Academic Degrees
Professional Positions
Leadership Positions
(With the assistance of the President of the organization, I solicited speakers and session leaders, organized the program, and wrote the annual report. With the help of Jim Evans at UPS,I recruited John Heilbron, a noted historian of science at UC Berkeley, to speak on aspects of astronomy and time keeping in European cathedrals. I enjoyed a rare opportunity to use my Kiswahili when I introduced the speaker on "Scientific Concepts in the Early Swahili Culture".)
(I assisted the Progam Chairman in organizing the annual program. I conducted the annual business meeting.)
(During this year the department of Mathematics and Computer Science experimented with a joint administration of the two disciplines within the same department. I handled matters pertaining to mathematics. The following year we formed two separate departments.)
(I was one of 10 faculty nominated, campus-wide, that year.)
(This grant helped fund the mathematics computer classroom, the Apple Pi Room. The proposal focused on training future teachers in the appropriate use of technology in teaching mathematics.)
(Proposals for CCLI grants are reviewed by colleagues from around the country. Awards are based on intellectual merit, creativity, and potential for positive impact on scientific and technological understanding and on society. More information on these criteria can be found at: http://www.nsf.gov/pubs/1999/nsf99172/nsf99172.htm . The proposal itself and a great deal of background information regarding preparation for writing the grant can be found at: http://www.plu.edu/~dornerbc/Grant/GrantPage.htm)
(We recruit, train, and send PLU mathematics students into local schools to help local teachers train teams of their students to take part in the Washington State Math Olympiad. Our intent is to build a community centered on mathematics that stretches from PLU down to the Elementary Schools and includes students, parents, teachers, and school administrators. This year we will coach about 150 mathletes in 6 local schools in 3 school districts.)
Publications
(The article presents a new method for computing roots of any order (square roots, cube roots, fourth roots, etc.) and its growth out of mathematics that can be used for computing square roots developed in renaissance Europe, medieval India-Pakistan, as well as ancient Greece, Egypt, India-Pakistan, and Iraq.)
(The article provides classroom suggestions for combining numerical, algebraic, and geometric techniques to understand a simple method for computing square roots. The historical origins of the method illustrate the debt we owe to ancient minds living in what are now India, Pakistan, Iraq, and Egypt.)
(The article explains a method for computing the sine and cosine functions that can be understood by students who are in their first trigonometry course. The method is a new one that I discovered. Usually no method is taught until students encounter Taylor Series in second semester calculus.)
(The article describes geometric puzzles that lead to algebraic and combinatorial problems. Chris Meyer spoke about our solutions at Branko Grunbaum's Combinatorics/Geometry seminar at the University of Washington. Moshe Rosenfeld corresponded with Stan Wagon and Raphael Robinson about the results.)
(Describes the architecture of Floating Point System's AP-120B and the hardware/software parallel processing techniques employed by the machine as well as its use and performance in some specific simulations.)
(An exposition of parallel processing methods applied to algorithms of interest in the field of computer tomography. These algorithms compute 3-dimensional structures from their 2-dimensional projections.)
(Expository account of the mathematical techniques used in the [then recent] computer assisted proof of the four color theorem. Not refereed.)
Presentations Outside PLU
(This conference covers all aspects of using technology in teaching college mathematics. I presented my paper,The Magic Calculator and The Sine Addition Formula. See http://archives.math.utk.edu/ICTCM/EP-11.html.)
(I spoke in the Technical Challenges Session, on "Curriculum Questions for a Symbolic Algebra Age".)
(I was a panel member, speaking about the design and intent of the grant that established the Apple Pi Room.)
(I gave a series of three lectures (two identical) on a visit to India in January 1994. I spoke twice on the Mandlebrot Set, a topic from dynamical systems and chaos theory, and once on the movement to reform teaching of undergraduate mathematics in the United States.)
(The mathematical community was discussing whether the calculus course should be replaced by the discrete structures course as the common student entry point into college mathematics.)
Presentations Inside PLU
(PLU Mathematics Department Seminars are public events. Notices are sent to all schools in the area.)- "Mathematical Writing", PLU Writing Forum, several years.
(Kate Grieshaber annually organizes the Writing Forum. She recruits speakers from a wide variety of disciplines across campus as an opportunity for students in freshman inquiry seminars to see both the common and distinct features of writing in different subjects. I have demonstrated the unique features of mathematical writing most of the years the Forum has been offered.)- "Roots: Do all roads lead to (1/2)(x+N)? What lies beyond?", PLU Mathematics Department Seminar, November, 2003.
(I described several methods for computing square roots from ancient and medieval India/Pakistan and Iraq that all lead to the same sequence of approximations. I explained how I generalized a modern approach that also leads to this sequence and created a new method that computes cube, fourth, and all higher roots.)- "Mean Math, Lesser Known Aspects of the Geometric Mean", PLU Mathematics Department Seminar, February, 2002.
(I showed the relation between the geometric mean and an ancient method for computing square roots. In particular I showed that a diagram of Euclid's for constructing the geometric mean can be considered a refinement of a more ancient method for computing square roots in India.)- "Unified Algorithms", PLU Mathematics Department Seminar, September, 1999.
