New Hillsdale Course Teaches Principles of Mathematics and Logic

Mathematics and Logic

“Mathematics and Logic: From Euclid to Modern Geometry” offers a profound answer for the relativistic age in which we live. This free online course is being offered by Hillsdale College starting on March 2, 2021. You can be one of the first to sign up!


I know, you probably recoil at the thought of calculations, equations, and formulas. While those are a vital part of any mathematics education, “Mathematics and Logic: From Euclid to Modern Geometry” will move beyond questions of how to calculate. Instead, it will explore the fundamental principles of mathematical logic and reasoning.

Hillsdale’s free course contains 11 lectures of 27 minutes each. It provides simple definitions and begins with Book I of Euclid’s Elements, so you can follow along. This course does not require previous knowledge of mathematics or logic.

Mathematics and Logic

“Mathematics and Logic: From Euclid to Modern Geometry” is taught by Thomas I. Treloar, Professor of Mathematics at Hillsdale College and David C. Murphy, Associate Professor of mathematics at Hillsdale College, with an introduction by Hillsdale College President Larry P. Arnn.

Modeled after Hillsdale’s core mathematics course, this free online course examines the significance of mathematics to the liberal arts—and to our intellectual development. Mathematics is central to the liberal arts because it contributes not only to practical purposes, such as commerce and algebra, but also extends to knowledge of the most fundamental and eternal things.

Students enrolled in the free course will study the transformation of mathematics by the ancient Greeks, the fundamentals of logic and deductive reasoning, the central proofs of Euclid, the birth of modern geometry, and much more.

Euclidean Geometry

We live in an age that requires logic and sound reasoning in defense of truth. One of the best ways to develop these skills is through the study of Euclidean Geometry.

The Greeks employed deductive reasoning because they sought certain knowledge about mathematics and geometry. Using deductive reasoning, mathematicians like Euclid were capable of attaining not just certain knowledge but even eternal truths.

Euclid’s Elements stands as one of the central texts of Western civilization. For more than 2,300 years, Euclid’s Elements has provided the foundation for countless students to learn how to reason with precision and pursue knowledge in all fields of learning.

The brilliance of his work has made it the second most published book in history because it provides profound tools to discover truth about the world and distinguish truth from error.

Larry P. Arnn says, “We do a disservice to young people by not teaching them all the steps in mathematics, because it’s liberating to know. And by discarding Euclid you have cut them off from the way to understand logic, from which all accurate reasoning comes. And you have cut them off also from understanding the beauty of the relationships in nature.”

Non-Euclidean Geometry

One segment of “Mathematics and Logic: From Euclid to Modern Geometry” features one of the most important figures in the history of mathematics, the 18th century mathematician Leonhard Euler. He developed what would become a new mathematic discipline: graph theory.

The final lecture tells how three mathematicians – Carl Friedrich Gauss, János Bolyai, and Nikolai Lobachevsky – each working independently of the others, all came to the same conclusions, which served as the foundations for non-Euclidean geometry.

The end result is an enjoyable study of mathematics that provides students with a foundation for reasoning with precision and clarity.

Watch the trailer for “Mathematics and Logic: From Euclid to Modern Geometry” here:

Secure your spot in this free course today at

1 Comment

Add a Comment

Leave a Reply

Your email address will not be published. Required fields are marked *

Time limit is exhausted. Please reload CAPTCHA.