SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
SPRING, 2009


EXPERIMENTS IN GENETICS AND MOLECULAR BACTERIOLOGY: By performing a sequence of experiments, students will be introduced to some of the fundamental principles and basic techniques of genetics and molecular bacteriology. Experiments will include: culturing bacteria, protein purification, DNA purification, construction of genomic libraries, bacterial conjugation, and transposon mutagenesis. There will also be discussions of recombinant DNA technology and mechanisms of bacterial pathogenesis.

THE CYTOSKELETON - DYNAMIC SCAFFOLDING OF THE CELL: This course will focus on the cytoskeleton, its importance in cellular activities, and its role in human diseases. The structure and function of the cytoskeleton will be presented with emphasis on cell migration, cell division, and intracellular transport. There will also be a discussion of the diseases that arise when there are defects in the major cytoskeletal networks: the actin-myosin network and cancer cell migration, the microtubule network and neurodegenerative diseases, and the intermediate filament network and rapid aging disorders.

HUMAN PHYSIOLOGY: This course will provide an introduction to the major systems of the human body, including the cardiovascular, respiratory, digestive, endocrine, immune, reproductive, excretory, skeletal, muscular, and nervous systems. Discussions will progress from general system structure to function on a cellular level. An overview of pathology and current research will also be presented.

NEUROBIOLOGY OF DEVELOPMENT AND DISEASE: This course will provide an introduction to the cellular and molecular mechanisms of how the brain is formed and how disorders can arise within the nervous system. The basic principles of nerve cell function and molecular biology will be reviewed prior to more in-depth discussions of neuronal differentiation and death. Special topics will include: stem cells and differentiation, programmed cell death in development and apoptosis in general, prions and mad cow disease, neurodegenerative diseases, and Alzheimer's disease.

MIND AND BRAIN: The primary goal of this course is to give students an understanding of current scientific views on how human beings think. Current and historical work in psychology, cognitive neuroscience, neuropsychology, psychiatry, and psychopharmacology will be used to illustrate the nature of human cognition as well as the way non-normative events in the brain disrupt or alter cognition. Topics will include: brain anatomy, visual perception, memory and learning, language, motor behavior, emotion, cognitive control, mirror neurons, neural classifiers and "mind reading," psychoactive drugs, and mental illness.

ORGANIC CHEMISTRY: Through lectures and laboratory experiments, this course will introduce students to the basic principles and exciting frontiers of organic chemistry. Topics will include: chemical bonds, structure, and reactivity; design and synthesis of organic molecules; and spectroscopic techniques for determining structure. There will also be background discussions of the physical and chemical laws which govern the behavior of molecular systems.

NANO - FROM SCIENCE TO TECHNOLOGY: Scientific discovery of new phenomena on the dimensional scale of nanometers is generating a revolution in technological development called "Nanotechnology." Members of Columbia University's Nanoscale Science and Engineering Center will present a basic description of these new scientific discoveries and will then explore some of the many resulting technological innovations. Topics to be covered will include: fundamental physics of electron confinement on the nanoscale, graphene, carbon nanotubes, nanoscale electronics, quantum dots, scanning probes, and self assembly. Examples will be given to illustrate the capabilities of nanotechnology to transform our society.

RELATIVITY, QUANTUM MECHANICS, AND STRING THEORY: This course will introduce students to the two main theoretical pillars of modern physics and recent attempts to unify them. The first part of the course will present Einstein's Special and General Theories of Relativity: time dilation, length contraction, the space-time continuum and its metric, Lorentz transformations, 4-vectors, relativistic energy-momentum, and gravity as space-time curvature. The second part of the course will present an overview of Quantum Mechanics: wave-particle duality, probability distributions, the Uncertainty Principle, and quantization. There will also be a discussion of String Theory, which addresses the difficulties encountered when applying quantum principles to Einstein's General Theory of Relativity.

