#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

Spring 2022

**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 branch of physics that studies the
Universe on its largest scales and endeavors to understand its origin,
evolution, and fate. In this course, we will review the key
ingredients and the main observations that contributed to our current
understanding of the Universe. We will discover that modern cosmology
not only provides an explanation of how structures formed during
cosmic history, and evolve on large scales, but that it also answers
questions about how nature is organized at a fundamental level. Topics
to be explored include: the expansion of the Universe, the Big Bang
model, the cosmic microwave background, the large-scale structure of
the Universe, dark matter and dark energy.

**RELATIVITY AND QUANTUM PHYSICS:** Relativity and quantum physics
underpin 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, Compton scattering, the Einstein and de
Broglie relations, 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, the Bohr-Einstein debates, Bohr's atomic model,
magnetic monopoles, particle in a box, and zero-point energy. Advanced
topics include the two-state quantum system, quantum tunneling, and
the Schrodinger equation. Students should have completed
pre-calculus.

**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 (complementary metal-oxide semiconductor)
technology. While the course is usually highly interactive, in light
of the pandemic, in-person activities will be replaced with virtual
experiences including a visit to see examples of fabrication
facilities as well as various metrology/microscopy tools (such as an
atomic force microscope) in quantum materials labs on the Columbia
campus. Students will have the opportunity to participate in a
virtually guided tour and preparation of single atom-thick materials
as well as write basic programs to run on IBM's quantum circuit
interface. The course will conclude with introductory lectures on
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, virtual 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. Recordings of experiments and follow-up discussions
will introduce common techniques employed in organic chemistry and
will include: extraction, recrystallization, thin layer and column
chromatography, reflux, and distillation.

**BIOINFORMATICS:** The study of biology is changing rapidly thanks to the
advent of DNA sequencing technology. This technique produces so much
data that researchers must use tools from computer science,
statistics, and physics to make sense of it all, in a new field
broadly referred to as bioinformatics. In this course, we will explore
diverse topics in bioinformatics ranging from genome wide association
studies, to functional cancer genomics, to the human microbiome. Our
goal is to showcase how data science can be applied to real-world
problems across many areas of biology. Some coding experience will be
helpful but is not required.

**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 cancer and hemorrhagic
fevers. Classes will explore the molecular biology of viruses, their
replication cycles and the unique features that distinguish them from
all other forms of life. The course will also cover vaccines,
host-pathogen interactions and gene therapy. While highly interactive
and including group work, the course is primarily lecture-based.

**HUMAN PHYSIOLOGY:** This course provides 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.

**UNDERSTANDING EARTH'S CLIMATE SYSTEM AND CLIMATE CHANGE:** In this
course, students will explore the Earth's climate system. We will
learn about the physics of climate, how it affects life on Earth, and
how humans are changing it. We will discuss the models and tools used
by climate scientists and apply one of these methods on real climate
data. Toward the end of the course, we will read from an international
climate assessment and consider possible solutions.

**INTRODUCTION TO ABSTRACT MATHEMATICS THROUGH KNOTS:** This course is an
invitation to several areas of pure mathematics. The starting point
will be the notion of a mathematical knot, and why it is important to
mathematicians. Each week, we will use knots as an excuse to visit a
different field of math: topology, group theory, combinatorics, modern
geometry, graph theory, commutative algebra, complexity theory,
etc. You will also learn to use math software, such as SageMath and
SnapPy, to perform computations and manipulate knots. The only
requirement is an affinity for drawing diagrams.

**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. The course will cover real world applications
like PageRank (ranking web pages), Maps, hashing in cryptocurrency
etc.

**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.

**ECONOMICS AND COMPUTATION:** How do we cut a cake fairly? How should we
match kidney patients to kidney donors? We will be exploring a variety
of economic concepts from a computational lens. Tentative topics
include: game theory, auctions, fair division, matching, and social
choice. No familiarity with economics is required and no special
mathematical or computer science background is assumed although some
exposure to algorithms or proofs will be helpful.