A HISTORY OF THE DEPARTMENT OF MATHEMATICAL SCIENCES 1888-1965
Walter P. Heinzman, Professor Emeritus
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| McFie Hall Original college building |
Early in 1888, a group of Las Cruces citizens established the Las Cruces College, with Hiram Hadley installed as the College’s first president. When the College opened on September 15, 1888 the student body numbered forty, the faculty, three — Hiram Hadley, Anna Hadley, and Matilda R. Koehler. From this College, a land grant college evolved, thanks to the efforts of a number of education-minded Mesilla Valley residents. Of this evolution, Hadley, in the 1908 edition of the Swastika, notes, “Encouraged by the success of the College, a few enterprising citizens of Las Cruces began laying plans for the capture of the Agricultural College, to which, by national legislation, New Mexico was entitled. In Las Cruces College was a nucleus for a greater one. the valley has long been regarded as possessing great agricultural possibilities; and it possessed a band of trained politicians. These made a combination difficult to defeat in such an enterprise. This new agricultural college was quite small, so small that, in the Spring of 1890, it was housed in a single building. From these pioneer beginnings, New Mexico State University evolved, surviving two World Wars and several name changes, growing in enrollment from the original forty to over 11,500 today, growing in number of faculty from three to over 500 today, in the process of this growth becoming one of the Southwest’s noted universities.
One of the earliest and most important departments of NMSU was the Department of Mathematical Sciences. The growth of this department closely parallels that of the University, evolving from a department with a faculty of one — Hiram Hadley — in 1888 to a department with a faculty of thirty-one today. Contrasted with its early offerings of preparatory and college work in the foundations of mathematics is the department’s current curriculum, which offers students of mathematics course work leading to the Bachelor of Science, the Master of Science, and the Doctor of Philosophy; included in its graduate offerings are concentrations both in mathematics and in statistics and probability. The purpose of this history is to chronicle the development of the Department of Mathematical Sciences from its beginnings in 1888 through 1965, the year in which Professor Walter P. Heinzman, author of this history, retired. Professor Heinzman, Professor Emeritus of Mathematics, taught mathematics at NMSU for forty years, from 1925 through 1965. During his tenure, Professor Heinzman was actively involved with the growth and the workings of the Department of Mathematical Sciences, and it is this involvement that has occasioned the writing of this history.
PIONEER BEGINNINGS–1888-1924
Until well into the twentieth century, the Department of Mathematical Sciences was primarily a service department. Students in the College’s early years could choose among three majors–the classical scientific course of study, mechanical engineering, or scientific agriculture–and the offerings of the Department of Mathematics and Astronomy supported all three. In addition, the department offered course work for the College’s preparatory and high school programs. In the 1890-91 catalogue of the Agricultural College at Las Cruces, Hiram Hadley, Professor of Mathematics, describes his department:
It is the intention to lay a thorough and practical foundation in elementary mathematics, embracing arithmetic, algebra, plane and spherical geometry and trigonometry, surveying and leveling. Our aim is to go deep rather than broad, to qualify the student to read, at his pleasure, more advanced works.The College is provided with a first-class transit, level, etc., and students in surveying, leveling, and trigonometry will have practical training in the use of these instruments.
As the College’s lone mathematician, Hadley found his duties to be rigorous, but his contribution to NMSU and to education in New Mexico extends far beyond his founding of the Department of Mathematical Sciences. From the College’s inception in 1888 through the end of the 1893-94 academic year, Hadley served as the President of the Las Cruces College as well as head of the Department of Mathematics, leaving the post of President in 1894 after his support among the College’s regents waned. Simply put, politics ousted Hadley from the presidency, and at least two of the College’s professors–Frederick F. Barker and A. J. Wiechardt–lost their positions in the political power struggle as well. Hadley subsequently became the Vice President of the University of New Mexico, and under Hadley’s guidance, UNM competed quite successfully with the Las Cruces College Then in 1898 Hadley returned to the College as a Professor, though of history and pedagogy rather than of mathematics. In 1905, Hadley was appointed territorial Superintendent of Instruction, and, prior to his retirement, he served on the Collage’s Board of Regents. Hadley served the College and education in New Mexico well in a number of positions–Professor of Mathematics, Head of the Department of Mathematics and Astronomy, President of the Las Cruces College, Vice President of the University of New Mexico, Professor of History and Pedagogy (LCC) , territorial Superintendent of Instruction, Las Cruces College Regent–but his particular influence on the College and the Department of Mathematics and Astronomy was profound.
Early in the life of the College, Hadley found his combined administrative and teaching load too heavy. Not only was he responsible for teaching all the course work in mathematics, he was also responsible for all course work in astronomy and for performing the duties of the College’s President. Thus, in the 1890-91 academic year, Hadley hired a second mathematician–Clarence T. Hagerty–who, in 1892, became Head of the Department of Mathematics and Astronomy, a post he held until his retirement in 1924, a total of thirty-two years. Not only did Hagerty direct the Department of Mathematics and Astronomy but the Department of Civil Engineering as well. During his tenure, Hagerty, as did all faculty, served on a number of committees, including Boarding and Accommodations, Catalogue, Course of Study, Entertainment, and Judiciary. In addition, he managed the College’s tennis program for a number of seasons. Hagerty, then, was very active in the life of the College and contributed greatly to it.
