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Applications open: 2018


Exploring The Brain

Whether it’s pleasure or pain, hope or regret, memories of things past or planning for the future, the workings of the human brain underpin what we do and experience. Find out what we are learning from modern neuroscience about the structure and activities underlying decision making.

Understanding Behavior

Our decisions are influenced by beliefs and biases, mood and age, context and culture. Understand what we are learning about how these variables shape our decisions.

Examining Influence

Every day, we try to influence the decisions of others, from families and colleagues to customers and leaders. Learn how we use persuasion, incentives and choice architecture to nudge people towards decisions we want them to make.

Improving Decision Making

We all want to make better decisions—on our own, and as members of teams or organizations. Explore approaches to better decision making that engage analytical reasoning, improved communication and team dynamics, and reliance on values.


The Brain: How the brain decides and the critical roles played by pleasure and pain, memory and experience

Behavior: How cultural, developmental, contextual and emotional influences play out in our brains and shape our choices.

Influence: How we use persuasion, incentives, choice architecture, and appeals to beliefs and values to influence the decisions of others.

Improvement: How new research and techniques can help you make creative, reasoned, satisfying, and responsible decisions—individually and with others.


  • David Demarest, vice president of public affairs, Stanford; former head of public affairs at Bank of America, Visa
  • Hazel Markus, social psychologist, Stanford University
  • Bill Newsome, neurobiologist, head of the Stanford Neuroscience Institute, and co-chair of Obama’s BRAIN Initiative


Applications open: 2018


$2600.00 ( covers online materials, on-campus program, and meals)

15% non-profit/governmnet/Stanford alumni discounts.



This course is offered through Worldview Stanford, which creates interdisciplinary media and learning experiences to engage and inform the public.

The science of decision making

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Tuesday, March 31, 2015
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This interdisciplinary course encompasses the fields of rock mechanics, structural geology, earthquake seismology and petroleum engineering to address a wide range of geomechanical problems that arise during the exploitation of oil and gas reservoirs.

The course considers key practical issues such as prediction of pore pressure, estimation of hydrocarbon column heights and fault seal potential, determination of optimally stable well trajectories, casing set points and mud weights, changes in reservoir performance during depletion, and production-induced faulting and subsidence. The first part of the course establishes the basic principles involved in a way that allows readers from different disciplinary backgrounds to understand the key concepts.

The course is intended for geoscientists and engineers in the petroleum and geothermal industries, and for research scientists interested in stress measurements and their application to problems of faulting and fluid flow in the crust.


Introductory Geology and Geophysics
Familiarity with principles of drilling and petroleum production


  • 20, 90 minute lectures (in ~20 minute segments). 2 lectures will be made available each week, starting April 1, 2014.
  • Lecture 1 is a course overview to introduce students to the topics covered in the course. Lectures 2-17 follow 12 chapters of Dr. Zoback’s textbook, Reservoir Geomechanics (Cambridge University Press, 2007) with updated examples and applications. Lectures 18 and 19 are on topics related to geomechanical issues affecting shale gas and tight oil recovery. Lecture 20 is on the topic of managing the risk of triggered and induced seismicity.
  • 8 Homework assignments (and associated video modules) are intended to give students hands-on experience with a number of the topics addressed in the course.
  • The course grade will be based solely on homework assignments. There will be no quizzes or exams.
  • Homework assignments will be graded electronically and will consist of multiple choice and numerical entry responses.
  • There will be an online discussion forum where students can discuss the content of the course and ask questions of each other and the instructors.


