#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

FALL 2015

**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.

**DNA DYNAMICS:** Deoxyribonucleic acid or DNA is the underlying
genetic instructions for development, function, and reproduction of
all living organisms. Although its structure may seem simple, DNA is
elegantly designed to promote proper replication, repair, and
transcription. This course will emphasize the basic function of DNA in
development, disease, and aging, and will investigate both genetic and
epigenetic modifications that influence DNA function. This course will
incorporate in-class discussions and several hands-on activities in
order to facilitate student understanding. At the end of this course,
students should have a fundamental comprehension of DNA
structure/function, and its role in development and disease.

**VIROLOGY:** This course will provide an understanding of how viruses
work, using both historical and current examples. Students will learn
about different types of viruses that infect animals, plants and
bacteria, causing diseases from cold sores to hemorrhagic fevers. The
course will also cover vaccines, host-pathogen interactions and gene
therapy.

**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.

**THERAPEUTICS - FROM DISEASE TO DISCOVERY:** Therapy, a cornerstone of
modern clinical practice, is defined as an attempt to solve a health
problem. This course will explore the evolution and integration of
numerous therapeutic approaches from a well-grounded understanding of
human physiology, pathology, pharmacology, and basic biology. Each
class will be centered on a particular disease; discussion will weave
through a brief history of the disease, disease etiology and
pathology, history of treatment approaches, and development of modern
treatments. Emphasis will be placed on the interplay between
understanding of disease and understanding of treatment in the
development of novel therapies. Examples of disease topics to be
covered include: bacterial infection, cancer, diabetes, depression,
and Parkinson's disease.

**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 explores the chemical basis of the essential
life processes that occur within an organism. Students will learn the
structural and functional properties of biological macromolecules,
such as DNA, RNA and proteins, the molecular basis for how the body
metabolizes carbohydrates and fatty acids, and signal transduction
processes crucial to regulating homeostasis of cells. These concepts
will be applied to an understanding of how the malfunction of critical
biochemical processes can lead to human disease. The course will
introduce students to cutting edge biochemical research and students
will learn how scientists clone genes, purify proteins, and use
biophysical technologies to examine macromolecular complexes at atomic
resolution. Finally, students will learn how such research is applied
to the discovery of small molecule medicines. By the end of the
course, students will be asked to present their own ideas on a current
cutting-edge research concept and its potential applications.

**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.

**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.

**FABRICATION OF CLASSICAL AND QUANTUM COMPUTING DEVICES:** This
course will introduce students to various techniques used to create
micro-/nano-structures, with an emphasis on devices for classical and
quantum information processing. Starting with the pioneering ideas
presented by Richard Feynman in his paper "Plenty of room at the
bottom", students will learn how those visionary proposals have
developed into a discipline undergoing an exponential growth and
extremely rapid innovation. The course will be highly interactive,
including short quizzes at the beginning and end of each class, and
visits to see examples of various metrology/microscopy tools (TEM,
STM, AFM), the cleanroom, and fabrication labs on the Columbia
campus. Basic notions of quantum physics and the physics of solids
will be taught on an as-needed basis, in order to maintain the focus
on the experimental and practical aspects of the discipline.

**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
geometry, Lorentz transformations, 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 and quantization. Lastly, we'll discuss some the cutting
edge research being done in theoretical physics today, much of which
centers on fully merging these two frameworks.

**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.

**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.

**KNOTS AND MANIFOLDS:** In mathematical language, a knot is an
embedding of a circle in 3-dimensional Euclidean space, and this
captures our intuitive idea of what a knot is in real life. The
central question of knot theory is to classify all knots: Can we come
up with a list of all possible knots? When presented with a knot, can
we tell which knot in our list it is? In the first part of this
course, we will develop some basic notions in knot theory, and also
learn about knot invariants, which are effective tools to tell
different knots apart. Knot theory belongs to a part of mathematics
called low-dimensional topology, in which we also study objects like
curves, surfaces and their generalizations to three and four
dimensions, called manifolds. In the second part of the course, we
will develop basic manifold theory. We will also discuss the
fascinating relationship between knots and 3-dimensional manifolds,
and the higher dimensional analog 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 ITS APPLICATIONS:** Group theory is the foundation of
modern abstract algebra. But where does it come from? Is it simply an
arcane field of study, or 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. 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.