In the 1892-93 yearbook, Hagerty describes the course of study in mathematics for students enrolled in the College:
The prescribed course in Mathematics, for all regular College students, comprises a year of algebra, a year of plane and solid geometry, including conic sections, and one term, three periods per week, of plane trigonometry. One term’s work in elementary mechanics is required of all except those who are taking the course in Science and Agriculture. All, except those in Classical Scientific course, have spherical trigonometry, one term, three periods per week, land surveying, one term, and analytical geometry and calculus, one year. In addition to the above, students taking Civil or Mechanical Engineering courses have two terms of analytical mechanics.Algebra is begun in the Freshman year, and, completed as far as the binomial theorem inclusive. Much attention is given to the demonstration of original theorems, and to the solution of original problems in geometry. The instruction in all branches of Mathematics will be made as practical as possible.
Hagerty also taught astronomy, and in the 1897-98 catalogue, he described his department’s equipment for the study of astronomy:
This department has a portable equatorial telescope with 5-inch objective and magnifying powers ranging from 100 to 400, a surveyor’s transit with solar attachment, planisphere, star lantern with slides, field glasses, star atlas, protractors, trigonometry, 24-inch stated globe, Kennedy’s dissected geometrical blocks.The departmental library contains many valuable books of reference, and several periodicals.
Students enrolled in the College paid a flat fee of $40.00 during the early years, and their books were provided for them. According to the 1901-02 catalogue, “Textbooks are furnished to all students after they have made a deposit of $2.50 with the registrar. These books are drawn out upon written orders from the several instructors. Students are charged for unreasonable damage to their books.” Several of the mathematics texts used at this time included these:
Arithmetic — Thompson’s
Elementary Algebra — Slaught and Lennes, High School Algebra
Descriptive Geometry — Phillips and Miller, Essentials of Descriptive Geometry (required); Tracy, Mechanical Drawing (reference)
Geometry — Wentorth, Plane and Solid Geometry
Algebra — Mime, High School Algebra
Calculus — Taylor, Elements of Calculus
Hagerty served, among others, on the Catalogue Committee, and due to his position on this committee, the catalogue began to incorporate course listings by number and by description. The first listing of such courses appeared in the 1899-1900 catalogue, and these were the courses listed under mathematics:
Math 1,2: Geometry (Plane). Required of all Freshmen, terms 1 and 2. 5 hours — nearly one-third of the time is given to original exercise.
Math 3: Geometry (Solid). Third term required of all Freshmen. 5 hours.
Math 4: Trigonometry (Plane), including introduction to Spherical. Required of all Sophomore students in Engineering and Agriculture. 3 hours.
Math 5: Algebra. Third term required of Sophomores in Engineering.
Math 6: Analytic Geometry. Required of Sophomores in Engineering. 3 hours
Math 7: Analytic Geometry. Required of Sophomores in Engineering. 3 hours.
Math 8: Differential Calculus. 3 hours.
Math 9: Integral Calculus. 3 hours
As the enrollment of the College fluctuated, so did the size of the faculty of the Department of Mathematics and Astronomy. In 1908, J. R. Burkey, a civil engineer from Ohio State University, joined the department, and in the 1908-09 school year, both Burkey and Hagerty are listed as the faculty of the Department of Mathematics and Astronomy and among that of the Department of Civil Engineers. Burkey instructed Descriptive Geometry, Topographical Drawing, Railroad Surveying, Topographical Surveying, Railroad Construction, Irrigation Field Work, and Bridge Design, while Hagerty taught Trigonometry, Analytic Geometry, Calculus, and Surveying. In 1910, George P. Stocker joined the faculty as an Assistant Professor of Mathematics and Civil Engineering; at the same time, Fannie Ford became an Assistant in Mathematics. In 1910, then, the Department of mathematics and Astronomy consisted of four faculty. In the 1912-13 academic year, that faculty remained at four, although this year’s catalogue indicates that during this year Mary F. Winninghan replaced Burkey as a mathematician. By the 1916-17 school year only two faculty were listed in the Department, Hagerty and Winningham with Winningham teaching Elementary Algebra and Plane Geometry and Hagerty teaching the remaining courses scheduled in mathematics. Two years later, Lucie V. Armitage was hired under a joint appointment with history, teaching Elementary Algebra and several history courses.
