Courses

COMAP is always looking for ways to encourage high school and college students to study mathematics and its applications. Those of us at COMAP also know that if we are to succeed, we must put good materials into the hands of students and faculty. The problem is compounded by the fact that many high school and college mathematics departments are small, with faculty who have little or no training in the applications of mathematics, and little time to create such courses, let alone to speak with authority on the vital role that mathematics plays at the cutting edge of science and technology. Little wonder then that many students miss a great opportunity at a career that embraces the mathematical sciences. The courses below are in a sequence of online courses dedicated to helping teachers and their students to see and embrace these opportunities. They are intended as course material for students in teacher training programs, as inspirational material for college teachers who may wish to develop parallel course work for their students, and as stand-alone course material for any college student who wants to take an online course to find out if the subject will excite an interest in a career. Notice our emphasis on the phrase stand-alone. Each course in the sequence will include core text, reading lists, problem sets, web links, projects, examinations, and appropriate software.

Bioinformatics

Biology undergraduates often spend an afternoon in a lab doing a DNA sequence. Molecular biologists have reconstructed the polio virus from materials commonly available from a biological supply house, while other are striving to find good measures of genetic distance between various genomes, and to trace the evolution of specific biomolecules. Still others, with the support of the pharmaceutical industry are using ligand field theory and molecular geometry to find small molecules that will “dock” on specific biosites, in the hope of finding treatments for a variety of diseases, many of which may be caused by irregularities in gene expression. There are even studies aimed at unlocking the feed back mechanism between our cellular DNA (inherited in equal parts from our parents) and our Mitochondrial DNA (inherited only from our mother), and regulating energy production in our cells. Every day, the list of discoveries, and the list of new questions increases. Such topics from DNA sequencing to genome interactions all owe their evolution to discovery of the double-helix geometry of genomes in the 1960s, that led, in turn, to the decoding of the small genomes, and finally the human genome around 2000. The storing, retrieval, and analysis of all this data is the concern of bioinformatics (aka computational molecular biology), which serves as the driving force for conjectures, and future discoveries in genetics, biomedicine, bionanotechnology, and host of other disciplines, some, as yet, unborn. The very words used in describing the content and question base of bioinformatics suggest a close connection between this discipline and biology, physics, computer science, and mathematics. In fact, the central paradigm of the discipline, inherited from biology, is that “form implies function,” a very geometric notion. Learn More