SPRING, 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: This course focuses on several key fundamentals of eukaryotic molecular genetics. Starting with DNA replication and repair we will branch into other more specific fields, including gene targeting, cell cycle checkpoint control, cancer, and aging. Students will be encouraged to participate in class discussions and some hands-on demonstrations. At the end of the course the students should have a broad knowledge of the field of DNA replication, mutagenesis, and repair.

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.

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.

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.

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.

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.

RADIATION - FRIEND AND FOE: This course on radiological science will introduce the fundamental physics of radiation absorption and radiation biology, including radiation-induced DNA damage, radiation carcinogenesis, etc. Students will learn about some of the clinical applications of radiation, including radiotherapy of cancer, diagnostics and imaging, and the impact of radiation for space exploration. There will also be discussion of radiation accidents, and a detailed study of solar radiation and energy, covering topics such as photovoltaics, off-grid power systems, and solar cooking.

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 CURIOSITIES: This course takes a range of basic mathematical proof methods - such as parity, invariants, the method of painting, search for winning position, combinatorics - and brings them to life in the form of small problems. Students will be engaged in solving problems illustrating different ideas of abstract mathematics hidden in situations close to everyday life.

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.