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.

This new version of the CCK adds capacitors, inductors and AC voltage sources to your toolbox! Now you can graph the current and voltage as a function of time.

Build circuits with capacitors, inductors, resistors and AC or DC voltage sources, and inspect them using lab instruments such as voltmeters and ammeters.

This course describes discrete mathematics, which involves processes that consist of sequences of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. Upon successful completion of this course, the student will be able to: Create compound statements, expressed in mathematical symbols or in English, to determine the truth or falseness of compound statements and to use the rules of inference to prove a conclusion statement from hypothesis statements by applying the rules of propositional and predicate calculus logic; Prove mathematical statements involving numbers by applying various proof methods, which are based on the rules of inference from logic; Prove the validity of sequences and series and the correctness or repeated processes by applying mathematical induction; Define and identify the terms, rules, and properties of set theory and use these as tools to support problem solving and reasoning in applications of logic, functions, number theory, sequences, counting, probability, trees and graphs, and automata; Calculate probabilities and apply counting rules; Solve recursive problems by applying knowledge of recursive sequences; Create graphs and trees to represent and help prove or disprove statements, make decisions or select from alternative choices to calculate probabilities, to document derivation steps, or to solve problems; Construct and analyze finite state automata, formal languages, and regular expressions. (Computer Science 202)

Treatment of electromechanical transducers, rotating and linear electric machines. Lumped-parameter electromechanics of interaction. Development of device characteristics: energy conversion density, efficiency; and of system interaction characteristics: regulation, stability, controllability, and response. Use of electric machines in drive systems. Problems taken from current research. Alternate years. 6.685 explores concepts in electromechanics, using electric machinery as examples. It teaches an understanding of principles and analysis of electromechanical systems. By the end of the course, students are capable of doing electromechanical design of the major classes of rotating and linear electric machines, and have an understanding of the principles of the energy conversion parts of Mechatronics. In addition to design, students learn how to estimate the dynamic parameters of electric machines and understand what the implications of those parameters are on the performance of systems incorporating those machines.

Treatment of electromechanical transducers, rotating and linear electric machines. Lumped-parameter electromechanics of interaction. Development of device characteristics: energy conversion density, efficiency; and of system interaction characteristics: regulation, stability, controllability, and response. Use of electric machines in drive systems. Problems taken from current research. This course explores concepts in electromechanics, using electric machinery as examples. It teaches an understanding of principles and analysis of electromechanical systems. By the end of the course, students are capable of doing electromechanical design of the major classes of rotating and linear electric machines and have an understanding of the principles of the energy conversion parts of Mechatronics. In addition to design, students learn how to estimate the dynamic parameters of electric machines and understand what the implications of those parameters are on the performance of systems incorporating those machines.

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.

"This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, and exam solutions."

Play with a bar magnet and coils to learn about Faraday's law. Move a bar magnet near one or two coils to make a light bulb glow. View the magnetic field lines. A meter shows the direction and magnitude of the current. View the magnetic field lines or use a meter to show the direction and magnitude of the current. You can also play with electromagnets, generators and transformers!

Light a light bulb by waving a magnet. This demonstration of Faraday's Law shows you how to reduce your power bill at the expense of your grocery bill.

Generate electricity with a bar magnet! Discover the physics behind the phenomena by exploring magnets and how you can use them to make a bulb light.