Dr. Mark D. Zoback

Dr. Mark D. Zoback is the Benjamin M. Page Professor of Geophysics at Stanford University. Dr. Zoback conducts research on in situ stress, fault mechanics, and reservoir geomechanics with an emphasis on shale gas, tight gas and tight oil production. He was one of the principal investigators of the SAFOD project in which a scientific research well was successfully drilled through the San Andreas Fault at seismogenic depth. He is the author of a textbook entitled Reservoir Geomechanics published in 2007 by Cambridge University Press. He is the author/co-author of over 300 technical papers and holds five patents. He was the co-founder of GeoMechanics International in 1996, where he was Chairman of the Board until 2008. Dr. Zoback currently serves as a Senior Executive Adviser to Baker Hughes. Dr. Zoback has received a number of awards and honors, including the 2006 Emil Wiechert Medal of the German Geophysical Society and the 2008 Walter H. Bucher Medal of the American Geophysical Union. In 2011, he was elected to the U.S. National Academy of Engineering and in 2012 elected to Honorary Membership in the Society of Exploration Geophysicists. He is the 2013 recipient of the Louis Néel Medal, European Geosciences Union and named an Einstein Chair Professor of the Chinese Academy of Sciences. He recently served on the National Academy of Engineering committee investigating the Deepwater Horizon accident and the Secretary of Energy’s committee on shale gas development and environmental protection. He currently serves on a Canadian Council of Academies panel investigating the same topic. Dr. Zoback is currently serving on the National Academy of Sciences Advisory Board on drilling in the Gulf of Mexico.

Arjun H. Kohli, Graduate Teaching Assistant

Arjun H. Kohli is a 4th year Ph.D. candidate in the Department of Geophysics at Stanford and laboratory manager of the Stress and Crustal Mechanics Laboratory. Arjun conducts research on fault mechanics and microstructure with applications to plate-boundary fault zones, geothermal and petroleum reservoirs, and induced and triggered seismicity. He completed a B.S. in Geology-Physics/Mathematics at Brown University in 2010 and was awarded the Brown University Department of Geological Sciences Undergraduate Research Award for his work on dynamic fault weakening mechanisms. In 2011, he received a National Science Foundation Graduate Research Fellowship to investigate controls on the transition from stable to dynamic fault slip with Dr. Zoback at Stanford. Arjun is currently engaged in collaborative research with numerous partners including the United States Geological Survey, University of Silesia, University of Minnesota, and Stanford University Department of Geological and Environmental Sciences.


Will I receive a Statement of Accomplishment

Yes. A Statement of Accomplishment will be given to students who obtain more than 70% of the maximum score on the homework assignments.

Do I need to purchase a textbook for the course?

While it is not required to purchase the Reservoir Geomechanics textbook for this course, it is recommended. Lectures 2-17 follow the 12 chapters of the book. The book provides significant additional detail and explanation of the course concepts. It is available through:
Cambridge University Press:
Amazon and Kindle:

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Thursday, January 29, 2015 to Friday, March 27, 2015
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About This Course

This course provides an overview of women's health and human rights, beginning in infancy and childhood, then moving through adolescence, reproductive years and aging. We consider economic, social, political and human rights factors, and the challenges women face in maintaining health and managing their lives in the face of societal pressures and obstacles.

We focus on critical issues, namely those that may mean life or death to a woman, depending on whether she can exercise her human rights. These critical issues include: being born female and discrimination; poverty; unequal access to education, food, paid work and health care; and various forms of violence. Topics discussed include son preference, education, HIV/AIDS, reproductive health, violence in the home and in war and refugee circumstances, women's work, sex trafficking, and aging.

Our MOOC will have a special focus on creating an international network of engaged students. We will ask students to take part in interactive discussions and cooperative exercises and to share their own experiences. We also ask students to engage with the communities they live in, in order to deepen their understanding of the issues and tie academic ideas to real-life circumstances.

To find out more details about this course and its principles, please visit our Project Page at

Course Staff

Anne Firth Murray

Anne Firth Murray, a New Zealander, was educated at the University of California and New York University in economics, political science and public administration, with a focus on international health policy and women’s reproductive health.

For the past twenty-five years, Anne has worked in the field of philanthropy, serving as a consultant to many foundations. From 1978-1987, she directed the environment and international population programs at the William and Flora Hewlett Foundation in California. She is the Founding President of The Global Fund for Women, which aims to seed, strengthen, and link groups committed to women’s well-being and human rights. In 2005, Anne was nominated along with a thousand activist women for the Nobel Peace Prize.

