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.

Columbia University Science Honors Program.