#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

Spring 2016

**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.

**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, particularly CMOS technology. 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 (SEM, AFM among others), the cleanroom, and
low dimensional materials labs on the Columbia campus. The second part
of the course will include an introduction to quantum mechanics and
the physics of solids, as it relates to quantum information science
and technology, while maintaining the focus on the experimental and
practical aspects of the discipline.

**INTRODUCTION TO ELECTRICAL ENGINEERING - ANALOG AND DIGITAL
COMMUNICATION USING A MODIFIED LASER POINTER:** In this course,
students will learn the operating principles of, and build, an analog
free-space laser music transmitter/receiver using a laser pointer
modified to produce a variable output, driven by a phone or other
audio source. As part of this project, students will study some basic
electronics and learn how to use electronics test equipment. Students
will also learn how to program an Arduino microcontroller, then design
the code to have an Arduino accept digital data via USB from a laptop,
transmit it using the laser system, and receive and display the
data. A final stage of the project will involve reconfiguring the
system to send and receive data simultaneously, setting up a series of
relay stations to transmit data over long distances.

**SUSTAINABLE ENGINEERING:** This course will focus on a range of
technologies that are available today for addressing challenges
relating to climate change. Lectures will explore renewable energy
solutions and other (ancient and novel) technologies associated with
sustainable development. The course will cover a number of innovative
and interdisciplinary solutions that are being developed to address
site-specific and global issues. This will be an interactive course;
students will be encouraged to participate in creative and imaginative
projects that they will present to the class on the final day.

**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, the course will address some of 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.

**RADIATION: FRIEND AND FOE:** Radiation is in the air we breathe, the
food we eat, and the water we drink. Ionizing radiation in particular
is a double-edged sword that it is used to cure cancer but can also
cause cancer: how could that be? This is an interdisciplinary course
that encompasses physics, chemistry, and biology. Starting from the
physics of radiation absorption, students will learn how radiation
interacts with DNA, cells, tissues and organs. We will discuss some of
the clinical applications of radiation, such as cancer radiotherapy
and why radiation is a threat for the health of astronauts in
space. With hands-on activities, students will learn to evaluate the
environmental and human health risks of exposure to radiation due to
accidents, nuclear disasters, or terrorism.

**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.

**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.

**EXPLORATIONS IN DATA SCIENCE:** In this course, students will carry out
a series of explorations in data science to learn about statistical
thinking, principles and data analysis skills used in data
science. These explorations will cover topics including: descriptive
statistics, sampling and estimation, association, regression analysis,
etc. Classes will be organized to have a lecture component and a
hands-on exploration component each session. In the lecture session,
an introductory curriculum on data science will be given. In the
exploration session, students will be led through data analysis
exercises using the statistical analysis language R. These exercises
are designed to use open data, such as NYC open data that contain
interesting information about neighborhoods of New York City. No prior
programming experience is required.