SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
FALL, 2013
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
biology, with particular emphasis on 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.
GENETICS AND BIODIVERSITY CONSERVATION: This course combines
lectures, computer labs and group activities to provide an introduction to
the cutting edge molecular techniques and genetic analyses that are being
used to address key problems in biodiversity conservation. After a review
of the basic principles of molecular genetics, evolutionary biology, and
population genetics, students will be introduced to the wide range of
methods used in conservation genetics including bioinformatics, forensics,
and genomics. Emphasis will be placed on the practical application of
genetic techniques to the development and support of national and
international biodiversity policies and strategies.
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.
NEUROSCIENCE - EXPLORING THE BRAIN: This course will provide a
comprehensive overview of what we currently know about the brain and how
we study it. We will explore the organization, structure, and function of
this fascinating organ which enables us to sense, move, sleep, feel, and
think. Going from single molecules to cells, from cells to neural
circuits, and from networks to behavior; our journey will feature a
description of how we perceive, process, store, and retrieve information,
as well as how these processes are altered during disease states such as
Alzheimer's, Parkinson's, depression, addiction, schizophrenia, and
autism. Topics will include: anatomical and cellular organization of the
brain, electrical impulses and signaling in neurons, neurodevelopment,
sensory perception, movement, sleep, and higher cognitive functions such
as language, emotions, 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.
ENERGY USE IN A MODERN ECONOMY: In this course, students will
develop an understanding of the fundamental and pervasive role that useful
forms of energy play in a modern society. Environmental concerns
associated with the use of different forms of primary energy, fossil fuels
in particular, will be addressed; and possible mitigation and replacement
technologies will be presented in a framework of engineering as well as
economics. Underlying biological, chemical, and physical principles will
also be discussed. Topics will include: basic energy concepts;
thermodynamics; the genesis, properties, and processing of fossil fuels;
the biogeochemical carbon cycle; alternative energy sources; elements of
basic finance and industrial engineering.
INTERNATIONAL CONSERVATION - ECOLOGICAL SCIENCE, ECONOMICS, AND THE
PUBLIC: In recent decades, conservation biology has emerged as a
multidisciplinary science in response to increasing pressures on the
world's ecosystems. Recently, concerns about issues such as climate
change, habitat loss, and the wildlife trade have become particularly
urgent. This course will investigate these concerns and will provide an
overview of integrated approaches to maintaining biological diversity in a
changing world. Students will critically examine current conservation
issues through scientific, socioeconomic, and political lenses. Lectures
will explore the drivers of biodiversity loss, the theoretical and
mathematical models used in ecology, and the economic valuation of
ecosystem services. The course will place these topics into the global
context with case studies from around the world. There will also be
interactive class discussions about environmental management, public
policy, and conservation education.
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 AND QUANTUM MECHANICS: 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, gravity as
space-time curvature, and black hole solutions. The second part of the
course will present an overview of Quantum Mechanics: wave-particle
duality, probability distributions, the Uncertainty Principle, and
quantization.
PARTICLE PHYSICS - EXPLORING MATTER AND FORCES: 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. This course will present an overview of the Standard Model
of Particle Physics, together with possible new physics at the
high-energy frontier. Topics will include: high-energy particle
accelerators and detectors, quarks and leptons, matter and antimatter,
unification of forces, neutrinos, the Higgs boson and the LHC,
supersymmetry, and string theory. There will also be a brief discussion of
special relativity, quantum mechanics, and the role of symmetries in
physics. Recent observations, including the discovery of a Higgs-like
particle, and evidence for dark matter in the universe, will also be
explored.
EXPERIMENTS IN MODERN PHYSICS: This course will have a combination
of laboratory and theoretical work on the properties of electrons and
photons, the interference and diffraction of waves, the structure and
dynamics of atoms, the radioactive decay of nuclei, the properties of
elementary particles, and the expansion of the universe. The laboratory
experiments will introduce students to key features of quantum mechanics,
relativity, and cosmology, and will include a visit to one or more
research laboratories on the Columbia campus.
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.
MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES: This course will
provide a survey of analytic techniques used at the forefront of
mathematical and scientific research. The course will introduce students
to topics in vector and integral calculus, complex analysis, linear
algebra, Fourier analysis, Green's functions, nonlinear dynamics, chaos
theory, and variational calculus. Students will develop an understanding
of mathematical methods used to solve differential and integral equations
occurring in the physical sciences. Depending on time and interest,
theoretical models describing electrical conductors, ferromagnetism,
electromagnetic radiation, population dynamics, biochemical switches,
autocatalytic reactions, geomagnetic reversals, vibrations on a string,
rocket propulsion, wave propagation in materials, laser thresholds, and
viscous fluid dynamics will be compared against classroom demonstrations
and numerical simulations. Some prior knowledge of elementary calculus
will be helpful but not required.
STATISTICAL MECHANICS - AN INTRODUCTION TO QUANTUM MANY-BODY
THEORY: In this course, statistical mechanics is used to examine how
behavior at the single particle (or quantum) level generalizes to the
macroscopic (or many-body) world. The course will develop descriptions
based on probabilities, introduce and exploit calculus, and then discuss
applications in thermodynamics, quantum mechanics, astrophysics, condensed
matter physics and chemistry. If time, the rich phenomenology of phase
transitions will also be discussed.
INFINITIES AND INFINITESIMALS: In physics, situations where one
quantity is much smaller than another are often encountered. This course
will consider the simplifications that are possible in such cases when the
small quantity is infinitely small or the large quantity is infinitely
large. Topics will include Taylor series expansions, power series, motion
down inclined planes, tidal forces, moments of inertia. The basic ideas of
calculus, such as the derivative and integral, will emerge naturally from
selected physics problems.
GRAPH THEORY BY EXAMPLE: Graph theory is a new and exciting area of
discrete mathematics. For our purposes, a graph is just a number of points
together with lines or curves joining certain pairs of these points.
Though at first glance graphs may seem like simple objects to study, the
field of graph theory contains some of the deepest and most beautiful
mathematics of the last fifty years. Being an extremely visual field, many
problems in graph theory are easily stated, yet have complex solutions
with far reaching implications and applications. Problem solving, class
discussions, and student examples will guide exploration not only of the
mathematics of graph theory, but also illustrate how graph theory arises
in fields such as computer science, linguistics, chemistry, game theory,
and many others.
GROUP THEORY AND ITS APPLICATIONS: Group theory is the foundation
of abstract algebra. In this course, the notion of a group is introduced
and used to understand a wide variety of problems. Various real-life
scenarios in which groups arise will be discussed, such as the symmetries
of a physical object. Mathematicians use groups in almost every field of
their subject, physicists use them to describe quantum mechanical systems
and fundamental forces, and the security of information exchange also
relies on group theory.
NUMBER THEORY: Number theory is the study of the natural numbers,
or integers. For example, one can ask which integers can be written as the
sum of two squares. In this course, we will learn some math that can be
used to solve this and related problems. In addition, we will study the
necessary background to understand the RSA cryptosystem. These topics
include: the Euclidean algorithm, modular arithmetic, the Chinese
Remainder Theorem, and primality testing. Depending on time and interest,
as small groups, students will investigate one or more additional topics
such as quadratic reciprocity, Pell's equations, Fibonacci numbers and/or
elliptic curves. The necessary background for the course is a good working
knowledge of algebra. There will be an emphasis on both the theoretical
and the computational aspects.
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, 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.