Anne is a Consulting Professor in Human Biology at Stanford University, where she teaches on women's health, human rights and love as a force for social justice. She is the author of the books Paradigm Found: Leading and Managing for Positive Change and From Outrage to Courage: The Unjust and Unhealthy Situation of Women in Poorer Countries and What They Are Doing About It, on international women's health.


Kevin Hsu

Kevin runs a design studio, Skyship Educational Design, developing open online courses (MOOCs) and deploying digital tools in the classroom. He is dedicated to crafting new experiences for students and helped launch one of Stanford’s first social science MOOCs for a global audience, featuring Professor Larry Diamond on the topic of “Democratic Development.” He also teaches for the Program on Urban Studies at Stanford University.


What basic principles form the foundation course?

Because we believe that what we do is important but that the way we do it is more important, we attempt to teach and learn according to a set of principles that will guide the content and processes of the course. These are: compassion, mutual learning, respect, transparency, trust, and truth.

What do I need to take this course?

An interest in health and social justice. It will be useful to have an open mind, willingness to hear different points of view, and a commitment to positive social change.

Access to the Internet. A stable internet connection will also be useful, as much of the other content, including video interviews and lectures will be delivered online.

The course already started! Is it too late to join?

No you don't have to worry.Because it is an online class, you can comfortably jump into this course the first couple weeks while it is running. You get to review the material and watch video lectures and interviews on your own time! However, you'll want to get up to speed so you can interact with the other students in this international online community.

Is there a textbook for the class?

The primary text for the class is a book on international health and human rights, From Outrage to Courage: The Unjust and Unhealthy Situation of Women in Poorer Countries and What They Are Doing About It (Second Edition), by Anne Firth Murray. If you are interested in having a copy of the book, you can obtain one from We will also make individual chapters available online during the course.

Can I receive a Statement of Accomplishment for this course?

Yes, participants who successfully complete the required elements of the course will receive a personalized Statement of Accomplishment. Please note that online courses do not include university credit.

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Wednesday, October 15, 2014
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About This Course

People depend on nature to sustain and fulfill human life, yet the values of nature are typically ignored in decisions. Mapping and modeling ecosystem services can help highlight the diverse benefits provided to people by nature (what and where) and explore how those benefits might change under different management options--thus bringing information about nature’s values into decisions in practical ways. With these approaches, we can improve the state of biodiversity and human well-being by motivating greater and more cost-effective investments in both.

This course introduces the Natural Capital Project’s (NatCap’s) approach to using ecosystem service information to inform decisions. It uses specific examples to illustrate how the approach has worked in each case and highlights key methods and tools used in implementation.

Split into four modules, NC101 first introduces the concepts of natural capital and ecosystem services, the stocks and flows of vital benefits flowing from nature to people. The second module describes InVEST, NatCap’s software tool for mapping, modeling, and valuing ecosystem services. In addition, it provides guidance on project scoping and on matching approaches and tools to a project’s goals, decision context, timeline, capacity, and quality of data available. Modules 3-4 offer an overview of the skills needed to use InVEST models, including recommendations for how to effectively summarize and communicate model outputs to stakeholders and other audiences.

Intended Audience

This course is intended for those interested in how natural capital approaches can inform decisions taken by governments, multi-lateral development institutions, the private and finance sectors, and non-governmental organizations. It can be a resource for individuals interested in simply learning about these concepts or for those interested in using the NatCap’s approaches and tools in research or to influence decisions. This course can also serve as a primer for those individuals planning to attend one of our in-person training workshops in the future.


There are no prerequisites for this course. However, we recommend that you download InVEST and GIS software (either QGIS or ArcGIS) if you intend to follow the technical examples or complete the optional assessments contained in modules 3 and 4.

