Generative AI (“GenAI") is reshaping the global economy and the future of work by revolutionizing problem-solving, optimizing complex systems, and enabling data-driven decision-making. Its profound impact spans across natural language understanding, image generation, and predictive analytics, marking a paradigm shift that necessitates a deep and rigorous understanding of its mathematical foundations. This course is designed to equip students with a comprehensive framework for exploring the mathematical principles underpinning GenAI. Emphasizing statistical modeling, optimization, and computational techniques, the curriculum provides the essential tools to develop and analyze cutting-edge generative models.
Throughout history, societies have discovered resources, designed and developed them into textiles,
tools and structures, and bartered and exchanged these goods based on their respective values.
Economies emerged, driven by each society’s needs and limited by the resources and technology
available to them. Over the last two centuries, global development accelerated due in large part to the
overextraction and use of finite resources, whether for energy or materials, and supported by vast
technological advancements. However, this economic model did not account for the long-term impacts of
the disposal or depletion of these finite resources and instead, carried on unreservedly in a “take-make’-
waste” manner, otherwise known as a linear economy. Despite a more profound understanding of our
planet’s available resources, the environmental impact of disposal and depletion, and the technological
advancements of the last several decades, the economic heritage of the last two centuries persists today;
which begs the question: what alternatives are there to a linear economy?
The premise of this course is that through systems-thinking, interdisciplinary solutions for an alternative
economic future are available to us. By looking at resources’ potential, we can shape alternative methods
of procurement, design, application, and create new market demands that aim to keep materials,
products and components in rotation at their highest utility and value. This elective course will delve into
both the theory of a circular economy - which would be a state of complete systemic regeneration and
restoration as well as an optimized use of resources and zero waste - and the practical applications
required in order to achieve this economic model. Achieving perfect circularity represents potentially
transformative systemic change and requires a fundamental re-think of many of our current economic
structures, systems and processes.
This is a full-semester elective course which is designed to create awareness among sustainability
leaders that those structures, systems and processes which exist today are not those which will carry us
(as rapidly as we need) into a more sustaining future. The class will be comprised of a series of lectures,
supported by readings and case-studies on business models, design thinking and materi
Market research is the way that companies identify, understand and develop the target market for their products. It is an important component of business strategy, and it draws on the research and analytics skills you have learned thus far in the program. Often market research consists of generating your own data, through quantitative and qualitative methodologies, in pursuit of the market research question.
This course is an elective that will expand on quantitative and qualitative methodologies that have been introduced previously, provide an introduction to other methodologies that are more specific to market research, and provide hands-on practice in defining a market research plan from start to finish. Students will also learn about particular types of market research studies and when and how they should be deployed. Students will generate and test their own research instruments. Through the use of case studies and simulations, students will learn how market research fits into an overarching marketing plan for a company.
This course is designed for students who have completed the Research Design and Strategy and Analytics core courses, and who are exploring how research fits into product marketing. You will leave this class understanding the essential aspects of market research, when and how they should be deployed, and the role you could play in small and large companies directing and executing on market research opportunities.
Gender and Communication in the Workplace offers professionals across sectors and industries the knowledge and skills needed to identify the social and linguistic practices enacted at work, and the opportunity to advance the interests of those who run up against barriers to advancement as a result of prejudice and stereotyping.
In recent years, data analytics and artificial intelligence (AI) have become essential to business intelligence and informed decision making. But to realize the impact of analytics and AI, effective visual communication of data insights via user interfaces (UI), such as web pages and app dashboards, is equally critical. Building effective UIs requires mastering the user experience (UX) design principles and certain front-end development technologies. Furthermore, the recent rise of multimodal Generative AI offers unprecedented opportunities for simplifying, automating, and scaling UX/UI development.
This course provides a comprehensive understanding of UX design principles and best practices for developing UIs while emphasizing ethical considerations and inclusivity. Students will learn to create intuitive and visually engaging websites and dashboards that leverage AI-generated insights, also considering data privacy, diversity, and accessibility. Key topics include the design, implementation, and evaluation of UIs, with hands-on experience in web development technologies like HTML, CSS, and JavaScript, as well as related cloud services. Students will apply state-of-the-art AI technologies to create intelligent and interactive UIs, all while critically assessing data sources and AI models for potential biases.
The course content comprises a blend of conceptual learning and practice assignments. Weekly lectures and reading materials will cover the fundamentals of data visualization and user experience designs. Students will put the gained knowledge into practice through individual design and coding assignments and a group term project.
The course will cover the fundamentals of Algorithmic Trading, the discipline that brings together computer software, and financial markets to open and close trades based on programmed code. The goal of the course is to help the students to get familiar with the different techniques and strategies used in algorithmic trading and to let them experiment with classical and new algorithms they will create.
