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The Department of Mathematics of the University of Wisconsin
In 1997 the Department of Mathematics of the University of Wisconsin celebrated the centenary of their first award of a Ph.D. in 1897. They organised a Ph.D. Centennial Conference and a document containing a wealth of information about these 100 years is available at
https://mathalumni.math.wisc.edu/wp-content/uploads/sites/1783/2023/09/1997_dept_centennial.pdf
We give below an extract from the Welcome section of the document. We also give an extract from the University of Wisconsin Calendar for 1899 giving details of the Department of Mathematics in that year. We have made some minor changes to the text. For example we have added the full names of those only given in the calendar by their surname.
https://mathalumni.math.wisc.edu/wp-content/uploads/sites/1783/2023/09/1997_dept_centennial.pdf
We give below an extract from the Welcome section of the document. We also give an extract from the University of Wisconsin Calendar for 1899 giving details of the Department of Mathematics in that year. We have made some minor changes to the text. For example we have added the full names of those only given in the calendar by their surname.
1. History of the Department of Mathematics, University of Wisconsin.
The history of the Department of Mathematics of the University of Wisconsin starts in 1848. Wisconsin became a state on 29 May 1848 and in the summer of that year, the legislature established the University of Wisconsin in Madison with its government vested in a Board of Regents elected by the legislature. According to the law the university was to consist of four departments: "First the department of science, literature and the arts; second, the department of law: third, the department of medicine; fourth, the department of the theory and practice of elementary instruction."
The Regents first met in August of 1848 and approved the immediate establishment of a preparatory department. It also elected the president of the University of Missouri, John H Lathrop, as the first chancellor of the University of Wisconsin. John W Sterling was appointed to be in charge of the preparatory department. Sterling assembled the first class of the university in a room of the Madison Female Academy on 4 February 1849. The class consisted of only seventeen boys, with three more arriving later.
In 1849 the Regents announced its plans for the organisation of the first and fourth departments of the University. The Department of Science, Literature, and the Arts was to consist of six professorships. One of these was the professorship of mathematics, natural philosophy, and astronomy to give instruction in "pure and mixed Mathematics, in Civil Engineering, Practical Surveying, and other field operations, in experimental Philosophy, and the use of apparatus, and in Theoretical and Practical Astronomy." This professorship (or chair) was given to Sterling, who received the Ph.D. from the College of New Jersey (now Princeton University). Thus it is fair to say that Sterling was the father of the faculty of the University of Wisconsin, the first member of the Mathematics Department and its first chair. He was Dean of the Faculty from 1860 to 1865, Vice-Chancellor from 1865 to 1869, and Vice-President from 1870 to 1884. In the early years, in addition to providing instruction, Sterling had a number of other duties. These included administering the boarding house, purchasing firewood, care of the furnaces, directing repairs, and assessing and collecting students' fines! Sterling died in Madison in 1895.
Sterling was primarily a teacher and did not keep very abreast of scientific developments. Scholarship in mathematics was given a big boost with the appointment in 1881 of Charles A Van Velzer as instructor in mathematics. He revised the curriculum, published scholarly papers, and in general stimulated interest in mathematics by giving popular lectures. (Van Velzer developed a coal business interest outside the university and this 'conflict of interest' led then university president Charles Van Hise to insist that Van Velzer choose between his business and academic interests. Van Velzer chose to resign from the University, in 1906.) An additional boost was given to mathematics with the arrival in 1886 of Charles S Slichter.
In 1906 Edward Burr Van Vleck was appointed Professor of Mathematics (he was an instructor from 1893 to 1895 and spent the intervening years at Wesleyan University). Van Vleck began a new emphasis on research in pure mathematics. With Van Vleck in pure mathematics and Slichter in applied mathematics, Wisconsin was a leader in uniting pure and applied mathematics. Slichter's efforts in applied mathematics were aided by the appointments of Herman W March in 1906, Max Mason in 1908 (who transferred to physics in 1925), Warren Weaver in 1918, and Ivan S Sokolnikoff in 1927.
The first Ph.D. granted by the Department of Mathematics went to Henry Freeman Stecker. Stecker was born in Sheboygan, Wisconsin on 3 June 1867. He received a B.S. in mathematics in 1893, a M.S. in 1894, and a Ph.D. in 1897. The title of his thesis was "On the roots of equations, particularly the imaginary roots of numerical equations." Although our records are incomplete (and no copy of his thesis has been found), it is highly likely that his thesis advisor was Van Velzer. Stecker's 1894 Masters' thesis "The 'Gebilde' ordinarily known as the circle" was approved by Van Velzer. The earliest reference that I could find to Stecker in the Bulletin of the American Mathematical Society (AMS) is that a paper of his, "Non-euclidean cubics" was read at the Fifth Summer Meeting of the AMS at the Massachusetts Institute of Technology on 19 and 20 August 1898. At that meeting was E B Van Vleck, then a Professor of Mathematics at Wesleyan University.
