Alumni Newsletter: Spring '98

Mike Gage wins Goergen award for teaching

This fall, the first winners of the University of Rochester's Goergen Awards were announced. The award is for innovation and artistry in teaching and comes with a prize of $5000. Professor Mike Gage of the Mathematics Department was one of the winners.

Mike has a long history of innovative teaching at the University of Rochester. He is a constant source of new ideas about the curriculum and how to use computer technology in the classroom. He pioneered the use of the worldwide web at the University of Rochester. The Math Department's web site (http://www.math.rochester.edu), filled with useful and interesting information for students, was started by Mike.

Mike and Professor Arnie Pizer, also of the Math Department, created WeBWorK, a computer program for doing homework on the Internet. By doing their homework through WeBWorK students get an immediate response telling them that their answer is right or wrong. Because WeBWorK makes homework more fun and encourages students to work hard to get the right answer, it may become a widely used teaching device all over the nation.

Mike has done the delicate balancing act of making his courses emphasize fundamental concepts while encouraging more use of computer computation. In teaching the Honors Advanced Calculus course , Gage taught differential equations with a strong emphasis on nonlinear problems. He realized that the existence of computer programs for doing phase plane analysis makes it possible to successfully cover more advanced topics like nonlinear problems in the initial introduction to differential equations. The new emphasis on qualitative behavior is both more interesting, and in these days of symbolic differential equation solvers, more useful, than the traditional approach. His use of very easy to use and small programs such as X Functions and MathPad instead of the larger and more obtrusive Mathematica or Maple has been a success. It has contributed to maintaining the focus of the course on the subject matter of differential equations rather than getting distracted by the problem of mastering more complicated software. This approach benefits non-majors as well as majors since it emphasizes ideas rather than techniques. Mike has been an important member of the Meliora Mathematica Committee. The purpose of this committee is to revitalize the teaching of undergraduate mathematics at the University of Rochester. Its most important initiative has been the introduction of several experimental calculus sections which are called "Quest Calculus" and differ considerably from our usual calculus. Students in these sections do some of their homework in supervised teams and the problems they are expected to solve are much more nonroutine than the usual calculus problems. These problems emphasize original thought in the sense that the major challenge of the problems is to devise the method of solution and to connect the problems to the techniques of calculus.

Mike finds the time to be an innovator in both teaching and research. He does research in the field called differential geometry and is one of the acknowledged experts on the problem of how elastic curves or surfaces contract to their minimal shape. As the name implies, differential geometry is a way of using calculus techniques to study geometric problems, especially those problems which deal with curvature. It has applications in many areas of mathematics and physics. For example, Einstein's theory of curved space and time, known as general relativity, is founded upon the techniques of differential geometry.