Pricing Options with Mathematical Models

<div dir="ltr" style="text-align: left;" trbidi="on"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiznyvuD6QH5SigvR-lyBIw3JTLWyzt5gWhyphenhyphencb3u67VDoFCSpS3Q_Jc6eV4SlpEitacknkaEPmTt3jSyDziBFqa5C80XZT7SSg5r5VafsWHV9rUzCrNoMO4BUvL51UhSXLQJzyfsOu89WJ/s1600/caltech-200x121.png" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhiznyvuD6QH5SigvR-lyBIw3JTLWyzt5gWhyphenhyphencb3u67VDoFCSpS3Q_Jc6eV4SlpEitacknkaEPmTt3jSyDziBFqa5C80XZT7SSg5r5VafsWHV9rUzCrNoMO4BUvL51UhSXLQJzyfsOu89WJ/s400/caltech-200x121.png" /></a><br /><br /><div class="course-start" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; font-weight: bold; line-height: 24px; margin: 12px 0px; text-align: center;"><span style="box-sizing: border-box;">Starts on September 18, 2016</span></div><div class="course-enroll-actions" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px;"><a class="btn btn-cta txt-center js-enroll-btn " href="https://courses.edx.org/register?course_id=course-v1%3ACaltechX%2BBEM1105x%2B3T2016&enrollment_action=enroll&email_opt_in=true" style="background: rgb(94, 162, 15); border-radius: 2px; border: 0px; box-sizing: border-box; color: #fafafa; cursor: pointer; display: inline-block; font-size: 1.3em; font-weight: bold; line-height: 1.5; margin-bottom: 12px; padding: 10px 20px; text-align: center; text-decoration: none; transition: background 0.2s; width: 276px;">Enroll Now</a><div class="form-field" style="box-sizing: border-box; padding-left: 20px; position: relative;"><label class="register-emails" style="box-sizing: border-box; color: #363636; display: block; font-size: 0.75em; line-height: 1.5;"></label></div></div><div><br /></div><div><div class="content-grouping" style="box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px; margin-bottom: 24px;"><h2 class="course-info-heading" style="border-bottom-width: 0px; box-sizing: border-box; color: #050505; display: inline-block; font-size: 1.25em; line-height: 1.45em; margin: 0px; padding: 0px 0px 0.45em;">About this course</h2><div class="course-description wysiwyg-content expanded" style="box-sizing: border-box; position: relative;"><div class="see-more-content" style="box-sizing: border-box; height: auto; overflow: hidden;" tabindex="-1"><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">This is an introductory course on options and other financial derivatives, and their applications to risk management. We will start with discrete-time, binomial trees models, but most of the course will be in the framework of continuous-time, Brownian Motion driven models. A basic introduction to Stochastic, Ito Calculus will be given. The benchmark model will be the Black-Scholes-Merton pricing model, but we will also discuss more general models, such as stochastic volatility models. We will discuss both the Partial Differential Equations approach, and the probabilistic, martingale approach. We will also cover an introduction to modeling of interest rates and fixed income derivatives.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">I teach the same class at Caltech, as an advanced undergraduate class. This means that the class may be challenging, and demand serious effort. On the other hand, successful completion of the class will provide you with a full understanding of the standard option pricing models, and will enable you to study the subject further on your own, or otherwise. You should have a working knowledge of basic calculus, statistics, and probability and be interested in the use of mathematical modeling. Please go to <a href="https://courses.edx.org/courses/course-v1:CaltechX+BEM1105x+3T2016/courseware/7da89918eaf24c3d964288b08a5cdf8b/aeb336e0c5304539b460e903ce354431/" style="box-sizing: border-box; color: #2968aa; text-decoration: none;" target="_blank">Unit 0</a> in the Course Outline to take the prerequisites assessment.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div></div><div aria-hidden="true" class="see-more-cta" style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em;"><br /></div></div></div><div class="content-grouping" style="box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px; margin-bottom: 24px;"><h3 class="course-info-heading" style="border-bottom-width: 0px; box-sizing: border-box; color: #050505; display: inline-block; font-size: 1.25em; line-height: 1.5em; margin: 0px; padding: 0px;">What you'll learn</h3><div class="course-info-list wysiwyg-content" style="box-sizing: border-box;"><ul style="box-sizing: border-box; margin: 0px 0px 20px; padding: 12px 0px 12px 16px;"><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Option pricing and risk-hedging methods in the binomial tree and Black-Scholes-Merton models</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Ability to price options and other financial derivatives in models beyond Black-Scholes-Merton</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Present interest rate models and the pricing of interest rate derivatives</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Evaluate the economics and mathematics behind the financial models presented</li></ul><div class="separator" style="clear: both; text-align: center;"><iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/JyKBLCQdQc4/0.jpg" src="https://www.youtube.com/embed/JyKBLCQdQc4?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div><div><br /></div></div></div></div></div>

Pricing Options with Mathematical Models

Starts on September 18, 2016 Enroll Now About this course This is an introductory course on options and other financial derivatives, and the...