From 1920 through 1924, Hagerty is listed as the only member of the faculty of the Department of Mathematics and Astronomy. Then, in the Spring of 1924, Hagerty was retired and forced to leave the College. In That All May Learn: New Mexico State University, 1888-1964, Simon F. Kropp writes of Hagerty’s separation from the College:
Perhaps the most unexplainable alteration within the faculty during the 1923-24 academic year] was the departure of Clarence T. Hagerty, who had served the College since 1891. Hagerty had taught at Silver City’s college during the summer and then secured a position at St. Louis University in the Fall [of 1924]. Since it was obvious that the old man had been shoved off the faculty, The Round-Up voiced the opinion that the Board of Regents could have been more generous than merely offering him a leave of absence. The non-existence of a pension system for New Mexico’s teachers became a glaring deficiency. In any case, before leaving the College Hagerty carefully arranged for the mounting of his telescope which he then placed under the supervision of his students. About one year later Hagerty received his reward by being granted emeritus status and a pension that was derived from a fund created by the state legislature for all retired teachers with thirty years or more years of service. Hagerty was honored by The Round-Up in a very laudatory article noting his influence on a number of the College’s students: “Under (Hagerty’s) expert tutelage hundreds of men and women of all classes, of all grades of intelligence have passed, emerging better men and women, better mathematicians, more logical thinkers, and greatest of all — for after all, that is the most valuable boon one can derive from contact with right-thinking perception might well be proud–far better citizens. A service the equal of which few men can boast. From Las Cruces Collage, Hagerty went to the University of St. Louis for one year, then to John Carroll University at Cleveland where he taught until his death in 1931.
With the death of Hadley in 1922, with the College’s dropping its high school and preparatory programs in 1924, and with the departure of Hagerty in 192U, the era which may be labeled “Pioneer Beginnings” came to a close. During this period, the Department was primarily a service department, but its course offerings expanded from the fairly general foundations in basic principles as set forth by Hadley in the College’s first catalogue to offerings which included a number of specific courses for specific majors. And during this period, the Department of Mathematics and Astronomy became a college level department, offering a more comprehensive course of study than it had been able to when, like other departments in the College, it was responsible for educating not only students of the College but students in the preparatory and high school division as well. Thus, under the direction first of Hadley and then of Hagerty, the Department of Mathematics and Astronomy grew. (For tributes to both Hadley and Hagerty, see Appendices C and D, respectively.)
THE MIDDLE YEARS — 1925-1947
Until the Fall semester of 192~, the College had had only two heads of the Department of Mathematics and Astronomy, and both, coincidentally, were from Indiana So, too, was the third scholar hired to lead the department Ralph V. Pritchard. In his first year on the College’s faculty, Pritchard was Domed by Daniel S. Robbins, who was Head of the Department of Physics, and Mr. Raymond of the Department of Civil Engineering. These three faculty taught all courses in mathematics during the 192~-1925 school year. During this year, the mathematics curriculum and texts remained, for the most part, the same, although the text for trigonometry adopted was Palmer and Leigh’s Plane and Spherical Trigonometry while the text for analytic geometry and calculus was Woods Bailey’s Analytic Geometry and Calculus, Added to courses offered by the department during this year were Differential Equations, Fourier Series, Higher Trigonometry, Math of Finance, General Math Analysis I and II, Mathematical Reading, History of Mathematics, and Teaching of Secondary Mathematics. Under Pritchard’s direction, then, the department increased its offerings substantially.
Just as the course offerings under Pritchard’s direction grew, so did the faculty. During the Christmas holidays of 1924, Pritchard, who was an avid checker player, attended a national checker and chess tournament in Indianapolis, Indiana. Pritchard, while on this trip, arrived at Noblesville, Indiana on an interurban street car, on his way to visit his in-laws. Onto this car stepped Walter P. Heinzman. Pritchard and Heinzman began a conversation in which each talked of what he was doing, and Pritchard suggested that Heinzman apply for a position in his department. Heinzman did just that, and following the review of his credentials by the College’sPresident, Heinzman received his notice of employment immediately prior to his graduating from Depauw University. On September 1, 1925, he became the newest addition to the faculty of the Department of Mathematics and Astronomy employed as Instructor of Mathematics for a nine-month term at a salary of $1,600.
In the 1925-26 academic year, the department surrendered Descriptive Geometry to the Department of Civil Engineering, since neither Pritchard nor Heinzman cared to teach it. A new course was added, however, the Philosophy of Mathematics, with Kaiser�s Philosophy of Mathematics serving as the course’s principal text. In the following school year, no new courses were added to those already listed with the Department of Mathematics and Astronomy. There was, however, a change in faculty, as Pritchard left the College in May of 1927. Pritchard was replaced by John W. Branson, who came to the College as head of the department, serving in that position for the next fourteen years. Branson arrived on campus with his M.S. already in hand and became the first scholar to head the Department of Mathematics and Astronomy to hold the Master’s degree on his arrival. Recognizing the importance of a graduate education, Branson encouraged his faculty to enter or to return to graduate school; indicative of this encouragement is the fact that Heinzman earned both the M.S. from the New Mexico College of the Agriculture and Mechanic Arts (formerly the Las Cruces College) in 1929 and the M.A. from the University of Illinois in 1931.