During the course, the students will use a Trading Market Simulator: The Rotman Market Simulator – a platform which allows students to transact financial securities with each other on a real time basis. Using the simulator, the students will familiarize themselves with specific decision tasks associated with financial securities, market dynamics, and investment or risk management strategies and get ready for the Rotman Competition.
Students conduct research related to biotechnology under the sponsorship of a mentor within the University. The student and the mentor determine the nature and extent of this independent study. In some laboratories, the student may be assigned to work with a postdoctoral fellow, graduate student or a senior member of the laboratory, who is in turn supervised by the mentor. The mentor is responsible for mentoring and evaluating the students progress and performance. Credits received from this course may be used to fulfill the laboratory requirement for the degree. Instructor permission required. Web site: http://www.columbia.edu/cu/biology/courses/g4500-g4503/index.html
Students conduct research related to biotechnology under the sponsorship of a mentor within the University. The student and the mentor determine the nature and extent of this independent study. In some laboratories, the student may be assigned to work with a postdoctoral fellow, graduate student or a senior member of the laboratory, who is in turn supervised by the mentor. The mentor is responsible for mentoring and evaluating the students progress and performance. Credits received from this course may be used to fulfill the laboratory requirement for the degree. Instructor permission required. Web site: http://www.columbia.edu/cu/biology/courses/g4500-g4503/index.html
Intro to Moving Image: Video, Film & Art is an introductory class on the production and editing of digital video. Designed as an intensive hands-on production/post-production workshop, the apprehension of technical and aesthetic skills in shooting, sound and editing will be emphasized. Assignments are developed to allow students to deepen their familiarity with the language of the moving image medium. Over the course of the term, the class will explore the language and syntax of the moving image, including fiction, documentary and experimental approaches. Importance will be placed on the decision making behind the production of a work; why it was conceived of, shot, and edited in a certain way. Class time will be divided between technical workshops, viewing and discussing films and videos by independent producers/artists and discussing and critiquing students projects. Readings will be assigned on technical, aesthetic and theoretical issues. Only one section offered per semester. If the class is full, please visit http://arts.columbia.edu/undergraduate-visual-arts-program.
Students conduct research related to biotechnology under the sponsorship of a mentor outside the University within the New York City Metropolitan Area unless otherwise approved by the Program. The student and the mentor determine the nature and extent of this independent study. In some laboratories, the student may be assigned to work with a postdoctoral fellow, graduate student or a senior member of the laboratory, who is in turn supervised by the mentor. The mentor is responsible for mentoring and evaluating the students progress and performance. Credits received from this course may be used to fulfill the laboratory requirement for the degree. Instructor permission required. Web site: http://www.columbia.edu/cu/biology/courses/g4500-g4503/index.html
Students conduct research related to biotechnology under the sponsorship of a mentor outside the University within the New York City Metropolitan Area unless otherwise approved by the Program. The student and the mentor determine the nature and extent of this independent study. In some laboratories, the student may be assigned to work with a postdoctoral fellow, graduate student or a senior member of the laboratory, who is in turn supervised by the mentor. The mentor is responsible for mentoring and evaluating the students progress and performance. Credits received from this course may be used to fulfill the laboratory requirement for the degree. Instructor permission required. Web site: http://www.columbia.edu/cu/biology/courses/g4500-g4503/index.html
Examination of areas critical to an organization’s success from strategic, operational, financial, and insurance perspectives, and examines why many companies fail in spite of the vast knowledge of factors driving success. Several case studies examined in depth.
Prerequisites: all 6 MAFN core courses, at least 6 credits of approved electives, and the instructors permission. See the MAFN website for details. This course provides an opportunity for MAFN students to engage in off-campus internships for academic credit that counts towards the degree. Graded by letter grade. Students need to secure an internship and get it approved by the instructor.
This course equips students with essential mathematical foundations for understanding and working with artificial intelligence (AI) algorithms. After a brief introduction to the historical and social context that numbers arise in, students will learn about:
- Linear Algebra: Matrices, matrix-vector multiplication, linear models, change of basis, dimensionality, spectral decomposition, and principal component analysis (PCA).
- Calculus: Rates of change, derivatives, optimization techniques like gradient descent, with a brief touch upon linear approximation.
- Probability and Statistics: Mathematically deriving complex probability distributions out of simpler ones, mathematically deriving statistical testing methods
- Graph Theory: How graphs are used to find relationships between data as well as being a setting for AI-driven problem solving.
- Problem Solving and Algorithms: Applying mathematical concepts to find problem solutions.
Students will learn about search methods like uninformed search, informed search with the A* algorithm, and greedy algorithms.
- Computational Theory and Automata: Answering questions about what is computable, what is needed in order to compute something, and using this framework to state how much “information” is contained in a mathematical object.
By the end of this course, students will possess a strong mathematical toolkit to confidently tackle the complexities of modern AI algorithms.
