SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
SPRING, 2013


EXPERIMENTS IN GENETICS AND MOLECULAR BACTERIOLOGY: 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, construction of genomic libraries, bacterial conjugation, and transposon mutagenesis. There will also be discussions of recombinant DNA technology and mechanisms of bacterial pathogenesis.

BIOCHEMICAL PATHWAYS OF CELL LIFE AND CELL DEATH: The cells in our body require energy to perform essential processes to stay alive. This course will provide an overview of the biochemical pathways through which the foods we consume (such as sugars, fats, and proteins) are converted into energy within cells. There will also be a detailed discussion of what happens when cells do not produce enough energy, a deficiency which leads to cell death. Every cell in our body has the ability to die in an orderly way; and this is important for human development, for the prevention of infections, as well as for many other biological processes. When cell death does not occur properly, diseases can result, such as cancer, diabetes, neurodegeneration, and immune disorders. We will investigate the causes, symptoms, and treatments of these diseases in relation to cellular energy production and cell death.

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.

SURVEY OF MODERN PSYCHOLOGY: This course will provide an overview of the scientific study of human behavior. Major areas of psychology (cognitive, developmental, social, and abnormal psychology) will be described, together with the history of psychology, the physiology of the brain and nervous system, the methods used in research, and the statistical interpretation of data. The course will also explore mental illness (mood, anxiety, psychotic, and personality disorders) and therapeutic interventions.

ORGANIC CHEMISTRY: Through lectures and laboratory experiments, this course will introduce students to the basic principles and exciting frontiers of organic chemistry. Topics will include: chemical bonds, structure, and reactivity; design and synthesis of organic molecules; and spectroscopic techniques for determining structure. There will also be background discussions of the physical and chemical laws which govern the behavior of molecular systems.

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.

INTERNATIONAL CONSERVATION - ECOLOGICAL SCIENCE, ECONOMICS, AND THE PUBLIC: In recent decades, conservation biology has emerged as a multidisciplinary science in response to increasing pressures on the world's ecosystems. Recently, concerns about issues such as climate change, habitat loss, and the wildlife trade have become particularly urgent. This course will investigate these concerns and will provide an overview of integrated approaches to maintaining biological diversity in a changing world. Students will critically examine current conservation issues through scientific, socioeconomic, and political lenses. Lectures will explore the drivers of biodiversity loss, the theoretical and mathematical models used in ecology, and the economic valuation of ecosystem services. The course will place these topics into the global context with case studies from around the world. There will also be interactive class discussions about environmental management, public policy, and conservation education.

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." Members of Columbia University's Nanoscale Science and Engineering Center 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.

ACCELERATOR SCIENCE - FROM THE BIG BANG TO X-RAY VISION: The course will begin with an introduction to particle accelerators, and the production of high-energy particles and electromagnetic radiation in both natural and artificial processes. The characteristics of electromagnetic radiation of differing wavelengths will be examined, with a particular focus on X-ray radiation produced in synchrotron accelerators. Synchrotron observations have revealed details of materials unseen with the naked eye, from archeological relics to Archimedes' writings to neuroscience to next generation technology. The rest of the semester will involve a journey through recent scientific breakthroughs enabled by synchrotron facilities. This will involve exploration of some of the most exciting developments in biology, physics, chemistry, and material science and will include demonstrations of their influence on everyday life.

RELATIVITY AND QUANTUM MECHANICS: This course will introduce students to the two main theoretical pillars of modern physics and recent attempts to unify them. 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, and black hole solutions. The second part of the course will present an overview of Quantum Mechanics: wave-particle duality, probability distributions, the Uncertainty Principle, and quantization.

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. These explorations have resulted in the highly successful Standard Model of Particle Physics. This course will present an overview of the Standard Model, 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 a Higgs-like particle, and evidence for dark matter in the universe, will also be explored.

QUANTUM STATES AND QUBITS: This course will introduce students to the fundamental principles of quantum mechanics using the linear algebra of vectors and matrices. In this approach, the quantum state of a particle is represented by a vector, and physical properties of the particle (such as energy or spin) are represented by matrices. The course will cover the following topics: linear algebra and vector spaces, eigenvalues and eigenvectors, the axioms of quantum mechanics, probability in quantum mechanics, Schrodinger's equation, observables as operators, interference, measurement and collapse of the state vector, spin and angular momentum, entanglement, non-locality of quantum mechanics and Bell's theorem, the no-cloning theorem, and quantum computers. No prior knowledge of linear algebra is required for this course.

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 culminate with a tour of a modern atomic, molecular, and optical physics lab.

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.

CALCULUS IN THE COMPLEX PLANE: This course will provide an introduction to the differential and integral calculus for functions of a complex variable. Some prior knowledge of elementary calculus will be helpful but is not required. The concepts of differentiation and integration will be introduced using the advanced perspective of the complex plane. Topics will include: complex numbers, analytic functions, singularities, Riemann sheets, Taylor and Laurent series, analytic continuation, directional derivatives, contour integrals, and the theory of residues. Applications in the physical sciences and engineering will also be explored.

CONJECTURES IN MODERN MATHEMATICS: The past hundred years have been marked by incredible mathematical breakthroughs including proofs of Fermat's Last Theorem, the Poincare conjecture and most recently a proposed proof of the extremely believable yet very difficult ABC conjecture. Today, conjectures such as the Birch and Swinnerton-Dyer Conjecture or the Riemann Hypothesis and many others have left wide open many exciting avenues of research. The course will underscore some of the major philosophies that permeate modern mathematics, to give a taste of some of the above conjectures that so many mathematicians think about.

NUMBER THEORY: Number theory is the study of the natural numbers, or integers. For example, one can ask which integers can be written as the sum of two squares. In this course, we will learn some math that can be used to solve this and related problems. In addition, we will study the necessary background to understand the RSA cryptosystem. These topics include: the Euclidean algorithm, modular arithmetic, the Chinese Remainder Theorem, and primality testing. Depending on time and interest, as small groups, students will investigate one or more additional topics such as quadratic reciprocity, Pell's equations, Fibonacci numbers and/or elliptic curves. The necessary background for the course is a good working knowledge of algebra. There will be an emphasis on both the theoretical and the computational aspects.

COMPUTER PROGRAMMING IN JAVA: Students will learn the basics of programming using Java in a UNIX environment. 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.