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 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.
This is a guide to good practices for college and university open-access (OA) policies. It's based on the type of rights-retention OA policy first adopted at Harvard, Stanford, MIT, and the University of Kansas. Policies of this kind have since been adopted at a wide variety of institutions in North America, Europe, Africa, and Asia, for example, at public and private institutions, large and small institutions, affluent and indigent institutions, research universities and liberal arts colleges, and at whole universities, schools within universities, and departments within schools.
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.
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.
The Internet is at once a constructive and disruptive technology. As more and more of our lives move online, we are faced with opportunities to do new and amazing things. Concurrently, we encounter problems that no one anticipated as we collectively built the internet as we know it today. This seminar will consider some of the most intriguing of the issues to which the advent of the internet has given and continues to give rise. It will focus on a cluster of topics about which any computer user likely knows a good deal already: spam, spyware, peer-to-peer file sharing, personal privacy, and e-commerce. It will also venture into a few issues-like blogging, RSS (Really Simple Syndication), social software, and internet filtering-that may be less familiar. The internet and the practice of law are both increasingly global in nature, so the seminar will take special care to delve into basic topics in international law. A specific series of laws, regulations and policies related to online activities continues to evolve. In particular, the seminar will focus on the law of intellectual property related to the Internet-whether the IP relates to code, commercial data, music or other content-which has broad and complex application for anyone using the internet in the current multi-jurisdictional world. We'll consider who makes the laws in an environment that crosses national borders by its very nature and where enforcement is an extremely tricky matter. We will imagine what these new technologies might do to culture in the United States and to other cultures throughout the world, particularly those in developing countries. Participants should be willing to experiment with new information technologies in a learning environment.
- General Law
- Material Type:
- Harvard University
- Provider Set:
- Berkman Center for Internet and Society at Harvard law School
- John Palfrey
- Date Added:
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.
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.
The course World War and Society in the Twentieth Century: World War II is a thematic exploration of the war and its time through feature films, primary sources, and scholarly interpretations.
It seeks to provide a means for analyzing and evaluating what one reads or sees about World War II in terms of historical accuracy and for gaining a broader understanding of different perspectives. Themes include the impact of war on soldiers and civilians, on the home front, women in war, the Japanese and German viewpoints, and postwar issues. Films include Mrs. Miniver, The Pianist, The Winter War, So Proudly We Hail, Taking Sides, The Hiding Place, and The Cranes Are Flying.