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Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

Laszlo Tisza was Professor of Physics Emeritus at MIT, where he began teaching in 1941. This online publication is a reproduction the original lecture notes for the course "Applied Geometric Algebra" taught by Professor Tisza in the Spring of 1976. Over the last 100 years, the mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These sophisticated tools provide powerful machinery for describing the physical world, however, their physical interpretation is often not intuitive. These course notes represent Prof. Tisza's attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics. Prof. Tisza revisits many elementary problems with an advanced treatment in order to help develop the geometrical intuition for the algebraic machinery that may carry over to more advanced problems. The lecture notes came to MIT OpenCourseWare by way of Samuel Gasster, '77 (Course 18), who had taken the course and kept a copy of the lecture notes for his own reference. He dedicated dozens of hours of his own time to convert the typewritten notes into LaTeX files and then publication-ready PDFs. You can read about his motivation for wanting to see these notes published in his Preface below. Professor Tisza kindly gave his permission to make these notes available on MIT OpenCourseWare.

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I designed the course for graduate students who use statistics in their research, plan to use statistics, or need to interpret statistical analyses performed by others. The primary audience are graduate students in the environmental sciences, but the course should benefit just about anyone who is in graduate school in the natural sciences. The course is not designed for those who want a simple overview of statistics; we’ll learn by analyzing real data. This course or equivalent is required for UMB Biology and EEOS Ph.D. students. It is a recommended course for several of the intercampus graduate school of marine science program options.

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This course is an arithmetic course intended for college students, covering whole numbers, fractions, decimals, percents, ratios and proportions, geometry, measurement, statistics, and integers using an integrated geometry and statistics approach. The course uses the late integers model—integers are only introduced at the end of the course.

This course is particularly focused on helping you develop visual literacy skills, but all the college courses you take are to some degree about information literacy. Visual literacy is really just a specialized type of information literacy. The skills you acquire in this course will help you become an effective researcher in other fields, as well.

This course is an exploration of visual art forms and their cultural connections for the student with little experience in the visual arts. It includes a brief study of art history and in depth studies of the elements, media, and methods used in creative processes and thought. Upon successful completion of this course, students will be able to: interpret examples of visual art using a five-step critical process that includes description, analysis, context, meaning, and judgment; identify and describe the elements and principles of art; use analytical skills to connect formal attributes of art with their meaning and expression; explain the role and effect of the visual arts in societies, history, and other world cultures; articulate the political, social, cultural, and aesthetic themes and issues that artists examine in their work; identify the processes and materials involved in art and architectural production; utilize information to locate, evaluate, and communicate information about visual art in its various forms. Note that this course is an alternative to the Saylor FoundationĺÎĺ_ĺĚĺ_s ARTH101A and has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. This free course may be completed online at any time. (Art History 101B)

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

The Art of the Probable" addresses the history of scientific ideas, in particular the emergence and development of mathematical probability. But it is neither meant to be a history of the exact sciences per se nor an annex to, say, the Course 6 curriculum in probability and statistics. Rather, our objective is to focus on the formal, thematic, and rhetorical features that imaginative literature shares with texts in the history of probability. These shared issues include (but are not limited to): the attempt to quantify or otherwise explain the presence of chance, risk, and contingency in everyday life; the deduction of causes for phenomena that are knowable only in their effects; and, above all, the question of what it means to think and act rationally in an uncertain world. Our course therefore aims to broaden students’ appreciation for and understanding of how literature interacts with--both reflecting upon and contributing to--the scientific understanding of the world. We are just as centrally committed to encouraging students to regard imaginative literature as a unique contribution to knowledge in its own right, and to see literary works of art as objects that demand and richly repay close critical analysis. It is our hope that the course will serve students well if they elect to pursue further work in Literature or other discipline in SHASS, and also enrich or complement their understanding of probability and statistics in other scientific and engineering subjects they elect to take.

We will explore images that pertain to the emergence of Japan as a modern state. We will focus on images that depict Japan as it comes into contact with the rest of the world after its long and deep isolation during the feudal period. We will also cover city planning of Tokyo that took place after WWII, and such topics as the 1964 Tokyo Olympics.

A Critical Introduction to U.S. Government and Politics

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Description: This course pack is designed to meet the learning outcomes for Adult Literacy Fundamental English Level 1 (roughly equivalent to beginner to grade 1.5 in the K-12 system). Every of the nine chapters includes a level-appropriate, high-interest reading of approximately 100 words. The readings are freely available in a separate reader with convenient links to the readings in each chapter of this course pack. The online version of this course pack also contains audio recordings of each story in the reader. These recordings, combined with vocabulary and word pattern exercises, prepare the Level 1 student to read each paragraph-long text with greater independence. Font size and line spacing can be adjusted in the online view, and have been enhanced for the print and PDF versions for easier reading. This course pack has been reviewed by subject experts from colleges and universities.

This course pack is designed to meet the learning outcomes for Adult Literacy Fundamental English Level 2 (roughly equivalent to grades 1.5 to 3 in the K-12 system). Every of the eight chapters includes a level-appropriate, high-interest reading of approximately 200 words. The readings are freely available in a separate reader with convenient links to the readings in each chapter of this course pack. The online version of this course pack also contains audio recordings of each story in the reader. These recordings, combined with vocabulary and word pattern exercises, prepare the Level 2 student to read each chapter with greater independence. Font size and line spacing can be adjusted in the online view, and have been enhanced for the print and PDF versions for easier reading. This course pack has been reviewed by subject experts from colleges and universities.

This course pack is designed to meet the learning outcomes for Adult Literacy Fundamental English Level 3 (roughly equivalent to grades 3 to 4.5 in the K-12 system). Every chapter within the three units includes a level-appropriate, high-interest reading of between 350 and 500 words. The readings are freely available in a separate reader with convenient links to the readings in each chapter of this course pack. For students using this program in a self-paced format, there are audio clips embedded throughout the course pack. These clips narrate the denser sections of text. Font size and line spacing can be adjusted in the online view, and have been enhanced for the print and PDF versions for easier reading. This course pack has been reviewed by subject experts from colleges and universities.

This course pack is designed to meet the learning outcomes for Adult Literacy Fundamental English Level 4 (roughly equivalent to grades 4.5 to 6 in the K-12 system). Every chapter includes a level-appropriate, high-interest reading of between 400 and 500 words. The readings are freely available in a separate reader with convenient links to the readings in each chapter of this course pack. Font size and line spacing can be adjusted in the online view, and have been enhanced for the print and PDF versions for easier reading. This course pack has been reviewed by subject experts from colleges and universities.

This course pack is designed to meet the learning outcomes for Adult Literacy Fundamental English Level 5 (roughly equivalent to grades 6 to 7.5 in the K-12 system). Every chapter includes a level-appropriate, high-interest reading of between 500 and 800 words. The readings are freely available in a separate reader with convenient links to the readings in each chapter of this course pack. Font size and line spacing can be adjusted in the online view, and have been enhanced for the print and PDF versions for easier reading. This course pack has been reviewed by subject experts from colleges and universities.