Course Staff

Gregg Verutes

Geographer - Lead Instructor

Gregg Verutes leads NatCap's training program which hosts both introductory and technical workshops throughout the world. His current focus is developing innovative techniques that utilize maps, games, and problem-based exercises to teach students, scientists and practitioners about valuing nature. Gregg also serves as a GIS specialist for the marine team working on coastal zone management and spatial planning in Belize, Vietnam and the Americas. He worked previously for National Geographic as a GIS instructor and a visiting scientist with the World Wildlife Fund's Conservation Science Program. Gregg received his M.S. from San Diego State University and his B.S. in Policy Analysis and Management from Cornell University. 

Adrian Vogl

Senior Scientist

Adrian Vogl is leading the application of InVEST models for watershed services, and developing decision support models for spatial planning, permitting new infrastructure projects and mitigation, and targeting investments in watershed conservation. Adrian co-led development of the RIOS tool, in partnership with The Nature Conservancy and the Latin American Water Funds Platform. In addition, Adrian is leading efforts to link the InVEST economic valuation approach with outputs from other hydrologic models. Before joining the Natural Capital Project, Adrian worked in central Texas developing land-use planning decision support tools that incorporate freshwater and groundwater ecosystem services, land development, and conservation planning. Adrian received her Ph.D. in Aquatic Resources from Texas State University-San Marcos, and her B.A. from the University of Arizona in Cultural Anthropology.

Henry Borrebach

Training Coordinator

Henry Borrebach is on the Natural Capital Project's training team, overseeing online education and the annual Natural Capital Symposium, as well as coordinating NatCap trainings around the globe. Henry has extensive experience in applied pedagogy and international education, and he is passionate about making the science behind conservation accessible to the public. He is currently working with the team to develop online training courses that make NatCap's approach and tools available to a wider audience. Henry holds a B.F.A. from Carnegie Mellon University and an M.F.A. from Florida International University. Before joining the project, he co-founded the O, Miami international poetry festival. 

Frequently Asked Questions

Do I need to complete all the modules in the course?

While the lessons contained in each of the four modules are intended to stand alone, we strongly encourage all participants to begin by reading through the Course Roadmap. This section explains how the course is organized and provides important background information about the two case study examples included throughout. To launch the Course Roadmap, click the "Start here" button on the top-left panel of the Courseware.

Do you offer a Statement of Accomplishment for completing the course?

The course is structured to provide two levels of accomplishment. Students completing only Modules 1 and 2 will be provided with a Statement of Accomplishment for Intro to Ecosystem Services. Students who complete Modules 1 through 4 (including the 2 assessments) will receive a Statement of Accomplishment in Ecosystem Services and Applications.

Do I need to buy a textbook?

This course is completely free. Links to download all the necessary course materials and tools are provided within each unit.

How long should it take to complete this course?

The course is divided into four modules. It should take approximately one hour to finish each module and about four hours to complete the entire course.

What is the best way to ask questions or provide feedback?

Click on the "Discussion" tab to link to our online user forum. This forum is monitored daily by our software engineers and scientists.

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Sunday, September 21, 2014 to Sunday, November 23, 2014
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Social networks pervade our social and economic lives.   They play a central role in the transmission of information about job opportunities and are critical to the trade of many goods and services. They are important in determining which products we buy, which languages we speak, how we vote, as well as whether or not we decide to become criminals, how much education we obtain, and our likelihood of succeeding professionally.   The countless ways in which network structures affect our well-being make it critical to understand how social network structures impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do.  This course provides an overview and synthesis of research on social and economic networks, drawing on studies by sociologists, economists, computer scientists, physicists, and mathematicians.
The course begins with some empirical background on social and economic networks, and an overview of concepts used to describe and measure networks.   Next, we will cover a set of models of how networks form, including random network models as well as strategic formation models, and some hybrids.   We will then discuss a series of models of how networks impact behavior, including contagion, diffusion, learning, and peer influences.

