The use of multinuclear NMR spectroscopy in the determination of the structures of inorganic molecules and the use of dynamic NMR spectroscopy (variable temperature NMR and magnetization transfer techniques) to provide information concerned with reaction mechanisms.
An introduction to central concepts in narrative theory: plot, archetype, myth, story vs. discourse, Freudian analysis, history and narrative, chronotype and personal narrative. These are explored in the context of sustained investigation of a particular plot device: the time loop. Examples come from Russian modernist fiction, Soviet and American science fiction, and film. We compare being stuck in a time loop with being lost in space - a theme found in personal narratives shared orally and online, as well as in literary fiction. Students develop a final paper topic on time loop narrative of their choice.
Prerequisites: (COMS W3134) or (COMS W3137) or (COMS W3136) and fluency in Java); or the instructor's permission. The fundamentals of database design and application development using databases: entity-relationship modeling, logical design of relational databases, relational data definition and manipulation languages, SQL, XML, query processing, physical database tuning, transaction processing, security. Programming projects are required.
In this course, we will take modern Chinese poetry as a crucible in which we can observe the interacting forces of literary history and social change. From diplomats who saw poetry as a medium for cultural translation between China and the world, to revolutionaries who enlisted poetry in the project of social transformation, we will examine the lives and works of some of China’s most prominent poets and ask, what can we learn about modern China from reading their poetry? In addition to poems, the course will include fiction, essays, photographs, and films by both Chinese and non-Chinese artists that place our poets in a broader context; topics of discussion include national identity, revolution, translation, gender, the body, ethnicity, and technology.
Aims to develop and harness the modeling, analytical, and managerial skills of engineering students and apply them to improve the operations of both service and manufacturing firms. Structured as a hands-on laboratory in which students "learn by doing" on real-world consulting projects (October to May). The student teams focus on identifying, modeling, and testing (and sometimes implementing) operational improvements and innovations with high potential to enhance the profitability and/or achieve sustainable competitive advantage for their sponsor companies. The course is targeted toward students planning careers in technical consulting (including operations consulting) and management consulting, or pursuing positions as business analysts in operations, logistics, supply chain and revenue management functions, positions in general management, and future entrepreneurs.
This introductory course covers human development across the lifespan. The course will provide an overview of development and the complexity of human growth through physical, cognitive, emotional, and social capacities. A review of historical and modern-day developmental theories as well as more complex interpersonal constructs, such as cultural variations, will be discussed. Special emphasis is placed upon examining the dynamic interplay between biology and environment with relevant application to nursing practice. The role of social and cultural stressors such as racism and socioeconomics in shaping human development will be examined. This undergraduate-level course will lay the foundation for further advanced study of human development within a nursing curriculum.
Prerequisites: CHEE 3010 and CHEN E3110 or the equivalent. Develops and applies non-equilibrium thermodynamics for modeling of transport phenomena in fluids and their mixtures. Continuum balances of mass, energy and momentum for pure fluids; non-equilibrium thermodynamic development of Newtons law of viscosity and Fouriers law; applications (conduction dominated energy transport, forced and free convection energy transport in fluids); balance laws for fluid mixtures; non-equilibrium thermodynamic development of Ficks law; applications (diffusion-reaction problems, analogy between energy and mass transport processes, transport in electrolyte solutions, sedimentation).
Prerequisites: CHEE 3010 and CHEN E3110 or the equivalent. Develops and applies non-equilibrium thermodynamics for modeling of transport phenomena in fluids and their mixtures. Continuum balances of mass, energy and momentum for pure fluids; non-equilibrium thermodynamic development of Newtons law of viscosity and Fouriers law; applications (conduction dominated energy transport, forced and free convection energy transport in fluids); balance laws for fluid mixtures; non-equilibrium thermodynamic development of Ficks law; applications (diffusion-reaction problems, analogy between energy and mass transport processes, transport in electrolyte solutions, sedimentation).