This course examines post-financial crisis regulations including Basel III, Fundamental Review of the Trading Book (FRTB), Dodd-Frank Act, Supervision and Regulation Letter 11-7 (SR 11-7), and others. Case studies will explore the technical details of these new rules; and guest lectures from industry experts will bring the material to life. Areas of focus include: model risk management, stress testing, derivatives, and insurance. By the end of this course students will be able to:
Evaluate the purpose and limitations of risk regulations in finance.
Identify and communicate weaknesses in a financial firm.
Communicate with regulators.
Understand Recovery and Resolution Plans or “Living Wills” for a financial firm.
This course helps the students understand the job search process and develop the professional skills necessary for career advancement. The students will not only learn the best practices in all aspects of job-seeking but will also have a chance to practice their skills. Each class will be divided into two parts: a lecture and a workshop.
In addition, the students will get support from Teaching Assistants who will be available to guide and prepare the students for technical interviews.
ESG will be a driving force in risk management in upcoming years. ERM / Risk professionals need a solid understanding of emerging ESG trends and regulations and how they apply to day-to-day job responsibilities. The ESG and ERM course begins with an overview of the ESG landscape and framework. After a foundational understanding is established, the course focuses on incorporating ESG into enterprise risk management, including identification, quantification, decision making, and reporting of ESG-related risks.
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Operations Management (OM) is responsible for the efficient production and delivery of goods and services, serving as a cornerstone of successful organizations. This course emphasizes how analytical techniques, such as forecasting, queuing theory, and linear programming, provide critical tools for optimizing operational decision-making, improving efficiency, and addressing real-world challenges in operations management. In this course, you will gain essential skills to optimize processes, manage resources, and enhance productivity across various industries. The course will be delivered through a combination of interactive lectures, case studies, and hands-on coding exercises to ensure a balance between conceptual learning and practical application.
Through lectures, you will gain a solid foundation in OM principles and analytical techniques. Case studies will help illustrate real-world applications of OM in industries such as manufacturing, healthcare, retail, and logistics, allowing you to see how the concepts are applied in diverse contexts. This course will integrate the principles of OM with hands-on analytical techniques using Python, allowing you to model and solve real-world OM problems. You will learn to run simulations, perform optimizations, and analyze data to make data-driven decisions that enhance efficiency and overall performance.
OM practices are tailored to meet the specific needs of various sectors. In manufacturing, OM helps streamline production lines and minimize waste; in healthcare, it enhances patient flow and optimizes resource allocation; in retail, it improves inventory management and supply chain operations; and in logistics, it ensures timely deliveries while reducing transportation costs. This course will equip you with the skills to apply OM practices effectively in different industries.
Analytics for Business Operations Management is an elective that is intended for students who are interested in pursuing a career using analytics and operational insights to drive organizational success in a competitive global marketplace across various industries.
This course explores financial derivatives across different asset classes with in-depth analysis of several popular trades including block trades, program trades, vanilla options, digital options, and variance swaps. Their dynamics and risks are explored through Monte Carlo simulation using Excel and Python. The daily decisions and tasks of a frontline risk manager are recreated and students have the opportunity to see which trades they would approve or reject. Students will gain a working knowledge of financial derivatives and acquire technical skills to answer complex questions on the trading floor.
In this course, students study major concepts of management and organization theory to understand human behavior in an organizational context, and then learn how to apply this to better manage interactions with key ERM stakeholders. Students will learn how to accomplish key ERM activities effectively while preserving and enhancing key internal relationships.
The course provides a deep dive into how enterprise risk functions operate within organizations, blending theoretical frameworks with practical, real-world applications. Topics include individual and organizational psychology, risk culture, organizational structure and governance, and the dynamics of managing risk in complex institutions. Through case studies and class discussions, students explore the behavioral and structural dimensions that shape ERM practices.
This elective is open only to students within the ERM program. This course (MSRO) is analogous to Managing Human Behavior in the Organization (MHBO), but customized for an ERM role. As a result, ERM students may not register for MHBO and those that have already taken MHBO may not register for MSRO.
Financial securities analysis and portfolio management is the study of analyzing information to evaluate financial securities and design investment strategies. Studying the subject can provide a foundation for students entering the fields of investment analysis or portfolio management. This course provides an intensive introduction to major topics in investments. Part I of the course lays the theoretical foundation by introducing the Portfolio Theory and Equilibrium Asset Pricing models. Part II covers the valuation models and analysis of major asset classes: equity, fixed-income, and derivatives. Topics include bond valuation and interest rate models, equity valuation and financial statement analysis, options valuation, other derivatives, and risk management. Part III of the course focuses on the practice of active portfolio management.
Tools for Risk Management examines how risk technology platforms assess risks. These platforms gather, store, and analyze data; and transform that data to actionable information. This course explores how the platforms are implemented, customized, and evaluated. Topics include business requirements specification, data modeling, risk analytics and reporting, systems integration, regulatory issues, visualization, and change processes. Hands-on exercises using selected vendor tools will give students the opportunity to see what these tools can offer.