Like Hadley, Branson served the college as President as well as Head of the Department of Mathematics and Astronomy. As department head, Branson reintroduced the course work in astronomy which had not been offered since Hagerty’s departure in 1924. Branson ‘S term as President of the College was actually several terms, including three as Acting President and then one as President. On July 1, 193S, he was named Acting President, a post he held until he was replaced by Hugh N. Milton on September 19 of that year. In 1940, Branson was appointed to the newly created post of Dean of the College of Arts and Sciences, a position he held concurrently with that of Acting President from early September of 1941 until January 1, 1946. President rulton had been called to military service during World War II, and Branson filled the presidency during Milton’s absence. During this second term as Acting President, Branson helped.to move the College toward a liberal arts orientation by advocating strongly a “general education,” by which he meant a balanced education during a student’s first two years in college. To help study the feasibility of such an education, he appointed a committee, chaired by another mathematician, Earl Walden. Eventually, the report of Walden’s committee was adopted.
The years of World War II were especially trying ones for the College, as it struggled to maintain a student body. But despite outside pressures on him, Branson refused to sacrifice quality education for mere survival. At one point, the possibility of the College becoming a vocational school was seriously considered by the legislature. Of this particular situation, Simon Kropp writes in That All May Learn, “Despite the alleged presence of opportunities for quick gain, Dean Branson decided he would not ‘cater to the trade school market’ and would maintain academic standards ‘regardless of any immediate profit.’ ” Such insistence was a major step in the College’s becoming a full-fledged university. On April 2, 1949, Branson was named Acting President for the third time; then, on October 17, 1949, he was named President, which post he held until his retirement on August 14, 1955.
The mathematics faculty in the 1929-30 school year consisted of Branson, Heinzman, and Wren Stone, who had an appointment in mathematics and in chemistry. During this year, several new courses were added to the department’s offerings: Introduction to Mathematics, Space Geometry, Advanced Solid Analytic Geometry, and Theory of Equations. From the 1929-30 academic year till that of 1935-36, there were no changes either in faculty or in course offerings. Then, in the Fall semester of 1935, Paul K. Rees came as an Assistant Professor of Mathematics. Rees, who had earned the Ph.D. from Rice Institute in 1933, became the first mathematics faculty member at the College to hold an earned doctorate. Later in the year, Stone died; the position his death left vacant was filled by Emmet A. Hazelwood, who came to the College from Cornell University, at which university he was enrolled in doctoral work. And in 1936, Hazelwood was awarded the Ph.D. by Cornell.
The following academic year — 1936-37 — saw the largest mathematics faculty in the history of the College. In addition to Branson, Heinzman, Rees, and Hazelwood, Gordon Fuller, who earned the Ph.D. from the University of Michigan in 1932, joined the faculty. Fuller brought the number of the department’s faculty holding the Ph.D. to three, while the remaining two held the M.S. and/or the M.A.
The 1936-37 catalogue outlines an organized, four-year program for a major in mathematics, which shows clearly the degree to which the department had evolved from its beginnings:
Major in Mathematics may be combined with major in Chemistry or Physics, giving excellent foundation for scientific research, teaching.
Freshman Year
English Composition 6
College Algebra 4
Trigonometry (first semester) 3
Analytic Geometry (second semester) 3
History
Physics
Plane Surveying (second semester) 2
M.S. or P.E. 4
Sophomore Year
Differential Calculus (first semester) 3
Integral Calculus (second semester) 3
Chemistry or Biology 8
German or French 6
English Literature 6
Electives 6
M.S. or P.E. 4-2
Junior Year
Public Speaking 2
Education (or elective) 10
Major Subject 10
German or French 6
Electives 4
Senior Year
English 4
Major Subject 10
Education (or elective) 5
History 6
In addition to this outline of study, the 1936-37 catalogue carried these descriptions of courses offered by the Department of Mathematics:
Majors in Mathematics are required to take courses numbered 11, 12, 13, 14, 53, 63, 103. In addition to these required courses, the student must select seventeen semester hours of mathematics with the approval of the Head of the Mathematics Department. In most cases the courses numbered 113 and 151-152 will be included.
2. H.E. Mathematics. Sem. 11 — Cr. 3
A course for students of Home Economics, including units of measure, annuities, interest and discount, and other topics, designed to prepare the student for the situations of everyday life.
7. Mathematics for Teachers. Sem. 1 — Cr. 3
A course for teachers of elementary mathematics, including content and methods of presentation.
9. College Algebra. Sen. 1 Cr. 3
For Freshmen in Business Administration.
10. Trigonometry. Sem. 11 — Cr. 3
For Freshmen in Business Administration.
9A. College Algebra. Sen. 1 — Cr. 2
For Freshmen in Agriculture.
10A. Trigonometry. Sem. 11 — Cr. 2
For Freshmen in Agriculture.
11,12. College Algebra Sen. 1, 11 — Cr. 2, 2
For students in Engineering and majors in Mathematics.
13. Trigonometry, Sem. 1 or 11 — Cr. 3
For students in Engineering and majors in Mathematics.
14. Analytic Geometry. Sem. 1 or 11 — Cr. 3
For students in Engineering and majors in Mathematics.
