bayesian reasoning, offering new approaches to handle contradictory evidence and uncertainty in scientific and AI applications.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video

A Reassessment of Gödel's Doctrine - The Necessity of Infinity

Delve into the philosophical examination of Gödel's Doctrine, exploring the necessity of infinity in mathematical proofs and its implications for finitary mathematics through multiple proof approaches.

• YouTube
• 1 hour 56 minutes
• Self-Paced
• Free Video

Ultracompletions

Explore the concept of ultracategories in mathematics, from Makkai's original notion to Lurie's refinement, with insights on their applications, differences, and algebraic structures.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

Axiomatic Collaborations in the Foundations of Geometry at the University of Chicago, 1900-1905

Explore Professor Lorenat's examination of Oswald Veblen's archival notes from E.H. Moore's 1901 seminar, revealing how American scholars adapted European mathematics through graphic notation and postulate systems.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video

Cavalieri's Indivisibles and its Followers

Explore the historical development of Cavalieri's indivisibles in 17th century mathematics and how this concept influenced later mathematicians like Torricelli, Pascal, and Leibniz, leading to differential calculus.

• YouTube
• 1 hour 54 minutes
• Self-Paced
• Free Video

What is Homotopy Type Theory (HoTT)?

Discover the historical, philosophical, and mathematical foundations of Homotopy Type Theory (HoTT), a revolutionary branch of logic developed over the past 15 years.

• YouTube
• 2 hours
• Self-Paced
• Free Video

The Mathematical Concept of Residue and its Ubiquity

Explore the evolution of mathematical residue from Cauchy's 1825 concept to modern applications across algebra, geometry, and analysis in this comprehensive seminar.

• YouTube
• 2 hours 2 minutes
• Self-Paced
• Free Video

Foundational Aspects of Size and Dimension in Higher Categorical Structures

Explore foundational aspects of size and dimension in higher categorical structures, examining universes, smallness notions, and truncation hierarchies in HoTT.

• YouTube
• 1 hour 41 minutes
• Self-Paced
• Free Video

Exchangeability and Algorithmic Randomness - A New Proof of the Principal Principle

Explore algorithmic randomness and exchangeability to understand a novel proof of the Principal Principle, connecting long-run frequencies with short-term credences in probability theory.

• YouTube
• 1 hour 26 minutes
• Self-Paced
• Free Video

Agency Cannot Be a Purely Quantum Phenomenon

Explore the physical constraints on quantum agency and discover why purely quantum systems cannot satisfy minimal requirements for agential behavior due to fundamental quantum limitations.

• YouTube
• 1 hour 53 minutes
• Self-Paced
• Free Video