Spring 2016

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.

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, particularly CMOS technology. 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 (SEM, 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.

INTRODUCTION TO ELECTRICAL ENGINEERING - ANALOG AND DIGITAL COMMUNICATION USING A MODIFIED LASER POINTER: In this course, students will learn the operating principles of, and build, an analog free-space laser music transmitter/receiver using a laser pointer modified to produce a variable output, driven by a phone or other audio source. As part of this project, students will study some basic electronics and learn how to use electronics test equipment. Students will also learn how to program an Arduino microcontroller, then design the code to have an Arduino accept digital data via USB from a laptop, transmit it using the laser system, and receive and display the data. A final stage of the project will involve reconfiguring the system to send and receive data simultaneously, setting up a series of relay stations to transmit data over long distances.

SUSTAINABLE ENGINEERING: This course will focus on a range of technologies that are available today for addressing challenges relating to climate change. Lectures will explore renewable energy solutions and other (ancient and novel) technologies associated with sustainable development. The course will cover a number of innovative and interdisciplinary solutions that are being developed to address site-specific and global issues. This will be an interactive course; students will be encouraged to participate in creative and imaginative projects that they will present to the class on the final day.

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, the course will address some of 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.

RADIATION: FRIEND AND FOE: Radiation is in the air we breathe, the food we eat, and the water we drink. Ionizing radiation in particular is a double-edged sword that it is used to cure cancer but can also cause cancer: how could that be? This is an interdisciplinary course that encompasses physics, chemistry, and biology. Starting from the physics of radiation absorption, students will learn how radiation interacts with DNA, cells, tissues and organs. We will discuss some of the clinical applications of radiation, such as cancer radiotherapy and why radiation is a threat for the health of astronauts in space. With hands-on activities, students will learn to evaluate the environmental and human health risks of exposure to radiation due to accidents, nuclear disasters, or terrorism.

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.

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.

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.