The principles and practice of building large-scale database management systems. Storage methods and indexing, query processing and optimization, materialized views, transaction processing and recovery, object-relational databases, parallel and distributed databases, performance considerations. Programming projects are required.
Advanced Business Chinese II is the continuation of Advanced Business Chinese I, both of which are designed to help Columbia students who have achieved the advanced level of proficiency in Chinese use the language to communicate effectively in professional contexts. Topics to be discussed include, but are not limited to, the concept of Face, Guanxi/Interpersonal obligations, Chinese modesty and humility, and Chinese style of negotiation and decision making.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157 or COMS W4118 or CSEE W4119) Design and implementation of large-scale distributed and cloud systems. Teaches abstractions, design and implementation techniques that enable the building of fast, scalable, fault-tolerant distributed systems. Topics include distributed communication models (e.g. sockets, remote procedure calls, distributed shared memory), distributed synchronization (clock synchronization, logical clocks, distributed mutex), distributed file systems, replication, consistency models, fault tolerance, distributed transactions, agreement and commitment, Paxos-based consensus, MapReduce infrastructures, scalable distributed databases. Combines concepts and algorithms with descriptions of real-world implementations at Google, Facebook, Yahoo, Microsoft, LinkedIn, etc.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3157 or COMS W4118 or CSEE W4119) Design and implementation of large-scale distributed and cloud systems. Teaches abstractions, design and implementation techniques that enable the building of fast, scalable, fault-tolerant distributed systems. Topics include distributed communication models (e.g. sockets, remote procedure calls, distributed shared memory), distributed synchronization (clock synchronization, logical clocks, distributed mutex), distributed file systems, replication, consistency models, fault tolerance, distributed transactions, agreement and commitment, Paxos-based consensus, MapReduce infrastructures, scalable distributed databases. Combines concepts and algorithms with descriptions of real-world implementations at Google, Facebook, Yahoo, Microsoft, LinkedIn, etc.
Stress and deformation formulation in two-and three-dimensional solids; viscoelastic and plastic material in one and two dimensions energy methods.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) and (COMS W3261) and (CSEE W3827) or equivalent, or the instructors permission. Modern programming languages and compiler design. Imperative, object-oriented, declarative, functional, and scripting languages. Language syntax, control structures, data types, procedures and parameters, binding, scope, run-time organization, and exception handling. Implementation of language translation tools including compilers and interpreters. Lexical, syntactic and semantic analysis; code generation; introduction to code optimization. Teams implement a language and its compiler.
Prerequisites: (CSEE W3827) and knowledge of C and programming tools as covered in COMS W3136, W3157, or W3101, or the instructors permission. Design and implementation of operating systems. Topics include process management, process synchronization and interprocess communication, memory management, virtual memory, interrupt handling, processor scheduling, device management, I/O, and file systems. Case study of the UNIX operating system. A programming project is required.
Prerequisites: Comfort with basic probability. Programming fluency in Python, C++, Java, or Ruby (please see section course page for specific language requirements). Introduction to computer networks and the technical foundations of the Internet, including applications, protocols, local area networks, algorithms for routing and congestion control, security, elementary performance evaluation. Several written and programming assignments required.
Prerequisites: LING UN3101 In light of the predicted loss of up to 90% of the world languages by the end of this century, it has become urgent that linguists take a more active role in documenting and conserving endangered languages. In this course, we will learn the essential skills and technology of language documentation through work with speakers of an endangered language.
An introduction to computer architecture and distributed systems with an emphasis on warehouse scale computing systems. Topics will include fundamental tradeoffs in computer systems, hardware and software techniques for exploiting instruction-level parallelism, data-level parallelism and task level parallelism, scheduling, caching, prefetching, network and memory architecture, latency and throughput optimizations, specialization, and an introduction to programming data center computers.