PARTICLE PHYSICS - EXPLORING MATTER AND FORCES: For more than a century, physicists have been probing the inner workings of the atom and its nucleus in order to understand the fundamental constituents of matter and the forces which act between elementary particles. These explorations have resulted in the highly successful Standard Model of Particle Physics, which has been experimentally validated to unprecedented precision. This course will give an overview of the Standard Model and its possible extensions. Topics will include: matter and antimatter, quarks and leptons, relativity, quantum mechanics, the role of symmetries in physics, and the unification of forces.

EXPERIMENTS IN ATOMIC AND NUCLEAR PHYSICS: Through a combination of laboratory and theoretical work, this course will provide an introduction to the physics of the atom and its nucleus. Students will have the opportunity to perform a variety of experiments to investigate the properties of electrons and photons, the structure and dynamics of atoms, and the radioactive decay of nuclei.

MODERN COSMOLOGY: Cosmology is the study of the universe on its largest space-time scales and endeavors to understand the universe's origin, evolution, and fate. Starting from fundamental physical principles, this course will investigate the observations and theories relevant to modern-day cosmology. Topics to be explored will include: the special and general theories of relativity, the geometry and expansion of the universe, the Big Bang, the early universe, the cosmic microwave background, the large-scale structure of the cosmos, dark matter, dark energy, and the ultimate fate of the universe.

ASTRONOMY - THE SOLAR SYSTEM AND BEYOND: This course will present an overview of astronomy, progressing from the small scale of the earth and solar system to the large scale of the entire universe. Topics will include: motions of the celestial sphere, the earth-moon system, the sun, planets, comets, asteroids, Kepler's laws, Newton's laws of motion and gravitation, space travel, extrasolar planetary systems, stars, stellar evolution and nucleosynthesis, novae and supernovae, black holes, and galaxies.

CALCULUS IN THE COMPLEX PLANE: This course will provide an introduction to the differential and integral calculus for functions of a complex variable. No prior knowledge of calculus is needed, and the concepts of differentiation and integration will be introduced using the advanced perspective of the complex plane. Topics will include: complex numbers, analytic functions, singularities, Riemann sheets, Taylor and Laurent series, analytic continuation, directional derivatives, contour integrals, and the theory of residues. Applications in the physical sciences and engineering will also be explored.

GRAPH THEORY: This course will present some of the most famous problems in graph theory together with their many applications. The graphs to be studied are simply collections of vertices (points) with edges (lines) connecting some of the vertices. We will try to answer a variety of questions about different graphs. Which graphs can be drawn on a sheet of paper such that no edges cross? How many colors do we need to color the countries on a map such that two countries sharing a border get different colors? Why couldn't Euler take a walk around the city of Konigsberg and cross each of its seven bridges exactly once? How can we transport items from point A to point B and minimize the costs? Additional topics will include: bipartite graphs, interval graphs, perfect graphs, matchings, edge coloring, and the traveling salesman problem.

NUMBER THEORY: This course will give an overview of the algebraic theory of numbers from Euclid and Diophantus to Fermat and Gauss. Topics will include: prime numbers, factorization, rational and irrational numbers, Fibonacci numbers, modular arithmetic, primality testing, finite and infinite sums, Bernoulli numbers, the Riemann zeta function, p-adic numbers, Diophantine equations, and Fermat's Last Theorem. There will also be a discussion of several recently-solved problems as well as some open questions which are accessible to experiment and conjecture.

BRAIDS - AN INTRODUCTION TO TOPOLOGY AND GROUP THEORY: Braids and their close relatives, knots and links, have diverse applications in the sciences. For example: the F-ring of Saturn is braided; there are new codes in public key cryptography that are based upon braids; and pictures show that strands of DNA can be knotted. The mathematical theory that underlies braiding will be the focus of this course. A variety of examples and applications will also be discussed.

COMPUTER PROGRAMMING IN JAVA: Students will learn the basics of programming using Java in a UNIX environment. Topics will include: variables, operators, loops, conditionals, input/output, objects, classes, methods, basic graphics, client/server systems, and fundamental principles of computer science. Approximately half of the class time will be spent working on the computer to experiment with the topics covered. Some previous programming experience will be helpful but is not required.


Columbia University Science Honors Program.