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Free
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Course
Online
When: Flexible
Description
Solve equations, draw graphs, and play with quadratics in this interactive course!Opinions
E
Ex-student
12/05/2016
What I would highlightExtraordinary course for any individual who needs to enhance their maths abilities. Begins exceptionally essential level, and continuously increments in complexity. Incredible intuitive arrangement, and precise illustrations. Exceptionally suggested.
What could be improved
Nothing.
Course taken: May 2016 |
Recomendarías este centro?
Sí.
S
student
12/06/2016
What I would highlightWhat could be improved
Everything OK.
Course taken: June 2016 |
Recomendarías este centro?
Sí.
M
Maria M
12/07/2016
What I would highlightWhat could be improved
Nothing bad.
Course taken: July 2016 |
Recomendarías este centro?
Sí.
What you'll learn on the course
Mathematics
Algebra
Graphs
Math
Quadratics
Course programme
We live in a world of numbers. You see them every day: on clocks, in the stock market, in sports, and all over the news. Algebra is all about figuring out the numbers you don't see. You might know how fast you can throw a ball, but can you use this number to determine how far you can throw it? You might keep track of stock prices, but how can you figure out how much money you've made (or lost) in the market? And you may already know how to tell time, but can you calculate at what times a clock's hour and minute hands are exactly aligned? With algebra, you can answer all of these questions, using the numbers you already know to solve for the unknown. Algebra is an essential tool for all of high school and college-level math, science, and engineering. So if you're starting out in one of these fields and you haven't yet mastered algebra, then this is the course for you! In this course, you'll be able to choose your own path within each lesson, and you can jump between lessons to quickly review earlier material. AlgebraX covers a standard curriculum in high school Algebra I, and CCSS (common core) alignment is indicated where applicable.
Additional information
Zach Wissner-Gross Zach is the CEO of School Yourself. He completed his doctorate in Physics at Harvard, where he won multiple teaching awards, including Harvard's White Award for Excellence in Teaching. He is a Hertz Fellow, and has authored papers in neuroscience, biophysics, and biotechnology, as well as three interactive math textbooks with the School Yourself team. John Lee John is the CTO of School Yourself, and is a software engineer with a background in artificial intelligence and data mining. As a Senior Software Engineer at Google, he led the data extraction team on experimental projects to mine knowledge from the open Web and push the boundaries of open-domain question answering. He studied Physics and Computer Science at MIT and completed his Masters in Computer Science and Engineering at MIT.
Introduction to Algebra - SchoolYourselfedX
Free
Do you see something that is not right in this course? Let us know if there are any mistakes and you will help users like yourself. | 677.169 | 1 |
This text is designed for a one semester Introduction to Analysis course. One main difference is the chapter on set, functions and proofs. This book will be attractive when a Transition to Advanced Mathematics course is not offered. The first chapter covers an introduction to proofs. The text…
This book aims to bridge the gap between large amounts of data and appropriate computational and management methods for scientific discovery. It will explore technologies for media/data communication, elastic media/data storage, and cross-network media/data fusion. The book will also cover…
Newcomers to R are often intimidated by the command-line interface, the vast number of functions and packages, or the processes of importing data and performing a simple statistical analysis. The R Primer provides a collection of concise examples and solutions to R problems frequently encounteredThis is the second edition of a very popular applied reference/textbook on the analysis of data from surveys. It is one of the most well-regarded books in the field, and is widely used for research and teaching. The new edition has been updated with a new chapter on the analysis of longitudinal…
Probability for the Applied Researcher
This book presents a conceptual, albeit mathematical, understanding of probability theory in measure-theoretic terms. Although there are many books on measure theory and probability, they are written for a mathematically operational understanding—for those with strong backgrounds such as…
Algebra, Probability, and Number Theory
The 39 self-contained sections in this book present worked-out examples as well as many sample problems categorized by the level of difficulty as Bronze, Silver, and Gold in order to help the readers gauge their progress and learning. Detailed solutions to all problems in each section are provided…
"This would be an excellent book for undergraduate, graduate and beyond….The style of writing is easy to read and the author does a good job of adding humor in places. The integration of basic programming in R with the data that is collected for any experiment provides a powerful platform for | 677.169 | 1 |
Presentation (Powerpoint) File
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5.08 MB | 28 pages
PRODUCT DESCRIPTION
• understand the terms permutation and combination, and solve simple problems involving selections;
• solve problems about arrangements of objects in a line, including
those involving:
• repetition (e.g. the number of ways of arranging the letters of the
word 'NEEDLESS'),
• restriction (e.g. the number of ways several people can stand in
a line if 2 particular people must — or must not — stand next to
each other | 677.169 | 1 |
IB Math Studies
Course Code:
47530
Course Level:
Advanced
Credits:
5.0
Grade Level:
12
Prerequisite:
Advanced Algebra 2
Description:
In this course students will be exposed to a
variety of mathematical topics. These
include probability and statistics, sequences and series, basic set theory,
symbolic logic, and financial mathematics.
