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.

Current work on semantics and questions of logic and meaning for syntactic systems in generative grammar.

Device and circuit level optimization of digital building blocks. MOS and bipolar device models and second order effects. Circuit design styles and arithmetic structures. Estimation and minimization of energy consumption. Interconnect models and parasitics; driver design; timing issues (clock skew, self-timed circuits, etc.). Memory architectures, circuits (sense amplifiers) and devices. Testing of integrated circuits. Extensive use of circuit layout and SPICE in design projects and software labs.

" Western philosophy and theoretical mathematics were born together, and the cross-fertilization of ideas in the two disciplines was continuously acknowledged throughout antiquity. In this course, we read works of ancient Greek philosophy and mathematics, and investigate the way in which ideas of definition, reason, argument and proof, rationality and irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry."

This course includes materials on AI programming, logic, search, game playing, machine learning, natural language understanding, and robotics, which will introduce the student to AI methods, tools, and techniques, their application to computational problems, and their contribution to understanding intelligence. The material is introductory; the readings cite many resources outside those assigned in this course, and students are encouraged to explore these resources to pursue topics of interest. Upon successful completion of this course, the student will be able to: Describe the major applications, topics, and research areas of artificial intelligence (AI), including search, machine learning, knowledge representation and inference, natural language processing, vision, and robotics; Apply basic techniques of AI in computational solutions to problems; Discuss the role of AI research areas in growing the understanding of human intelligence; Identify the boundaries of the capabilities of current AI systems. (Computer Science 405)

Introducing technology CMOS, that means complementary MOS, including how to make p-channel transistor and how this one works.

Introducing technology CMOS, that means complementary MOS, including how to make p-channel transistor and how this one works.

What kind of coat will keep you the warmest, one made from cotton, steel wool or air? In this experiment, students test three materials to determine which one is the best insulator.

These are courses offered by Cousera in mathematics and statistics from partner institutions of higher education. These courses span Statistics 1 and Calculus to Cryptology, Logic, Machine Learning, Analytic Combinatorics. Coursera's wide range of courses allows students to explore topics from many different fields of study. Sign up for a class today and join a global community of students and scholars.

How should you build a boat so that it carries the most cargo? In this experiment, students form teams to solve an engineering problem.

This course covered the mathematical topics most directly related to computer science. Topics included: logic, relations, functions, basic set theory, countability and counting arguments, proof techniques, mathematical induction, graph theory, combinatorics, discrete probability, recursion, recurrence relations, and number theory. Emphasis will be placed on providing a context for the application of the mathematics within computer science. The analysis of algorithms requires the ability to count the number of operations in an algorithm. Recursive algorithms in particular depend on the solution to a recurrence equation, and a proof of correctness by mathematical induction. The design of a digital circuit requires the knowledge of Boolean algebra. Software engineering uses sets, graphs, trees and other data structures. Number theory is at the heart of secure messaging systems and cryptography. Logic is used in AI research in theorem proving and in database query systems. Proofs by induction and the more general notions of mathematical proof are ubiquitous in theory of computation, compiler design and formal grammars. Probabilistic notions crop up in architectural trade-offs in hardware design.

Students use a Although atoms contain both negatively and positively charged particles, they do so in equal amounts and carry no net charge. This balance can be temporarily disrupted by rubbing one material against another. One device, known as a Van de Graaff generator, uses a fast moving rubber belt to charge a metallic dome to nearly 200,000 Volts. This activity uses a Van de Graaff generator to study the behavior of electrical charges.

This course provides a challenging introduction to some of the central ideas of theoretical computer science. It attempts to present a vision of "computer science beyond computers": that is, CS as a set of mathematical tools for understanding complex systems such as universes and minds. Beginning in antiquity--with Euclid's algorithm and other ancient examples of computational thinking--the course will progress rapidly through propositional logic, Turing machines and computability, finite automata, Gödel's theorems, efficient algorithms and reducibility, NP-completeness, the P versus NP problem, decision trees and other concrete computational models, the power of randomness, cryptography and one-way functions, computational theories of learning, interactive proofs, and quantum computing and the physical limits of computation. Class participation is essential, as the class will include discussion and debate about the implications of many of these ideas.

What do one mathematician, one artist, and one musician all have in common? Are you interested in zen Buddhism, math, fractals, logic, paradoxes, infinities, art, language, computer science, physics, music, intelligence, consciousness and unified theories? Get ready to chase me down a rabbit hole into Douglas Hofstadter's Pulitzer Prize winning book Gödel, Escher, Bach. Lectures will be a place for crazy ideas to bounce around as we try to pace our way through this enlightening tome. You will be responsible for most of the reading as lectures will consist primarily of motivating the material and encouraging discussion. I advise everyone seriously interested to buy the book, grab on and get ready for a mind-expanding voyage into higher dimensions of recursive thinking.

Examines the development of computing techniques and technology in the nineteenth and twentieth centuries, particularly critical evaluation of how the very idea of "computer" changes and evolves over time. Emphasis is on technical innovation, industrial development, social context, and the role of government. Topics include Babbage, Hollerith, differential analyzers, control systems, ENIAC, radar, operations research, computers as scientific instruments, the rise of "computer science," artificial intelligence, personal computers, and networks. Includes class visits by members of the MIT community who have made important historical contributions. This course focuses on one particular aspect of the history of computing: the use of the computer as a scientific instrument. The electronic digital computer was invented to do science, and its applications range from physics to mathematics to biology to the humanities. What has been the impact of computing on the practice of science? Is the computer different from other scientific instruments? Is computer simulation a valid form of scientific experiment? Can computer models be viewed as surrogate theories? How does the computer change the way scientists approach the notions of proof, expertise, and discovery? No comprehensive history of scientific computing has yet been written. This seminar examines scientific articles, participants' memoirs, and works by historians, sociologists, and anthropologists of science to provide multiple perspectives on the use of computers in diverse fields of physical, biological, and social sciences and the humanities. We explore how the computer transformed scientific practice, and how the culture of computing was influenced, in turn, by scientific applications.

Jefferson Lab's accelerator only works if all of its thousands of components work together. In this experiment, students work together to move 'electrons' down their 'accelerator'.

Logic provides a way to talk about truth and correctness in a rigorous way, so that we can prove things, rather than make intelligent guesses and just hope they are correct.

Logic, as an academic subject, is the systematic study of the standards of correct reasoning. In short, logic is the theory of reasoning. This fully online course is a comprehensive introduction to logic with an emphasis on modern logical theory.

Login: guest_ocl
Password: ocl

This is an introductory course to Philosophy, which is the study of general and fundamental problems such as those connected with existence, knowledge, values, reason, mind, and language. Students will be introduced to the primary branches of Philosophy - ethics, logic, metaphysics, and epistemology. The course considers philosophers and works of Western Philosophy, including Plato, Hebrew scripture, Schopenhauer, Swedenborg, Buber, Kant, Hume, Locke and Berkeley.