Course Syllabus

  • Week 1: Introduction, Empirical Background and Definitions
Examples of Social Networks and their Impact, Definitions, Measures and Properties: Degrees, Diameters, Small Worlds, Weak and Strong Ties, Degree Distributions

  • Week 2: Background, Definitions, and Measures Continued
Homophily, Dynamics,  Centrality Measures: Degree, Betweenness, Closeness, Eigenvector, and Katz-Bonacich. Erdos and Renyi Random Networks: Thresholds and Phase Transitions,

  • Week 3: Random Networks 
Poisson Random Networks, Exponential Random Graph Models, Growing Random Networks, Preferential Attachment and Power Laws, Hybrid models of Network Formation

  • Week 4:   Strategic Network Formation 
Game Theoretic Modeling of Network Formation, The Connections Model, The Conflict between Incentives and Efficiency, Dynamics, Directed Networks, Hybrid Models of Choice and Chance
  • Week 5:  Diffusion on Networks. 
Empirical Background, The Bass Model, Random Network Models of Contagion, The SIS model, Fitting a Simulated Model to Data

  • Week 6:  Learning on Networks. 
Bayesian Learning on Networks, The DeGroot Model of Learning on a Network, Convergence of Beliefs, The Wisdom of Crowds, How Influence depends on Network Position.

  • Week 7: Games on Networks. 
Network Games, Peer Influences:  Strategic Complements and Substitutes, the Relation between Network Structure and Behavior, A Linear Quadratic Game, Repeated Interactions and Network Structures.

Recommended Background

The course has some basic prerequisites in mathematics and statistics.  For example, it will be assumed that students are comfortable with basic concepts from linear algebra (e.g., matrix multiplication), probability theory (e.g., probability distributions, expected values, Bayes' rule), and statistics (e.g., hypothesis testing), and some light calculus (e.g., differentiation and integration).  Beyond those concepts, the course will be self-contained.

Suggested Readings

The course is self-contained, so that all the definitions and concepts you need to solve the problem sets and final are contained in the video lectures.  Much of the material for the course is covered in a text: Matthew O. Jackson  Social and Economic Networks, Princeton University Press (Here are Princeton University Pressand Amazon pages for the book).  The text is optional and not required for the course.  Additional background readings, including research articles and several surveys on some of the topics covered in the course can be found on my web page.

Course Format

The course will run for eight weeks.  Each week there will be video lectures available, as well as a standalone problem set and some occasional data exercises, and there will be a final exam at the end of the course for those who wish to earn a course certificate.  




Will I get a Statement of Accomplishment after completing this class?

Yes. Students who successfully complete the class (above 70 percent correct on the problem sets and final exam) will receive a Statement of Accomplishment signed by the instructor - and those earning above 90 percent credit on the problem sets and final will earn one with distinction.

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Tuesday, June 24, 2014 to Tuesday, September 2, 2014
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This course is designed as an eight-week introduction to the study of economics. Participants will be exposed to the economic way of thinking and learn about the functioning of a modern market economy. The early part of the course focuses on microeconomic analysis including the behavior of consumers and firms. We analyze markets for goods and services and policy choices that affect these markets. The later part of the course moves on to macroeconomic concepts such as national production, employment, inflation and interest rates. We explore models that determine long-run growth and short-term fluctuations in national economies. We then discuss the role of government regulation, monetary policy, and fiscal policy.


Part 1

  • The Basic Core
  • Getting Started
  • Observing and Explaining the Economy
  • The Supply and Demand Model
  • Using the Supply and Demand Model

Part 2

  • The Competitive Equilibrium Model
  • Deriving Demand
  • Deriving Supply
  • Market Equilibrium and Efficiency
  • Firms and Industries Changing Over Time
  • Cost and Changes at Firms Over Time
  • The Rise and Fall of Industries

Part 3

  • Deviations from Competition
  • Monopoly and Market Power
  • Between Monopoly and Competition
  • Antitrust Policy and Regulation