(I described my research extending my algorithm, the chordic algorithm, for computing sines and cosines to the computation of hyperbolic sines, hyperbolic cosines, exponential and logarithmic functions. I also gave a new, geometric interpretation of a well-known algorithm, the CORDIC algorithm, for doing these same computations. This interpretation showed clearly the relation between the chordic and the CORDIC algorithms. The chordic method uses chords in a circle while the CORDIC uses tangents.)- "The Magic Calculator and the Sine Addition Formula", PLU Mathematics Department Seminar, September, 1998.
(I gave a preliminary, but expanded, version of the talk that I later presented at the Eleventh Annual International Conference on Technology in Collegiate Mathematics. I described a new algorithm to compute arbitrary values of the sine and cosine functions suitable for use in a trigonometry class.)- "Active Learning Strategies in a J-term Course", PLU Workshop on the role of J-term in the Freshman Experience, 1997.
(I was invited to share some of the techniques I used to involve students in activities and group work in the Math 107 course I taught in J-term. This approach effectively used the freshman J-term experience to reinforce the intentions of the critical conversations course.)- "The Historical Setting of the Development of Trigonometry", PLU Mathematics Department Seminar, Fall 1995.
(I spoke on some topics I learned during my sabbatical.)- "T/L a Teaching, Learning Environment for the Calculus Class", PLU Mathematics Department Seminar, September 1990.
(I demonstrated computer modules I wrote for teaching calculus using the instructional application Calculus T/L.)- "Some Instructional Innovations and Experiments in Math 128", PLU Mathematics Department Seminar, March 1990.
- "The Birth of the Turing Machine", PLU Mathematics Department Seminar, 1986.
(I gave a series of four lectures on Alan Turing's seminal paper "On the Computable Numbers with an Application to the Entscheidungs Problem" in which he introduced the theoretical notion known as a Turing Machine. The Turing Machine is the conceptual foundation of what we now call a computer.)
Courses, Workshops
(This workshop presents cutting edge academic uses of the computer algebra system, Maple. See http://www.maplesoft.com/msw/ for more information.)
(We were updating the Apple Pi Room and the new computers would be using the new operating system OS X. Since OS X is based on UNIX, I wanted to learn that system. The course also included a brief introduction to PERL which I used when creating the online version of the mathematics placement system.)
(It had been several years since I had taught CS 144 and I wanted to learn JAVA.)
(The workshop provided hands on experience with activities from a sophomore course introducing students to the major in mathematics developed by the faculty at Mount Holyoke College in Massechuttes. Their book, Laboratories in Mathematical Experimentation describes the activities. I subsequently used their text when I taught Math 317, Introduction to proof. I translated some of their programs to run in Maple and used them in Math 245, Discrete Structures, as well.)
(Geometer's Sketchpad (GSP) is a computer application that allows one to create dynamic and animated constructions in Euclidean geometry. It is one of the finest uses of the computer as a tool that I have seen. In GSP, one guides and interacts with one's creation. I much prefer such uses over those where the computer acts as a machine that proceeds autonomously. I frequently use GSP to create demonstrations and instructional modules.)
(We discussed various forms of assessment in mathematics classes. We paid particular attention to the problem of assessing new approaches to teaching calculus and the difficulty of comparing new methods with traditional methods.)
(This project was organized by Washington Center for the Improvement of Undergraduate Education and sponsored by the National Science Foundation. Authors of leading calculus reform efforts led us in hands on experience using their textbooks and projects. The following year PLU adopted one of these and have used it, and subsequent editions, ever since.)
(This intensive workshop, sponsored by the National Science Foundation, gave participants hands on experience with two pieces of mathematical software: Maple and Calculus T/L. We explored effective ways to use such software in teaching mathematics. Maple is widely used in education and industry. I used T/L for several years, but it is now obsolete.)
(I took this workshop early in my career at PLU. It has had a strong influence on my teaching ever since.)
Collaborations
(We studied portions of Three-dimensional geometry and topology by William P. Thurston and investigated models of non-Euclidean geometry. Dr. Heath wrote and submitted a paper based largely on these discussions. He graciously aknowledged my contribution by including me as co-author of the paper.)
(We worked through portions of Coding and Information Theory, by Steven Roman and Introduction to the Theory of Error-Correcting Codes by Vera Pless.)
Seminars
(This seminar which ran over 20 years brought together mathematicians and physicists from PLU and UPS over questions of common interest at the dynamic frontiers of both subjects. Each year we chose a book or set of papers and took turns reading and/or leading discussion. Major topics included cosmology, catastrophe theory, dynamical systems, and chaos.)
(This seminar, organized by Jim Evans of UPS, had a similar format to the PLU-UPS joint seminar. We read John Sacrobosco's medieval astronomy text, in translation.)
Conferences Attended
(This national conference set the direction and tone for the calculus reform movement. The visions expressed here inspired and guided much of the work in following years. Several specific efforts to reform the teaching of calculus grew out of this conference.)
