#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

Fall 2018

**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, the
creation of the elements, and the evolution of the universe.

**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.

**RELATIVITY AND QUANTUM PHYSICS:** Relativity and quantum physics
underpins much of our modern understanding of the universe. The first
part of the course will present Einstein's special relativity,
including topics such as Galilean relativity, Einstein's postulates,
time dilation, length contraction, failure of simultaneity at a
distance, Lorentz transformations, space-time, four-vectors, the
relativistic Doppler effect, and mass-energy equivalence. A brief
interlude to general relativity covers the equivalence principle and
gravitational redshift. The second part begins with a historical
introduction to quantum physics, before moving on to topics such as
wave interference, the double-slit experiment, complementarity, the
Heisenberg uncertainty principle, Einstein and de Broglie relations,
Compton scattering, Bohr's atomic model, magnetic monopoles, particle
in a box, zero-point energy, quantum tunneling, and the Schrodinger
equation. The course culminates with a discussion of the Bohr-Einstein
debates and quantum entanglement. Students should have completed
pre-calculus.

**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.

**EXPERIMENTS IN PHYSICS:** This course will have a combination of
laboratory and theoretical work on the properties of electrons and
photons, electromagnetism, the interference and diffraction of waves,
the structure and dynamics of atoms, the radioactive decay of nuclei
and the properties of elementary particles. The laboratory experiments
will introduce students to key features of the fundamental particles
and forces in nature, and will include a visit to one or more research
laboratories on the Columbia campus.

**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.

**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 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.

**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.

**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 their structure confers their 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
structure. Students will be exposed to cutting-edge technologies such
as X-ray diffraction, cryo-electron microscopy, and nuclear magnetic
resonance used to determine protein structures at atomic
resolution. The course will also cover fundamental metabolic pathways
involving the break down of carbohydrates, lipids and fatty acids and
the crucial biological machines that carry out these
processes. Students will learn how perturbation in molecular processes
leads to complex pathologies, and understand how protein structures
can be used to design novel therapeutic compounds 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
innovative research concept and its potential applications.

**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.

**STEM CELL BIOLOGY AND ITS APPLICATIONS:** The course is an
introduction to the main concepts in stem cell biology as well as the
application of stem cells in experimental and clinical context. The
main focus will be on the basic biochemical and
physiological/pathophysiological mechanisms regulating stem cell
biology (neuroscience, lung, pancreas, liver/intestine,
cancer). Topics to be covered include: disease modeling, regeneration
(hands-on lab work) and legal and ethical issues related to stem cell
biology. The course will discuss the use of the most important
practical tools (e.g.: CRISPR-Cas9), methods (e.g.: organoids) and
experimental protocols needed to study and characterize stem
cells. Finally, the use of stem cell technologies will be presented in
novel medical therapies through coursework, scientific interactions,
and research.

**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.

**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 Poincare-Hopf theorem. We
will also see applications to modern physics, but no special knowledge
of mathematics or physics will be assumed.

**TOPICS IN ALGEBRA:** The aim of this course is to show the
beautiful interaction between topology, complex analysis, group theory
and the geometry of regular polyhedra. The course will start with the
basics of group theory, including groups of permutations, conjugacy
classes, Lagrange theorem and solvability. We will then move on to
complex analysis and discuss Riemann surfaces of algebraic functions -
surfaces where the multivalued functions naturally live. In this
interpretation, the Galois group has a clear meaning as the group of
permutations corresponding to loops on the surfaces - the monodromy
group. This will allow students to understand the theory of coverings
and the fundamental group. The course will culminate in an overview of
Abel's "impossibility theorem", which is the fundamental theorem of
the algebra of complex numbers.

**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.

**COMPUTER PROGRAMMING IN PYTHON:** Students will learn the basics
of programming using Python. 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.

**INTRODUCTION TO ALGORITHMS:** This course motivates algorithmic
thinking. The key learning objectives are the notions of run-time
analysis of algorithms, computational complexity, algorithmic
paradigms and data structures. Content will primarily be based on
high-school algebra and calculus. A tentative list of topics includes:
run-time analysis of algorithms, sorting, searching, hashing,
computational complexity and complexity classes, graph algorithms, and
dynamic programming.

**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.