FALL 2015

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.

DNA DYNAMICS: Deoxyribonucleic acid or DNA is the underlying genetic instructions for development, function, and reproduction of all living organisms. Although its structure may seem simple, DNA is elegantly designed to promote proper replication, repair, and transcription. This course will emphasize the basic function of DNA in development, disease, and aging, and will investigate both genetic and epigenetic modifications that influence DNA function. This course will incorporate in-class discussions and several hands-on activities in order to facilitate student understanding. At the end of this course, students should have a fundamental comprehension of DNA structure/function, and its role in development and disease.

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, 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.

THERAPEUTICS - FROM DISEASE TO DISCOVERY: Therapy, a cornerstone of modern clinical practice, is defined as an attempt to solve a health problem. This course will explore the evolution and integration of numerous therapeutic approaches from a well-grounded understanding of human physiology, pathology, pharmacology, and basic biology. Each class will be centered on a particular disease; discussion will weave through a brief history of the disease, disease etiology and pathology, history of treatment approaches, and development of modern treatments. Emphasis will be placed on the interplay between understanding of disease and understanding of treatment in the development of novel therapies. Examples of disease topics to be covered include: bacterial infection, cancer, diabetes, depression, and Parkinson's disease.

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 explores the chemical basis of the essential life processes that occur within an organism. Students will learn the structural and functional properties of biological macromolecules, such as DNA, RNA and proteins, the molecular basis for how the body metabolizes carbohydrates and fatty acids, and signal transduction processes crucial to regulating homeostasis of cells. These concepts will be applied to an understanding of how the malfunction of critical biochemical processes can lead to human disease. The course will introduce students to cutting edge biochemical research and students will learn how scientists clone genes, purify proteins, and use biophysical technologies to examine macromolecular complexes at atomic resolution. Finally, students will learn how such research is applied to the discovery of small molecule medicines. By the end of the course, students will be asked to present their own ideas on a current cutting-edge research concept and its potential applications.

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.

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.

FABRICATION OF 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. The course will be highly interactive, including short quizzes at the beginning and end of each class, and visits to see examples of various metrology/microscopy tools (TEM, STM, AFM), the cleanroom, and fabrication labs on the Columbia campus. Basic notions of quantum physics and the physics of solids will be taught on an as-needed basis, in order to maintain the focus on the experimental and practical aspects of the discipline.

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 geometry, Lorentz transformations, 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 and quantization. Lastly, we'll discuss some the cutting edge research being done in theoretical physics today, much of which centers on fully merging these two frameworks.

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.

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.

KNOTS AND MANIFOLDS: In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, and this captures our intuitive idea of what a knot is in real life. The central question of knot theory is to classify all knots: Can we come up with a list of all possible knots? When presented with a knot, can we tell which knot in our list it is? In the first part of this course, we will develop some basic notions in knot theory, and also learn about knot invariants, which are effective tools to tell different knots apart. Knot theory belongs to a part of mathematics called low-dimensional topology, in which we also study objects like curves, surfaces and their generalizations to three and four dimensions, called manifolds. In the second part of the course, we will develop basic manifold theory. We will also discuss the fascinating relationship between knots and 3-dimensional manifolds, and the higher dimensional analog 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 ITS APPLICATIONS: Group theory is the foundation of modern abstract algebra. But where does it come from? Is it simply an arcane field of study, or 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. 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.