# Walter Rudin

Walter Rudin (May 2, 1921 – May 20, 2010[2]) was an Austrian-American mathematician and professor of Mathematics at the University of Wisconsin–Madison.[3]

Walter Rudin
BornMay 2, 1921
DiedMay 20, 2010 (aged 89)
NationalityAmerican
Alma materDuke University (B.A. 1947, Ph.D. 1949)
Known forMathematics textbooks; contributions to harmonic analysis and complex analysis[1]
AwardsAmerican Mathematical Society Leroy P. Steele Prize for Mathematical Exposition (1993)
Scientific career
FieldsMathematics
InstitutionsProfessor Emeritus, University of Wisconsin–Madison
Doctoral advisorJohn Jay Gergen
Doctoral studentsCharles Dunkl
Daniel Rider

In addition to his contributions to complex and harmonic analysis, Rudin was known for his mathematical analysis textbooks: Principles of Mathematical Analysis,[4] Real and Complex Analysis,[5] and Functional Analysis[6] (informally referred to by students as "Baby Rudin", "Papa Rudin", and "Grandpa Rudin", respectively). Rudin wrote Principles of Mathematical Analysis only two years after obtaining his Ph.D. from Duke University while he was a C. L. E. Moore Instructor at MIT. Principles, acclaimed for its elegance and clarity,[7] has since become a standard textbook for introductory real analysis courses in the United States.[8]

Rudin's analysis textbooks have also been influential in mathematical education worldwide, having been translated into 13 languages, including Russian,[9] Chinese,[10] and Spanish.[11]

## Biography

Rudin was born into a Jewish family in Austria in 1921. They fled to France after the Anschluss in 1938. When France surrendered to Germany in 1940, Rudin fled to England and served in the Royal Navy for the rest of World War II. After the war he left for the United States, and earned his B.A. from Duke University in North Carolina in 1947, and two years later earned a Ph.D. from the same institution. After that he was a C.L.E. Moore instructor at MIT, briefly taught in the University of Rochester, before becoming a professor at the University of Wisconsin–Madison. He remained at the University for 32 years.[2] His research interests ranged from harmonic analysis to complex analysis.

In 1970 Rudin was an Invited Speaker at the International Congress of Mathematicians in Nice.[12] He was awarded the Leroy P. Steele Prize for Mathematical Exposition in 1993 for authorship of the now classic analysis texts, Principles of Mathematical Analysis and Real and Complex Analysis. He received an honorary degree from the University of Vienna in 2006.

In 1953, he married fellow mathematician Mary Ellen Estill, known for her work in set-theoretic topology. The two resided in Madison, Wisconsin, in the eponymous Walter Rudin House, a home designed by architect Frank Lloyd Wright. They had four children.[1]

Rudin died on May 20, 2010 after suffering from Parkinson's disease.[2]

## Selected publications

Ph.D. thesis
• Rudin, Walter (1950). Uniqueness Theory for Laplace Series (Thesis). Duke University.[13]
Selected research articles
Books

Textbooks:

Monographs:

• Fourier Analysis on Groups.[16] (1962)
• Function Theory in Polydiscs. (1969)
• Function Theory in the Unit Ball ofn.[17] (1980)

Autobiography:

• The Way I Remember It. (1991)

## References

1. ^ a b
2. ^ a b c Ziff, Deborah (May 21, 2010). "Noted UW-Madison mathematician Rudin dies at 89". Wisconsin State Journal. Retrieved May 21, 2010.
3. ^ "Remembering Walter Rudin (1921–2010)" (PDF). Notices of the AMS. 60 (3): 295–301. 2013. doi:10.1090/noti955.
4. ^ Rudin, Walter (1976) [1953]. Principles of Mathematical Analysis (3rd ed.). New York: McGraw-Hill. ISBN 007054235X.
5. ^ Rudin, Walter (1987) [1966]. Real and Complex Analysis (3rd ed.). New York: McGraw-Hill. ISBN 0070542341.
6. ^ Rudin, Walter (1991) [1973]. Functional Analysis (2nd ed.). New York: McGraw-Hill. ISBN 0-07-100944-2.
7. ^ a b Munroe, M. E. (2016-11-06). "Review: Casper Goffman, Real Functions, and Walter Rudin, Principles of mathematical analysis, and Henry P. Thielman, Theory of functions of real variables". Bulletin of the American Mathematical Society. 59 (6): 572–577. doi:10.1090/s0002-9904-1953-09765-8. ISSN 0002-9904.
8. ^ a b Locascio, Andrew (13 August 2007). "Book Review: Principles of Mathematical Analysis". Mathematical Association of America. Retrieved 12 October 2016.
9. ^ Rudin, Walter; Havin, V. P. (translator) (1976). Principles of Mathematical Analysis (Russian translation of 2nd edition). Moscow: Mir Publishers.
10. ^ Rudin, Walter; Zhao, Cigeng (translator); Jiang, Duo (translator) (1979). Principles of Mathematical Analysis (simplified Chinese translation). Beijing: People's Education Press, China Machine Press (reprint, 2004). ISBN 7-111-13417-6.
11. ^ Rudin, Walter; Irán Alcerreca Sanchez, Miguel (translator) (1980). Principles of Mathematical Analysis (Spanish translation). México: Libros McGraw-Hill. ISBN 968-6046-82-8.
12. ^ Rudin, Walter. "Harmonic analysis in polydiscs." Actes Congr. Int. Math., Nice 2 (1970): 489–493.
13. ^ Bilyk, Dmitriy; De Carli, Laura; Petukhov, Alexander; Stokolos, Alexander M.; Wick, Brett D., eds. (2012). "remarks on Walter Rudin's PhD thesis". Recent Advances in Harmonic Analysis and Applications: In Honor of Konstantin Oskolkov. Vol. 25. Springer Science & Business Media. p. 59.
14. ^ Shapiro, Victor L. (1968). "Review: Walter Rudin, Real and complex analysis". Bull. Am. Math. Soc. 74 (1): 79–83. doi:10.1090/s0002-9904-1968-11881-6.
15. ^ Kadison, Richard V. (1973-01-01). "Review of Functional Analysis". American Scientist. 61 (5): 604–604. JSTOR 27844041.
16. ^ Kahane, J.-P. (1964). "Review: Walter Rudin, Fourier analysis on groups". Bull. Am. Math. Soc. 70 (2): 230–232. doi:10.1090/s0002-9904-1964-11092-2.
17. ^ Krantz, Steven G. (1981-11-01). "Review: Walter Rudin, Function theory in the unit ball of $\mathbf {C}^n$". Bulletin (New Series) of the American Mathematical Society. 5 (3): 331–339. doi:10.1090/s0273-0979-1981-14951-x. ISSN 0273-0979.