Part 4

  • Labor Markets
  • The Labor Supply and Demand Model
  • Labor Model Cont. – Min. Wage and Discrimination
  • Key Economic Policy Issues
  • Taxes, Transfers and Income Distribution
  • Public Goods and Externalities
  • Government Failure and Success

Part 5

  • Financial and Capital Markets
  • Markets for Physical Capital
  • Financial Markets: Risk and Return
  • Macro Facts and Measures
  • Getting Started with Macroeconomic Ideas
  • Measuring Production, Income and Spending of Nations

Part 6

  • Long Run Macro
  • Determining Consumption, Investment and Govt. Shares
  • Employment and Unemployment
  • Productivity, Econ. Growth and Determining Factors
  • A Look at Money, Inflation and the Fed

Part 7

  • Short Run Macro
  • Introduction to Economic Fluctuations
  • Economic Fluctuations Model
  • Using the ADIA Model

Part 8

  • Macro Policy Issues
  • Intro to Macroeconomic Policy
  • Fiscal Policy
  • Monetary Policy
  • Monetary Policy Analysis
  • International Economic Issues
  • Gains from Trade
  • International Trade Policy – Tariffs and Quotas


Do I need to buy a textbook?

No. All required course materials will be provided through the online platform. The textbook Principles of Economics, Seventh Edition, by John B. Taylor and Akila Weerapana, may be used as a study resource, but is not required. Used books, earlier editions, rentals, or e-books versions of this book are options to keep the cost down.

Will I receive Stanford credit for this course?

No. For those interested in a for-credit, Stanford Summer Session course covering similar material, see Econ 1V.


John B. Taylor

John B. Taylor is the George P. Shultz Senior Fellow in Economics at the Hoover Institution and the Mary and Robert Raymond Professor of Economics at Stanford University. He was previously the director of the Stanford Institute for Economic Policy Research and was founding director of Stanford's Introductory Economics Center. He has a long and distinguished record of public service. Among other roles, he served as a member of the President’s Council of Economic Advisors from 1989 to 1991 and as Under Secretary of the Treasury for International Affairs from 2001 to 2005.

Ryan Triolo (Head TA)

Ryan is a Master's student in Public Policy and International Policy Studies, and has 2 years experience as a Teaching Assistant for Introductory Economics at Stanford.

Nick Pataki

Nick is a Master's student in Public Policy and International Policy Studies, and has 2 years experience as a Teaching Assistant for Introductory Economics at Stanford.

Constantine Yannelis

Constantine is a PhD student in Economics, and has one year experience as a Teaching Assistant for Introductory Economics at Stanford.

Jessie Li

Jessie is a PhD student in Economics, and has one year experience as a Teaching Assistant for Introductory Economics at Stanford

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Tuesday, June 24, 2014 to Monday, September 1, 2014
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This course aims to provide a firm grounding in the foundations of probability and statistics. Specific topics include:

1. Describing data (types of data, data visualization, descriptive statistics)
2. Statistical inference (probability, probability distributions, sampling theory, hypothesis testing, confidence intervals, pitfalls of p-values)
3. Specific statistical tests (ttest, ANOVA, linear correlation, non-parametric tests, relative risks, Chi-square test, exact tests, linear regression, logistic regression, survival analysis; how to choose the right statistical test)

The course focuses on real examples from the medical literature and popular press. Each week starts with "teasers," such as: Should I be worried about lead in lipstick? Should I play the lottery when the jackpot reaches half-a-billion dollars? Does eating red meat increase my risk of being in a traffic accident? We will work our way back from the news coverage to the original study and then to the underlying data. In the process, students will learn how to read, interpret, and critically evaluate the statistics in medical studies.

The course also prepares students to be able to analyze their own data, guiding them on how to choose the correct statistical test and how to avoid common statistical pitfalls. Optional modules cover advanced math topics and basic data analysis in R.


