ISC/CHM/COS/MOL/PHY 231, 232, 233, 234
An Integrated, Quantitative Introduction to the Natural Sciences
Lecture: Mon–Fri, 10:00–10:50 a.m.
Lab: Mon or Tues, 1:30–4:20 p.m.
Precept: Wed or Thurs, 1:30–4:20 p.m.
Problem Session (Class) Wed: 7:30-8:50 p.m.
This course presents an integrated, mathematically and computationally sophisticated introduction to physics and chemistry, drawing on examples from biological systems. It offers an alternative to the combination of PHY 105/106, CHM 201/202, COS 126, and MOL214/215. Students must enroll in ISC 231 and ISC 232 in the fall, and ISC 233 and ISC 234 in the spring.
Prerequisites: familiarity with calculus at the level of MAT 103/104 or Advanced Placement Calculus BC, and solid high school physics and chemistry courses.
Peter Andolfatto (Ecology and Evolutionary Biology and Lewis-Sigler Institute)
William Bialek (Physics and Lewis-Sigler Institute)
Carlos Brody (Molecular Biology and Neuroscience Institute)
Chase Broedersz (Lewis-Sigler Institute)
Pablo Debenedetti (Chemical and Biological Engineering)
Jennifer Gadd (Lewis-Sigler Institute)
Thomas Gregor (Physics and Lewis-Sigler Institute)
Andrew Leifer (Lewis-Sigler Institute)
Benjamin Machta (Lewis-Sigler Institute)
Robert Sedgewick (Computer Science)
Joshua Shaevitz (Physics and Lewis-Sigler Institute)
Stas Shvartsman (Chemical and Biological Engineering and Lewis-Sigler Institute)
Olga Troyanskaya (Computer Science and Lewis-Sigler Institute)
Eric Wieschaus (Molecular Biology and Lewis-Sigler Institute)
Ned Wingreen (Molecular Biology and Lewis-Sigler Institute)
Haw Yang (Chemistry)
This course provides an integrated, mathematically sophisticated introduction to the natural sciences. Rather than being organized around the historical progression of physics, chemistry and biology, our teaching is organized around the kinds of mathematical models that we use in describing and understanding the world around us. We hope to provide students with a unified and powerful approach to thinking about science, while at the same time exposing them to the richness and diversity of the different disciplines.
Fall of freshman year
The course begins with an overview of the different disciplines in the natural sciences (physics, chemistry, biology) and our strategy for providing a unified understanding of them. The rest of the semester is arranged around two major classes of quantitative models: dynamical and probabilistic (see below). The power of these models to describe key phenomena in physics, chemistry and biology will be taught. Through applying these models, students will learn both the most critical facts and fundamentals of these disciplines and the key unifying features that cut across them. In addition, students will dramatically expand their skills in solving quantitative problems.
A key tool in quantitative problem solving is the computer. For the first portion of the fall semester, students will attend the regular lectures of COS 126 in parallel with the Integrated Science lectures. The schedule is arranged such that COS 126 fits neatly into a portion of the allotted Integrated Science time. The computational background built over the first ~ six weeks of COS 126 will be used throughout the Integrated Science sequence, where the utility of computers for testing our mathematical description of the world (even when we cannot find exact solutions to the relevant equations) will be repeatedly emphasized. Additional lectures and problem sets introducing specific computer programming concepts of special utility to emerging scientists (with a focus on computational biology) will also permeate the entire freshman year, largely in the spring semester (see below).
Dynamical models. Classical mechanics provides the great historical example of using calculus to describe how things change in time; indeed this desire to understand dynamics was a major driving force in the invention of calculus. We will describe the fundamental mechanics of physics in a rigorous mathematical form, show how things you measure in the laboratory (e.g., the exponential approach to terminal velocity for a small object falling in a viscous fluid) emerge from Newton's equations, and then go on to show that the same equations describe chemical kinetics, the dynamics of electrical circuits and the growth of bacterial populations (which you will measure using an instrument that you construct yourself). These simple equations have far- reaching implications, allowing us to determine the age of the solar system from measurements of radioactive decay or the complexity of our DNA from time required for fragments to find one another in solution. The simple mechanical problem of a mass on a spring provides an introduction to the general questions of response and stability, which reappear as we think about the way cells regulate the expression of genes or the way neurons in our brain generate electrical signals. The power of conservation laws, which allow us to make global statements about the nature of many systems (be them planets or living cells) will be emphasized.
