A Primer of Real Analysis
After understanding this book, mathematics will now seem as though it is incomplete and lacking in concepts that maybe you have wondered before. In this book, we will provide glimpses of something more to mathematics than the real numbers and real analysis.
After all, the mathematics we talk about here always seems to only involve one variable in a sea of numbers and operations and comparisons. Note: A table of the math symbols used below and their definitions is available in the Appendix. A select list of chapters curated from other books are listed below.
They should help develop your mathematical rigor that is a necessary mode of thought you will need in this book as well as in higher mathematics. This part of the book formalizes the various types of numbers we use in mathematics, up to the real numbers. This part focuses on the axiomatic properties what we have defined to be true for the sake of analysis of not just the numbers themselves but the arithmetic operations and the inequality comparators as well.
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This part of the book formalizes the definition and usage of graphs, functions, as well as trigonometry. The most curious aspect of this section is its usage of graphics as a method of proof for certain properties, such as trigonometry. These methods of proof are mostly frowned upon due to the inaccuracy and lack of rigorous definition when it comes to graphical proofs , but they are essential to derive the trigonometric relationships, as the analytical definition of the trigonometric functions will make using trigonometry too difficult—especially if they are described early on.
The following chapters will rigorously define the trigonometric functions. They should only be read after you have a good understanding of derivatives, integrals, and inverse functions. This part of the book formalizes sequences of numbers bound by arithmetic, set, or logical relationships. This part focuses on concepts such as mathematical induction and the properties associated with sets that are enumerable with natural numbers as well as a limit set of integers.
Are calculus and real analysis the same thing? - Mathematics Stack Exchange
This part of the book formalizes the concept of distance in mathematics, and provides an introduction to the analysis of metric space. The text is changing constantly, and your comments are very welcome: please sign our guest book. Sets and Relations 2. Infinity and Induction 3.
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Sequences of Numbers 4. Series of Numbers 5. Topology 6. Also includes a glossary of calculus terms and biographies, with definitions, theorems, and problems. Teaching Resources Online - Bert G. Wachsmuth Seton Hall University professor's syllabi, online handouts, sample programs, scripts and software to download, exams and answers, general information, and other teaching resources for his computer science and mathematics courses: Intro to Computer Science, Parts 1 and 2, Java and Network Programming, Java and Internet Programming, Calculus I for Science Majors, Junior Seminar in Mathematics, and Real Analysis.
Latex, Maple, and Derive notes. Mark McClure Mark McClure is an assistant professor at the University of North Carolina at Asheville researching real analysis, specifically fractal measure and dimension.
Papers on these topics may be downloaded in gzipped PostScript format; a paper involving Julia MatematicasVisuales - Roberto Cardil, Miguel Cardil Interactive visualizations of mathematical concepts, in the topics of geometry, real analysis, complex analysis, probability, and history. An English version is also available. Mathematical Analysis I - Elias Zakon This online text covers the basic topics of undergraduate real analysis: metric spaces, continuity, differentiation and integration.