The course will trace the appearance of the avant-garde on the territory of the Russian Empire with a focus on Ukrainian art as compared to Russian. Examining the art aspiring not only to reflect but to alter the reality originating both in the center and the periphery, the class will explore the array of strategies employed by art for that end. The foundational theories of avant-garde, non-conformism, and dissident art will be studied alongside the most celebrated and influential examples of innovative and radical art from the region. Beginning with socially minded realist practices, the class will consider the impact of the collapse of the Russian and then Soviet Empires on art and reflect on how the societal upheavals affect the understanding of the function and the definition of art. The appearance of Socialist Realism and the versions of opposition to it will be studied, from dissident undermining to neglect and escapism of the second avant-gardes. Ukrainian art of recent decades will be studied in the context of several revolutions (Granite, Orange, Euromaidan) that defined its contemporary history. The class is offered for graduate and advanced undergraduate students. Knowledge of Russian or Ukrainian is not required.
This is an introduction to the interdisciplinary approaches of historical anthropology, in sources, methods and conceptualizations. Taking studies of differing Muslim societies by leading anthropologists as examples, we will examine the possibilities of this mode of inquiry. Students will give seminar presentations on the readings and complete a semester paper.
Prerequisites: the instructors permission. Introduction to the ecology and epidemiology of infectious diseases of humans and wildlife.
Introduction to the principles, methods and tools necessary to manage design and construction processes. Elements of planning, estimating, scheduling, bidding and contractual relationships. Valuation of project cash flows. Critical path method. Survey of construction procedures. Cost control and effectiveness. Field supervision.
Prerequisites: (CIEN E3125) equivalent, or the instructors permission. Introduction to the design of systems that support construction activities and operations. Determination of design loads during construction. Design of excavation support systems, earth retaining systems, temporary supports and underpinning, concrete formwork and shoring systems. Cranes and erection systems. Tunneling systems. Instrumentation and monitoring. Students prepare and present term projects.
A new approach to the classical problems of the sociology of knowledge - the social determination of knowledge and the social roles of those who create, possess, and distribute knowledge. This new approach rejects the current boundaries of inquiry and reunifies them as a network of practices straddling the boundaries of science and the professions.
Prerequisites: (CIEN E4129) or equivalent. Current methods of construction, cost-effective designs, maintenance, safe work environment. Design functions, constructability, site and environmental issues.
This seminar takes mental health and illness in socialist and postsocialist countries as objects of anthropological investigation. It explores the ways in which mental health care, diagnostics, suffering, and therapeutic systems are constituted by and constitutive of the post/socialist cultural, political, and socioeconomic contexts. Topics include critical approaches to psychiatric diagnostics; the development of the Soviet psychiatric complex, neuropharmaceuticals, and addiction treatment practice; the constitution and treatment of mental disabilities; institutional and communal mental healthcare; deinstitutionalization; experimental treatments; healing and injurious socioeconomic and political forces; social abandonment and death. Class readings will present a mixture of theoretical texts and ethnographic/historical material from post/socialist regions.
Core concepts of strategic planning, management and analysis within the construction industry. Industry analysis, strategic planning models and industry trends. Strategies for information technology, emerging markets and globalization. Case studies to demonstrate key concepts in real-world environments.
Capstone practicum where teams develop strategies and business plans for a new enterprise in the engineering and construction industry. Identification of attractive market segments and locations; development of an entry strategy; acquisition of financing, bonding and insurance; organizational design; plans for recruiting and retaining personnel; personnel compensation/incentives. Invited industry speakers. Priority given to graduate students in Construction Engineering and Management.
Prerequisites: (IEOR E4003) and (CIEN E4133) or IEOR E4003, CIEN E4133, or equivalent. Examination of the fundamentals of infrastructure planning and management, with a focus on the application of rational methods that support infrastructure decision-making. Institutional environment and issues. Decision-making under certainty and uncertainty. Capital budgeting and financing. Group decision processes. Elements of decision and finance theory. Priority given to graduate students in Construction Engineering and Management.
