FALL, 2014

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 molecular bacteriology. Experiments will include: culturing bacteria, protein purification, DNA purification, DNA amplification, construction of genomic libraries, bacterial conjugation, and transposon mutagenesis. There will also be discussions of recombinant DNA technology and mechanisms of bacterial pathogenesis.

GENETICS AND BIODIVERSITY CONSERVATION: This course combines lectures, computer labs, and group activities to provide an introduction to the cutting edge molecular techniques and genetic analyses that are being used to address key problems in biodiversity conservation. After a review of the basic principles of molecular genetics, evolutionary biology, and population genetics, students will be introduced to the wide range of methods used in conservation genetics including bioinformatics, forensics, and genomics. Emphasis will be placed on the practical application of genetic techniques to the development and support of national and international biodiversity policies and strategies.

HUMAN PHYSIOLOGY: This course will provide an introduction to the major systems of the human body, including the cardiovascular, respiratory, digestive, endocrine, immune, reproductive, excretory, skeletal, muscular, 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.

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 carbohydrates, lipids, and fatty acids are metabolized in the human body, with a focus primarily on protein structure and 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 three-dimensional structure. Students will also be exposed to cutting-edge technology such as X-ray diffraction, cryo-electron microscopy, and nuclear magnetic resonance to determine protein structures at atomic resolution. Some crucial biological machines such as those that generate energy, metabolize fatty acids, and make proteins will be examined. Finally, students will learn how protein structures can be used to design modern drugs.

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.

HISTORY OF THE EARTH: This course traces the history of the Earth from the origin of its constituents in the earliest moments of our universe to the influences that have made it a habitable planet today. Covering nearly fourteen billion years of cosmological history, from the early formation of the elements to the beginning of the Solar System, Earth accretion and chemical differentiation, topics will include: the Big Bang, nucleosynthesis, radioactive decay, mass segregation, plate tectonics, petrology, volcanism, and climate, among others.

ENERGY USE IN A MODERN ECONOMY: In this course, students will develop an understanding of the fundamental and pervasive role that useful forms of energy play in a modern society. Environmental concerns associated with the use of different forms of primary energy, fossil fuels in particular, will be addressed; and possible mitigation and replacement technologies will be presented in a framework of engineering as well as economics. Underlying biological, chemical, and physical principles will also be discussed. Topics will include: basic energy concepts; thermodynamics; the genesis, properties, and processing of fossil fuels; the biogeochemical carbon cycle; alternative energy sources; elements of basic finance and industrial engineering.

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.

RELATIVITY AND QUANTUM MECHANICS: This course will introduce students to the two main theoretical pillars of modern physics: relativity and quantum mechanics. The first part of the course will present Einstein's Special and General Theories of Relativity: time dilation, length contraction, the space-time continuum and its metric, Lorentz transformations, 4-vectors, relativistic energy-momentum, gravity as space-time curvature, black holes, and cosmology. The second part of the course will present an overview of quantum mechanics: wave functions, probability distributions, the Uncertainty Principle, quantization, entanglement, and the sum over histories picture.

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, and evidence for dark matter in the universe, will also be explored.

EXPERIMENTS IN MODERN PHYSICS: This course will have a combination of laboratory and theoretical work on the properties of electrons and photons, the interference and diffraction of waves, the structure and dynamics of atoms, the radioactive decay of nuclei, the properties of elementary particles, and the expansion of the universe. The laboratory experiments will introduce students to key features of quantum mechanics, relativity, and cosmology, and will include a visit to one or more research laboratories on the Columbia campus.

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.

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, dark matter and dark energy, the creation of the elements, and the evolution of the universe.

MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES: This course will provide a survey of analytic techniques used at the forefront of mathematical and scientific research. The course will introduce students to topics in vector and integral calculus, complex analysis, linear algebra, Fourier analysis, Green's functions, nonlinear dynamics, chaos theory, and variational calculus. Students will develop an understanding of mathematical methods used to solve differential and integral equations occurring in the physical sciences. Depending on time and interest, theoretical models describing electrical conductors, ferromagnetism, electromagnetic radiation, population dynamics, biochemical switches, autocatalytic reactions, geomagnetic reversals, vibrations on a string, rocket propulsion, wave propagation in materials, laser thresholds, and viscous fluid dynamics will be compared against classroom demonstrations and numerical simulations. Some prior knowledge of elementary calculus will be helpful but not required.

INFINITIES IN PHYSICS: In physics, situations where one quantity is much smaller than another are often encountered. For example, the size of the Earth can be treated as infinitely large in many physical problems on the Earth's surface, but conversely can be treated as infinitely small when speaking about the motion of bodies in our Solar System. This course will consider the simplifications that are possible in such cases when the small quantity is infinitely small or the large quantity is infinitely large. Topics will include: Taylor series expansions, power series, motion down inclined planes, tidal forces, moments of inertia, and many others. The basic ideas of calculus, such as the derivative and integral, will emerge naturally from selected physics problems.

KNOT THEORY: Knot theory considers questions such as the following: given a tangled loop of string, is it really knotted or can it, with enough ingenuity and/or luck, be untangled without having to cut it? More generally, given two tangled loops of string, when are they deformable into each other? Is there an effective algorithm to make these determinations? In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space. A common method of describing a knot is a planar diagram called a knot diagram. Any given knot can be drawn in many different ways using a knot diagram. The course will also discuss knot invariants, links, and higher dimensional generalizations of knots.

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 and most beautiful 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.

GROUP THEORY AND CRYPTOGRAPHY: Group theory is the foundation of modern abstract algebra. But where does it come from? Is it simply an arcane field of study, or is it machinery applicable to a wide range of real-world problems? To answer the first question, we do not need to go too far. We have worked with groups, in a sense, since the dawn of mathematics. As for its usefulness, group theory covers a vast range of problems. Questions about the constructability of regular polygons, or discovering general prescriptions like the quadratic formula to find the roots of polynomials, were answered using group theory. Group theory has also proven to be extremely useful in the field of cryptography, whether giving us ways to secure our information or to break its defenses. The course will explore these topics in depth, and include detailed examples and problem solving.

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.

Columbia University Science Honors Program.