Algebra is the language of modern mathematics. This course introduces students to that language through a study of groups, group actions, vector spaces, linear algebra, and the theory of fields.
Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.
Note: this is a 57 MB PDF Document.
Biomedical research today is not only rigorous, innovative and insightful, it also has to be organized and reproducible. With more capacity to create and store data, there is the challenge of making data discoverable, understandable, and reusable. Many funding agencies and journal publishers are requiring publication of relevant data to promote open science and reproducibility of research.
In order to meet to these requirements and evolving trends, researchers and information professionals will need the data management and curation knowledge and skills to support the access, reuse and preservation of data.
This course is designed to address present and future data management needs.
Modern China presents a dual image: a society transforming itself through economic development and social revolution; and the world’s largest and oldest bureaucratic state, coping with longstanding problems of economic and political management. Both images bear the indelible imprint of China’s historical experience, of its patterns of philosophy and religion, and of its social and political thought.
In this free Chinese studies online course, these themes are discussed to understand China in the modern world and as a great world civilization that developed along lines different from those of the Mediterranean.
This semester, we will explore the nuts and bolts of advising and defending Internet-related businesses, organizations and individuals. With the help of practicing cyberlawyers and other outside participants, we will delve into some of the most contested issues involving intellectual property, speech, and privacy on the Net, and the means by which courts and legislatures are asked to take sides and, at times, affect the course of the Internet's evolution.
This site invites you to explore the process of piecing together the lives of ordinary people in the past. It is an experimental, interactive case study based on the research that went into the book and film A Midwife’s Tale, both based upon the remarkable diary of 18th-century midwife/healer Martha Ballard. Although DoHistory is centered on the life of Martha Ballard, you can learn basic skills and techniques for interpreting fragments that survive from any period in history.
This book addresses the following topics: Iterations and fixed points; bifurcations; conjugacy; space and time averages; the contraction fixed point theorem; Hutchinson's theorem and fractal images; hyperbolicity; and symbolic dynamics. 151 page pdf file.
Photography has exploded in recent years as digital cameras have become affordable and easier to use. There are many courses that teach students the artistic aspect of "how to become a better photographer" or "how to improve your eye," but this is not one of them. Instead, students—from one-time users to professionals—become better photographers through an understanding of the technical aspects and terms of a digital camera. Learn why photos look blurry at night, why color management is important, what the difference between sports mode and portrait mode on the camera's dial is, and how to manipulate the camera without the need of these modes in the first place. Topics include exposure and metering, flash, dynamic range, CMOS and CCD sensors, color filter arrays, RAW versus JPEG formats, color spaces and profiles, editing photos with Photoshop, and optical and computational artifacts. Through lectures and hands-on assignments, students understand the jargon and compromises of digital photography that ultimately expose the workings of digital cameras. You are not required to own a digital camera, but if you do, one with a manual mode and an option for RAW is recommended.
The true “hero” of this ancient Greek literature course is the logos, or word, of logical reasoning, as activated by Socratic dialogue. The logos of dialogue requires careful thinking, realized in close reading and reflective writing. The last “word” read in the course comes from Plato’s memories of the last days of Socrates. These memories depend on a thorough understanding of concepts of the hero in all their varieties throughout the history of Greek civilization and beyond. This course is driven by a sequence of dialogues that lead to such an understanding, guiding the attentive reader through some of the major works of the ancient Greek classics, from Homer to Plato.
This free online computer science course is an introduction to the intellectual enterprises of computer science. Topics include algorithms (their design, implementation, and analysis); software development (abstraction, encapsulation, data structures, debugging, and testing); architecture of computers (low-level data representation and instruction processing); computer systems (programming languages, compilers, operating systems, and databases); and computers in the real world (networks, websites, security, forensics, and cryptography). The course teaches students how to think more carefully and how to solve problems more effectively. Problem sets involve extensive programming in C as well as PHP and JavaScript.
This course examines current legal, political, and technical struggles for control/ownership of the global Internet and its content. The course will draw upon a growing body of cyberlaw cases and commentary, class members' research, and participation by invited guests, including lobbyists, politicians, journalists, and scholars from the HLS faculty and elsewhere. Course themes include the interaction between emerging Internet self-governance regimes and rule by traditional sovereigns; the expression of conflicting interests of commercial and individual Internet speakers/broadcasters; new modes of control over widely distributed intellectual property ("privication"); and the potential for market giants and other architects of Internet technologies to constrain behavior online in ways governments find difficult to assimilate. Classroom discussion of these topics will be augmented by online discussion software through which students will have one-on-one exchanges about issues in the course. No specialized technical expertise or prerequisite required, but students should be prepared to use and experiment with new technologies as part of their coursework and participation.
