Fall 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 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.

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, 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.

APPLIED NEUROSCIENCE: This course provides an introduction to basic computational methods for understanding how the brain works. Students will have the chance to learn about experimental and analytical tools used in the field. For instance, students will learn how to code simple models of the brain and explore how scientists use genetic tools and optical imaging to study the brain in detail. We will illustrate the use of theoretical models in diseases such as schizophrenia and epilepsy. In this way, we aim to show how theory is applied to neuroscience. No prior knowledge of neuroscience or programming is required for this course.

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 different organisms, 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 (CryoEM), and nuclear magnetic resonance (NMR) 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 novel therapeutic compounds such as 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 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.

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.

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 (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.

SUSTAINABLE ENGINEERING: This course will focus on a range of technologies that are available now to address our environmental issues. 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 applied for site-specific and global issues. This will be an interactive course; students will be encouraged to participate in creative 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.

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.

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.

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 Poincaré-Hopf theorem. We will also see applications to modern physics, but no special knowledge of mathematics or physics will be assumed.

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.

REPRESENTATION THEORY: Representation theory is a branch of modern mathematics that studies abstract algebraic structures by viewing them as linear transformations of vector spaces (e.g we can view a circle as rotations of a plane). Representation theory is one of the most beautiful areas in mathematics, and has numerous applications in physics and chemistry, as well as in other branches of mathematics. This course will focus primarily on the representation theory of finite groups and the classification of Lie algebras. Instead of showing complete proofs, the class will work together on many concrete examples. Those examples will finally enable students to answer questions such as: What is a representation? What is a Lie group/Lie algebra? What is an oscillator in mathematics? What are hydrogen atoms in a mathematician's eyes?

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.