The following free book is intended for all those who wish to learn to wander in mathematics.
About the book (by the author)
The primary purpose of this work is to serve as a supplement and support to the various mathematics degree courses of our science faculty.
On the following pages you will find a set of exercises aimed at drawing attention to a particular aspect of a particular theorem, validity or not, interrelationships with each other, etc. It also includes problems whose appeal is that, to solve them, the help of various branches of mathematics is needed; Thus, for example, they appear to be engaged in a specific exercise: actual analysis, group theory, topology.
Also, we will find connections between very different subjects, perhaps unexpected, such as: magic square and linear algebra, espionage and matrix theory, real numbers and dove’s nest, Archimedes’ principle, and deviation theorem.
Similarly, we will find sections dedicated to topics that are not usually addressed in class due to time constraints; Let us cite as an example: the equivalence of the analytical form and the geometric form of the Han-Banach theorem; We have another pattern when using the same word for different aspects of the surface of a mathematical object. This happens when, in our first analysis courses, we are introduced to a set of real numbers, as a whole sorted field. Then we are told about R as the whole metric space. What is the relation between one idea and another?
Special mention deserves the chapter on “Fauna’s Theorem”. In it we will travel through different branches of mathematics: geometry, algebra of exact sequences, nonlinear analysis, combination theory.
Content (subject)
- Analysis
- Functional analysis
- Algebra linear
- Math Entertainment
- Different equations
Information sheet
Year: 2005
Editor: University of the Andes
English: Español
Size: 611 KB
License: Pending review
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