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Differential Calculus of Functions of Several Variables
Ráž, Adam ; Mlček, Josef (advisor) ; Balcar, Bohuslav (referee)
The thesis follows on Petr Vopìnka's alternative theory of sets and semisets by extending notions of in nite closeness and monad for real spaces of several variables. It speci es and explains on examples the basic terminology of this theory, namely notions of sets, semisets and domains. It brings up two worlds | an ancient and a classical one | by which it shows a dual way of looking at real functions of several variables. That is used for examining local properties like continuity, limit or derivative of a function at a point. The peak of the thesis is an alternative formulation of the implicit function theorem and the inverse function theorem. The thesis also contains translation rules, which allow us to reformulate all these results from an alternative into a traditional formulation used in mathematical analysis.
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Differential Calculus of Functions of Several Variables
Ráž, Adam ; Mlček, Josef (advisor) ; Balcar, Bohuslav (referee)
The thesis follows on Petr Vopìnka's alternative theory of sets and semisets by extending notions of in nite closeness and monad for real spaces of several variables. It speci es and explains on examples the basic terminology of this theory, namely notions of sets, semisets and domains. It brings up two worlds | an ancient and a classical one | by which it shows a dual way of looking at real functions of several variables. That is used for examining local properties like continuity, limit or derivative of a function at a point. The peak of the thesis is an alternative formulation of the implicit function theorem and the inverse function theorem. The thesis also contains translation rules, which allow us to reformulate all these results from an alternative into a traditional formulation used in mathematical analysis.
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Imagination of infinity
Semerád, Martin ; Pauza, Miroslav (advisor) ; Sak, Petr (referee) ; Jirků, Petr (referee)
This work deals with a basic question of modern science and it is its indefectibility. Quality of education is reduce to an evaluation of conformity to a common known knowledge and its quantity representation. Seeds of this long process go back to an ancient academia of Gondisapur established in an Arabic world. Author proclaims that the main goal of philosophy is to show, that this is not the only way of thinking and in the same time that the main goal and power of phenomenology is to apply the transcendental epoche to overcame the truth in its regularization shape. The hardcore of modern science is located in the world of mathematics and a lot of thinkers find the Math as a land of pure sureness - the core of this work in an opposite proofs, that in fact nowadays math is all, but the correct way of thinking. The two examples are explicit: the Pythagorean Theorem and the Sum of the geometric row. This work brings a quite new view on the mathematical problem of "the point" and "the nothing" as a border of things. In the second part uses as a frame of its topic the first 18 §§ of the work "Paradoxes of the infinite" by Czech mathematician of German mother tongue Bernard Bolzano. The important idea of this study is a new ontological view on the set of prime numbers.
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