Given the ever growing reliance on models, Model risk affects financial institutions at almost every level of their organization including pricing, risk, finance, and marketing. Model risk management (MRM) is now one of the primary focuses of operational risk management at modern financial institutions. In this class, the ERM skill sets of risk identification, risk quantification, and risk decision making are applied to the kinds of models seen in large, complex financial institutions. Through readings, lecture, assignments, and in-class discussions, students learn the principles and concepts that a robust MRM function uses to manage model risk.
Equips students with the basics of risk measurement and simulation using a hands-on approach to ERM modeling. Using industry-standard simulation software, students build systems of risk drivers for finance and insurance companies. Topics include risk correlations, VaR and TVaR, capital modeling, capital allocation, and parameter, process, and model Risk. Students acquire both quantitative experience building models and qualitative appreciation for model weaknesses.
This new course aims to provide advanced undergraduate and graduate students with a critical history of Palestine-related archaeology from the mid-19th century to the present, and (b) an examination of how archaeological narratives relating to Palestine have been impacted by state nationalism, colonialism and conflicting local, regional and global religious interests from the "Classical World" to the 21st century.
The exponentially increasing availability of data and the rapid development of information technology and computing power have inevitably made Machine Learning part of the risk manager’s toolkit. But, what are these tools? This class provides the driving intuitions for machine learning. Students will see how many of the algorithms are extensions of what we already do with our human minds. These algorithms include regularized regression, cluster analysis, naive bayes, apriori algorithm, decision trees, random forests, and boosted ensembles.
Through practical and real-life applications of ML to Risk Management, students will learn to identify the best technique to apply to a particular risk management problem, from credit risk measurement, fraud detection, portfolio selection to climate change, and ESG applications.
This course will explore the ethics and politics of using oral history methods for documenting injustice, oppression, and human rights issues. The course is open to graduate students of oral history, human rights, journalism, and related fields; no prior experience with oral history interviewing is required. Oral history can be a powerful means of documenting oppression, human rights abuses, and crisis “from the bottom up” and facilitating the understanding and possible transformation of conditions of injustice. It can open the space for people and narratives that have been marginalized to challenge official narratives and complicate narrow accounts of injustice and crisis. The course will first explore what is distinct about oral history as a response to harm or injustice, comparing it to more familiar forms of testimony and narrative used within the realm of human rights, social justice organizations and courts of law. With its commitment to life narrative interviews and archival preservation, oral history situates injustice within the broader context of a life, a historical trajectory, and a political and cultural setting. Weaving together conceptual and practical approaches, we will examine different potential goals of oral history, such as documenting the experiences of people who have been marginalized; seeking justice; fostering dialogue and healing; and/or supporting activism and advocacy. The course covers interviewing skills and project planning specifically for oral history projects about injustice and human rights, and explores various dimensions of how power, politics, and ethics come into play — how politics and power shape the way a narrative is heard; the challenges of realizing ideals of collaboration and shared authority amid uneven power dynamics; contending with the effects of trauma on both narrators and interviewers; and critical considerations for projects produced with activist and advocacy aims. We will explore how oral history can work alongside other forms of memory and witnessing that go beyond words, such as activism, film, and memorials.
A study of financial, economic, and engineering disasters from a common systems engineering perspective, to better understand and model risk in complex process systems. Course topics will introduce process systems engineering concepts and tools such as digraphs, fault trees, probabilistic risk assessment, HAZOP, FMEA, etc., for modeling enterprise-wide risk. We will develop risk models and analyze them for real-life inspired examples and case studies. Several disaster case studies will also be discussed.
Over the past decade, the Internet of Things (IoT) has transformed industries by enabling real-time data collection, analysis, and automated control through interconnected devices. Advancements in networking, cloud computing, and robotics have expedited IoT adoption, impacting a wide range of fields from home safety and industrial automation to healthcare and autonomous driving. Additionally, the rise of artificial intelligence (AI) led to the emergence of the Artificial Intelligence of Things (AIoT), which combines IoT connectivity with AI-driven decision-making to enhance smart systems.
This course provides a comprehensive understanding of IoT technologies and their integration with AI and robotic systems. Students will explore IoT architecture, key components, and communication protocols while gaining hands-on experience with IoT platforms, sensors, and data acquisition devices. The curriculum emphasizes practical AIoT applications for real-time decision-making in manufacturing, public safety, smart cities, healthcare, etc., and addresses the ethical considerations of these technologies.
Students will learn how to better identify and manage a wide range of IT risks as well as better inform IT investment decisions that support the business strategy. Students will develop an instinct for where to look for technological risks, and how IT risks may be contributing factors toward key business risks. This course includes a review of IT risks, including those related to governance, general controls, compliance, cybersecurity, data privacy, and project management. Students will learn how to use a risk-based approach to identify and mitigate cybersecurity and privacy related risks and vulnerabilities. No prior experience or technical skills required to successfully complete this course.
