I do not recall feeling disadvantaged while growing up.

In presenting this volume the author endeavours to set forth matter which will give training and drill in all of the fundamental processes of arithmetic. The matter contained herein has all been taken by Mr D W Woodard, the author, from the industrial and business operations of the Institute. He has visited every department of the Institution, has examined all the books, and has had numerous conferences with every instructor. He has not found a single practical, workable operation in arithmetic that has not ben exemplified in some of the work connected with the Institution. The problems are therefore local in their setting. The Accounting Department, the Mechanical department with its various construction operations, and the Agricultural Department, through its planting, harvesting and productive endeavours, together with the various industries for the training of young women, have all furnished the material for the operations in this volume.

This book has been prepared in response to a long felt need of the students of the Tuskegee Normal and Industrial Institute. At this institution, the attempt is made to connect the arithmetic in a vital manner with the everyday interests and exercises of the students. The subject is presented as a necessary tool for doing certain things, for solving specific problems. Under this conception of the function of arithmetic, the course centres about the problems. Attention is called to the very large number of problems in which the data must be gathered at first hand by teacher and student. In fact, it is impossible to carry out the purposes of this book within the narrow confines of the classroom.

One day a group of Tuskegee students was engaged in putting the finishing touches to a new building on the Institute grounds. To one young man, who was learning the carpenter's trade, was assigned the work of laying some molding. For quite a while he pursued his work quickly and successfully. then his job led him to a certain corner of the building which deviated considerably from the usual right angle. What was he to do? Never before had he laid molding round such a corner. Now the problem consisted in finding the angle for cutting the molding so as to make a proper fit. Failing to think out the problem, the student by a trial and error method was finally able to make the molding fit as desired. But this trial and error method involved not only a loss of time but also a waste of material. This happened in Friday, a day on which this particular carpenter was wholly engaged in industrial work. According to the Tuskegee system, a "day" student in a week spends three days at his trade and three days in academic work, the "trade" days alternating with the "academic" days. On the day after the incident mentioned, the student reported the affair to his class in geometry. After he had attempted to give a statement of his difficulties, the class visited the scene of the event. Again the student explained the situation. Finally, a method was worked out on the spot whereby the molding could be cut without waste. But the method arrived at, while it eliminated all waste, was unsatisfactory in that it was very slow in operation. On the next "academic" day the problem was again discussed and referred for further discussion to a committee of three carpenters (students) who were members of this class in geometry. This committee consulted the instructors in carpentry and all other available sources of information. Altogether three methods were propose for the task. A model representing the corner of the room was brought into the classroom together with pieces of molding, a saw, and the like. Each method was actually exhibited before the class and the geometrical principles concerned in each were thoroughly discussed.

In the early 1920s Dudley Woodard began taking advanced mathematics courses in the summer sessions at Columbia University. It then became clear that he was among the gifted mathematicians in the nation.

R L Moore, in his paper, "On the Foundations of Plane Analysis Situs", Transactions of the American Mathematical Society, Volume 17, 1916, proposed three systems of axioms, $S_{1}, S_{2}, S_{3}$, for the development of two-dimensional analysis situs. ... In Axiom 8, which belongs to all three systems, Moore assumes that every simple closed curve is the boundary of at least one region, that is, that every simple closed curve defines a bounded connected set of connected exterior having further properties implied by certain other axioms of the three systems. The chief purpose of this investigation is to replace Moore's Axiom 8 by another axiom of such nature that no property of the simple closed curve is assumed. The Jordan curve theorem in its most general form appears as the fundamental theorem of the set of theorems. Two systems, I and II, are presented. It is proved that (1) all of Moore's theorems follow as consequences of each of the systems of axioms, (2) every simple closed curve is the boundary of a set of points having all the properties of a region, (3) every space satisfying the set designated as Axiom I is homeomorphic with the Euclidean plane and (4) there exist spaces satisfying Axiom II that are "neither metrical, descriptive, nor separable". The proof of the Jordan curve theorem for spaces of the type described in (4) constitutes perhaps the most interesting result in the development that follows. ... I wish to express my deep obligation to Dr J R Kline who suggested the problem and whose helpful criticism has been of inestimable value.

... obtained the necessary resources and administrative support for a mathematics library, and sponsored visiting professorships and scholarly seminars. When he retired in 1947 as chairman of the department, he had led Howard's mathematics faculty through a quarter century of steady advancement. In an age of discrimination, Dudley Weldon Woodard had competed and triumphed in the face of overwhelming odds. Penn is proud to claim him among its most distinguished alumni.

Among his colleagues and students, Woodard excelled and was very popular as professor and as an administrator. Additionally, he was apparently highly respected by those who knew him in the mathematical sciences community. Deane Montgomery, former president of the American Mathematical Society and the International Mathematical Union described Woodard as, "an extremely nice man, well-balanced personally." Leo Zippin, who was an internationally known specialist in Woodard's field, said that he was "one of the noblest men I've ever known." Dr Woodard was not only a brilliant mathematician, but a man of high intelligence and dignity; he enjoyed life in spite of his racial environment. He used the phrase, "black is beautiful" in the 1930s; he often ignored the "colored" signs and visited any men's room of his choice. He also ate at many "nice" restaurants and enjoyed the theatres of his choice in New York. He and his family once moved in what had been an all-white neighbourhood because it was aesthetically nice and it was near Howard.