16. Introduction to Astronomy. Sen. 11 — Cr. 3
A careful study of the solar system and a brief study of the sidereal universe.
53. Differential Calculus. Sem. 1 or 11 — Cr. 3
For students in Engineering and majors in Mathematics.
57,58. Mechanics (See Physics 5758). Sem. 1 or 11 — Cr 3, 3
Acceptable toward a major in Mathematics.
63. Integral Calculus. Sem. 1 or 11 — Cr. 3
For students in Engineering and majors in Mathematics.
90. Statistics. Sem. I –Cr. 3
For students in Business Administration and elective for others.
103. Applications of Calculus. Sem. 1 or 11 — Cr. 3
For students in Engineering and majors in Mathematics.
110. Vector Analysis (See Physics 110). Sem. 11 — Cr. 3
112. Space Geometry. Sem. 11 — Cr. 3
An advanced course in solid analytical geometry, including some work in differential geometry.
113. Theory of Equations. Sem. 1 — Cr. 3
115. Spherical Trigonometry Sem. 1 Cr. 2
122. Advanced Calculus. Sem. 1 — Cr. 3
151,152. Differential Equations. Sem. 1, 11 — Cr. 3, 3
157. Methods of Teaching High School Mathematics. Sem. 1 — Cr. 2
Pre-requisite, 15 semester hours of college mathematics.
160. Celestial Mechanics. Sem. 11 — Cr. 3
Prerequisite, Physics 57, Mathematics 151.
During the first ten years of Branson’s direction, then, the Department of Mathematics made great strides, increasing substantially the number and variety of its course offerings and increasing the size of its faculty as well. But the faculty was to remain at five for some time. In the 1938-39 academic year, Frederick H. Bailey and Paul M. Swingle were hired to replace Hazelwood and Fuller. With this change, the faculty of the department remained at five, with two — Rees and Swingle — holding the Ph.D. and three — Branson, Heinzman, and Bailey — holding the M.S. and/or the M.A.
Over the next few years, the Department of Mathematics experienced a number of personnel changes, although the general program and course offerings remained the same. In 1939, flees left the College and was replaced by Gerald Harrison. In addition to Harrison, Anna H. Gardiner joined the faculty as an instructor. (Mrs. Gardiner, wife of George Gardiner, Head of the Department of Physics, stepped in whenever needed over the next several years to teach lower division courses in mathematics.) Then, in 1940, Branson became Dean of Arts and Sciences; to teach those courses which would otherwise be taught by Branson, Rudolph D. Delehanty became a member of the mathematics faculty. In 1941, Harrison left, and Roy B. McKay joined the faculty as am Associate Professor of Mathematics. Only a year and a half later McKay died. In the 1941-42 academic year, Branson became Acting President of the College, although he still taught courses in the Department of Mathematics during this year. The 1942-43 school year found Heinzman as acting head of the department, and he served in this capacity for three years. Also in 1942, Earl Walden joined the mathematics faculty. The College experienced a drop in enrollment as World War II broke out and continued, and at least one member of the mathematics department — F. Homer Bailey — left the College to enter military service. To take Bailey’s place, James V. Boyd was hired, and Ruth Nees joined the faculty to help instruct students in the Army Program which Branson had helped secure for the College to boost enrollment.
When the war ended, Branson, while still Dean of Arts and Sciences, returned to the department when the College’s President, General Hugh Milton, returned to the College from the service. At this time, then, the Department of Mathematics consisted of four faculty — Branson, Heinzman, Swingle, and Walden — since Bailey, who had returned from the service, resigned his position in 1946. Branson headed the department from 1945 through 1947, at which time Walden was named to head the department to fill Bailey’s position, Robert D. Westhafer joined the faculty, keeping the number of mathematics faculty at five.
In the 1946-47 academic year, which marks the end of the second era in the history of the Department of Mathematical Sciences, the College’s catalogue lists course work offered by the Department of Mathematics, and the offerings show that the department had both expanded and contracted its course offerings. New courses included Solid Geometry, Mathematics of Finance, and Actuarial Theory, but course work in such lower division courses as algebra had been consolidated. In the 1936-37 catalogue, the department lists a course in algebra for majors in Business Administration, another in algebra for majors in Agriculture, and a third in algebra for majors in Engineering and in Mathematics. The 1946-47 catalogue, however, makes no such distinction among these lower division courses. Further, the 1946-47 catalogue shows that a minor in mathematics had been developed:
Majors in Mathematics are required to take courses numbered 12, 13, 51, 105, and 106. In addition to these required courses, the student must select thirteen semester hours of mathematics with the approval of the Head of the Mathematics Department.
A student whose minor is Mathematics will take courses 12 or 17, 13 , 51, and not less than five additional hours selected with the approval of the student’s major and minor professors. Courses in Mathematics which carry College credit have as prerequisites one unit of High School Algebra and one unit of Plane Geometry. Those who do not have the prerequisites will be given the opportunity to make up deficiencies.
Any of the following courses are offered either semester.0. Algebra.