Computer Science 50: Introduction to Computer Science I is a first course in computer science at Harvard College for concentrators and non-concentrators alike. More than just teach you how to program, this course teaches you how to think more methodically and how to solve problems more effectively. As such, its lessons are applicable well beyond the boundaries of computer science itself. That the course does teach you how to program, though, is perhaps its most empowering return. With this skill comes the ability to solve real-world problems in ways and at speeds beyond the abilities of most humans.
This book addresses the following topics: The Campbell Baker Hausdor formula; sl(2) and its Representations; classical simple algebras; Engel-Lie-Cartan-Weyl; conjugacy of Cartan subalgebras; simple finite dimensional algebras; cyclic highest weight modules; Serre's theorem; Clifford algebras and spin representations; The Kostant Dirac operator; The center of U(g); and Chevalley's theorem.
Professors Lessig and Zittrain will teach a research seminar on the Microsoft case. The seminar will meet at least once a week, beginning the week of 9/21. It will review the proceedings leading up to the present antitrust action, and then shadow the current trial. We will collect transcripts from the case, which will be assigned each week, as well as other readings to be determined. In addition to the ultimate question of liability, we will consider whether there are special issues that cyberspace raises for antitrust. The most significant requirement of the course will be classroom participation; a short paper at the end will be required.
This resource is a playlist containing pointers to other resources. This will be a collection of information and resources for Beowulf.
As visitors to River City, students travel back in time, bringing their 21st century skills and technology to address 19th century problems. With funding from the National Science Foundation, we have developed an interactive computer simulation for middle grades science students to learn scientific inquiry and 21st century skills. River City has the look and feel of a video game but contains content developed from National Science Education Standards, National Educational Technology Standards, and 21st Century Skills. All middle grades (6-9) teachers in North America are invited to participate in the River City Project.
This book represents course notes for a one semester course at the undergraduate level giving an introduction to Riemannian geometry and its principal physical application, Einstein’s theory of general relativity. The background assumed is a good grounding in linear algebra and in advanced calculus, preferably in the language of differential forms.
This book covers the following topics: The principal curvatures; rules of calculus; Levi-Civita Connections; bundle of frames; connections on principal bundles; Gauss's lemma; special relativity; Die Grundlagen der Physik; submersions; Petrov types; and Star.
This online math course develops the mathematics needed to formulate and analyze probability models for idealized situations drawn from everyday life. Topics include elementary set theory, techniques for systematic counting, axioms for probability, conditional probability, discrete random variables, infinite geometric series, and random walks. Applications to card games like bridge and poker, to gambling, to sports, to election results, and to inference in fields like history and genealogy, national security, and theology. The emphasis is on careful application of basic principles rather than on memorizing and using formulas.
I have taught the beginning graduate course in real variables and functional analysis three times in the last five years, and this book is the result. The course assumes that the student has seen the basics of real variable theory and point set topology. The elements of the topology of metrics spaces are presented (in the nature of a rapid review) in Chapter I. The course itself consists of two parts: 1) measure theory and integration, and 2) Hilbert space theory, especially the spectral theorem and its applications. In Chapter II I do the basics of Hilbert space theory, i.e. what I can do without measure theory or the Lebesgue integral. The hero here (and perhaps for the first half of the course) is the Riesz representation theorem. Included is the spectral theorem for compact self-adjoint operators and applications of this theorem to elliptic partial di erential equations. Chapter III is a rapid presentation of the basics about the Fourier transform. Chapter IV is concerned with measure theory.
This course is all about understanding: understanding what's going on inside your computer when you flip on the switch, why tech support has you constantly rebooting your computer, how everything you do on the Internet can be watched by others, and how your computer can become infected with a worm just by turning it on. In this course we demystify computers and the Internet, along with their jargon, so that students understand not only what they can do with each but also how it all works and why. Students leave this course armed with a new vocabulary and equipped for further exploration of computers and the Internet. Topics include hardware, software, the Internet, multimedia, security, website development, programming, and dotcoms. This course is designed both for those with little, if any, computer experience and for those who use a computer every day.