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As organizations increasingly rely on external vendors and service providers, managing third-party risks becomes paramount to ensure operational resilience, regulatory compliance, and strategic success. Challenges include:
The evolving nature of technology risks.
The impact of geopolitical tensions.
The lessons learned from disruptive events like pandemics.
By offering a comprehensive curriculum covering everything from the basics of vendor management to advanced predictive TPRM models and emphasizing regulatory requirements specific to the financial services sector, the course equips professionals with the knowledge and tools needed to navigate the intricate web of third-party relationships.
Students taking this course are prohibited from taking Supply Chain Risk Management for Non-Financials (ERMC PS5585) at any time. Contact your advisor for more information.
This course is designed to immerse students in the intersection of cybersecurity and data analytics. The course explores how modern data-driven approaches are revolutionizing the way organizations detect and manage cyber threats. Students will engage deeply with core cybersecurity concepts, such as network security, vulnerability management, and threat intelligence, while also learning to leverage cutting-edge data analytics and artificial intelligence to solve real-world security problems. Through hands-on exercises, coding assignments, and case studies, students will gain practical skills in analyzing logs and telemetries, building detection systems, and applying machine learning to security operations.
The Pandemic made us all aware of the fragility of supply chains and how significant the consequences of failure of our supply chains can be. It is paramount to note that global and local economies can break down, and scarcity of essential resources can foment wars. Risk professionals must know what best practices bring security to supply chains and related companies, governments, and other institutions.
Students taking this course are prohibited from taking Third-Party Risk Management (ERMC PS5575) at any time. Contact your advisor for more information.
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Cancer is the second leading cause of death in the US and most affluent countries. It represents a complex group of
diseases with heterogeneity in biology, incidence, prevalence, and outcomes. And unlike other complex and
potentially life-threatening maladies, a cancer diagnosis is regularly received by patients as a death sentence. It
elicits dread, despair, hopelessness, and sometimes stigma in patients and their families. The emotional toll of a
cancer diagnosis and vulnerability that ensues, can profoundly impact patients’ approaches to research and
treatment.
The Cancer Bioethics course offers a comprehensive exploration of the diverse ethical issues that arise in the context
of cancer care and research, providing students with an analytic framework for complex moral dilemmas faced by
patients, clinicians, researchers, and policymakers. Through case studies, theoretical discussions, and critical
analysis, students will employ key bioethical principles and their application to cancer care - from diagnosis to
survivorship or decisions about end-of-life care. Topics will include unique ethical challenges in oncology such as
the “right not to know” and other challenges associated with disclosures of genomic testing of cancer; the moral
uncertainty of conducting research in minors diagnosed with cancer and the downstream use of their oncologic data;
the unbridled optimism and therapeutic illusion among a number of cancer specialists; therapeutic misconception
among participants in oncologic clinical trials; and the increasing integration of artificial intelligence into new
models of cancer care and prognostication. The course will also examine the intersection of social determinants of
health, cultural beliefs and value systems, and healthcare access, addressing the ethical concerns of disparities in
cancer care.
The course incorporates curricular elements of clinical ethics, law and bioethics, research ethics, reproductive ethics,
pediatric ethics, global ethics, environmental ethics, race and bioethics, organ transplant ethics, health policy and
bioethics, etc. This is an elective course open to cross-registrants from other fields and/or Columbia University
programs. Students do not need to have medical background to take this course. Students pursuing a degree in
medicine or pre-medicine, nursing, behavioral sciences, biotechnology, genetics, data science, public policy,
journalism, law, and governme
The Capstone Project is an opportunity for students to synthesize and apply learnings from throughout the Strategic Communication program. Under the guidance of expert advisers, you’ll investigate a real-world communication issue, devising solutions and strategies that bridge the gap between theory and practice.
Introductory course to analog photographic tools, techniques, and photo criticism. This class explores black & white, analog camera photography and darkroom processing and printing. Areascovered include camera operations, black and white darkroom work, 8x10 print production, and critique. With an emphasis on the student’s own creative practice, this course will explore the basics of photography and its history through regular shooting assignments, demonstrations, critique, lectures, and readings. No prior photography experience is required.
As far back as Walter Benjamin’s “work of art in the age of mechanical reproduction” (1935), photography has always been challenged by
mechanical means
of image processing. Photographers and Institutions have first resisted and then (mostly) embraced each of these changes. This class explores Artificial Intelligence Photography as the latest in a series of earthquakes in the history of the photographic image, accompanying the desires of business, globalization, and science. This class seeks an ethically guided, globally representative model for photography and artificial intelligence. Debates around authorship and creativity (e.g., Supreme Court case with Andy Warhol) now face a radically new context of an “authorless” photograph. As crowdsourced imagemaking begins, the bias of massive datasets have taken techno-utopians by surprise, underlining that the task of building an equitable image-bank of the world cannot be left to algorithms and entrepreneurs. This class will explore the ethics and aesthetics of Artificial Intelligence and Imagery. There will be equal emphasis on reading and writing papers, as there will be on learning new software and tools.
