# William Marvin Whyburn

### Quick Info

Born
12 November 1901
Lewisville, Denton County, Texas, USA
Died
5 May 1972
Greenville, North Carolina, USA

Summary
William Whyburn was an American mathematician best known for his work on ordinary differential equations.

### Biography

William Whyburn's parents were the farmers Thomas Whyburn and Eugenia Elizabeth McLeod. Thomas Whyburn had been born in Devonshire, England, but had emigrated with his family to the United States when he was two years old. Eugenia was a native of Alabama. William was brought up on the farm, near to Lewisville, North Texas. He had a younger brother, Gordon Thomas Whyburn, who also has a biography in the archive. William attended Bethel School in the small settlement of Bethel which was situated near the present intersection of Bethel School Road and Moore Road to the east of Coppell. This school, which had existed since 1858, only taught pupils up to the ninth grade so, in 1916, when William was not yet fifteen years old, he entered North Texas State College in Denton. He had sat the college qualifying examinations to gain admission to this College.

North Texas State College was a liberal arts college, mainly aimed at training teachers, but its President from 1906 to 1923 was William Hershel Bruce who had organised the starting of Bachelor of Arts and Bachelor of Science degree programmes in 1917-18. Let us note that William Hershel Bruce was a mathematician who had been a mathematics professor at North Texas State College for five years before becoming President. Whyburn studied at North Texas State College until 1920 when he went to the University of Texas in Austin. After two years, during which he majored in mathematics, he was awarded a Bachelor of Arts degree and he continued to study there for his Master of Arts degree which he received one year later in 1923. We note that Whyburn's younger brother, Gordon Whyburn, was also a student at the University of Texas from 1921, but he majored in chemistry for his Bachelor's degree.

In the year that William Whyburn was awarded his Master's degree, 1923, he married Marie Barfield (1900-1988). Marie, the daughter of Joseph Purcell Barfield and Mary Jane Powers, was a fellow student at the University of Texas. They had two children, Willa Marie Whyburn (born 1928) and Clifton Thomas Whyburn (born 1937). We note that Clifton Thomas Whyburn studied mathematics and was awarded a Ph.D. in 1964 from The University of North Carolina at Chapel Hill. His thesis advisor was Alfred Brauer and his thesis was entitled On the Second Smallest Quadratic Non-Residue.

Returning to our description of William Whyburn's career, after the award of his Master's degree he continued to study at University of Texas for his Ph.D. His thesis advisor was Hyman Joseph Ettlinger (1889-1986), who had been a student of G D Birkhoff, and Whyman was awarded a doctorate in June 1927 for his thesis Linear Boundary Value Problems for Ordinary Differential Equations and Their Associated Difference Equations. However, Whyburn had already published three papers before submitting his doctoral thesis, namely An extension of the definition of the Green's function in one dimension (1924), On the Green's function for systems of differential equations (1927) and On the polynomial convergents of power series (1927). In the first of these Whyburn appended the note:-
This paper was written at the suggestion of and under the supervision of Professor H J Ettlinger.
Whyburn introduces the paper by writing:-
The Green's function in one dimension was defined by Bôcher in 1901. This definition applies to linear differential systems of the nth order where the coefficients of the differential equation are continuous functions and the coefficients of the $n$ linearly independent boundary conditions are constants. It is the purpose of this paper to extend this definition to apply to linear differential systems of the second order whose coefficients are analytic functions of a parameter. This extended definition of the Green's function is used to carry over the results that have been obtained for these differential systems to integral equations whose kernels are in general analytic functions of a parameter.
Although not published until after his thesis had been submitted, he had also submitted (on 26 February 1927) the paper Second-Order Differential Systems with Integral and k-Point Boundary Conditions for publication; it appeared in 1928. Whyburn was still at the University of Texas when he submitted a further paper Existence and oscillation theorems for non-linear differential systems of the second order for publication on 7 September 1927 but, shortly after that, he went to Harvard where he spent the academic year 1927-28 as a National Research Fellow.

