Moore Teaching Method and Mary Ellen Rudin Aidy Segura October 15, 2014 The Moore method is named after Robert Lee Moore, a topologist, and it is used in advanced mathematics courses. Robert Lee Moore was born on November 14, 1882 in Dallas, Texas and died in Austin, Texas on October 4, 1974. Moore's father fought for the Confederacy and was a proud Southerner, it wasn't until much later that Moore found out that his uncles fought for the Union. Moore is considered as a founder of his own school of topology which had many contribution to that field. He was president of the American Mathematical Society in the late 30s. Three of his 50 graduate students were also presidents of the AMS and five were presidents of the Mathematical Association of America. The majority of his graduate students became academics and he has almost 1,700 mathematical descendants. There are various forms to teach the course. In general, the students are given a list of theorem and definitions and are expected to prove them and present in class. Usually, in using the Moore Method there are limitaitions to the amount of material the class is able to cover. The Moore Method has its pros and cons but in the end it is just another teaching method that involves more than just listening to lectures. F. Burton Jones was a student of Moore and practiced his method. Jones recalls that "when a student stated that he could prove Theorem x, he was asked to go to the blackboard and present his proof. Then the other students, especially those who had not been able to discover a proof, would make sure that the proof presented was correct and convincing. Moore sternly prevented heckling. This was seldom necessary because the whole atmosphere was one of a serious community effort to understand the argument." You could imagine the amount of pressure these students had on themselves. The students were for- bidden to read any book or article about the subject. They were even forbidden to talk about it outside of class. Some believe that the Moore method is a reminiscent of an old method of teaching swimming called "sink or swim." In 1920 after Moore became an associate-professor at the University of Texas at Austin the Moore Method became more popular. Today, the University of Texas at Austin continues using the method in various courses in their math department. Other institutions that use the Moore Method are : 1 • The University of Chicago offers the following Moore method classes: hon- ors calculus, analysis, algebra, geometry, and number theory along with one or two Moore method electives each year. • Professor Arnold Lebow uses the Moore method in his Advanced Calculus, Probability, and Discrete Structures courses at Yeshiva University in New York. • Professor Bryan Snyder at Sault Ste. Marie, Michigan's Lake Superior State University, has introduced the Moore Method to the university in a course named "Fundamental Concepts of Mathematics." • Professor Ronald D. Taylor at Berry College in Rome, Georgia successfully uses the Moore method in his Real Analysis course. • The Physics Department of Berry College successfully uses the Moore method in numerous upper level courses. • Professor Don Chalice at Western Washington University regularly uses a modified Moore method in all the upper level courses he teaches. • Professor Lawrence Fearnley of Brigham Young University has, over the course of several decades, thoroughly implemented the Moore method in several of the analysis, topology and Calculus courses. • Professor Mike Brilleslyper of the United States Air Force Academy uses the Moore Method to teach Real Analysis. • Professor Ed Parker of James Madison University uses a modified Moore Method in Calculus and Analysis courses. • Professor Elena Marchisotto of California State University, Northridge uses a modified Moore method in her "Foundations of Higher Mathemat- ics" course. • Many topology professors in the Mathematics Department of Auburn Uni- versity use varying modifications of the Moore method. • Professor David W. Cohen of Smith College implemented a modified Moore method for courses in Infinite-dimensional Linear Algebra and Real Anal- ysis. • Professor Vladimir N. Akis of California State University, Los Angeles uses the Moore Method to teach graduate Topology courses. • Professor Thomas Wieting of Reed College uses a Moore method in his Real Analysis and Differential Equations courses. • Professor Glenn Hurlbert of Arizona State University, uses the Moore Method to teach Introduction to Proofs, Combinatorics, and Linear opti- mization courses, and has written a Springer textbook to facilitate its use in Linear Optimization. 2 • Professor Gordon Johnson of University of Houston utilizes the Moore method to instruct Calculus and Analysis courses. • Professor Genevieve Walsh of Tufts University uses a modified Moore method in her Point-set topology course. • Different instructors have used the Moore method at Canada/USA Math camp to teach various topics on algebra, topology, number theory, logic, and set theory. • Mike Cullerton used a modified Moore Method to teach the quadrangles unit of a high school Geometry class at Ute Creek Secondary Academy in Longmont, CO. • Professor Dylan Retsek uses this method at Cal Poly San Luis Obispo to teach Calculus, Introduction to Proofs, and Real Analysis. • Professor Padraig McLoughlin uses this method at Kutztown University of Pennsylvania to teach Calculus, Set Theory, Foundations of Mathematics, Real Analysis, Topology, and Probability and Statistics. Mary Ellen Rudin was born on December 7, 1924 and died on March 18, 2013, her maiden name is Mary Ellen Rudin and is an American mathematician. She attended the University of Texas under Robert Lee Moore. Rudin completed her Bachelors in 1944 and her Ph.D in 1949. At the University she was a member of the Phi Mu Women's Fraternity and was elected to the Phi Beta Kappa society. Mary Ellen's dad was a civil engineer and her mother was an English teacher in High School, both of Mary Ellen's grandmothers had graduated from Mary Sharp College in Winchester, Tennessee. She married Walter Rudin a mathematician. It is said that Rudin ran into mathematics by accident on the day of reg- istration at the University of Texas in 1941. Because there were few people at the math table, she went to it and discussed many things with the man sit- ting there for a long time and it turned out to be Moore. Even though Mary Ellen benefited from the Moore teaching method, she did not believe it was for everyone. Mary Ellen Rudin's research centered on point-set topography. It was only until 1971 that Rudin was appointed as professor of Mathematics at the Uni- versity of Wisconsin. She served as the vice president of the American Mathe- matical Society from 1980-1981. Rudin was selected to be a Noether Lecturer in 1984, an award given annually to honor women who have made fundamental and sustained contributions to the mathematical sciences. She was an honorary member of the Hungarian Academy of Sciences in 1995 and became a member of the American Mathematical Society in 2012. Rudin was the firs to create a ZFC Dowker space. ZFC stands for Zermelo-Fraenkel set theory with the axiom of choice and it is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox, today it is the standard form of axiomatic set theory. In 3 topography Dowker space is a topological space that is T4 but not countably paracompact. With this contribution she disproved a conjecture of Dowker's that had stood, and helped drive topological research, for more than twenty years. She also proved the first Morita conjecture and a restricted version of the second. A Morita conjecture is a certain problem about normal spaces. Her last major contribution was a proof of Nikiel's conjecture. Rudin's Erdos num- ber is 1 and to be assigned an Erdos number you have to be a coauthor of a research paper with another person who has a finite Erdos number. Mary Ellen published two works: • (1975). Lectures on set theoretic topology (Rep. with corr. ed.). Provi- dence: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society. ISBN 082181673X. • (1984). Dowker spaces (in the Handbook of set-theoretic topology). Am- sterdam u.a. North-Holland. pp. 761-780. ISBN 0444865802. 4.