Week 1 - Descriptive statistics and looking at data
Week 2 - Review of study designs; measures of disease risk and association
Week 3 - Probability, Bayes' Rule, Diagnostic Testing
Week 4 - Probability distributions
Week 5 - Statistical inference (confidence intervals and hypothesis testing)
Week 6 - P-value pitfalls; types I and type II error; statistical power; overview of statistical tests
Week 7 - Tests for comparing groups (unadjusted); introduction to survival analysis
Week 8 - Regression analysis; linear correlation and regression
Week 9 - Logistic regression and Cox regression


There are no prerequisites for this course.

Students will need to be familiar with a few basic math tools: summation sign, factorial, natural log, exponential, and the equation of a line; a brief tutorial is available on the course website for students who need a refresher on these topics.



Can I get CME credit for this course?

This free version of the course does not offer CME credits, but there is a fee-based CME version available as well. Go to the Stanford online CME course page for more information. You are welcome to take this free version of the course before the CME course, but note that you will still need to create an account on the CME site, pay the registration fee, and complete the CME Pre-test, Post-test, Evaluation Survey, and Activity Completion Attestation statement in order to receive your credits.

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Welcome to the world’s first online course for deforestation and forest degradation mapping. This course is designed to equip government, academic and non-commerical, non-government organizations with the knowledge needed to monitor forests using the Carnegie Landsat Analysis System-lite or CLASlite. The course provides the scientific basis for each module in CLASlite, along with other information to make forest monitoring easy using Earth observing satellite data.

Background information available from the Carnegie Institute for Science at

To take the course, please begin by completing the Pre-Course Survey.


We only provide CLASlite training and licensing to non-profit, non-commercial organizations. To successfully complete the course, you should have a basic familiarity with geospatial data and Windows PCs.

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Monday, February 3, 2014
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NOTE: For the Winter 2014 session, the course website will go live at 10:00 AM US-PST on Saturday February 1, two days before the course begins, so you have time to familiarize yourself with the website structure, watch some short introductory videos, and look at some preliminary material.

The goal of the course is to help you develop a valuable mental ability – a powerful way of thinking that our ancestors have developed over three thousand years.
Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.
The course is offered in two versions. The eight-week-long Basic Course is designed for people who want to develop or improve mathematics-based, analytic thinking for professional or general life purposes. The ten-week-long Extended Course is aimed primarily at first-year students at college or university who are thinking of majoring in mathematics or a mathematically-dependent subject, or high school seniors who have such a college career in mind. The final two weeks are more intensive and require more mathematical background than the Basic Course. There is no need to make a formal election between the two. Simply skip or drop out of the final two weeks if you decide you want to complete only the Basic Course.

Subtitles for all video lectures available in: Portuguese (provided by The Lemann Foundation), English

Course Syllabus

Instructor’s welcome and introduction
 1.  Introductory material
 2.  Analysis of language – the logical combinators
 3.  Analysis of language – implication
 4.  Analysis of language – equivalence
 5.  Analysis of language – quantifiers
 6.  Working with quantifiers
 7.  Proofs
 8.  Proofs involving quantifiers
 9.  Elements of number theory
10.  Beginning real analysis

Recommended Background

High school mathematics. Specific requirements are familiarity with elementary symbolic algebra, the concept of a number system (in particular, the characteristics of, and distinctions between, the natural numbers, the integers, the rational numbers, and the real numbers), and some elementary set theory (including inequalities and intervals of the real line). Students whose familiarity with these topics is somewhat rusty typically find that with a little extra effort they can pick up what is required along the way. The only heavy use of these topics is in the (optional) final two weeks of the Extended Course.

A good way to assess if your basic school background is adequate (even if currently rusty) is to glance at the topics in the book Adding It Up: Helping Children Learn Mathematics (free download), published by the US National Academies Press in 2001. Though aimed at K-8 mathematics teachers and teacher educators, it provides an excellent coverage of what constitutes a good basic mathematics education for life in the Twenty-First Century (which was the National Academies' aim in producing it).