Prerequisites: (IEOR E2261) and (CIEN E3129) or instructors permission. Introduction to financial mechanics of public and private real-estate development and management. Working from perspectives of developers, investors and taxpayers, financing of several types of real estate and infrastructure projects are covered. Basics of real-estate accounting and finance, followed by in-depth studies of private, public, and public/private-partnership projects and their financial structures. Focused on U.S.-based financing, with some international practices introduced and explored. Financial risks and rewards, and pertinent capital markets and their financing roles. Impacts and incentives of various government programs, such as LEED certification and solar power tax credits. Case studies provide opportunity to compare U.S. practices to several international methods.
Prerequisites: (IEOR E2261) and (CIEN E3129) or instructors permission. Introduction to financial mechanics of public and private real-estate development and management. Working from perspectives of developers, investors and taxpayers, financing of several types of real estate and infrastructure projects are covered. Basics of real-estate accounting and finance, followed by in-depth studies of private, public, and public/private-partnership projects and their financial structures. Focused on U.S.-based financing, with some international practices introduced and explored. Financial risks and rewards, and pertinent capital markets and their financing roles. Impacts and incentives of various government programs, such as LEED certification and solar power tax credits. Case studies provide opportunity to compare U.S. practices to several international methods.
Delivery of infrastructure assets through Public-Private Partnerships (PPP). Value for Money analysis. Project organization. Infrastructure sector characterization. Risk analysis, allocation and mitigation. Monte Carlo methods and Real Options. Project finance and financing instruments. Case studies from transportation, water supply and energy sectors.
This course has multiple aims: to introduce students to the broad historiographical trends in the study of urban Africa, to acquaint students with some of the key issues and problems that have dominated studies of African cities, to examine key fulcrums of generational struggle in 20th century Africa, and to inspire deep thought and appreciation for the ways in which both theoretic questions and empirical methods impact our understanding of the past. This is a research seminar. Students will produce a research paper, focused in an African city, based on their original analysis of primary sources. We will explore the processes by which urban communities were built, and the various ways states and common people shaped the physical, material, social and cultural life of African cities. Gender and generation will be central foci in our analysis. Our readings will include both ‘classic texts’ and more recent scholarship on urban Africa. Our aims are to understand how the questions and concerns dominating urban studies have changed over time, as well as how scholars from various disciplines have utilized primary sources to approach the study of Africa’s urban past.
Prerequisites: elementary organic chemistry. Introduction to theory and practice of NMR spectroscopy. Instrumental aspects, basic NMR theory, NOE, and a survey of 2D methods are covered.
Israel has a unique and constantly-evolving national cinema, the product of its diverse immigrant population, influences from neighboring nations, and dramatic national history. Beginning with artistic influences from abroad and culminating with native self-examinations, this course will provide a survey of Israeli film history, recurring foci of Israeli cinema, and introductions to influential filmmakers from early director and impresario Menahem Golan to Orthodox writer/director Rama Burshtein. Each class meeting will include a complete screening of an Israeli feature film, as well as clips of related works. Readings will include critical essays and histories which elaborate on in-class screenings and cover additional topics and films. Written assignments will be three analytical essays which will encourage critical thinking, close analysis of films, and independent research beyond the materials presented in class. All readings are in English. All feature films and film clips are in Hebrew (some include Arabic), and will be presented with English subtitles. Students fluent in Hebrew and Arabic are encouraged to interpret the dialogue for additional meaning that may not be translated in the subtitles.
Focused on broadening knowledge of AEC data management. Use of industry data sets from the design, construction, and operations of buildings to learn and practice data management and solve problems by aggregating industry data and creating data-driven reports in dashboard format. Exploration of industry data through ELT (Extract, Load, Transform) Services. Hands-on learning experiences through a series of workshops and case studies. Guides where predictive analysis is performed and how it is used for Project Management Information System (PMIS) and Facility Management (FM), leading to Digital Twin data management, data processing, and data visualization.