A three-hour, non-credit course for students in Engineering who have had only one unit of High School Algebra.1. Solid Geometry — Cr. 3
Students in Engineering, who lack the one-half unit of High School credit in solid geometry necessary for entrance to the School of Engineering must take this course during their first year in college, without credit, to remove such deficiency.
12. College Algebra — Cr. 3
The topics studied are quadratics, systems of quadratics, equations of higher degree, variation, progressions, partial fractions, permutations, combinations, probability, mathematical induction, the binomial theorem, and determinants. Required for students in Engineering and majors in Mathematics.
13. Trigonometry — Cr. 3
Systematic study of triangles, trigonometric equations and identities with emphasis on analysis. Required for students in Engineering and majors in Mathematics.
17. College Algebra — Cr. 3
A study of the algebraic processes necessary in obtaining the solutions of polynomial equations in one unknown and systems of equations. Progression, compound interest, annuities, and other topics are considered. Required of Freshmen in Business Administration.
18. Mathematics of Finance — Cr. 3
Simple interest, compound interest, annuities, amortization, sinking funds, depreciation, bonds, and life insurance. Prerequisites, Math 17 or equivalent. Required of all Business Administration students.
51. Analytic Geometry — Cr. £4
A study of relations which can be stated in the form of an equation in two variables and represented by a curve in a plane; also a brief study of relations which can be stated in the form of an equation in three variables and represented by a surface in three-dimensional space. Various systems of coordinates are used. Required of students in Engineering and majors in Mathematics.
55. Introduction to Astronomy — Cr. 3
A careful study of the solar system and a brief study of the sidereal universe.
90. Statistics — Cr. 3
Collection and tabulation of data, construction of simple graphs, sampling, averages, dispersion, index numbers, probability, normal curve, estimation with application to economic problems, and simple correlation. Prerequisites, Math 12 or 17, Math 13 or 18. Required of all Business Administration students.
104. Actuarial Theory — Cr. 3
Theory of probability as related to life insurance, construction of mortality tables, expectation of life annuities, net premiums, net level reserve, modern reserve systems, and gross premiums. Prerequisites, Math 12 or 17, Math 13 or 18.
105. Calculus I — Cr. 4
Derivatives and differentials of the usual algebraic, trigonometric, logarithmic, and exponential forms with applications to problems dealing with maxima, minima, curve tracing, rates, and an introduction to integral calculus.
106. Calculus II — Cr. 4
Integration of the forms studied in differential calculus with applications to problems dealing with areas, volumes, lengths, etc. infinite series; introduction to differential equations. Pre-requisite, Math 105.
107 a-b. Logic and Scientific Method — Cr. 3, 3
A study of traditional logic, scientific method and symbolic logic. The content will be determined in part by the interest of those taking the course.
109. Foundations of Modern Math — Cr. 3
A study of the philosophy, and development of mathematics; of interest to those desiring a general education. Prerequisite, Math 106
115. Spherical Trigonometry — Cr. 3
A study of right and oblique spherical triangles with applications in problems in astronomy and navigation. Prerequisite, Math 13.
151. Differential Equations — Cr. 3
The types of ordinary and partial differential equations encountered in such subjects as biology, chemistry, physics, and engineering are treated by various methods. Pre-requisite, Math 106.
152. Differential Equations — Cr. 3
Existence theorems, numerical solutions of differential equations, and certain classical equations are studied. Prerequisites, Math 151 or consent of instructor.
160 a-b. Celestial Mechanics — Cr. 3, 3Speed, velocity, and acceleration in rectilinear and curvilinear motion, central forces, potential and attractions of bodies; problem of two bodies, determination of orbits, differential equations of motion of n bodies; perturbations. Prerequisites, Phys 117, Math 151.
171 a-b. Higher Algebra — Cr. 3, 3
Pre-requisite, Math 105.
181 a-b. Higher Geometry — Cr. 3, 3
Prerequisite, Math 105.
191 a-b. Higher Analysis — Cr. 3, 3
Prerequisite, Math 105.
During the Middle Years, the Department of Mathematics became a full-fledged department with standing in Arts and Sciences and within the College as a whole as more than a service department. The contributions of several of the department’s faculty had great impact on the College and its students: Branson served as Head of the Department of Mathematics, as Dean of Arts and Sciences, and as Acting President of the College during World War II, years which were trying ones for the college as it struggled to maintain its enrollment and standing as a college. Walden helped to form a program of liberal studies, which clarified and codified a two-year course of study for all students in the College of Arts and Sciences, thereby providing more coherence in existing degree programs than there had been before. And it was Walden who helped to bring to the Department of Mathematics an emphasis on graduate programs, which, in turn, increased student enrollment in mathematics and faculty positions as well.
