List of Analysis Texts   for Math 5210 - 1

  1. N. L. Carothers, Real Analysis, Cambridge U. Press 2000. Written for senior and beginning graduate students. Fairly detailed alternative to my chosen text.
  2. G. Folland, Real Analysis, Modern Techniques and their Applications, 2nd. ed., Wiley & Sons, Inc., 1999. A graduate text in real analysis with applcations to partial differential equations, Fourier series and probability.
  3. N. Haaser & J. Sullivan, Real Anaslysis, Dover Publ., 1991 (orig. van Norstrand, 1971). I used this inexpensive text for Math 5210 in 1995. It has an excellent treatment of real numbers and metric spaces. It is unusual in that it takes the Denjoy approach to Lebesgue integral, which is perhaps not the best for beginners. Prof. Brooks used this text but switched to Royden to cover integration.
  4. F. Jones, Lebesgue Integration on Euclidean Space, Jones and Bartlett, Publ., 2001. A slow introduction to Lebesgue integration with application to Fourier series. Good alternative to our text.
  5. C. Pugh, Real Mathematical Analysis, 2nd. ed., Springer, 2015. A highly visual and intuitive treatment of real analysis aimed at juniors and seniors. An alternative to our current text.
  6. H. Royden, Real Analysis, Macmillan 1968. Granddaddy real analysis text. It presents the Lebesgue measure on the line before doing it for abstract spaces. It covers metric spaces and some functional analysis. Text used in my first analysis class in grad school.
  7. W. Rudin, Priciples of Mathematical Analysis, 3rd. ed., McGraw-Hill, Inc., 1964. This book is widely known as "Baby Rudin" or "Blue Rudin," since he also has a graduate text in real and complex analysis, "Big Rudin," as well as a functional analysis text, "Funky Ann." It is sometimes used at Utah in the honors sections of math 3210 / 20 as well as for Math 5210. It covers an introduction to analysis in Euclidean n-dimensional space including a chapter on Lebesgue integration. Rudin is a very precise and compact writer. It gave me great satisfaction to teach from this text in a beginning analysis course at Berkeley. But students think Rudin's presentation to be "terse" or "slick" and find his books difficult going.

Last updated: 12 - 30 - 21