Natural Sciences

The Dynamic Earth This course explores how the paradigm of plate tectonics organizes a study of the Earth. Earth scientists see the world as ever-changing, and we will adopt that outlook. Thus, we will put classical geology into the context of plate tectonics, and seek relationships between processes deep in the Earth, such as magnetic field generation and mantle convection, with surface manifestations such as earthquakes and volcanoes. The course is lab-based to give a feel for Earth processes and for how one makes inferences about the deep Earth. Topics include the age and composition of the Earth and solar system, minerals and rocks, plate tectonics, conduction and convection, seismology and the structure of the Earth, and magnetic field generation. This course satisfies the college science requirement.

Skepticism and the Scientific Method The course will teach general critical thinking skills: reading and writing argumentative essays, how to assess the reliability of information, and the uses and abuses of statistics. Special focus will be placed on the application of these skills to analyze issues in science, technology, and medicine. Topics will include case studies from the history of science (e.g., evolution and the Big Bang), as well as current events (e.g., the safety of nuclear power, genetically modified foods, etc). Prerequisite: Math 101 or equivalent. This course satisfies the science requirement.

Science Seminar: Global Climate Change This course examines the science behind what could be the most pressing issue affecting life on Earth. Topics include the heat budget (the balance of incoming and outgoing radiation) of the Earth, the greenhouse effect, past climate change, climate modeling, the carbon cycle, and the impact of global climate change on human society and the biological world. Students will actively engage in scientific investigation, including collecting and analyzing data, and hypothesis forming and testing. They will also use mathematics and mathematical modeling, which will be introduced as needed. The course satisfies the science requirement, and is designed to be suitable for all students, regardless of previous science background. Lab required. Prerequisite: Placement into a credit-bearing mathematics course.

Data Analysis: Methods, Application, Examples Do you have a dataset you want to analyze thoroughly, methodically, and in a sophisticated and rigorous manner? No matter which of the life, social, and physical sciences this dataset or your interests represent (e.g., psychology, computer science, applied mathematics, earth sciences, economics, biology, ecology), this course will teach you how to perform those analyses. This course is an excellent preparation for most research projects, in particular a Senior Thesis, as well as the Columbia 3-2 program. The course addresses many of the most often applied methods of data analysis. Since the basic unit of analysis is a real, rectangular matrix of data, the first part of the class will simultaneously introduce the problem of data reduction and preferred coordinate systems, and build the linearalgebraic tools needed to analyze such multi-dimensional datasets. We will first introduce diagonalization of square matrices as a generalization of the real numbers, and discuss the stability of diagonalization under perturbations and uncertainty. We will next introduce square covariance matrices, and discuss their structure, meaning, and limits of determination. We will then combine both parts by bringing to bear the analysis methods developed earlier on the analysis of square covariance matrices. Rectangular cross-covariance matrices of several datasets, and their decomposition, will be introduced, derived, and discussed next. This will naturally lead to some basics of filtering and truncation. Reconstruction methods and their limitations will conclude the course. Prerequisites: Calculus I or Introduction to Statistics. Because this course will be as self-contained as realistically possible, linear algebra is not required.

Introduction to Paleontology This course investigates the nature of fossil organisms and the information we can gain from them. Discussions center on interpretations of the fossil record and hypotheses about the history of life. Field trips are required. Some will be relatively long. This course is open to all students and satisfies the sciences requirement.

Research Methods This course prepares students for research in the natural sciences and helps prepare them for Senior Thesis work. Topics covered include the nature of scientific methods and the philosophy of science, parametric and non-parametric statistics, and the review and critique of current scientific literature. The course is required for natural science majors and is strongly recommended for environmental studies majors.

Natural Science Tutorial Under these course numbers, juniors and seniors design tutorials to meet their particular interests and programmatic needs. A student should see the prospective tutor to define an area of mutual interest to pursue either individually or in a small group. A student may register for no more than one tutorial in any semester.