#
SCIENCE HONORS PROGRAM

COURSE DESCRIPTIONS

Spring 2023

**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.

**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,
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.

**SCIENCE OF MATERIALS:** Almost every major technological
advancement has depended on a leap in our understanding of Materials
Science- we even name eras after their most important materials, from
the stone and bronze ages to our modern age of steel and silicon. We
will cover the main classes of materials (metals, ceramics,
polymers/plastics, and functional-electronic) by understanding their
structure at different length scales, from atomic bonds, to crystals,
to steel in skyscrapers and silicon in transistors. We will see how
the structure and defects in materials determine their properties, and
how physics and chemistry can be used to engineer the materials to
build the modern world, answering questions ranging from "Why are
rubies red?" to "How does tempered glass protect my phone?" Topics to
be covered include: atoms and bonding; crystals and defects;
mechanical, electronic, and optical properties; band theory and
electronic devices; graphene and 2D materials.

**CLASSICAL AND QUANTUM COMPUTING DEVICES:** This course will begin
with the principles of quantum mechanics, showing how entanglement and
superposition could usher in a new era of quantum information
devices. Students will be exposed to the math underlying quantum
physics, learn about the many platforms being used to build qubits in
research and industry, and have the opportunity to visit a quantum
optics lab at Columbia. The second part of the course will introduce
students to the theory and applications of modern CMOS (complementary
metal-oxide semiconductor) technology with an emphasis on devices for
classical and quantum information processing. Students will examine
the fabrication and implementation of conventional 3D semiconductor
devices as well as the "new-age" 2D Van der Waal (VdW) materials for
multi-layered heterostructure analysis. The course will also include
visits to see fabrication facilities and metrology/microscopy tools in
quantum materials labs on the Columbia campus.

**ORGANIC CHEMISTRY:** This course combines lectures, collaborative
discussions surrounding laboratory experiments and theory, and online
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. Research work conducted by graduate students will
introduce common techniques employed in organic chemistry and will
include: extraction, recrystallization, thin layer and column
chromatography, reflux, and distillation.

**BIOTECHNOLOGY AND BIOENGINEERING:** Biotechnology and
bioengineering have transformed the world around us for countless
fields, from medicine to agriculture. In this course, students will
learn the fundamentals of biology and biochemistry and how scientists
have taken these biological systems and engineered them to produce
life-saving insulin, drought-resistant crops, COVID-19 tests, and many
more topics. In each class we will learn about at least one
biotechnology breakthrough, how it works, and have discussions on the
greater impacts of these breakthroughs.

**CODE OF LIFE: EXPLORING COMPUTATIONAL BIOLOGY*:** Over the past
few decades, computer science has revolutionized our approach to
studying biology. In this course, we will embark on an exciting
journey into the world of bioinformatics. Through interactive
lectures, hands-on activities and case studies, students will gain a
deeper appreciation of how computational tools are used to decode the
complex biological processes that govern life on earth. The course
will begin with an introduction to DNA sequencing and its applications
in various fields, followed by a discussion of single-cell RNA
sequencing and its role in understanding cellular diversity. We will
then delve into cancer genomics and learn how to identify genetic
mutations and develop targeted therapies. Next, we will explore novel
machine learning approaches for predicting protein structure and
function. We will also discuss computational immunology and population
genetics, and their applications in personalized medicine. By the end
of the course, students will have a solid foundation in the principles
and applications of computational biology, and will be equipped with
the skills to pursue further studies in this rapidly evolving
field. Prior coding experience is useful but not
required. ***Students will need to be able to
bring a personal laptop for this course.**

**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.

**TISSUE ENGINEERING: AN INTRODUCTION TO THE WORLD OF REGENERATIVE
MEDICINE:** This course is designed to provide a comprehensive
overview of the field of tissue engineering, from the basics of cell
biology to the forefront of cutting-edge clinical developments. At the
start of the course, students will learn about the composition of the
extracellular matrix and its impact on how cells interact with their
environment. We will then move on to discuss the potential of tissue
engineering to address major medical issues and bridge the gap in
transplantation by growing tissues ex vivo. Later, students will
explore the various tissue engineering solutions that have been
approved for clinical use, as well as the organ-on-a-chip systems and
their implication for pharmaceutical development. At the conclusion of
the course, students will hold a strong grasp of core tissue
engineering principles, preparing them for research experiences and
advanced study.

**EXPLORING THE COMPLEX: AN INTRODUCTION TO COMPLEX ANALYSIS:**
This course will provide an introduction to the fascinating field of
complex analysis. Complex analysis is a branch of mathematics that
studies complex functions, which are functions that map complex
numbers to other complex numbers. In this course, we will explore the
properties and behavior of these functions, which can help us
understand and solve problems in many different fields. After
examining the basic properties of complex numbers, including complex
arithmetic, complex conjugation, and the geometry of the complex
plane, we will move on to more advanced topics, such as complex
differentiation and integration, the Cauchy-Riemann equations, and the
Cauchy integral theorem. One of the key concepts we will study in this
course is analyticity, which is the property that allows us to
differentiate complex functions. We will explore the relationship
between analytic functions and the geometry of the complex plane, and
see how analytic functions can be used to solve problems in physics,
engineering, and other fields. Other topics that we may cover include
complex power series, Laplace and Fourier transforms, and
singularities. We will also examine the application of complex
analysis to a variety of different problems, including fluid dynamics,
electrical engineering, and number theory. No special mathematical
background is required for this course.

**SPACES AND SYMMETRIES:** A large part of modern mathematics deals with
understanding spaces and their symmetries. This course will serve as
an introduction to the mathematical formulation of these ideas,
starting with spaces (geometry and topology): when are two spaces "the
same" and how can we tell when they are "intrinsically" different? In
order to answer this question, we will often look at the structures
arising from symmetry (group theory, algebraic topology). On the way,
we will explore the mathematics of knots, singularities, alternative
number systems, non-Euclidean geometries, and much more!

**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. ***Students will need to be able to
bring a personal laptop for this course.**

**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, basic sorting algorithms, quick sort,
binary sort, heap sort and hash table. If time permits, graph
algorithms and dynamic programming will be covered. Students will
need to be able to bring a personal laptop for this
course. ***Students will need to be able to
bring a personal laptop for this course.**

**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. ***Students
will need to be able to bring a personal laptop for this
course.**