A corrected version of the paper is available below. You are identified by the last four digits of your ID number. You can also download it from here. I have fixed a couple of typos in question 2. In the hint for question 2 the rational number q should be nonzero, and in question 3 the numbers p and q appearing in the definition of the field should be rationals, rather than any real.
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Two detailed appendices, covering nearly thirty pages, are references for the prerequisite number theory and linear algebra. This is a dense work, light on illustrations and with little in the way of flavoring asides.
Exercises are sprinkled throughout the chapters, rather than gathered at the end. No solutions are provided, which is fine for a work that is not intended as a self-sufficient resource for independent readers.
This also makes it an efficient reference or adjunct work to any assigned text. I would have been glad to have had it myself when I first encountered this material. Preceding this is often a paragraph-length introduction to the subject at hand. Typically, this is from a related important work by authors such as Banach and Toeplitz. Following are the expected definitions, theorems, and proofs seasoned with the aforementioned exercises.
Examples of these projects include an exploration of spectral theory for compact self-adjoint operators on a Hilbert space and differentiability of a monotone function.
Sally begins by constructing the real and complex numbers, then explores metric theory, normed linear spaces, and differentiation in separate chapters. The chapter on integration follows Lebesgue, not Riemann, and the seven-chapter work concludes with Fourier analysis. Terms and notation are helpfully indexed separately. The elegant, complete, and rigorous presentation makes this an idea work for capable undergraduate and graduate students interested in learning and even teaching real analysis.
Fundamentals of mathematical analysis
Fundamentals of Mathematical Analysis