SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
SPRING, 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.
BIOCHEMICAL PATHWAYS OF CELL LIFE AND CELL DEATH: The cells in our
body require energy to perform essential processes to stay alive. This
course will provide an overview of the biochemical pathways through which
the foods we consume (such as sugars, fats, and proteins) are converted
into energy within cells. There will also be a detailed discussion of what
happens when cells do not produce enough energy, a deficiency which leads
to cell death. Every cell in our body has the ability to die in an orderly
way; and this is important for human development, for the prevention of
infections, as well as for many other biological processes. When cell
death does not occur properly, diseases can result, such as cancer,
diabetes, neurodegeneration, and immune disorders. We will investigate the
causes, symptoms, and treatments of these diseases in relation to cellular
energy production and cell death.
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.
ACCELERATOR SCIENCE - FROM THE BIG BANG TO X-RAY VISION: The course
will begin with an introduction to particle accelerators, and the
production of high-energy particles and electromagnetic radiation in both
natural and artificial processes. The characteristics of electromagnetic
radiation of differing wavelengths will be examined, with a particular
focus on X-ray radiation produced in synchrotron accelerators. Synchrotron
observations have revealed details of materials unseen with the naked eye,
from archeological relics to Archimedes' writings to neuroscience to next
generation technology. The rest of the semester will involve a journey
through recent scientific breakthroughs enabled by synchrotron facilities.
This will involve exploration of some of the most exciting developments in
biology, physics, chemistry, and material science and will include
demonstrations of their influence on everyday life.
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. 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: 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.
QUANTUM STATES AND QUBITS: This course will introduce students to
the fundamental principles of quantum mechanics using the linear algebra
of vectors and matrices. In this approach, the quantum state of a particle
is represented by a vector, and physical properties of the particle (such
as energy or spin) are represented by matrices. The course will cover the
following topics: linear algebra and vector spaces, eigenvalues and
eigenvectors, the axioms of quantum mechanics, probability in quantum
mechanics, Schrodinger's equation, observables as operators, interference,
measurement and collapse of the state vector, spin and angular momentum,
entanglement, non-locality of quantum mechanics and Bell's theorem, the
no-cloning theorem, and quantum computers. No prior knowledge of linear
algebra is required for this course.
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 culminate with a tour of a modern
atomic, molecular, and optical physics lab.
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.
CALCULUS IN THE COMPLEX PLANE: This course will provide an
introduction to the differential and integral calculus for functions of a
complex variable. Some prior knowledge of elementary calculus will be
helpful but is not required. 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.
CONJECTURES IN MODERN MATHEMATICS: The past hundred years have been
marked by incredible mathematical breakthroughs including proofs of
Fermat's Last Theorem, the Poincare conjecture and most recently a
proposed proof of the extremely believable yet very difficult ABC
conjecture. Today, conjectures such as the Birch and Swinnerton-Dyer
Conjecture or the Riemann Hypothesis and many others have left wide open
many exciting avenues of research. The course will underscore some of the
major philosophies that permeate modern mathematics, to give a taste of
some of the above conjectures that so many mathematicians think
about.
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.