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The Evolving Universe

<div dir="ltr" style="text-align: left;" trbidi="on"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjazXlgPd5EFqH93LiSGDrkrJsuc0Hih6D6wkItGD62Q19TyS08NSor5tYBPwRGltNgqH8FTr_GmjfFhY3cpp0Yfzsuo3lr9DRkRcAaTGLCEyylxAljnV1BODUYEFuASfygguhEZfLS1TC1/s1600/caltech-200x121.png" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjazXlgPd5EFqH93LiSGDrkrJsuc0Hih6D6wkItGD62Q19TyS08NSor5tYBPwRGltNgqH8FTr_GmjfFhY3cpp0Yfzsuo3lr9DRkRcAaTGLCEyylxAljnV1BODUYEFuASfygguhEZfLS1TC1/s400/caltech-200x121.png" /></a><br /><div class="course-start" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; font-weight: bold; line-height: 24px; margin: 12px 0px; text-align: center;"><div style="box-sizing: border-box;">Archived</div><span style="box-sizing: border-box;">Future Dates To Be Announced</span></div><div class="course-enroll-actions" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px;"><a class="btn btn-cta txt-center js-enroll-btn " href="https://courses.edx.org/register?course_id=CaltechX%2FAy1001x%2F2T2014&enrollment_action=enroll&email_opt_in=true" style="background: rgb(53, 92, 9); border-radius: 2px; border: 0px; box-sizing: border-box; color: white; cursor: pointer; display: inline-block; font-size: 1.3em; font-weight: bold; line-height: 1.5; margin-bottom: 12px; outline: 0px; padding: 10px 20px; text-align: center; text-decoration: none; transition: background 0.2s; width: 276px;">Enroll Now</a></div><div class="course-enroll-actions" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px;"><br /></div><div class="course-enroll-actions" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px;"><div class="content-grouping" style="box-sizing: border-box; margin-bottom: 24px;"><div class="course-description wysiwyg-content expanded" style="box-sizing: border-box; position: relative;"><div class="see-more-content" style="box-sizing: border-box; height: auto; outline: none; overflow: hidden;" tabindex="-1"><span style="box-sizing: border-box; color: #303030; font-weight: 700;">This is an Archived Course</span><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">EdX keeps courses open for enrollment after they end to allow learners to explore content and continue learning. <em style="box-sizing: border-box;">All features and materials may not be all available</em>. Check back often to see when new course start dates are announced.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">This is an introductory astronomy survey class that covers our understanding of the physical universe and its major constituents, including planetary systems, stars, galaxies, black holes, quasars, larger structures, and the universe as a whole. We will learn how modern astronomical observations and applications of physics we know from the planet Earth reveal the nature of these objects and explain their observed properties, and tell us how they form and evolve. We will also examine various cosmic phenomena, from variable or exploding stars to the expansion of the universe and the evidence for dark matter, dark energy, and the big bang. The universe as a whole and all of its major constituents are evolving, and we now have a fairly complete and consistent picture of these processes that is based on the objective evidence from observations and the laws of physics. The goal of this class is both to learn about the fascinating objects and phenomena that populate the universe, and to understand how we know all that.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div></div><div aria-hidden="true" class="see-more-cta" style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em;"><a class="see-more-reveal" href="https://www.edx.org/course/evolving-universe-caltechx-ay1001x#!" style="box-sizing: border-box; color: #2968aa; text-decoration: none;"><span aria-hidden="true" class="fa-stack fa-lg" style="box-sizing: border-box; display: inline-block; font-size: 1.33333em; height: 2em; line-height: 2em; position: relative; vertical-align: middle; width: 20px;"><span class="fa fa-circle-o fa-stack-1x" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: inherit; font-stretch: normal; left: 0px; line-height: inherit; position: absolute; text-align: center; text-rendering: auto; transform: translate(0px, 0px); width: 20px;"></span><span class="fa fa-minus fa-stack-1x" style="-webkit-font-smoothing: antialiased; box-sizing: border-box; display: inline-block; font-family: FontAwesome; font-size: 0.5em; font-stretch: normal; left: 0px; line-height: inherit; position: absolute; text-align: center; text-rendering: auto; transform: translate(0px, 0px); width: 20px;"></span></span> Hide</a></div></div></div><div class="content-grouping" style="box-sizing: border-box; margin-bottom: 24px;"><h3 class="course-info-heading" style="border-bottom-width: 0px; box-sizing: border-box; color: #050505; display: inline-block; font-size: 1.25em; line-height: 1.5em; margin: 0px; padding: 0px;">What you'll learn</h3><div class="course-info-list wysiwyg-content" style="box-sizing: border-box;"><ul style="box-sizing: border-box; margin: 0px 0px 20px; padding: 12px 0px 12px 16px;"><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Gain an understanding of the physical universe, including planetary systems, stars, galaxies, black holes, quasars, larger structures, and the universe as a whole</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Learn how modern astronomical observations and applications of physics reveal the nature of the physical universe</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Examine various cosmic phenomena, from variable or exploding stars to the expansion of the universe and the evidence for dark matter, dark energy, and the big bang</li></ul><div class="separator" style="clear: both; text-align: center;"><iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/WzliYGGSVlg/0.jpg" src="https://www.youtube.com/embed/WzliYGGSVlg?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div><div><br /></div></div></div></div></div>

