Positive Definite Matrices
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This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
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Introduction to applied linear algebra and linear dynamical systems, with applications to circuits, signal processing, communications, and control systems. Topics include: Least-squares aproximations of over-determined equations and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm and singular value decomposition. Eigenvalues, left and right eigenvectors, and dynamical interpretation. Matrix...more
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This is a basic course on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.
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Professor Diamond continues her discussion of the nervous system and begins by revisiting her discussion of the ascending path. She notes the presence of substantia gelatinosa in the area of the second neuron and describes the concept of homunculus, which is the upside-down representation of the body in the brain, and notes that this does not occur in the face for reasons unknown to neurologists. Professor Diamond then begins describing...more
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In order for Social Security to work, people have to believe there's some possibility that the world will last forever, so that each old generation will have a young generation to support it. The overlapping generations model, invented by Allais and Samuelson but here augmented with land, represents such a situation. Financial equilibrium can again be reduced to general equilibrium. At first glance it would seem that the model requires a...more
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SARS, avian influenza and swine flu are the first new diseases of the twenty-first century. They are all diseases of globalization, or diseases of modernity, and while relatively limited in their impact, they have offered dress-rehearsals for future epidemics. As information about SARS spread internationally in 2002, in spite of China's campaign of silence, the global response had a curiously twofold character: on one hand, the...more
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Recap: Example: Minimum Cardinality Problem, Interpretation As Convex Relaxation, Interpretation Via Convex Envelope, Weighted And Asymmetric L_1 Heuristics, Regressor Selection, Sparse Signal Reconstruction, L_1-Norm Methods For Convex-Cardinality Problems Part II, Total Variation Reconstruction, Total Variation Reconstruction, TV Reconstruction, L_2 Reconstruction, Iterated Weighted L_1 Heuristic, Sparse Solution Of Linear Inequalities,...more
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The stock market is the information center for the corporate sector. It represents individuals' ownership in publicly-held corporations. Although corporations have a variety of stakeholders, the shareholders of a for-profit corporation are central since the company is ultimately responsible to them. Companies offer dividends, stock repurchases and stock dividends to give profits back to shareholders or to signal information. Companies can...more
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The last lecture in the course wraps up the discussion of clinical psychology with a discussion of treatment efficacy. Does therapy actually work? Professor Bloom summarizes the different types of influences that clinical interventions might have on people who receive therapy. Professor Bloom ends with a review of one of the most interesting research topics in "positive psychology," happiness. What makes us happy? How does happiness...more
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This lecture is an introduction to kinematics which ultimately leads (in Lecture 4) to trajectories in three-dimensions. Professor Lewin begins with a description of one-dimensional motion of a particle. He talks about average velocity, the importance of + and - signs, and our free choice of origin. He moves into a conversation about average speed vs. average velocity, instantaneous velocity (reviewing when velocity is zero,...more
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In this lecture, Professor Donald Kagan explores the rise, fall, and significance of tyrannies in the Greek polis. He argues that the various tyrannies in the Greek world had both negative and positive aspects, which need to be appreciated. For instance, on the one hand, tyrannies promoted economic, commercial and artistic advances. On the other hand, tyrannies ruled absolutely and curbed the freedom of the polis. Finally, Professor...more
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Guest Lecturer: Jacob Mattingley, Logistics, Agenda, Convex Set, Convex Cone, Polyhedra, Positive Semidefinite Cone, Operations That Preserve Convexity, Intersection, Affine Function, Generalized Inequalities, Minimum And Minimal Elements, Supporting Hyperlane Theorem, Minimum And Minimal Elements Via Dual Inequalities