Probabilistic models. Freshman physics and chemistry each tackle the conceptually difficult problems of thermodynamics and the statistical description of heat. The underlying mathematical structure is probabilistic: what we see in the world are samples drawn at random out of a probability distribution, and the theory specifies the form of this distribution. Mendelian genetics is also a probabilistic model, and related ideas permeate modern approaches to the analysis of large data sets in computer science. Starting with genetics, we introduce the ideas of probability and proceed through a rigorous view of statistical mechanics as it applies to the gas laws, chemical equilibrium, etc. In the laboratory, you will do experiments that verify the fundamentally probabilistic nature of mutations and observe directly the phenomenon of Brownian motion, following Einstein's path to determine the size of molecules. Entropy will be traced from its origins in thermodynamics to its statistical interpretation up through its role in information theory and coding, highlighting the startling mathematical unity of these diverse fields. We will introduce the ideas of coarse-graining and approximation, explaining how the same formalism applies to ideal gases and to complex biological molecules. Some of these topics will spill over into the spring semester.
Spring of freshman year
The spring term of Integrated Sequence continues and expands upon the basic themes laid out in the Fall. Students will apply and refine their growing quantitative science and computational skills in three principal domains: computational biology, electric and magnetic fields and chemical bonding. In each case, connections will be made from the central topic to diverse areas of science that normally are taught separately but are intellectually closely aligned.
Computational biology. We will build upon COS 126 to teach the full scope of core computational skills required to function as a modern scientist. Students will write code to pull closely related gene sequences out of large databases, finding for themselves genes that are conserved between yeast and human cancers. They will also learn to analyze systems biology data; a homework problem might involve identifying patterns in the levels of thousands of proteins in a cell and thereby gaining understanding of the underlying biology.
Fields. The study of electricity and magnetism will be placed in the larger content of models where the basic variables vary not just in time but also in space. Students will learn about electric and magnetic fields and their unification in the form of light as an electromagnetic wave. This will lead into more extensive study of both waves and light, progressing to microscopy and diffraction, two of the most important experimental tools for the investigation of life. An understanding of fields will also be used to examine the motion of fluids and the diffusion of molecules. Students will learn how the fundamentals of diffusion influence our thinking about the rates of chemical reactions and the even emergence of spatial patterns during embryonic development. Thus, students will use concepts from basic physics not just to understand electric circuits (normal freshman science) but also to answer questions like, “How did the zebra get its stripes?” (freshman Integrated Science).
The quantum world. In the latter portion of the course, dynamics, fields and probability will all come together in the strange and wonderful world of quantum phenomena. We will discuss its foundations, give simple examples and outline how quantum mechanics predicts the structure of orbitals in atoms and chemical bonds in molecules. This lays the groundwork for a richer discussion of chemical bonding and reactivity and for understanding how the structures of complex molecules, such as those relevant for life, emerge from the basic rules. (Just wait for the sophomore year…)
Readings for the Fall Term will be based primarily on lecture notes, which will be available through Blackboard. Students will also need to follow readings from course COS126 for the first half of the fall semester.
SUGGESTED reading (Please see instructors for updates and complete reading list):
Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements, Taylor, John R., 1997, University Science Books, ISBN-9780935702750
Introduction to Programming in Java: An Interdisciplinary Approach, Sedgewick, Robert & Kevin Wayne, 2001, Addison-Wesley Longman, ISBN-9780321498052
Molecular Driving Forces. Statistical Thermodynamics in Biology, Chemistry, Physics, and Nanoscience, Ken A. Dill and Sarina Bromberg, 2nd edition, ISBN 978-0-8153-4430-8
Physics: Vol. 1, Halliday, David, et al., 2001, John Wiley & Sons, ISBN-9780471320579
Physics: Vol. 2, Halliday, David, et al., 2001, John Wiley & Sons, ISBN-9780471401940
**All textbooks will be on reserve at the Lewis Library**