The Evolving Universe

Archived Future Dates To Be Announced Enroll Now This is an Archived Course EdX keeps courses open for enrollment after they end to allow le...

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Quantum Cryptography

<div dir="ltr" style="text-align: left;" trbidi="on"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjSurLxRohpXz6b2mmnl7DxJith1YcuyIZN7jyemy25x68y6WYwAoAn-OCZXwcvSK-BiHu8HHVLpHPkh7whkRbF5nc0uq91S2aak6_TwSyp8G0WKavtpv81QnAftMaitqrpa6sbEBBZTV1/s1600/caltech-200x121.png" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjSurLxRohpXz6b2mmnl7DxJith1YcuyIZN7jyemy25x68y6WYwAoAn-OCZXwcvSK-BiHu8HHVLpHPkh7whkRbF5nc0uq91S2aak6_TwSyp8G0WKavtpv81QnAftMaitqrpa6sbEBBZTV1/s400/caltech-200x121.png" /></a><br /><div class="course-start" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; font-weight: bold; line-height: 24px; margin: 12px 0px; text-align: center;"><span style="box-sizing: border-box;">Starts on October 10, 2016</span></div><div class="course-enroll-actions" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px;"><a class="btn btn-cta txt-center js-enroll-btn " href="https://courses.edx.org/register?course_id=course-v1%3ACaltechDelftX%2BQuCryptox%2B3T2016&enrollment_action=enroll&email_opt_in=true" style="background: rgb(53, 92, 9); border-radius: 2px; border: 0px; box-sizing: border-box; color: white; cursor: pointer; display: inline-block; font-size: 1.3em; font-weight: bold; line-height: 1.5; margin-bottom: 12px; outline: 0px; padding: 10px 20px; text-align: center; text-decoration: none; transition: background 0.2s; width: 276px;">Enroll Now</a><div class="form-field" style="box-sizing: border-box; padding-left: 20px; position: relative;"><label class="register-emails" style="box-sizing: border-box; color: #363636; display: block; font-size: 0.75em; line-height: 1.5;"></label></div></div><div><h2 class="course-info-heading" style="background-color: white; border-bottom-width: 0px; box-sizing: border-box; color: #050505; display: inline-block; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 1.25em; line-height: 1.45em; margin: 0px; padding: 0px 0px 0.45em;">About this course</h2><span style="background-color: white; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px;"></span><div class="course-description wysiwyg-content expanded" style="background-color: white; box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px; position: relative;"><div class="see-more-content" style="box-sizing: border-box; height: auto; overflow: hidden;" tabindex="-1"><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">How can you tell a secret when everyone is able to listen in? In this course, you will learn how to use quantum effects, such as quantum entanglement and uncertainty, to implement cryptographic tasks with levels of security that are impossible to achieve classically.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">This interdisciplinary course is an introduction to the exciting field of quantum cryptography, developed in collaboration between QuTech at Delft University of Technology and the California Institute of Technology.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">By the end of the course you will</div><ul style="box-sizing: border-box; margin: 1em 0px; padding: 0px 0px 0px 40px;"><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Be armed with a fundamental toolbox for understanding, designing and analyzing quantum protocols.</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Understand quantum key distribution protocols.</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Understand how untrusted quantum devices can be tested.</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Be familiar with modern quantum cryptography – beyond quantum key distribution.</li></ul><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">This course assumes a solid knowledge of linear algebra and probability at the level of an advanced undergraduate. Basic knowledge of elementary quantum information (qubits and simple measurements) is also assumed, but if you are completely new to quantum information additional videos are provided for you to fill in any gaps.</div></div></div></div></div>

Quantum Cryptography

Starts on October 10, 2016 Enroll Now About this course How can you tell a secret when everyone is able to listen in? In this course, you wi...

