SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
Fall 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.
RELATIVITY: 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.
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.
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. The course will include virtual
experiences including a visit to see fabrication facilities and
metrology/microscopy tools in quantum materials labs on the Columbia
campus. Students will have the opportunity to 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.
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.
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.
GRAPH THEORY BY EXAMPLE: Graph theory is a new and exciting area of
discrete mathematics. Simply put, a graph is just a collection of
points joined by certain pairs of these points, yet many real-world
problems (i.e. traffic flow, school admissions, scheduling) can be
formulated as such. Although many problems in graph theory can be
easily stated, these problems often have complex solutions with far
reaching implications and applications. Problem solving, class
discussions, and student examples will be the major proportion of this
course. Rigorous proofs will also be presented in the lecture. In
addition to exploring the mathematics of graph theory, we will also
see how graph theory arises in fields such as computer science,
chemistry, game theory, and many others.