This course will cover the science needed to understand hydrology, the link between hydrology and climate, and why climate change will affect the hydrologic cycle. It will then look at what changes have occurred in the past, and what changes are projected for the future and how these changes may affect other sectors, such as agriculture. The final module of the course will look at adaptation measures to adapt to climate change. The course will be formatted to be a mixture of lectures and seminars, with the lecture portion used to introduce scientific concepts and the seminar portion to discuss and evaluate the readings assigned. At the end of this course, students will the hydrologic cycle and its connection to climate, how changes in climate have affected/will affect how much water is available on land, how water impacts ecosystem services, and how to diagnose the cause of a climate-related water problem and develop solutions to address it.
Recommended for archaeology and physical anthropology students, pre-meds, and biology majors interested in the human skeletal system. Intensive study of human skeletal materials using anatomical and anthropological landmarks to assess sex, age, and ethnicity of bones. Other primate skeletal materials and fossil casts used for comparative study.
Introduction to modern tools in functional analysis that are used in the analysis of deterministic and stochastic partial differential equations and in the analysis of numerical methods: metric and normed spaces. Banach space of continuous functions, measurable spaces, the contraction mapping theorem, Banach and Hilbert spaces bounded linear operators on Hilbert spaces and their spectral decomposition, and time permitting distributions and Fourier transforms.
Covers the following topics: fundamentals of probability theory and statistical inference used in engineering and applied science; Probabilistic models, random variables, useful distributions, expectations, law of large numbers, central limit theorem; Statistical inference: pint and confidence interval estimation, hypothesis tests, linear regression. For IEOR graduate students.
Formal background in economics is not required. A review of the basic concepts and methods of urban economics, with a major emphasis on location and land-use economics. Examination of both equilibrium-based models and the new critical models derived from analyses of the production process and spatial organization.
Prerequisites: the instructors permission. This course covers various topics in Medieval Latin Literature.
Prerequisites: MATH GU4061 or MATH UN3007 A rigorous introduction to the concepts and methods of mathematical probability starting with basic notions and making use of combinatorial and analytic techniques. Generating functions. Convergence in probability and in distribution. Discrete probability spaces, recurrence and transience of random walks. Infinite models, proof of the law of large numbers and the central limit theorem. Markov chains.
Generation, composition, collection, transport, storage and disposal of solid and hazardous waste. Impact on the environment and public health. Government regulations. Recycling and resource recovery.
This course – the first of its kind at Columbia – introduces students to a vital subfield of ethics focusing on patent and regulatory law in the biotech and pharmaceutical sectors. The course combines lectures, structured debate, and research to best present this fascinating and nuanced subject. Properly exploring this branch of bioethics requires an in-depth understanding of biotech and pharmaceutical patent and regulatory law. Students can gain this understanding by first completing Biotechnology Law (BIOT GU4160), formerly the prerequisite for this course. Now, they can also gain it by reading the appropriate chapters of
Biotechnology Law: A Primer for Scientists
(the textbook for BIOT GU4160 published earlier this year) prior to each class. A number of students in the biotechnology fields (such as those in biotechnology, biomedical engineering, and bioethics programs) have shown a keen interest over the years in taking this course, yet were unable to do so because they hadn’t taken BIOT GU4160. Given the recent publication of
Biotechnology Law
and the desirability of making BIOT GU4161 accessible to more students having the appropriate science background, BIOT GU4160 has been removed as a prerequisite.
Fundamentals of water pollution and wastewater characteristics. Chemistry, microbiology, and reaction kinetics. Design of primary, secondary, and advanced treatment systems. Small community and residential systems.
