Walter Rudin

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

In addition to his contributions to complex and harmonic analysis, Rudin is known for his mathematical analysis textbooks: Principles of Mathematical Analysis, Real and Complex Analysis, and Functional Analysis (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, has since become a standard textbook for introductory real analysis courses in the United States.

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

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. 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. 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.

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

Ph.D. thesis

• Rudin, Walter (1950). Uniqueness Theory for Laplace Series (Thesis). Duke University.

Selected research articles

• "Uniqueness theory for Laplace series". Trans. Amer. Math. Soc. 68 (2): 287–303. 1950. doi:10.1090/s0002-9947-1950-0033368-1. MR 0033368.
• "Factorization in the group algebra of the real line". Proc Natl Acad Sci U S A. 43 (4): 339–340. 1957. doi:10.1073/pnas.43.4.339. PMC 528447. PMID 16578475.
• "Zero-sets in polydiscs". Bull. Amer. Math. Soc. 73 (4): 580–583. 1967. doi:10.1090/s0002-9904-1967-11758-0. MR 0210934.
• "Holomorphic maps that extend to automorphisms of a ball" (PDF). Proc. Amer. Math. Soc. 81 (3): 429–432. 1981. doi:10.1090/s0002-9939-1981-0597656-8. MR 0597656.
• "Totally real Klein bottles in ${\displaystyle {\mathbb {C} }^{2}}$"(PDF)". Proc. Amer. Math. Soc. 82 (4): 653–654. 1981. doi:10.1090/s0002-9939-1981-0614897-1. MR 0614897.

Books

Textbooks:

• Principles of Mathematical Analysis. (1953; 3rd ed., 1976, 342 pp.)
• Real and Complex Analysis. (1966; 3rd ed., 1987, 416 pp.)
• Functional Analysis. (1973; 2nd ed., 1991, 424 pp.)

Monographs:

• Fourier Analysis on Groups. (1962)
• Function Theory in Polydiscs. (1969)
• Function Theory in the Unit Ball of ℂ. (1980)

Autobiography:

• The Way I Remember It. (1991)

• Steele Prize for Mathematical Exposition (1993)