The reader may have noticed that Whyburn took four years before submitting his Ph.D. thesis after the award of his Master's degree. This is not a particularly long time but, in Whyburn's case, his doctoral studies had only been a small part of his commitments since he was also teaching. In fact he began teaching while studying at North Texas State College for, between 1918 and 1920, he taught at various schools in Denton County. It is worth noting that Samuel Wilks's first school was Little Elm School, a local one-room primary school, and when he was in the 7th grade at this school he was taught by Whyburn. For the first of the four years between his Master's degree and his Ph.D., 1923-24, he taught full-time as an Instructor at South Park Junior College, Beaumont, Texas, and for the next, 1924-25, he was an Assistant Professor at Texas A&M College. In the third of these years, 1925-26, he was an Associate Professor at the Texas Technological College in Lubbock, Texas. This looks as though he had not even begun his doctoral studies until 1926 but he had spent the summers at the University of Texas during these years. He was awarded a Louis Lipsitz Fellowship for the academic year 1926-27 so he was able to work full-time at his thesis during that year. He retained his position at the Texas Technological College in Lubbock, taking leave from the College and, in 1927-28 while he was at Harvard he was still on the faculty at the Texas Technological College but on leave. We should marvel that, with such a limited amount of research time over his four years at the University of Texas, not only did he write a thesis but also the series of major papers we mentioned above.

In 1928 Whyburn was appointed as an Assistant Professor of Mathematics at the University of California at Los Angeles. He spent sixteen years at the University of California, steadily being promoted until he became a full professor on 1938. He served as the chairman of the Mathematics Department for seven years from 1937 to 1944. Of course, some of these seven years were the years of World War II and Whyburn undertook various war related duties in addition to his role as chairman of department. He served as Chairman of the Supervisors Committee, Los Angeles Area, University of California, for Engineering, Science, Management War Training Programs from 1941 to 1944. He also held the role of Chief of the Operations Analysis Section of the Third Air Force in 1944. During the war years he wrote the paper Mathematics for production and war (1943) and the book (with Paul H Daus and John W Gleason) Basic mathematics for war and industry (1944). A preliminary edition of the book (reproduced from a typewritten copy) was published in 1943 under title Mathematics for war and industry. The authors write in the Preface:-
The war program has given rise to extensive training and educational activities designed to meet needs of essential industries and the armed forces. Skill in the use of mathematics, particularly arithmetic, algebra, geometry, and trigonometry, is an integral part of all phases of a highly technical war. Similarly, but to a less spectacular degree, basic mathematical skills are indispensable to peace-time activities. The experiences of serious investigators lead to the uniform conclusion that the same principles of elementary mathematics are needed for the armed forces, for war industry, and for ordinary civilian activities. ... This book is written to provide a single text in which selected principles of elementary mathematics are presented in a carefully organised manner. The book has been made thoroughly practical - both in the choice and treatment of topics. The practical aspects have been introduced without sacrifice of mathematical rigour or accuracy of statement.
We note that, in 1921, Paul Harold Daus (1894-1973) had received his doctorate from the University of California where his thesis advisor was Derrick N Lehmer. He was associated with the University of California until he retired in 1961. He wrote a number of texts in collaboration with Whyburn in addition to the one we have just mentioned: First year college mathematics with applications (1949), Algebra for college students (1955), Introduction to mathematical analysis, with applications to problems of economics (1958), and Algebra with applications to business and economics (1961). In the first of these texts the authors write:-
This book is written with the intention of providing a single text for the study of first year college mathematics, especially in engineering and technical schools. Its purpose is to provide a strong and ample background for the study of the calculus, and to integrate the subjects of college algebra, analytic geometry, and analytic trigonometry. At the same time the text illustrates all principles by applications taken from science and engineering, so that the course is completely independent of its future use.... Suggested lesson outlines for a ninety-hour course (three days a week for two semesters) and for a seventy-five-hour course are given....
E M Beesley writes in the review [1]:-
Those who prefer to give relatively strong training in analytic geometry should welcome this book with enthusiasm. In sharp contrast with recent works which combine analytics with calculus and thereby effect a de-emphasis of the former subject, this text retains most of the traditional geometrical topics. Moreover, it provides a vigorous and well-motivated presentation which, in the opinion of the reviewer, is superior to that of many established books.
For extracts from more reviews of this book, and of Whyburn's other books, see THIS LINK.

In 1944 Whyburn was appointed as President of Texas Technological College [10]:-
As President of Texas Tech he recruited able people, and provided leadership in advancing that school to a higher academic level and its recognition by such agencies as the American Association of Universities and the American Association of University Women. The institution also profited by Whyburn's contacts with government agencies, as reflected by the excellent support that was obtained for certain programs.
He held this position for four years before resigning in 1948 when he was appointed Kenan Professor of Mathematics at the University of North Carolina in Chapel Hill. He also became chairman of the mathematics Department from the time of his appointment. In 1956 he gave up the chairmanship of the department when he became Acting Provost for the academic year 1956-1957, and he then served as Vice President for Research from 1957 to 1960. In January 1967, when aged 65, he retired from the University of North Carolina but was appointed as Frensley Professor of Mathematics at the Southern Methodist University in Dallas. He undertook his duties in Dallas until June 1970 when he took a "second retirement" returning to live again in Chapel Hill in the home he had lived in for over twenty years. Even after two retirements, Whyburn found it difficult to leave the academic world and he was happy to accept a part-time position teaching in East Carolina University in Greenville, North Carolina. He taught there until his sudden death from a heart attack in May 1972.

