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.