Traditional topics involving the study of linear, quadratic, and exponential
functions will be presented with an emphasis on applications. Elementary procedures from differential calculus
will be introduced. The use of graphing calculators and appropriate computer software
will be encouraged throughout the course.
IB Math Studies is designed to assist students preparing
for the IB Math Studies Standard Level exam and requires a major project (math
term paper) to be completed by all students. | 677.169 | 1 |
Powers and Exponents Glossary
PDF (Acrobat) Document File
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0.49 MB | 6-7 pages
PRODUCT DESCRIPTION
The five valuable learning activities that this glossary provides will assist your grade eight and nine academic math students in their understanding of the following mathematical laws and vocabulary words:
Power,Base,exponent,Exponential form,Factored form,Negative base,Volume of a Cylinder,Volume of a Cube,Area of a Square, Area of of a Cube, Surface Area of a Cylinder, Area (rectangle),
Multiplying Powers With the Same Base,Dividing Powers With the Same Base,Raise Powers to An Exponent Law,Raising a Product to an Exponent Law,Raising a Quotient to an Exponent Law,
Raising a Quantity to an Exponent of Zero,Coefficient, Order of Operations ,Length of A Circumference, pi.
This glossary is also a valuable problem solving tool for ESL, EAP students, as it keeps the necessary vocabulary fresh in their minds | 677.169 | 1 |
Thirty-Five Years of Teamwork in Indiana
Product Description:
A Friendly Mathematics Competition tells the story of the Indiana College Mathematics Competition (ICMC) by presenting the problems, solutions, and results of the first 35 years of the ICMC. The ICMC was organized in reaction to the Putnam Exam - its problems were to be more representative of theundergraduate curriculum, and students could work on them in teams. Originally participation was originally restricted to the small, private colleges and universities of the state, but was later opened up to students from all of the schools in Indiana. The competition was quickly nicknamed the "Friendly" Competition because of its focus on solving mathematical problems, which brought faculty and students together, rather than on the competitive nature of winning. Organized by year, the problems and solutions in this volume present an excellent archive of information about what has been expected of an undergraduate mathematics major over the past 35 years. With more than 245 problems and solutions, the book is also a must buy for faculty and students interested in problem-solving.The index of problems lists problems in: Algebraic Structures; Analytic Geometry, Arclength, Binomial Coefficients, Derangements, Differentiation, Differential Equations, Diophantine Equations, Enumeration, Field and Ring Theory, Fibonacci Sequences, Finite Sums, Fundamental Theorem of Calculus Geometry, Group Theory, Inequalities, Infinite Series, Integration, LimitEvaluation, Logic, Matrix Algebra, Maxima and Minima Problems,Multivariable Calculus, Number Theory, Permutations, Probability, PolarCoordinates, Polynomials, Real Valued Functions Riemann Sums, Sequences,Systems of Equations, Statistics, Synthetic Geometry, Taylor Series, Trigonometry, and Volumes.
REVIEWS for A Friendly Mathematics | 677.169 | 1 |
Introduction to Algebra session-1
NCERT Math book solution. All NCERT text book questions and questions from premium reference books are discussed in detail in these video lectures. Watch the videos and learn the basics of algebra. There are lots of worksheets on algebra so students are suggested to take print of the worksheets and solve them after watching the video lectures. | 677.169 | 1 |
Offers a systematic, step-by-step approach, building on concepts throughout the book and facilitating easier learning
Includes sections on common pitfalls and programming guidelines to direct students toward best practices
Combines basic programming concepts, built-in functions, and advanced topics for problem solving with MATLAB to make this book uniquely suitable for a wide range of courses teaching or using MATLAB across the curriculum
NEW: Expanded content in the chapters "Defining the Problem," "Generation of 'Alternative Concepts'," and "Detailed Design"
NEW: Material on sustainability issues in engineering
Introduces students to the engineering profession, emphasizing the fundamental physical, chemical, and material bases for all engineering work
Includes an Engineering Ethics Decision Matrix used throughout the book to pose ethical challenges and explore decision-making in an engineering context
Lists of "Top Engineering Achievements" and "Top Engineering Challenges" help put the material in context and show engineering as a vibrant discipline involved in solving societal problems
Companion Web site includes links to several new drawing supplements, including "Free-hand Engineering Sketching," (detailed instructions on free-hand engineering sketching); "AutoCAD Introduction," (an introduction to the free AutoCAD drawing software); and "Design Projects," (new freshman-level design projects that complement the "Hands-On" part of the textbook).