This course will provide a real-time exposition of an emerging area of study that is at the interface between chemistry, physics, engineering, and biology to understand and control how electric fields can be used to catalyze chemical transformations. The course will be taught by a cross-disciplinary group of faculty and will contain the following components: (1) the theoretical underpinnings for catalysis in nanoscale electrical environments, (2) the experimental tools used to study these chemical transformations, (3) experimental demonstrations of catalysis in electric fields. For each of these three elements the course will draw on elements of organometallic/organic catalysis, quantum mechanics, enzymatic catalysis, and nanoelectronics to form the basis for understanding this new branch of catalytic science.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) Introduction to the theory and practice of computer user interface design, emphasizing the software design of graphical user interfaces. Topics include basic interaction devices and techniques, human factors, interaction styles, dialogue design, and software infrastructure. Design and programming projects are required.
Prerequisites: (COMS W3134 or COMS W3136 or COMS W3137) Introduction to the theory and practice of computer user interface design, emphasizing the software design of graphical user interfaces. Topics include basic interaction devices and techniques, human factors, interaction styles, dialogue design, and software infrastructure. Design and programming projects are required.
Prerequisites: (COMS W4160) or (COMS W4170) or the instructors permission. Design, development, and evaluation of 3D user interfaces. Interaction techniques and metaphors, from desktop to immersive. Selection and manipulation. Travel and navigation. Symbolic, menu, gestural, and multimodal interaction. Dialogue design. 3D software support. 3D interaction devices and displays. Virtual and augmented reality. Tangible user interfaces. Review of relevant 3D math.
Advanced security. Centralized, distributed, and cloud system security. Cryptographic protocol design choices. Hardware and software security techniques. Security testing and fuzzing. Blockchain. Human security issues. Note: May not earn credit for both W4182 and W4180 or W4187.
Prerequisites: LING UN3101 How discourse works; how language is used: oral vs. written modes of language; the structure of discourse; speech acts and speech genres; the expression of power; authenticity; and solidarity in discourse, dialogicity, pragmatics, and mimesis.
This course builds on core economics courses and addresses issues of environmental, resource and sustainable economics. It focuses on the interaction between markets and the environment; policy issues related to optimal extraction and pricing; property rights in industrial and developing countries and how they affect international trade in goods such as timber, wood pulp, and oil. An important goal of the class is to have students work in groups to apply economic concepts to current public policy issues having to do with urban environmental and earth systems. The use of the worlds water bodies and the atmosphere as economic inputs to production are also examined. The economics of renewable resources is described and sustainable economic development models are discussed and analyzed. Some time will also be devoted to international trade and regulation, and industrial organization issues. Students not only learn economic concepts, but they will also learn how to explain them to decision-makers. The instructor will tailor this course to the skill level of the students in order to most effectively suit the needs of the class.
Techniques of solution of partial differential equations. Separation of the variables. Orthogonality and characteristic functions, nonhomogeneous boundary value problems. Solutions in orthogonal curvilinear coordinate systems. Applications of Fourier integrals, Fourier and Laplace transforms. Problems from the fields of vibrations, heat conduction, electricity, fluid dynamics, and wave propagation are considered.
This taxon-based course provides students with a basic understanding of the diversity and natural history of the mammals. Broad coverage of mammalian biology includes: morphological adaptations, evolutionary history and biogeography.
Open to SEAS graduate and advanced undergraduate students, Business School, and GSAPP. Students from other schools may apply. Fast-paced introduction to human-centered design. Students learn the vocabulary of design methods, understanding of design process. Small group projects to create prototypes. Design of simple product, more complex systems of products and services, and design of business.
Prerequisites: BIOT W4200 (OK without prerequisite). This course will provide a practical definition of the current role of the Regulatory Professional in pharmaceutical development, approval and post-approval actions. This will be illustrated by exploration, and interactive discussion of regulatory history, its evolution, current standards, and associated processes. The course will seek to clarify the role of Regulatory in development and lifecycle opportunities, demonstrating the value Regulatory adds by participation on research, development and commercial teams. The course will utilize weekly case studies and guest lecturers to provide color to current topical events related to the areas.
