SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
FALL, 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, DISEASE, AND BEHAVIOR: 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.
Complex mental processes and behavior will also be discussed. Topics will
include: neurons and the nervous system, neuronal differentiation,
programmed cell death in neurons during development, apoptosis in general,
neurodegenerative diseases (such as mad cow disease and Alzheimer's
disease), sensory and motor systems, consciousness, learning, and
memory.
SURVEY OF MODERN PSYCHOLOGY: This course will provide an overview of
the scientific study of human behavior. Major areas of psychology
(cognitive, developmental, social, and abnormal psychology) will be
described, together with the history of psychology, the physiology of the
brain and nervous system, the methods used in research, and the statistical
interpretation of data. The course will also explore mental illness (mood,
anxiety, psychotic, and personality disorders) and therapeutic
interventions.
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.
FOSSIL FUELS AND GLOBAL CHANGE: In this course, students will develop
an understanding of the environmental challenges which fossil fuels pose for
our planet. Aspects of environmental problems will be addressed with
attention to the interplay among the atmosphere, biosphere, geosphere, and
hydrosphere. Underlying biological, chemical, and physical principles will
also be discussed. Topics will include: basic energy concepts; the genesis,
properties, and processing of fossil fuels; the biogeochemical carbon and
sulfur cycles; anthropogenic interference with these cycles; climate change,
global warming, and acid rain; engineering solutions to some environmental
problems.
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.
EXPLORING BLACK HOLES: This course will introduce students to
Einstein's theory of General Relativity by using one of nature's most exotic
objects, the black hole, as a guide. Consider the following questions: Can I
see a black hole? What does it feel like as I fall toward a black hole? What
happens to me once I have fallen into a black hole? How do particles and
light travel in the vicinity of a black hole? These and many other questions
will be answered by investigating the geometry of space-time, flat in
special relativity and curved in general relativity. Some background in
elementary calculus (differentiation and integration) is needed for this
course.
PARTICLE PHYSICS: For more than a century, physicists have probed the
inner workings of the atom in order to understand the fundamental
constituents of matter and the forces that act between them. These
explorations have resulted in the highly successful Standard Model of
Particle Physics. This course will present an overview of the Standard
Model, together with possible new physics at the high-energy frontier.
Topics will include: quarks and leptons, matter and antimatter, unification
of forces, the Higgs boson, supersymmetry, gravity, and extra space-time
dimensions. There will also be a brief discussion of special relativity,
quantum mechanics, and the role of symmetries in physics. Recent
observations, including evidence for dark matter and dark energy in the
universe, will also be explored.
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 AND ASTROPHYSICS: This course will trace our knowledge of
the universe from astronomy's ancient roots in naked-eye observations of the
sky to the twenty-first-century studies of extrasolar planetary systems,
black holes, and cosmology. Initial topics will include: Newton's laws of
motion and gravitation, orbits and space travel, and the properties of
planets' surfaces, interiors, and atmospheres. The course will then combine
atomic and nuclear physics with stellar and galactic astronomy to describe
stars, supernovae, black holes, the interstellar medium, galaxies, dark
matter and dark energy, the creation of the elements, and the evolution of
the universe.
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.
FIRST STEPS IN ALGEBRAIC TOPOLOGY: Algebraic topology is the study of
geometric objects (such as spheres, donuts, and Mobius strips) by means of
algebraic tools. For a taste of the questions that one can answer using
algebraic topology, consider the following: Why does every person's head
have a "bald spot"? Do there always exist two points on the surface of the
earth that are diametrically opposite each other and have exactly the same
temperature? The purpose of this course is to develop the mathematical tools
necessary to answer these types of innocuous but very deep questions. Topics
will include: groups, topological spaces, metrics, openness, homotopy, the
fundamental group, Brouwer's fixed point theorem, and covering
spaces.
GROUPS, SYMMETRIES, AND GAMES: The theory of groups plays a central
role in modern mathematics, with far-reaching applications in all of the
sciences. This course will begin by showing how groups arise in everyday
life: in the symmetries of geometric objects and in combinatorial games such
as Rubik's cube. The course will then move on to a more abstract point of
view and to general group theory. Applications to problems in number theory
and topology, including the solvability of polynomial equations and the
recently-proven Poincare Conjecture, 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.