Suggested Readings

There is one reading assignment at the start, providing some motivational background.
There is a supplemental reading unit describing elementary set theory for students who are not familiar with the material.
There is a course textbook, Introduction to Mathematical Thinking, by Keith Devlin, available at low cost (under $10) from Amazon, in hard copy and Kindle versions, but it is not required in order to complete the course.

For general background on mathematics and its role in the modern world, take a look at the five week survey course on mathematics ("Mathematics: Making the Invisible Visible") Devlin gave at Stanford in fall 2012, available for free download from iTunes University (Stanford), and on YouTube (1234,5), particularly the first halves of lectures 1 and 4.

Course Format

The Basic Course lasts for eight weeks, comprising ten lectures, each with a problem-based work assignment (ungraded, designed for group work), a weekly Problem Set (machine graded), and weekly tutorials in which the instructor will go over some of the assignment and Problem Set questions from the previous week. 

The Extended Course consists of the Basic Course followed by a more intense two weeks exercise called Test Flight. Whereas the focus in the Basic Course is the development of mathematically-based thinking skills for everyday life, the focus in Test Flight is on applying those skills to mathematics itself. 




  • Will I get a certificate after completing this class?

    The course does not carry Stanford credit. If you complete the Basic Course with more than a minimal aggregate mark, you will get a Statement of Accomplishment. If you go on to complete the Extended Course with more than a minimal mark, you will receive a Statement of Accomplishment with Distinction.

  • What are the assignments for this class?

    At the end of each lecture, you will be given an assignment (as a downloadable PDF file, released at the same time as the lecture) that is intended to guide understanding of what you have learned. Worked solutions to problems from the assignments will be described the following week in a video tutorial session given by the instructor.

    Using the worked solutions as guidance, together with input from other students, you will self-grade your assignment work for correctness. The assignments are for understanding and development, not for grade points. You are strongly encouraged to discuss your work with others before, during, and after the self-grading process. These assignments (and the self-grading) are the real heart of the course. The only way to learn how to think mathematically is to keep trying to do so, comparing your performance to that of an expert and discussing the issues with fellow students.

  • Is there a final exam for this course?

    No. The Test Flight exercise in the final two weeks of the Extended Course is built around a Problem Set similar to those used throughout the course, and your submission will be peer evaluated by other students, but the focus is on the process of evaluation itself, with the goal of developing the ability to judge mathematical arguments presented by others. Whilst not an exam, Test Flight is an intense and challenging capstone experience, and is designed to prepare students for further study of university level mathematics.

  • How is this course graded?

    In the Basic Course, grades are awarded for the weekly Problem Sets, which are machine graded. The aggregate grade is provided in the cover note to the Statement of Accomplishment, with an explanation of its significance within the class. In the Extended Course, additional grades are awarded for a series of proof evaluation exercises and for the Test Flight Problem Set (peer evaluated). The aggregate grade is provided in the cover note to the Statement of Accomplishment with Distinction, with an explanation of its significance within the class.

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Tuesday, January 21, 2014
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This is an introductory-level course in supervised learning, with a focus on regression and classification methods. The syllabus includes: linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, model selection and regularization methods (ridge and lasso); nonlinear models, splines and generalized additive models; tree-based methods, random forests and boosting; support-vector machines. Some unsupervised learning methods are discussed: principal components and clustering (k-means and hierarchical).

This is not a math-heavy class, so we try and describe the methods without heavy reliance on formulas and complex mathematics. We focus on what we consider to be the important elements of modern data analysis. Computing is done in R. There are lectures devoted to R, giving tutorials from the ground up, and progressing with more detailed sessions that implement the techniques in each chapter.

The lectures cover all the material in An Introduction to Statistical Learning, with Applications in R by James, Witten, Hastie and Tibshirani (Springer, 2013). As of January 5, 2014, the pdf for this book will be available for free, with the consent of the publisher, on the book website.

Trevor Hastie
Rob Tibshirani
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