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.

Columbia University Science Honors Program.