In this course, the student will first learn about waves and oscillations in extended objects using classical mechanics. The course will then examine the sources and laws that govern static electricity and magnetism. A brief look at electrical measurements and circuits will help establish how electromagnetic effects are observed, measured, and applied. These topics lead to an examination of how Maxwell's equations unify electric and magnetic effects and how the solutions to Maxwell's equations describe electromagnetic radiation, which will serve as the basis for understanding all electromagnetic radiation, from very low frequency radiation emitted by power transmission lines to the most powerful astrophysical gamma rays. The course also investigates optics and launches a brief overview of Einstein's special theory of relativity. A basic knowledge of calculus is assumed. (Physics 102; See also: Biology 110, Chemistry 002, Mechanical Engineering 006)

This course provides an introduction to critical thinking, informal logic, and a small amount of formal logic; its purpose is to provide students with the basic tools of analytical reasoning. Upon successful completion of this course, students will be able to: Understand what critical thinking is and why it is valuable; Distinguish between good and bad definitions, Recognize the differences between explicit and implicit meaning, and remove ambiguities of meaning from unclearly worded statements; Recognize arguments in writing, pick out good and bad arguments by their form, and construct sound arguments of their own; Diagnose the most common reasoning errors and fallacies, as well as identify ways of improving them; Understand the basics of sentential and predicate logic and gain practice manipulating meaning symbolically; Understand the rudiments of scientific methodology and reasoning; Evaluate arguments that rely on specific types of visual representation; Understand the basics of strategic reasoning and problem solving; Understand the particular challenges involved in reasoning about values and morality; Diagnose fallacies and evaluate arguments about values and morality. (Philosophy 102)

Mathematical tools and methods for computer science and engineering. Emphasis on development of rigorous thinking, analytical skills, and mathematical sophistication while learning elementary discrete mathematics. Topics: mathematical proofs; induction and well-ordering; divisibility and congruences; asymptotic notation and growth of functions; sets, relations, functions, and graphs; counting theory; recurrences and generating functions; and discrete probability. This is an introductory course in Discrete Mathematics oriented toward Computer Science and Engineering. The course divides roughly into thirds: Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations Discrete Structures: Modular Arithmetic, Graphs, State Machines, Counting Discrete Probability Theory.

This course covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.

Mathematical tools and methods for computer science and engineering. Emphasis on development of rigorous thinking, analytical skills, and mathematical sophistication while learning elementary discrete mathematics. Topics: mathematical proofs; induction and well-ordering; divisibility and congruences; asymptotic notation and growth of functions; sets, relations, functions, and graphs; counting theory; recurrences and generating functions; and discrete probability.

In his analysis of inference into three types, deduction, induction, and abduction, C. S. Peirce maintains that probability plays an essential role in the first two, but not in the third. For a deductive argument, probability tells us the frequency with which the conclusion will hold given the premises; for an inductive argument, probability tells us the frequency with which the argument will hold true. However, probability has no role to play in abduction because there is, in Peirce's view, no common ground between the conclusion and the premises on which to base a calculation of frequencies. Nevertheless, there is something in the argument that makes the conclusion plausible to our mind. I will argue that this something is a probability which is, in many cases, quantifiable. This probability is the significance level of the statistical logic developed by R. A. Fisher in the 1920's.

Main emphasis on electricity and magnetism. Topics include currents and DC circuits; capacitance, resistance, and nonsteady currents; Coulomb's Law and electrostatic fields; Gauss's Law; electric potential; magnetic fields of currents; electromagnetic induction; magnetism and matter; AC circuits and resonance; Maxwell's equations; electromagnetic fields in space; electromagnetism and relativity; electromagnetic radiation as waves and photons. Kits of equipment are provided for the performance of a relevant take-home experiment as part of the homework each week. This course is an introduction to electromagnetism and electrostatics. Topics include: electric charge, Coulomb's law, electric structure of matter, conductors and dielectrics, concepts of electrostatic field and potential, electrostatic energy, electric currents, magnetic fields, Ampere's law, magnetic materials, time-varying fields, Faraday's law of induction, basic electric circuits, electromagnetic waves, and Maxwell's equations. The course has an experimental focus, and includes several experiments that are intended to illustrate the concepts being studied.

In this exercise, students examine several components of reasoning with the purpose of helping the student see how these are used in developing a personal problem solving technique. The students work through three exercises: determining an object in a sealed box, identifying a series of unknown household chemicals, and identifying the rules that determine responses in a computer simulation.