An integrated, quantitative introduction to the natural sciences

 

Note: This is not an official course website.  Rather the goal is to provide some informal sharing of what we have done in the first few times through the course.  Current students should find all of the relevant (and up-to-date!) material on Princeton’s blackboard.  Colleagues interested in making use of these materials should contact our course coordinator, Jennifer Brick, jbrick@princeton.edu. Last updated 14 October 2008.

 

 

Princeton’s integrated science course is an experiment in science education for undergraduates.  It is a collaboration among faculty from many departments, and is now in its fifth year.  The freshman course, which we describe here, is a double course that provides an alternative to the usual introductory courses in physics, chemistry and computer science. Rather than following the historical divisions of these subjects, we organize the course around the kinds of mathematical models that we use in describing Nature.   Thus, the fall semester begins with a discussion of dynamical models, starting with Netwonian mechanics but connecting to chemical kinetics, population growth, genetic networks, … .  We continue with probabilistic models, introducing the concepts of probability via genetics and then turning to statistical physics and chemical thermodynamics, tracing the concepts of entropy from Carnot to Boltzmann to Shannon and highlighting the fundamental role of these ideas in demonstrating the atomic character of matter.  The Spring semester takes up models in which the basic variables are fields—electromagnetism, but also fluid motion, diffusion, and waves more generally—aiming at an understanding of the diffraction and interference phenomena that are so central to visualization of the microscopic world and its molecular structure.  Finally, the threads of dynamics, fields and probability come together in an introduction to quantum mechanics and its implications for molecular structure, chemical bonding and reactivity.

 

Throughout the course we teach at a relatively high level of mathematical sophistication, as expected in honors physics courses.  We reach, wherever possible, toward examples that make contact with the phenomena of life, not least to emphasize that the intellectual style of the traditionally mathematical sciences knows no arbitrary borders.  Although many of us involved in the course have research interests at the interface of the physical and biological sciences, we view this as an introduction to science more generally, not just a training ground for students who share our particular interests; we also note that, in its mathematical level and outlook, this course is almost the opposite of a traditional “physics and chemistry for biologists” course.  We are pleased that students who pass through the freshman course have gone on to concentrate in many different disciplines:  chemistry, computer science, ecology and evolutionary biology, geosciences, molecular biology, physics, and various engineering fields; a few brave souls have even taken the course just to provide an integrated view of science, then going on to work outside the sciences.   While we reach toward biology, the freshman course takes no responsibility for transmitting the factual knowledge that comes with a real introduction to biology; a course for sophomores plays this role.

 

To make our task manageable, we assume that our students have a solid mastery of calculus, roughly at the level tested by the “BC” Advanced Placement exam.  Most students have had some exposure to physics and chemistry in high school, but little specific knowledge from those courses is assumed.  We try, as soon as possible, to go beyond the usual exactly solvable examples from the traditional introductory courses; students learn to approximate, and to use the computer to get answers when analytic methods fail.  We assume no prior experience in programming.  Most students seem to know (if only from popular television programs) that our genetic identity is coded in our DNA, and many know that much of the work of cells is done by proteins, so we try to use this common knowledge rather than revisiting in detail how these basic facts were established.

 

To get a more detailed sense of what we are doing, one can look at our plan for Fall 2008; this document also introduces the faculty involved in the course and gives a feeling for some of the more practical issues that we have encountered in our teaching thus far.  As indicated in the plan, the course involves lectures, laboratories, precepts and problem sessions, totaling nearly fourteen contact hours per week.  The labs deserve special mention, since they were constructed, from scratch, for the course, and have been widely acclaimed by the students; responsibility for the labs has been taken by the Lewis–Sigler Fellows, with modest assistance from the more senior faculty.    None of this would be possible without the support of the University and many departments, which have provided resources not only to staff the course but also to support our efforts in creating the course.

 

There is as yet no textbook for the course.  Lecture notes (including a wide selection of problems drawn from assignments and exams given in the previous versions of the course) are in varying states of refinement, and will be posted here as they reach some threshold of completeness; please check back regularly for updates.  We’re starting with the first segment of the course, on dynamical models. Again, current students should go blackboard.