#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

Fall 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 recombinant DNA. Experiments
include: culturing bacteria, protein purification, DNA purification,
restriction digest, DNA amplification, construction of genomic
libraries, bacterial conjugation, and transposon mutagenesis as well
as other techniques that are used to investigate the structure,
function, and transmission of inheritable information in flies and
plants. There will also be discussions of recombinant DNA technology
and how to rigorously interpret and analyze results.

**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, 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.

**APPLIED NEUROSCIENCE:** This course provides an introduction to
basic computational methods for understanding how the brain
works. Students will have the chance to learn about experimental and
analytical tools used in the field. For instance, students will learn
how to code simple models of the brain and explore how scientists use
genetic tools and optical imaging to study the brain in detail. We
will illustrate the use of theoretical models in diseases such as
schizophrenia and epilepsy. In this way, we aim to show how theory is
applied to neuroscience. No prior knowledge of neuroscience or
programming is required for this course.

**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
different organisms, 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 (CryoEM), and nuclear magnetic resonance
(NMR) 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 novel
therapeutic compounds such as in the fields of metabolic engineering
and synthetic biology. 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.

**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.

**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 (STM, 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.

**SUSTAINABLE ENGINEERING:** This course will focus on a range of technologies that are available now to address our environmental issues. 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 applied for site-specific and global issues. This will be an interactive course; students will be encouraged to participate in creative 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.

**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, neutrino oscillations, and evidence for dark
matter in the universe, will also be explored.

**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.

**GEOMETRY AND TOPOLOGY:** This course will introduce the fields of
geometry and topology, which are used to study the "shapes" of
objects. We will discuss what "shape" means, and different notions of
whether two objects, say a sphere and a cube, have the same shape. One
main problem we will tackle is to find properties of objects that can
distinguish between objects of different shapes. For example, why is a
donut different from a sphere? Properties such as the Euler
characteristic, homotopy groups, and curvature allow us to answer
questions such as "Why is it impossible to fold a piece of paper over
a globe without crumpling it?" and to prove statements like "There
always exists some location on Earth with no wind." Other topics we
will explore include: non-Euclidean geometry, orientability, the
Gauss-Bonnet theorem, vector fields, and the Poincaré-Hopf theorem. We
will also see applications to modern physics, but no special knowledge
of mathematics or physics will be assumed.

**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 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.

**REPRESENTATION THEORY:** Representation theory is a branch of
modern mathematics that studies abstract algebraic structures by
viewing them as linear transformations of vector spaces (e.g we can
view a circle as rotations of a plane). Representation theory is one
of the most beautiful areas in mathematics, and has numerous
applications in physics and chemistry, as well as in other branches of
mathematics. This course will focus primarily on the representation
theory of finite groups and the classification of Lie
algebras. Instead of showing complete proofs, the class will work
together on many concrete examples. Those examples will finally enable
students to answer questions such as: What is a representation? What
is a Lie group/Lie algebra? What is an oscillator in mathematics? What
are hydrogen atoms in a mathematician's eyes?

**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.