A look at the extracts from the reviews of Whyburn's books at THIS LINK will show immediately how much he was concerned about teaching at all levels. It is clear that he had thought deeply about how to enthuse students, particularly those who were users of mathematics rather than those studying the subject for its own sake. William Reid, who had been a research student at the University of Texas advised by H J Ettlinger at the same time as Whyburn, writes [10]:-
Whyburn was interested in teaching at all levels, and according to one of his former colleagues he prided himself upon carrying a balanced load of courses at all levels from freshman to advanced graduate. In the classroom, one of his precepts was "give the student something that he can do", and he was always concerned with the development of the student's initiative. In supervising dissertation research, he carefully adapted his tactics to the individual student. Out of the classroom, he was sincerely concerned with the welfare of students and faculty, and was readily accessible to all.
We must not let the fact that Whyburn wrote low level undergraduate texts lead us to believe that he did not contribute much in high-level research. On the contrary, he wrote around 40 papers on differential equations. These are discussed in [1] under the areas: Boundary value problems; Systems of difference equations; General existence theorems, and functional properties of solutions; Specific properties of Green's functions and Green's matrices; and Nonlinear matrix differential equations. Closely related to this work on differential equations is his papers on the theory of the Lebesgue integral following Frigyes Riesz's approach of approximation by step functions.

Among the honours Whyburn received for his contributions, we mention that he served as Vice President of the Mathematical Association of America for 1943-1945. He was elected to the National Academy of Peru in December 1943, and in 1948 he was awarded the honorary doctorate by Texas Technological College.

### References (show)

1. E M Beesley, Review: First year college mathematics with applications, by P H Daus and W M Whyburn, Amer. Math. Monthly 57 (2) (1950), 124-126.
2. R W Clower, Review: Introduction to Mathematical Analysis with Applications to Problems of Economics, by P H Daus and W M Whyburn, Econometrica 27 (4) (1959), 715-716.
3. I K Feinstein, Review: Algebra for College Students, by W M Whyburn and P H Daus, The Mathematics Teacher 48 (8) (1955), 571.
4. V D Gokhale, Review: Algebra for College Students, by W M Whyburn and P H Daus, Amer. Math. Monthly 63 (4) (1956), 265-266.
5. G Kade, Review: Introduction to Mathematical Analysis with Applications to Problems of Economics, by P H Daus and W M Whyburn, Journal of Economics and Statistics 172 (5) (1960), 466-467.
6. G Kade, Review: Algebra with Applications to Business and Economics, by P H Daus and W M Whyburn, Journal of Economics and Statistics 175 (3) (1963), 278-279.
7. E J Mishan, Review: First year college mathematics with applications, by P H Daus and W M Whyburn, Economica, New Series 27 (108) (1960), 375-376.
8. P C Nicola, Review: Introduction to Mathematical Analysis with Applications to Problems of Economics, by P H Daus and W M Whyburn, Rivista Internazionale di Scienze Sociali (III) 40 (77) (5/6) (1969), 586-587.
9. C Oakley, Review: Introduction to Mathematical Analysis with Applications to Problems of Economics, by P H Daus and W M Whyburn, Amer. Math. Monthly 67 (2) (1960), 196.
10. W T Reid, William M Whyburn, Bull. Amer. Math. Soc. 79 (6) (1973), 1175-1183.
11. H A Simmons, Review: Basic Mathematics for War and Industry, by P H Daus, J M Gleason and W M Whyburn, National Mathematics Magazine 18 (6) (1944), 253-254.
12. M E Stark, Review: First year college mathematics with applications, by P H Daus and W M Whyburn, Mathematics Magazine 23 (5) (1950), 268-269.
13. L A Wolf, Review: Basic Mathematics for War and Industry, by P H Daus, J M Gleason and W M Whyburn, Amer. Math. Monthly 51 (8) (1944), 469.

### Additional Resources (show)

Other pages about William Whyburn:

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Written by J J O'Connor and E F Robertson
Last Update April 2015