(This meeting brought together mathematicians from all over the world as well as North America. I renewed contact with Ajit Chalana, the head of the mathematics department at Delhi University in New Delhi, India. This contact led to my visit and lectures at her institution in 1994. Informal conversations with the representative from the National Science Foundation provided valuable input regarding strategies for the grant we were preparing for submission that fall.)
(This conference brings together educators concerned about teaching mathematics in the secondary school. Faculty from colleges and high schools throughout Oregon, Washington, British Columbia, Alaska, Idaho, and Montana attend.)
(This special symposium honored the 100th birthday of the idea of the quantum. Leading thinkers in the history of science and impacts of science on society, John Heilbron and Freeman Dyson, gave valuable historical perspectives.)
(This conference covers all aspects of using technology in teaching college mathematics. In addition, I met a colleague who had been at the Mount Holyoke workshop with me and had written a successful NSF CCLI proposal, similar to the one I was writing. She later sent me a copy. Our proposal benefitted from seeing a successful model.)
(This conference brings together faculty from colleges and universities across the state of Washington who teach future teachers of mathematics to discuss with teachers and state officials ways to best train and support teachers of mathematics in the state of Washington.)
Service to the University
(I regularly met with other members of the committee and archetects to discuss the design of the new building. I wrote up room descriptions and requirements and confered with colleagues in the department about room locations, furnishings, classroom desk organization, multimedia and equipment needs for each room, and a host of other considerations.)
(I created and demonstrated a prototype online version of the mathematics placement test. I organized meetings between representatives from Admissions, CATS, Mathematics, and Natural Sciences System Administration. Together we eliminated almost all mailings of paper exam booklets and manual processing of scantron forms.)
(I stepped into this role when computing was new to academics. In the early days it demanded a great deal of time to obtain the equipment and keep it current and functioning. I helped institutionalize the purchasing and maintenance of equipment for the mathematics department by working with CATS and the Business office on the current leasing program for the Apple Pi Room. I developed a good working relationship with Natural Sciences System Administrators and helped hire one of them.)
(I worked with the chair on issues relating to transfer students and course equivalencies. I advised transfer students and went to meetings for prospective students.)
(The committee investigated the feasibility of creating a joint degree in Mathematics and Computer Science.)
(I worked with Wanda Wentworth, head of Academic Assistance, to accomplish the transition of the mathematics department evening help session workers to their current position in Academic Assistance including running evening sessions in the Apple Pi Room.)
(This was the forerunner of the Governance Committee. We prepared slates of candidates, ran elections, and counted ballots. I was chair of the committee in academic year 89-90 and in that capacity also served on a specially convened Grievance Committee.)
(This committee was subsumed into the Instructional Resource Committee. I was chair of the committee in academic year 1982-1983. As chair I was also a representative on the TLC committee and the Computer Selection committee. The TLC committee was a University Committee, conceived in the dawn of the Information Age, that attempted to come to grips with the role of technology in a liberal arts environment. The Computer Selection committee picked the VAX system to replace the DEC computer PLU had outgrown.)
Service to the Profession
(By invitation of the National Science Foundation, I reviewed grant proposals in the same category as the one we received last year. The panel reviews are a major step in the decision process for funding new proposals.)
(Project TEACH [Teacher Education Alliance of Colleges and High Schools] seeks to identify, recruit and prepare future teachers of mathematics. Project Teach is centered at Green River Community College. The Advisory Board provided input and feedback during the planning stage of the program. The project is supported by NSF Grant: DUE-9876589.)
(I helped plan the program and schedule talks. I helped identify, recruit, and introduce presenters. I helped arrange refreshments, etc.)
Service to the Community
(We recruit, train, and send PLU mathematics students into local schools to help local teachers train teams of their students to take part in the Washington State Math Olympiad. Our intent is to build a community, enthusiastic about mathematics, that stretches from PLU down to the Elementary Schools and includes students, parents, teachers, and school administrators. This year we will coach about 150 mathletes in 6 local schools in 3 school districts.)
(The group began as a discussion group centered on the low success rate of Washington High School students in mathematics. The work of the group is supported by a GEAR UP grant. My contributions helped move the group from discussion to committed action. On May 20, 2004 the first annual "Math Day" was held that brought together students, teachers, and parents from elementary school through high school. The goal is to create a connected community focused on enthusiasm for mathematics. The "Math Day" will be an opportunity to exhibit and celebrate student work that illustrates common themes stretching from elementary school through high school.)
(Gary Peterson and I put on a daylong workshop for Upward Bound students who visited the campus. We designed a series of events and activities including a "Mathematical Scavenger Hunt". For example, we asked the students to find the distance "as the crow flies" between two points separated by a chasm; from the furthest pillar on the Music Building portico to a point in the building on the opposite side of the open air summer performance area. We had previously given them a hint that the Pythagorean Theorem would be useful for some items on the hunt.)
(I helped prepare the Annie Wright Middle School Math Counts teams and served as scoring room supervisor for the annual Pierce County competition.)
Other Professional Activities