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Since Walter Benjamin’s concept of “work of art in the age of mechanical reproduction” (1935), photography has been continuously changed by mechanical, and then digital, means of image capture and processing. This class explores the history of the image, as a global phenomenon that accompanied industrialization, conflict, racial reckonings, and decolonization. Students will study case studies, read critical essays, and get hands-on training in capture, workflow, editing, output, and display formats using digital equipment (e.g., DSLR camera) and software (e.g., Lightroom, Photoshop, Scanning Software). Students will complete weekly assignments, a midterm project, and a final project based on research and shooting assignments. No Prerequisites and no equipment needed. All enrolled students will be able to check out Canon EOS 5D DSLR Camera; receive an Adobe Creative Cloud license; and get access to Large Format Print service.
Prerequisites: (STAT GR5701) working knowledge of calculus and linear algebra (vectors and matrices), STAT GR5701 or equivalent, and familiarity with a programming language (e.g. R, Python) for statistical data analysis. In this course, we will systematically cover fundamentals of statistical inference and modeling, with special attention to models and methods that address practical data issues. The course will be focused on inference and modeling approaches such as the EM algorithm, MCMC methods and Bayesian modeling, linear regression models, generalized linear regression models, nonparametric regressions, and statistical computing. In addition, the course will provide introduction to statistical methods and modeling that addresses various practical issues such as design of experiments, analysis of time-dependent data, missing values, etc. Throughpout the course, real-data examples will be used in lecture discussion and homework problems. This course lays the statistical foundation for inference and modeling using data, preparing the MS in Data Science students, for other courses in machine learning, data mining and visualization.
Advanced analog photography & darkroom printing. Students will work with analog cameras and learn how to refine black-and-white printing techniques, produce larger prints, etc. Emphasis will be placed on the editing, sequencing, and display of images while cultivating a theoretical and historical context to situate the work. Students will engage with an array of photographic practices through presentations, critiques, guest artist lectures and printing assignments. This course will explore critical issues in contemporary photography and advanced camera and production techniques through regular shooting assignments, demonstrations, critique, lectures, readings, and field trips. Prerequisites:
Intro Darkroom Photography
(Columbia) or equivalent experience
Electricity is the lifeblood of human society. Decarbonization of global economies through electrification is seen as the most viable path for reducing GHG emissions and addressing the worst effects of climate change. Though generally accepted as the best path forward, an understanding of the operational parameters of the electric system is essential to understanding both the benefits and limitations of current and future actions. This includes the highly visible investments in renewable energy generation, less visible but equally important investments in transmission and distribution infrastructure, and the largely personal, private choices of individual households and businesses.
The course will examine pathways for the transition from fossil fuel-based electricity generation to one dominated by electricity generated by renewable energy. Students will examine the drivers of past energy transitions and various factors influencing current energy systems. At the conclusion of the course, students will be able understand the drivers of past energy transitions, the impact of those drivers on the overall energy supply chain, and how new technologies (e.g. distributed energy resources, smart meters, internet of things (IOT), etc.), consumer adoption of mass market products (e.g. Electric Vehicles, battery backup, etc,) and evolving consumer expectations (e.g. fast charging) are altering long held assumptions about energy production and use. Through this work, students will be able to infer practical steps to support current efforts to decarbonize and the potential impacts of those actions on the modern energy supply chain.
Modernizing energy systems is essential for achieving a sustainable future. This course provides an in-depth exploration of intelligent energy systems, emphasizing the transformative role of Artificial Intelligence (AI) and Battery Energy Storage Systems (BESS) in advancing grid operations and sustainability objectives. Designed to integrate theoretical foundations with real-world application, the course highlights innovative methodologies and cutting-edge tools, enabling students to tackle critical challenges such as renewable energy intermittency, curtailment, grid reliability, and resilience. Through a challenging yet approachable curriculum, students will develop both the knowledge and hands-on expertise required to lead innovations in the renewable energy industry within an increasingly complex and interconnected world. This elective course is designed for students interested in the intersection of renewable energy, technology, and environmental stewardship. This course will emphasize transformative technologies in grid modernization, highlighting the pivotal roles of AI and BESS.