[After receiving the Ph.D. Stecker was an Instructor in Algebra, Academy of Northwestern University in Evanston, Illinois. In 1901 he was appointed Instructor in Mathematics at Cornell University. Afterwards he moved to the Pennsylvania State University and held the following positions: Instructor (1903-06), Assistant Professor (1906-07), Associate Professor (1907-17), and Professor (1917-23) He died in Baltimore, Maryland, on 29 October 1923. Since 1950, Pennsylvania State has awarded the H Freeman Stecker Scholarship to a student of any school who excels in the subject of mathematics.]
The second Wisconsin Ph.D. was granted to Theodore Running in 1899 with a thesis entitled "On systems of circles derived from three and four base circles." At the end of his thesis, Running thanks Van Velzer and Dowling for their interest in his work, so Van Velzer and Dowling were most likely joint advisors to Running. Running was an assistant in mathematics from 1898-1900.
At the commencement in 1897 in which Stecker was granted a Ph.D., Charlotte Elvira Pengra received a B.S. in Mathematics with honours for a thesis "General rational fractional linear transformations of plane curves." Pengra went on to receive in 1901 the third Wisconsin mathematics Ph.D. ("in pure mathematics, applied mathematics, and economics") with thesis "On the conformal representation of plane curves, particularly for the cases = 4, 5, and 6." At the end of her thesis, Pengra acknowledges her "indebtedness to Dr Dowling for his valuable suggestions and assistance in connection with the preparation of this paper." I can only conclude that Dowling was her advisor. Pengra was an assistant in the Department of Mathematics from 1899-1901.
At the 1901 commencement, Florence Eliza Allen received a Master of Letters in Mathematics and Philosophy for her thesis "The abelian integrals of the first kind upon the Riemann's surface ". Allen later received, in 1907, a Ph.D. with a thesis "The cycle involutions of third order determined by nets of curves of deficiency 0, l, and 2." Our records indicate that Allen was the first Ph.D. student of Edward Burr Van Vleck, but at the end of her thesis she expresses her gratitude only to Professor L W Dowling. Allen was a member of the Department of Mathematics of Wisconsin for 45 years and was named Assistant Professor Emerita in 1948. She died in Madison at the age of 84 on 31 December 1960.
There were three more Ph.D.s granted, for a total of seven, up to the end of World War I in 1918. Before the war, most American students received their doctorates in Europe, most notably in Germany. Following the war the training of doctorates became an increasingly important function of the Wisconsin Department of Mathematics. At least one doctorate has been granted each year since 1926. With the impending retirements of Slichter and Van Vleck, the department was augmented by the arrival of the algebraist Mark H Ingraham in 1919 and the analyst Rudolph E Langer in 1927. During the years immediately preceding and following the war, the Department also had on it's staff some notable teachers such as Arnold Dresden, L W Dowling, and E B Skinner.
The appointment of C C MacDuffee in 1933, followed by those of Stephen C Geene in 1935, Richard H Bruck in 1942, R H Bing and Laurence C Young in 1946, and R Creighton Buck in 1950 greatly enhanced a tradition of excellence in graduate training and led to the Department of Mathematics at Wisconsin becoming one of the very important centres in the world for graduate education and mathematical research. Since 1950 there have been a great many people who have played a major role in mathematical research and graduate education at Wisconsin.
2. University of Wisconsin Calendar 1899.
Department of Mathematics.
Staff.
Professor Charles Ambrose Van Velzer, Professor Charles Sumner Slichter, Assistant Professor Ernest Brown Skinner, Assistant Professor Linneaus Wayland Dowling, Mr Theodore Running, and Mr Elwyn Francis Chandler.
Elementary Courses.
1. Algebra. Progressions, arrangements and groups, binomial theorem, theory of limits, undetermined coefficients, derivatives and series.
Text-book: Van Velzer and Slichter's University Algebra.
First semester; three tines a week.
Course given by: Professor Van Velzer, Assistant Professor Skinner, Assistant Professor Dowling, and Mr Running.
This course will be repeated in the second semester if a sufficient number of students desire it at that time to form a class.
2. Trigonometry. In this course the ratio system is used exclusively and special stress is laid upon goniometry.
Second semester; three times a week.
Course given by: Professor Van Velzer, Assistant Professor Skinner, Assistant Professor Dowling, and Mr Running.
3. Algebra (continuation of course 1).
This course is elective for all students who have taken course 1.
Second semester; twice a week.
Assistant Professor Skinner.
4. Analytic Geometry (elementary course). Straight line, conic sections, general equations of the second degree, transcendental curves, and an introduction to geometry of three dimensions.
Twice a week for one year.
Course given by: Assistant Professor Dowling.
5. Calculus (elementary course). Differentiation and integration of functions of one variable with the usual geometric applications.
Three times a week for one year.
Course given by: Assistant Professor Dowling.
Advanced and Graduate Courses.
6. Elliptic Functions. This course must be preceded by course 9.
Twice a week for one year.
Course given by: Assistant Professor Dowling.
8. Calculus (advanced course). Partial derivatives and multiple integrals with the usual geometric applications.
Twice a week for one year.
Course given by: Assistant Professor Dowling.
9. Differential Equations. Ordinary and partial differential equations with a few geometric and mechanical applications.
This course must be preceded by course 8 or taken along with it.