Prerequisites: BIOT W4200 (OK without prerequisite). This course will provide a practical definition of the current role of the Regulatory Professional in pharmaceutical development, approval and post-approval actions. This will be illustrated by exploration, and interactive discussion of regulatory history, its evolution, current standards, and associated processes. The course will seek to clarify the role of Regulatory in development and lifecycle opportunities, demonstrating the value Regulatory adds by participation on research, development and commercial teams. The course will utilize weekly case studies and guest lecturers to provide color to current topical events related to the areas.
This course examines psychoanalytic movements that are viewed either as post-Freudian in theory or as emerging after Freuds time. The course begins by considering the ways Freuds cultural and historical surround, as well as the wartime diaspora of the European psychoanalytic community, shaped Freudian and post-Freudian thought. It then focuses on significant schools and theories of psychoanalysis that were developed from the mid 20th century to the present. Through readings of key texts and selected case studies, it explores theorists challenges to classical thought and technique, and their reconfigurations, modernizations, and total rejections of central Freudian ideas. The course concludes by looking at contemporary theorists moves to integrate notions of culture, concepts of trauma, and findings from neuroscience and attachment research into the psychoanalytic frame.
Review of laws of thermodynamics, thermodynamic variables and relations, free energies and equilibrium in thermodynamic system. Statistical thermodynamics. Unary, binary, and ternary phase diagrams, compounds and intermediate phases, solid solutions and Hume-Rothery rules, relationship between phase diagrams and metastability, defects in crystals. Thermodynamics of surfaces and interfaces, effect of particle size on phase equilibria, adsorption isotherms, grain boundaries, surface energy, electrochemistry.
Review of thermodynamics, irreversible thermodynamics, diffusion in crystals and noncrystalline materials, phase transformations via nucleation and growth, overall transformation analysis and time-temperature-transformation (TTT) diagrams, precipitation, grain growth, solidification, spinodal and order-disorder transformations, martensitic transformation.
Phenomenological theoretical understanding of electrons in crystalline materials. Both translational and point symmetry employed to block diagonalize the Schrödinger equation and compute observables related to electrons. Topics include nearly free electrons, tight-binding, electron-electron interactions, transport, magnetism, optical properties, topological insulators, spin-orbit coupling, and superconductivity. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials.
Phenomenological theoretical understanding of electrons in crystalline materials. Both translational and point symmetry employed to block diagonalize the Schrödinger equation and compute observables related to electrons. Topics include nearly free electrons, tight-binding, electron-electron interactions, transport, magnetism, optical properties, topological insulators, spin-orbit coupling, and superconductivity. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials.
Prerequisites: At least one semester, and preferably two, of calculus. An introductory course (STAT UN1201, preferably) is strongly recommended. A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov’s inequality.
Prerequisites: At least one semester, and preferably two, of calculus. An introductory course (STAT UN1201, preferably) is strongly recommended. A calculus-based introduction to probability theory. A quick review of multivariate calculus is provided. Topics covered include random variables, conditional probability, expectation, independence, Bayes’ rule, important distributions, joint distributions, moment generating functions, central limit theorem, laws of large numbers and Markov’s inequality.
Prerequisites: STAT GU4203. At least one semester of calculus is required; two or three semesters are strongly recommended. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.
Prerequisites: STAT GU4203. At least one semester of calculus is required; two or three semesters are strongly recommended. Calculus-based introduction to the theory of statistics. Useful distributions, law of large numbers and central limit theorem, point estimation, hypothesis testing, confidence intervals maximum likelihood, likelihood ratio tests, nonparametric procedures, theory of least squares and analysis of variance.
Prerequisites: STAT GU4204 or the equivalent, and a course in linear algebra. Theory and practice of regression analysis. Simple and multiple regression, testing, estimation, prediction, and confidence procedures, modeling, regression diagnostics and plots, polynomial regression, colinearity and confounding, model selection, geometry of least squares. Extensive use of the computer to analyse data.