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This is a document about the course “Geometric Algebra”. The document is in Spanish. The instructor for this course was Barnet Rich. The topics discussed are geometric, algebraic, and abstract, but all of them contain a degree of abstraction from the real world. Barnet Rich is an American mathematician who has written some books on mathematical topics that have been translated into many languages. He studied at Harvard University and then went on to teach at the University of Chicago for over two decades before retiring in 2009. In 2010 he started teaching at Cornell University, where he teaches courses such as "Geometric Algebra" and "Presents A First Course In Topology. ” This book is a Spanish translation of a book that was originally published in English. Geometric algebra is a branch of mathematics that uses geometric objects as the focus rather than the traditional problems that are solved using equations and numbers. Abstract algebra as well as real algebra are also topics of this course, but it is important to note that Barnet Rich is not simply explaining the results of these branches to his audience, he is helping them understand what they mean and how they relate to each other. This uses the geometric algebra as the point from which to explain abstract algebra and real algebra by relating it to concepts known by his students. The chapters play off each other using examples from one chapter in order understand concepts in another chapter. This is a useful way to teach mathematics; while often times we learn equations and numbers, we can also learn how to think about them in such a way as to facilitate learning other concepts. All of this is possible because Barnet Rich explains these ideas using geometric objects and doesn’t simply explain what the results of the arithmetic mean. Barnet Rich’s greatest contribution to mathematics is his use of geometric algebra as a means for understanding abstract algebra and real algebra. Geometric algebra was a very abstract approach that dealt with geometric objects rather than equations or numbers. This book begins discussing fundamental ideas in geometry, sets, and sequences before going on to discuss functions. Sets are the focus of this first chapter. The idea of a set is very simple, but it provides the foundation for the concept of an ordered discrete manifold. The discrete manifold is a mathematical object that represents any point in space or abstract space as a point in itself. The next chapter discusses sequences, which deal with numbers that go on forever without repeating themselves. These are known as infinite sequences, but the discussion does not dwell on this fact because for Barnet Rich it is clear that there are many points that are not finite or infinite. These points are created by drawing lines through points which are, in reality, discrete. This is the main idea of the chapter; anything that is infinite is really just comparison to another point that is not infinite. At the end of the chapter, Barnet Rich explains how to take a sequence and do Arithmetic with it. The next two chapters take his audience through an explanation of the concept of function and how it relates to ordered discrete manifolds. As he explains later in the book, Barnet Rich uses geometric algebra as a means to understand abstract algebra and real algebra by relating them back to geometry. cfa1e77820
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