Three times a week for one year.
Course given by: Professor Van Velzer.
10. Higher Trigonometry.
This course must be preceded by course 5.
Second semester; twice a week.
Course given by: Assistant Professor Skinner.
11. Analytic Geometry of Two Dimensions (advanced course). Modern methods in plane analytic geometry.
This course must be preceded by course 4.
Three times a week for one year.
Course given by: Professor Van Velzer.
12. Theoretical Mechanics. An elementary course in analytical mechanics.
This course may be taken by those who have had analytic geometry and course 11.
Three times a week for one year.
Course given by: Professor Slichter.
13. Newtonian Potential Function. Lectures and required readings on the theory of potential with an introduction to spherical harmonics.
Three times a week for one year.
Course given by: Professor Slichter.
14. Projective Geometry.
Twice a week for one year.
Course given by: Assistant Professor Dowling.
15. Analytic Geometry of Three Dimensions.
This course should be preceded by courses 8 and 11.
Twice a week for one year.
Course given by: Professor Van Velzer.
16. Quaternions.
Twice a week for one year, in alternate years.
This course will not be given in 1898-99.
Course given by: Assistant Professor Skinner.
17. Theory of Functions.
Three times a week for one year, in alternate years.
Course given by: Assistant Professor Dowling.
18. Partial Differential Equations of Mathematical Physics.
Based on Riemann's Lectures, and Byerly's Spherical Harmonics.
This course will be given in 1899-1900.
Twice a week for one pear in alternate years.
Course given by: Professor Slichter.
19. Theoretical Hydrodynamics. Lectures on fluid motion.
Twice a week for one pear in alternate years.
This course will be given in 1900-1901.
A course in Theory of Elasticity may be substituted for this course.
Course given by: Professor Slichter.
20. Modern Algebra. Invariants, covariants, etc.
This course must be preceded by courses 3 and 8.
Twice a week for one year in alternate years.
Course given by: Professor Van Velzer.
21. Theory of Substitutions.
Three times a week for one year in alternate years.
Course given by: Assistant Professor Skinner.
22. Theory of Numbers.
Twice a week for one year in alternate years.
Course given by: Professor Van Velzer.
Other Advanced Courses.
To graduates and others prepared to take them, courses will be given when desired in definite integrals, advanced differential equations, Abelian functions, and higher plane curves.
Mathematical Group.
Students who desire to take the degree of B.A., B.L., or B.S. in mathematics will be admitted to the mathematical group at the beginning of the sophomore year. Such students may omit studies prescribed for the sophomore year of the course to an amount not exceeding six hours a week and substitute five hours a week of mathematics therefor. Students expecting to write theses in applied mathematics should take the course in mathematics in their junior year.
Summer Session.
Mathematics.
Staff.
Professor Van Velzer, Professor Slichter, and Mr Running.
1. Algebra. Course in algebra planned with reference to the special needs of high school instructors and those who are preparing for examination.
Five times per week.
Course given by: Professor Slichter.
Three-fifths credit may be obtained by making up some additional work.
2. Geometry. A review of the important theorems in plane geometry, and a study of solid geometry.
No previous knowledge of solid geometry will be required.
Five times a week.
Completion of this course satisfies the entrance requirement of geometry to the University.
Course given by: Mr Running.
3. Plane Trigonometry and Logarithms.
No previous knowledge of the subject will be assumed, but plane geometry
and algebra though quadratics are prerequisites to the course.
Five times a week.
Course given by: Professor Van Velzer.
Two-fifths credit.
4. Analytic Geometry. (Elementary course.)
Five times a week.
Course given by: Mr Running.
Two-fifths credit.
Advanced Courses.
5. Calculus. Differentiation and integration of functions of one variable with geometric applications.
Five times a week.
Course given by: Mr Running.
Two-fifths credit.
6. Theoretical Mechanics. A course in analytical mechanics for students who have had the calculus.
Five times per week.
Course given by: Professor Slichter.
Two-fifths credit.
7. Theoretical Hydrodynamics. A course of reading on the motion of perfect fluids.
The conference will be held two or three times a week, and credit will be given on the basis of the work accomplished.
Course given by: Professor Slichter.
8. Theory of Equations. The properties of equations of the nth degree. Solution of cubic and biquadratic equations and numerical equations of higher degrees.
Five times a week.
Course given by: Professor Van Velzer.
Two-fifths credit.
9. Differential Equations. Solution of differential equations of the first order with geometric applications.
Five times a week.
Course given by: Professor Van Velzer.
Two-fifths credit.
10. Theory of Numbers. Elementary treatment of congruences, primitive roots and quadratic forms.
Lectures based on Dirichlet's Zahlentheorie.
Five times a week.
Course given by: Professor Van Velzer.
Two-fifths credit.
11. Substitutions. Elementary treatment of substitutions and substitution groups.
Lectures, based on Serret's Algèbre Supérieure and Netto's Substitutions.
Five times a week.
Course given by: Professor Van Velzer.
Two-fifths credit.
Of the courses 9, 10, 11, only two will be given.
Last Updated March 2025