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Fundamentals of Mathematics
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The first dilemma of the authors, when preparing this textbook was its future volume. Most textbooks are thick, with plenty of material, in most cases more than it would be presented in lectures. The reader, either lecturer or student, has to make certain choice for every particular course and to accordingly adjust the order of its presenting. For that reason, fat books usually serve as en-cyclopedia, where from certain knowledge might be sometimes extracted. Since the Internet can serve the same purpose, who reads fat books these days? For that reason, we have chosen this book to be thin. However, the majority of thin mathematical books provide only cursory information. In most cases, terms and statements are distorted and only short and trivial facts are being proven, more serious omitted or, in the best case, only mentioned due the prejudice that mathematical rigor is not for beginners and non-mathematicians, that they are notable to comprehend more complex statements or their proofs, in these books.In such a manner, mathematics is reduced to usage of prefabricated boring pat-terns. But the whole truth is that, without thorough insight of the proof details,it is often not possible to achieve neither the full comprehension nor the correct application of mathematics, particularly in other disciplines!
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