GRADUATE WORK BEGINS IN EARNEST—1948-1965
In the 1947-48 academic year, Earl Walden became Head of the Department of Mathematics, and, under his direction, the department rejuvenated the Master of Science in Mathematics. Both Walden and Westhafer recruited graduate students to enroll in the department’s M.S. program, and the first group of these students numbered six. During the following year, the number of graduate students, all of whom were graduate assistants, increased to eight. And the mathematics faculty grew from five to six. Branson was listed both as Dean of the College of Arts and Sciences and as Professor of Mathematics; the remaining mathematicians were Walden, Heinzman, Westhafer, Goethals, and Crouch. Late in 1948, Manfred Fliess joined the faculty, as did Max Kramer the following year. And in 1949, Frank A. Kros became the first student to receive the M.S. in Mathematics from NMSU since Heinzman was awarded the M.S. in 1929.
Until the mid-50’s, the department remained essentially the same, its faculty numbered between six and eight, its graduate assistants eight. And the department offered both the B.S. and the M.S. in Mathematics. The 1956-57 academic year, however, saw a very important change in the department, as the 1956-57 graduate bulletin notes:
The Department of Mathematics offers graduate work leading to the Master of Science and to the Doctor of Philosophy degrees and cooperates with the Departments of Physics and Electrical Engineering in offering the degree of Doctor of Applied Science.
During this year, then, the Department of Mathematics began its doctoral program, offering this advanced course work:
Courses for Advanced Undergraduates and Graduates
152 a-b. Advanced Calculus–Cr. 3, 3
A more rigorous discussion of the topics introduced in the calculus. Prerequisite: Math 106.
153.a-b. Advanced Calculus for Engineers — Cr. 3, 3
Topics of advanced calculus with emphasis on physical and engineering applications; ordinary differential equations, Laplace transforms Fourier series and boundary value problems, introduction to complex variable theory. Prerequisite: Math 107 or Math 106 and consent of instructor
158. Elementary Number Theory — Cr. 3
An introduction to the theory of primes, congruences and related topics. Prerequisite: Math 106.
161 a-b. Foundations of Mathematics — Cr. 3, 3
A survey of the nature of mathematics and its basic unifying concepts and disciplines. The fundamental concepts underlying the fields of number, algebra, geometry, and analysis. Prerequisite: Math 106 or consent of instructor.
162. Professional Subject Matter in Mathematics — Cr. 3
A re-examination of secondary school and junior college mathematics from an advanced viewpoint. Topics covered will include theory of equations and analysis of the methods of analytic geometry and calculus with their applications to the mathematics taught at those levels. Prerequisite: Math 106 or consent of instructor.
163. The Teaching of Secondary School Mathematics — Cr. 3
A seminar on the best modern practices in the teaching of mathematics in the junior and senior high schools. An analysis of the curriculum and its objectives. The relation of the knowledge of mathematical foundations to the teaching of secondary mathematics and the uses of mathematics in current times. Prerequisite: Math 161 taken previously or concurrently. Credit for this course may be counted toward meeting departmental requirements in the Department of Education.
164. Topics in Modern Mathematics — Cr. 3
Selections will be chosen from modern analysis, topology, modern algebra, geometry, and number theory. Designed to acquaint secondary teachers with modern trends in mathematics.
168. Vector Analysis — Cr. 3
Calculus of vectors, with applications to mechanics and electricity. Taught by the Physics Department.
171 a-b. Introduction to Higher Algebra — Cr. 3, 3
An introduction to the basic ideas and methods of abstract algebra. Prerequisite: Math 106.
179 a-b. Theory of Statistics — Cr. 3, 3
An introduction to the underlying principles of statistics. Prerequisite: Math 106.
180 a-b. Treatment of Experimental Data — Cr. 3, 3
A study of finite differences and the analysis of discrete and continuous data. Prerequisite: Math 179a.
181 a-b. Introduction to Higher Geometry — Cr. 3, 3
An introduction to the basic ideas and methods of higher geometry. Prerequisite: Math 106.
Courses for Graduates
201 a-b. Advanced Applied Mathematics — Cr. 3, 3
A selection from the following topics: theory of linear operators, Green’s functions, eigen-value problems of ordinary differential equations, partial differential equations of mathematical physics, variational methods, integral equations. Prerequisite: Math 152b or Math 153b.
203 a-b. Numerical Analysis — Cr. 3, 3
The study of numerical methods for the solution of algebraic, transcendental, differential and partial differential equations. Prerequisite: Math 152b or Math 153b or consent of instructor.
208. Topology I — Cr. 3
Introduction to set theory. Algebra of sets. Cardinal and ordinal numbers. Topological spaces and Frechet (V) spaces. Normal Topological spaces. Prerequisites: Math 171 a-b or consent of instructor.
209. Topology II — Cr. 3
Metric spaces. Complete spaces. Hilbert spaces. Prerequisite Math 208.
251 a-b. Differential Equations — Cr. 3, 3
Existence theorem for ordinary and partial differential equations. A study of some of the differential equations of mathematical physics. Prerequisite: Math 152b or Math 153b and consent of instructor.
260. Design of Experiments — Cr. 3
261. Sequential Analysis — Cr. 3
271 a-b. Advanced Algebra — Cr. 3, 3
Topics studied will include groups, rings, integral domains, fields and matrices. Prerequisite: Math 171 a-b, or consent of instructor.