“It could have been otherwise.” -Noël Burch
With this brief yet generative statement from a foundational film theorist we are introduced to a major theme of this course, a graduate level seminar concerning the still-in-formation field of media archeology. Pursuing the material traces left by false starts, wrong moves, misbegotten speculation, and dead formats, this course will dig into the historical past in order to better understand our current media ecology, prepare for the computational future, and imagine how things could be otherwise. Archeology in this sense refers to the study of a technical object through investigating its origins (its arché), as a means of breaking down traditional linear accounts of history and reconstructing them along new, more lacunary, less teleological lines. This will be our goal. We will be introduced to media archeology as both a method and an aesthetics. Our approach will look for the old in the new and the new in the old, while locating recurring topoi, ruptures, and discontinuities. Marking a departure from more hermeneutical, text-based film and media studies models, we will instead focus on questions of hardware, materiality, and physical inscription—technological research that sticks close to the signal of mediatic events, close to the metal, close to the silicon. We will perform close reading and thick description, as in established humanities disciplines like literary studies and anthropology, but with radically different, non-phenomenological, non-discursive object formations. Topics we will consider include, for example, analog waveforms and digital pulses, mathematical versus narrative modes of epistemology, and what Thomas Elsaesser calls a “poetics of obsolescence.” Our readings will draw from the corpus of media archeology studies as well as consonant fields such as material culture studies, computer engineering, and the history of science.
This course will provide students with an understanding of the ways and extent to which climate change law and policy is relevant to businesses, as well as the role of sustainability professionals in practical implementation. The course is divided into several core topics, including: (i) an overview of international and U.S. climate change policy and law, including the Paris Agreement, the Inflation Reduction Act and energy transition policy support, and human rights/environmental justice; (ii) market-led, voluntary initiatives such as the Task Force on Climate-related Financial Disclosures (TCFD), and related developments including the mainstreaming of ESG investing, sustainable finance, and the proliferation of corporate net zero goals; (iii) corporate governance, shareholder activism, and the emergence of mandatory regulation on climate disclosures, such as the E.U.’s Taxonomy Regulation and the U.S. Securities & Exchange Commission’s proposed climate disclosure rule; (iv) carbon pricing, carbon markets, and “offsets”; (v) greenhouse gas emissions accounting and data challenges; and (vi) climate-related litigation and enforcement actions against corporations and financial institutions in the U.S. and other key markets, including “greenwashing” litigation and “anti- energy company boycott” investigations by several U.S. states.
Data does not have meaning without context and interpretation. Being able to effectively present data analytics in a compelling narrative to a particular audience will differentiate you from others in your field. This course takes students through the lifecycle of an analytical project from a communication perspective. Students develop written, verbal, and visual deliverables for three major audiences: data experts (e.g., head of analytics); consumer and presentation experts (e.g., chief marketing officer); and executive leadership (e.g., chief executive officer).
Students get ample practice in strategic interactions in relevant social and professional contexts (e.g., business meetings, team projects, and one-on-one interactions); active listening; strategic storytelling; and creating persuasive professional spoken and written messages, reports, and presentations. Throughout the course, students create and receive feedback on data storytelling while sharpening their ability to communicate complex analytics to technical and nontechnical audiences with clarity, precision, and influence.
This course is designed to introduce pre-licensure students to relevant and emergent topics which affect the practice of nursing in the national and international healthcare system. The focus will be on issues confronting professional nurses including global health, cultural awareness, gender identity, and evidence-based wellness. State mandated topics for licensure will be covered.
Visiting artists and critics are invited over the course of the academic year to give a one-hour lecture followed by discussion, and conduct 3 40-minute studio visits. These lecturers will join the previously listed Visiting Critics and will be available as one of your allotted studio visits each semester.
The Actuarial Methods course explores models for evaluating and managing risks of life contingent contracts, their theoretical basis and applications. Topics include survival models, life insurance and annuity benefits, premium and reserve calculations related to policies on a single life, as well as option pricing. This course also covers materials relevant to the long-term section of the Fundamentals of Actuarial Mathematics (FAM) exam of the Society of Actuaries. This is a core course of the M.S. in Actuarial Science program.
The purpose this class is to develop the student’s knowledge of the theoretical basis of certain actuarial models and the application of those models to insurance and other financial risks. A thorough knowledge of calculus, probability, and interest theory is assumed. Knowledge of risk management at the level of Exam P is also assumed.
The combination of these two classes covers the material for the FAM-L and ALTAM examinations of the Society of Actuaries. This is a core class of the Actuarial Science program. Students who have already taken and passed the MLC or LTAM exam for SOA are exempted from this class and can substitute an elective.
This course provides an introduction to the tools for pricing and reserving for short term insurance. We will discuss methods for calculating IBNR reserves, ratemaking, frequency and severity models used for modeling coverage modifications, statistical methods for fitting, evaluating, and selecting parametric models for frequency and severity, and three credibility methods.
This class covers the short-term material of Exam FAM and also covers the material of Exam ASTAM of the Society of Actuaries, and some of the material on Exams MAS I, MAS II, and 5 of the Casualty Actuarial Society. This is a core class of the Actuarial Science program. Students who have already taken and passed the FAM exam (or its short term portion) and the ASTAM exam administered by the SOA are exempted from this class and can substitute an elective.