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Principles of Economics with Calculus

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFVS4DLrVOUk-Xo8AwfF6adkgfY4k4VbEojpQjSFVQ30KyPYKq7icA04CUTaQ-iR-H6fKnFBgPJvORCpQKJyNLdG5IelIku4sFtZGvW4D1RmgasKPlruJbKqTsHF4S8ICmK56pWlNHMVqO/s1600/caltech-200x121.png" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFVS4DLrVOUk-Xo8AwfF6adkgfY4k4VbEojpQjSFVQ30KyPYKq7icA04CUTaQ-iR-H6fKnFBgPJvORCpQKJyNLdG5IelIku4sFtZGvW4D1RmgasKPlruJbKqTsHF4S8ICmK56pWlNHMVqO/s400/caltech-200x121.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="content-grouping" style="box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px; margin-bottom: 24px;"><h2 class="course-info-heading" style="border-bottom-width: 0px; box-sizing: border-box; color: #050505; display: inline-block; font-size: 1.25em; line-height: 1.45em; margin: 0px; padding: 0px 0px 0.45em;">About this course</h2><div class="course-description wysiwyg-content expanded" style="box-sizing: border-box; position: relative;"><div class="see-more-content" style="box-sizing: border-box; height: auto; overflow: hidden;" tabindex="-1"><span style="box-sizing: border-box; color: #303030; font-weight: 700;">This is an Archived Course</span><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">EdX keeps courses open for enrollment after they end to allow learners to explore content and continue learning. <em style="box-sizing: border-box;">All features and materials may not be all available</em>. Check back often to see when new course start dates are announced.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;">This course provides a quantitative and model-based introduction to basic economic principles, and teaches how to apply them to make sense of a wide range of real world problems. Examples of applications include predicting the impact of technological changes in market prices, calculating the optimal gasoline tax, and measuring the value of new products. This is a real Caltech class. It will be taught concurrently to Caltech and on-line students. This has two implications. On the costs side: the class is challenging, makes extensive use of calculus, and will demand significant effort. On the benefit side: successful completion of the class will provide you with an in-depth understanding of basic economics, and will permanently change the way you see the world.</div><div style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 1em;"></div></div><div aria-hidden="true" class="see-more-cta" style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em;"><br /></div></div></div><div class="content-grouping" style="box-sizing: border-box; color: #4e4e4e; font-family: "Open Sans", Arial, Helvetica, sans-serif; font-size: 16px; line-height: 24px; margin-bottom: 24px;"><h3 class="course-info-heading" style="border-bottom-width: 0px; box-sizing: border-box; color: #050505; display: inline-block; font-size: 1.25em; line-height: 1.5em; margin: 0px; padding: 0px;">What you'll learn</h3><div class="course-info-list wysiwyg-content" style="box-sizing: border-box;"><ul style="box-sizing: border-box; margin: 0px 0px 20px; padding: 12px 0px 12px 16px;"><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;">Understand, apply, and analyze calculus-based economic models</li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;"><span data-sheets-userformat="[null,null,8320,null,null,null,null,null,null,null,2,null,null,null,null,null,10]" data-sheets-value="\n- Understand, apply, and analyze calculus-based economic models\n- Translate economic principles to the investigation of a wide range of real world problems\n- Elaborate on an in-depth understanding of basic economics and its applications"]" style="box-sizing: border-box;">Translate economic principles to the investigation of a wide range of real world problems</span></li><li style="box-sizing: border-box; font-size: 1em !important; line-height: 1.5em; margin-bottom: 5px;"><span data-sheets-userformat="[null,null,8320,null,null,null,null,null,null,null,2,null,null,null,null,null,10]" data-sheets-value="\n- Understand, apply, and analyze calculus-based economic models\n- Translate economic principles to the investigation of a wide range of real world problems\n- Elaborate on an in-depth understanding of basic economics and its applications"]" style="box-sizing: border-box;">Elaborate on an in-depth understanding of basic economics and its applications</span></li></ul></div></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><iframe width="320" height="266" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/Y7C6Zthx4lE/0.jpg" src="https://www.youtube.com/embed/Y7C6Zthx4lE?feature=player_embedded" frameborder="0" allowfullscreen></iframe></div><br /></div>

Principles of Economics with Calculus

About this course This is an Archived Course EdX keeps courses open for enrollment after they end to allow learners to explore content and c...

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