281 a-b. Differential Geometry — Cr. 3, 3
Differential geometry of curves and surfaces. Prerequisites: Math 106 and consent of instructor.
283. Algebraic Geometry — Cr. 3
The topics considered will include projective spaces, plane algebraic curves, transformations of a curve and linear series. Prerequisite: Math 181 a-b or consent of instructor.
291 a-b. Functions of a Complex Variable — Cr. 3, 3
This course covers functions of a complex variable, singularities, poles, residues, conformal transformation, Riemann surfaces, Laplace transformations, and integral representations of non-elementary functions. Prerequisite: Math 152b or Math 153b or consent of instructor.
293 a-b. Advanced Analysis — Cr. 3, 3
Theory of a real variable including a rigorous discussion of the real number system, continuity, differentiation, integration and convergence. Prerequisite: Math 152b or Ma~h 153b or consent of the instructor.
295. Special Problems — Cr. 2-6
300. Master’s Thesis — Cr. 2-6
301 a-b-c-d. Topics in Algebra — Cr. 3, 3, 3, 3
302 a-b-c-d. Topics in Analysis — Cr. 3, 3, 3, 3
303 a-b-c-d. Topics in Applied Mathematics — Cr. 3, 3, 3, 3
400. Doctor’s Thesis
As it began offering course work leading to both the M.S. and the Ph.D. in Mathematics, the Department of Mathematics listed a total of fifty-three possible courses for its graduate students, with nineteen of those fifty-three available for the department’s advanced undergraduates. To teach these courses, the graduate faculty of the Department of Mathematics numbered nine, with the 1956-57 graduate bulletin listing Walden, Heinzman, Westhafer, Crouch, Kramer, Olin B. Ader, Delmar L. Boyer, Randall M. Conkling, and A. V. Fend as the faculty.
The next major change in the offerings of the department appears in the 1961-62 graduate bulletin, which indicates that the department no longer offered course-work in Engineering. Apparently, during this year the department dropped its role in the Doctor of Applied Science degree, opting instead to concentrate its efforts on the Ph.D. in Mathematics.
Over the next few years, the number of students graduating with advanced degrees in mathematics increased substantially. And in 1960, the department graduated Allan B. Gray, Jr., its first Ph.D. and the first student to be awarded the Ph.D. by NMSU. In 1961, Ralph Crouch was appointed Head of the Department of Mathematics, a post he held until 1967. Under his direction, the department’s graduate program continued to flourish. By 1964, twelve students took the Ph.D. in Mathematics; in 1965, five more did so. In addition to these seventeen Ph.D. students, sixteen students took the M.S. in Mathematics between 1960 and 1965.
In the 1964-65 undergraduate catalogue, the mathematics faculty comprised twenty-eight members; in addition, fifteen graduate assistants were enrolled. Thus, during this academic year, the year in which this history ends, a total of forty-three teachers of mathematics offered undergraduate courses. And during this year, the mathematics graduate faculty numbered eighteen. By the end of the 1964-65 academic year, then, the Department of Mathematics was well on its way to becoming one of the major departments in Arts and Sciences, offering a broad range of courses leading to the B.S., the M.S., and the Ph.D. in Mathematics.
It is frequently difficult to measure the contribution a single department makes to a college or university. And while a list of achievements and activities in which the faculty of a department engage can, at best, only imply the scope of that department’s work the following list shows that the Department of Mathematical Sciences has indeed made a substantial contribution to NMSU from its beginnings in 1888 through 1965, the year in which this history ends:
1888 – Hiram Hadley, Head of the Department of Mathematics and Astronomy and first President of Las Cruces College.
1938-40, 1940-46, 1949 – John W. Branson, Head of the Department of Mathematics and Acting President of the New Mexico College of Agriculture and Mechanic Arts.
1940-46 – John W. Branson, Dean of the College of Arts and Sciences.
1947 – Earl Walden, Chairman of a committee which gives shape to the curriculum of the College of Arts and Sciences.
1949-55 – John W. Branson, President of NMCAMA.
1956-66 – Earl Walden, Dean of the College of Arts and Sciences and first Dean of the Graduate School.
1929, 1949-65 – Seventy-nine graduates with M.S. in Mathematics.
1960 – Allan B. Gray, Jr. first graduate with the Ph.D. in Mathematics and first graduate with the Ph.D. from New Mexico State University.
1960-65 – Twenty-six graduates with the Ph.D. in Mathematics.
Since 1965, unprecedented growth and development has occurred. Today, the faculty of the Department of Mathematical Sciences numbers thirteen, an increase of thirty positions since 1898. And far from offering the preparatory and college work in the foundations of mathematics, the department today offers a broad curriculum, with students enrolled in B.S., M.S., and Ph.D. programs in such fields as Applied Statistics, Operations Research, Numerical Analysis, Algebra, Topology, Applied Mathematics, Functional Analysis, and Logic. With its diverse offerings and its large, active faculty, the Department of Mathematical Sciences remains among NMSU’s most important departments.
