Brno, Czech Republic

Algebra, Number Theory and Mathematical Logic

Algebra, teorie čísel a matematická logika

Table of contents

Algebra, Number Theory and Mathematical Logic at MU

Language: Czech Studies in Czech
Subject area: mathematics and statistics
University website: www.muni.cz/
Years of study: 4

Definitions and quotes

Logic
Logic (from the Ancient Greek: λογική, translit. logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference. A valid inference is one where there is a specific relation of logical support between the assumptions of the inference and its conclusion. (In ordinary discourse, inferences may be signified by words like therefore, hence, ergo, and so on.)
Theory
A theory is a contemplative and rational type of abstract or generalizing thinking, or the results of such thinking. Depending on the context, the results might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings.
Theory
I firmly believe people have hitherto been a great deal too much taken up about doctrine and far too little about practice. The word doctrine, as used in the Bible, means teaching of duty, not theory. I preached a sermon about this. We are far too anxious to be definite and to have finished, well-polished, sharp-edged systems — forgetting that the more perfect a theory about the infinite, the surer it is to be wrong, the more impossible it is to be right.
George MacDonald, in a letter to his father, quoted in George MacDonald and His Wife (1924) by Greville MacDonald
Theory
How can we possibly test, or improve upon the truth of a theory if it is built in such a manner then any conceivable event can be described, and explained, in terms of its principles? The only way of investigating such all-embracing principles would be to compare them with a different set of equally all embracing principles- but this procedure has been excluded from the very beginning.
Paul Feyerabend, Against Method (1975) pp. 44-45
Theory
Great theories are expansive; failures mire us in dogmatism and tunnel vision.
Stephen Jay Gould, Eight Little Piggies (1993), "More Light on Leaves".
In June 1770, the explorer James Cook ran aground on the Great Barrier Reef in Australia and became the first European to experience the world's largest coral reef, today a paradise for scientists and holidaymakers alike. Last year, the James Cook research vessel set out to encounter unique and unexplored corals, this time in the deep ocean. Led by ERC grantee Dr Laura Robinson (University of Bristol, UK), the team on board crossed the equatorial Atlantic to take samples of deep-sea corals, reaching depths of thousands of meters. On the expedition, Dr Robinson collected samples that are shedding light on past climate changes and she will share her findings at TEDx Brussels.
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