Continues 18.100, in the direction of manifolds and global analysis. Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, differential forms, n-dimensional version of Stokes' theorem. 18.901 helpful but not required.
Includes the study of the gross and microscopic structure of the systems of the human body with special emphasis on the relationship between structure and function. Integrates anatomy and physiology of cells, tissues, organs, the systems of the human body, and mechanisms responsible for homeostasis.
Includes sections on the Endocrine System, the Cardiovascular System, the Lymphatic and Immune System, the Respiratory System, the Digestive System, Nutrition, the Urinary System, the Reproductive System, and Development and Inheritance.
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.
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; well 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.
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 modelintegers 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_ĺĚĺ_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.
This course is a review of basic mathematics skills. Here's what's covered:
-fundamental numeral operations of addition, subtraction, multiplication
division of whole numbers, fractions, and decimals
-ratio and proportion
-systems of measurement
-an introduction to geometry
NOTE: Open Campus courses are non-credit reviews and tutorials and cannot be used to satisfy requirements in any curriculum at BPCC. (Basic Mathematics Course by Bossier Parish Community College is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Based on a work at http://bpcc.edu/opencampus/index.html.)
"A lot of people thought we were an overnight sensation," says The Beatles' Paul McCartney in The Beatles: Eight Days a Week “The Touring Years," "but they were wrong." Indeed, though to many fans The Beatles seem to have been a big bang, bursting from Liverpudlian obscurity to international stardom with their 1963 debut album Please Please Me, quite the opposite is true. Between 1960-63, The Beatles worked. They were, after all, young men from the working classes of Liverpool, a city still recovering from World War II. They worked to earn money for basic necessities, playing pub sets both day and night and performing lengthy residencies in Hamburg, Germany, one of which included a stretch of 104 consecutive shows. They worked on repertoire, learning dozens of "cover" songs spanning several genres. They worked on their group sound, playing several sets a night and fine tuning the skills that helped them "hold" audiences at the dance floor, even those who may not have come specifically to see them.
In this lesson, students learn about the impact of The Beatles on their teenage audience, particularly in relation to the group's image as a "rock band."
Essential Question: How did The Beatles establish a new paradigm for the image of "the star," and how did that image support their global success?
In this lesson, students learn about the Beatles active stance against segregation and consider what the band's example meant for an emerging youth culture.
This lesson explores first the role Brian Epstein played in helping craft The Beatles' visual presence, group identity and team unity, the way he helped the group transition from successful nightclub act to international sensation.