This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination.

Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently.

This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

“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.

An introductory series by Marianne Talbot exploring bioethical theories and their philosophical foundations. These podcasts will explain key moral theories, common moral arguments, and some background logic.

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 is a critical thinking evaluation report that may be used as an assignment resource, free of charge, by any educator for the purposes of higher learning. It has been utilized as a resource in:2022-2023 UNC Undergraduate Research Program. Fostering Critical Thinking in Human Motion Analysis. Brown, J., Chandler, R., Fiaud, V., and Armitano, C. This resource was recently featured in a presentation at the National Association for Kinesiology in Higher Education in January of 2024 and disseminated for public use. For more information, please email:jjbrown@ecsu.edu

This is an in class activity created for Organic Chemistry I at LaGuardia Community College.

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)

This course teaches the principles and analysis of electromechanical systems. Students will develop analytical techniques for predicting device and system interaction characteristics as well as learn to design major classes of electric machines. Problems used in the course are intended to strengthen understanding of the phenomena and interactions in electromechanics, and include examples from current research.

After this course the student can:
Understand mechanical system requirements for Electric Drive
Understand and apply passive network elements (R, L, C), laws of Kirchhof, Lorentz, Faraday
Understand and apply: phasors for simple R,L,C circuits
Understand and apply real and reactive power, rms, active and reactive current, cos phi
Describe direct current (DC), (single phase) alternating current (AC) and (three phase) alternating current systems, star-delta connection
Understand the principle of switch mode power electronic converters, pole as a two quadrant and four quadrant converter
Understand principles of magnetic circuits, inductances and transformers

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.

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.
Acknowledgement
The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams.

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.

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.

This video lesson uses the technique of induction to show students how to analyze a seemingly random occurrence in order to understand it through the development of a mathematical model. Using the medium of a simple game, Dr. Lodhi demonstrates how students can first apply the 'rules' to small examples of the game and then, through careful observation, can begin to see the emergence of a possible pattern. Students will learn that they can move from observing a pattern to proving that their observation is correct by the development of a mathematical model. Dr. Lodhi provides a second game for students in the Teacher Guide downloadable on this page. There are no prerequisites for this lesson and needed materials include only a blackboard and objects of two different varieties - such as plain and striped balls, apples and oranges, etc. The lesson can be completed in a 50-minute class period.

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 is a PBL project that had students design, build, and explain an electrical device that would safely and accurately demonstrate their mastery of the principles of electricity and magnetism. It was specifically designed to help students increase their depth of knowledge of electrostatics, electrical circuits, and the fundamentals of electromagnetism and induction. The project required students to design an electrical prototype that (upon safety validation), could be built and used to authentically justify their level of mastery to local engineers, electricians, and other experts from the community. Note that the project was designed and delivered per the North Carolina honors Physics curriculum and it can be customized to meet your own specific curriculum needs and resources.

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

A version of this course from a previous term was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5512 (Mathematics for Computer Science).