#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

FALL, 2014

**EXPERIMENTS IN GENETICS AND MOLECULAR BIOLOGY:** 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,
DNA amplification, 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.

**BIOCHEMISTRY:** This course will provide a foundation for
understanding the chemical basis of biological processes. The course will
explore how molecules such as DNA, RNA, and proteins are made, and how
carbohydrates, lipids, and fatty acids are metabolized in the human body,
with a focus primarily on protein structure and function. Students will
learn how biochemists clone out a selected gene from the entire genome of
any organism, mass-produce protein from the gene, and purify it in order
to study its biochemical properties and determine its three-dimensional
structure. Students will also be exposed to cutting-edge technology such
as X-ray diffraction, cryo-electron microscopy, and nuclear magnetic
resonance to determine protein structures at atomic resolution. Some
crucial biological machines such as those that generate energy, metabolize
fatty acids, and make proteins will be examined. Finally, students will
learn how protein structures can be used to design modern drugs.

**ORGANIC CHEMISTRY:** This course combines lectures, laboratory
experiments, and demonstrations to provide an introduction to the
principles and exciting frontiers of organic chemistry. Students will be
introduced to the synthesis of organic compounds and the reaction
mechanisms. Lecture topics will include: chemical bonds, structural theory
and reactivity, design and synthesis of organic molecules, and
spectroscopic techniques (UV-Vis, IR, NMR) for structure determination.
Experiments will introduce common techniques employed in organic chemistry
and will include: extraction, recrystallization, thin layer and column
chromatography, reflux, and distillation.

**HISTORY OF THE EARTH:** This course traces the history of the Earth
from the origin of its constituents in the earliest moments of our
universe to the influences that have made it a habitable planet today.
Covering nearly fourteen billion years of cosmological history, from the
early formation of the elements to the beginning of the Solar System,
Earth accretion and chemical differentiation, topics will include: the Big
Bang, nucleosynthesis, radioactive decay, mass segregation, plate
tectonics, petrology, volcanism, and climate, among others.

**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.

**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." The
course 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: relativity
and quantum mechanics. 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, black holes, and cosmology. The second part of the
course will present an overview of quantum mechanics: wave functions,
probability distributions, the Uncertainty Principle, quantization,
entanglement, and the sum over histories picture.

**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 the Higgs 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.

**INFINITIES IN PHYSICS:** In physics, situations where one quantity is
much smaller than another are often encountered. For example, the size of
the Earth can be treated as infinitely large in many physical problems on
the Earth's surface, but conversely can be treated as infinitely small
when speaking about the motion of bodies in our Solar System. 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, and many others.
The basic ideas of calculus, such as the derivative and integral, will
emerge naturally from selected physics problems.

**KNOT THEORY:** Knot theory considers questions such as the following:
given a tangled loop of string, is it really knotted or can it, with
enough ingenuity and/or luck, be untangled without having to cut it? More
generally, given two tangled loops of string, when are they deformable
into each other? Is there an effective algorithm to make these
determinations? In mathematical language, a knot is an embedding of a
circle in 3-dimensional Euclidean space. A common method of describing a
knot is a planar diagram called a knot diagram. Any given knot can be
drawn in many different ways using a knot diagram. The course will also
discuss knot invariants, links, and higher dimensional generalizations of
knots.

**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 CRYPTOGRAPHY:** Group theory is the foundation of
modern abstract algebra. But where does it come from? Is it simply an
arcane field of study, or is it machinery applicable to a wide range of
real-world problems? To answer the first question, we do not need to go
too far. We have worked with groups, in a sense, since the dawn of
mathematics. As for its usefulness, group theory covers a vast range of
problems. Questions about the constructability of regular polygons, or
discovering general prescriptions like the quadratic formula to find the
roots of polynomials, were answered using group theory. Group theory has
also proven to be extremely useful in the field of cryptography, whether
giving us ways to secure our information or to break its defenses. The
course will explore these topics in depth, and include detailed examples
and problem solving.

**COMPUTER PROGRAMMING IN JAVA:** Students will learn the basics of
programming using Java. 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.