The Department of Mathematics invites you to the next seminar in the series “Mathematics Among Us”
On Friday, June 5, another seminar will be held for math teachers, student teachers, and others interested in mathematics as part of the series “Mathematics Among Us: From School to Life.” The seminar will take place from 8:45 a.m. to 3:30 p.m. at the Center for Natural Sciences and Technical Fields (CPTO).
The goal of this seminar series is to present teachers with various perspectives on how mathematics can be integrated into everyday life—whether in science, work, or personal contexts. It offers teachers inspiration and evidence that mathematics is not merely a school subject, but an effective and beautiful tool for solving a wide variety of problems and understanding the world around us.
The seminars take place at least once per semester (usually in June and September) and always feature at least three speakers from a wide range of fields, academic institutions, and the private sector. The next seminar will take place on Friday, June 5, and the program includes the following three lectures:
Mgr. Luděk Spíchal, Ph.D. (Czech Forestry Academy, Trutnov): How the Length of the Day Changes: Connecting Trigonometric Functions and Derivatives to a Real-World Natural Phenomenon
Abstract: The lecture focuses on the connection between mathematics and a real-world natural phenomenon—the change in the length of the day throughout the year. Using specific data, it demonstrates how the length of the day can be modeled using trigonometric functions and how the rate of its change relates to the derivative of the function. Attendees will learn to interpret the derivative as the instantaneous rate of change and will see that even commonly observed phenomena have a precise mathematical description. The presentation also includes a comparison of empirical models with models created using artificial intelligence.
Bc. Anna Kimlová (CTU): Mathematics in Materials Engineering: From Functions and Derivatives to Material Failure
Abstract: Materials engineering is a concrete example of a field where mathematics becomes a tool for describing physical reality. Many seemingly abstract mathematical concepts find application in the analysis of material behavior. The lecture will reveal where mathematics is hidden in this field and how it helps us understand the mechanical properties of materials or their failure. It will also provide insight into why an understanding of mathematics—and especially the assumptions underlying the validity of results—is essential for engineers. At the same time, it will highlight the serious consequences of mathematical errors for the safety of structures and equipment. Concrete examples from the engineering field will offer inspiration for linking high school mathematics education with technical practice.
Bc. Kotlan and Bc. Falta (UJEP): Computer Processing of Medical Data Using Data Analysis and Machine Learning Methods
Abstract: Two data analysts will take you into the world of computer processing of medical data for diagnostic purposes, specifically microscope images and physiological signals, where derivatives become filters, matrices become algorithms, and machine learning becomes a detector of hidden patterns. We will attempt to clearly explain, through two examples, how we use mathematics to teach machines to assist in diagnosis.
Prof. and Lecturer RNDr. Ladislav Kvasz, Ph.D., DSc. (UK): Aristotle’s Logic, Frege’s Reform of Logic, and the Genetic Method, or Why Logic Cannot Be Taught
Abstract: There is a paradox associated with Aristotelian logic. On the one hand, the theory of syllogisms is generally considered the first system of formal logic in history, but on the other hand, this logic was not used by ancient scholars such as Euclid, Archimedes, or Ptolemy, nor did Aristotle himself use it in his scientific writings. The aim of this lecture is to attempt to clarify this paradox through an analysis of the language in which Aristotle’s logic is formulated. In the lecture, we will distinguish three types of theories—theories of the physical type, theories of the mathematical type, and theories of the arithmetic type. We will attempt to show that syllogistic logic is a theory of the arithmetic type, and therefore cannot be used in the analysis of the logical structure of mathematical and physical theories. Based on this analysis, we will then attempt to understand the transition from Aristotelian syllogistic logic to Fregean mathematical logic. If our reconstruction of the history of logic is correct, it provides an explanation for why formal logic is, in fact, “unteachable.” It did not arise through an organic development from Aristotle’s original theory, but rather through its replacement by a ready-made abstract theory.