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This course introduces to the students, generalized linear models (GLM), time series models, and some popular statistical learning models such as decision trees models as well as random forests and boosting trees. The aim for GLM is to provide a flexible framework for the analysis and model building using the likelihood techniques for almost any data type. The aim for the statistical learning models is to build and predict or understand data structure (if unsupervised) using statistical learning methods such as tree-based for supervised learning and the Principle Component Analysis and Clustering for unsupervised learning. It develops a student’s knowledge of the theoretical basis in predictive modeling, computational implementation of the models and their application in finance and insurance. Tools such as cross-validation and techniques such as regularization and dimension reduction for fitting and selecting models are explored. We also implement these models using a combination of Excel and R.
The class covers the material of Exams, Statistics for Risk Modeling (SRM) and Predictive Analytics (PA) of Society of Actuaries, and some material of Exams, Modern Actuarial Statistics I (MAS-I) and MAS II by the Casualty Actuarial Society. This is a core course for the Actuarial Science students. Students who have already taken and passed the SRM and PA exams administered by the SOA are exempted from this class and can substitute an elective.
The Data Science in Finance and Insurance course explores machine learning models, their theoretical basis, computing implementation and applications in finance and insurance. Topics include machine learning models for regression, classification and unsupervised learning; tools such as cross validation and techniques such as regularization, dimension reduction and ensemble learning; and select algorithms for fitting machine learning models.
This course offers students an intensive hands-on experience where they combine theoretical understanding, domain knowledge and coding skills to better inform data-driven decision making. Prior exposure to linear algebra, calculus and statistics is helpful. A working knowledge of a spreadsheet program and R is a plus. Students will use spreadsheets and R for validation and prototyping and Python to implement algorithms and apply models to applicable data.
Some topics covered are also relevant to the statistical learning portion of the Society of Actuaries (SOA) and the Casualty Actuarial Society (CAS) curricula, and the quantitative methods section of the Chartered Financial Analyst (CFA) Institute curriculum. This is a core course of the Actuarial Science program.
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The Advanced Data Science Applications in Finance and Insurance course covers topics in object-oriented programming with python, the relational theory and relational database navigation with SQL, deep learning (including traditional machine learning tasks, computer vision, recurrent networks, natural language processing, and large language models), as well as interpretable machine learning.
Some topics covered are relevant to the Advanced Topics in Predictive Analytics (ATPA) exam of the Society of Actuaries. Topics in deep learning are also relevant to the statistical learning portion of the Casualty Actuarial Society (CAS) curriculum, and the quantitative methods section of the Chartered Financial Analyst (CFA) Institute curriculum.
Familiarity with machine learning models covered in the Data Science in Finance and Insurance (ACTU PS5841) course is helpful. Prior exposure to linear algebra, calculus, statistics, and a working knowledge of python and spreadsheets are necessary.
This course will introduce students to major issues currently of concern to all investors. It can give you the skills to conduct a sophisticated assessment of current issues and debates covered by the popular media as well as more-specialized finance journals. These skills are essential for people who pursues a financial service career, especially in today’s rapidly evolving environment. The material presented in this course are both practical important and intellectually interesting.
This course is consistent with and relevant to Chartered Financial Analyst (CFA) curriculum. It covers all subjects in CFA test and most of problems are in the same format as the CFA examination questions. This course will also provide a foundation for further study in Financial Risk Management and Financial market related courses.
Prerequisites: EEEB G4850. Incoming M.A. students aiming for the thesis-based program are guided through the process of defining a research question, finding an advisor, and preparing a research proposal. By the end of the semester the students will have a written research proposal to submit to potential advisors for revision. Subject to a positive review of the research proposal, students are allowed to continue with the thesis-based program and will start working with their advisor. The course will also provide an opportunity to develop basic skills that will facilitate the reminder of the students stay at E3B and will help in their future careers.
The Graduate Seminar in Sound Art and Related Media is designed to create a space that is inclusive yet focused on sound as an art form and a medium. Class time is structured to support, reflect, and challenge students as individual artists and as a community. The course examines the medium and subject of sound in an expanded field, investigating its constitutive materials, exhibition and installation practices, and its ethics in the 21st century. The seminar will focus on the specific relations between tools, ideas, and meanings and the specific histories and theories that have arisen when artists engage with sound as a medium and subject in art. The seminar combines discussions of readings and artworks with presentations of students' work and research, as well as site visits and guest lectures.
While the Columbia Visual Arts Program is dedicated to maintaining an interdisciplinary learning environment where students are free to use and explore different mediums while also learning to look at, and critically discuss, artwork in any medium, we are equally committed to providing in-depth knowledge concerning the theories, histories, practices, tools and materials underlying these different disciplines. We offer Graduate Seminars in different disciplines, or combinations of disciplines, including moving image, new genres, painting, photography, printmaking, sculpture, as well as in Sound Art in collaboration with the Columbia Music Department through their Computer Music Center. These Discipline Seminars are taught by full-time and adjunct faculty, eminent critics, historians, curators, theorists, writers, and artists.