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]]> Tools – The Third Way
22 Feb 2017 16:00:57 +0000 significant factor in getting any job done properly is having the right tools. This is true whether...
A significant factor in getting any job done properly is having the right tools. This is true whether you are building a kitchen, fixing your car or developing embedded software. Of course, it is the last of these that I am interested in here. I have been evangelizing on this topic for years (decades!). The problem is that there is a similarity – arguably superficial – between programming an embedded system and programming a desktop computer. The same (kind of) languages are used and software design techniques are fairly universal. However, there are really some major differences …
There are three key areas of difference between desktop and embedded programming:
The degree of control required by the embedded developer is much greater, in order to utilize resources (time and memory) effectively.
The approaches to verification and debugging and quite different, as an external connection and/or a selection of instruments need to be employed. Also, further tools may be needed to optimize the performance of the application.
Every embedded system is different, whereas every PC is basically the same. This means that the tools (like the programmers) need to be much more flexible and adaptable.
Because there are so many desktop programmers, who are all working in the same environment, there is a huge demand for tools. The result is that very good tools are effectively (or literally) free. The apparent similarity of embedded to desktop programming means that developers have a misguided expectation that their tools should be free too – regardless of their specialized needs and much lower demand level. In the electronic design (EDA) world, there is no such expectation. Tools are valued and price tickets are commonly in five figures.
There are essentially three ways that embedded developers can currently get tools:
They can purchase commercial tools that are dedicated to the needs of the embedded developer. This is undoubtedly the best approach, but their costs are not insubstantial. There is a reasonable expectation that the tools will work "out of the box" and that technical support is available.
They can take open source ("free") tools, which have been adapted for embedded use, or do the adaptation themselves. The direct costs are, of course, lower, but the extra time needed to get the tools in shape and to obtain support from the open source community cannot be ignored.
But, maybe there is a third way. What if a vendor were to take the best-in-class open source tools, comprehensively adapt them to the needs of the embedded developer, add some additional tools that fulfill their specialized requirements and offer this as a reasonably priced package? This package might be available in various editions, recognizing the diverse needs of embedded developers, and be available for immediate purchase and download on the Web. High quality technical support would also be available. For users with particularly specialized needs, services would be available to further adapt the tools to fit their specific requirements.
In his 2007 address to the Annual Security Conference in Munich, Vladimir Putin threw down a gauntlet to the West. Attacking what he called "illegal" unilateral military action by the US, he hinted that Russia would build its capability in information warfare to counter American and NATO expansion.
In the same year, a Russian policy doctrine noted that as the world became more digitally connected, the well-being of nation states would become dependent on data and and its rapid movement. Back then, information warfare was just a sideshow, and Putin's emphasis was on more traditional weapon systems. But things have changed. In the decade since, Russia has rapidly developed its information warfare capability and deployed it in conflicts in Estonia, Georgia, and Ukraine.
But what exactly do we mean by the term "information warfare"? Dan Kuehl of the National Defence University in the US defined it as the "conflict or struggle between two or more groups in the information environment". You might think that just sounds like a fancy way of describing computer hacking. In fact, it's a far more sinister and dangerous proposition. The free flow of information within and between nation states is essential to business, international relations and social cohesion.
Communications today lean heavily on the internet, or via communications using various parts of the electromagnetic spectrum (such as wireless and microwaves) through terrestrial communications networks or satellite networks in space. We live in a highly connected world, and it doesn't take much to tip a nation state into instability.
There have already been questions raised about possible Russian interference in government elections in the US. So will it use its new-found warfare capability to influence international relations to its own advantage in the future?
A study by the World Bank stated that Russia boasts more than 1m software specialists involved in research and development. Russian illegal cyber warriors (hackers) are among the most proficient in the world with around 40 large criminal cyber rings operating within the country's borders. The Russian government has long been known to source its technology, world-class hacking talent and even some intelligence information from local cyber crime rings. What's more, this criminal fraternity probably receives state immunity for cyber crimes committed outside Russia in return for offering services to the Russian state. It is estimated that these criminal rings have recruited nearly 1,000 software engineers since 2012.
Hacking activities include the penetration of national infrastructure systems, and money markets, and the stealing of state secrets and intellectual property. All of these destabilising attacks can be considered as preparation for any future conflict.
Russia is carrying out a sustained campaign of cyber attacks targeting democracy and critical infrastructure in the West.
Russia, or its proxy cyber warriors, have been accused of a number of high-profile attacks, all of which can be regarded as attempts to undermine democracy by fuelling doubt or creating distrust through misinformation or "false reporting". In military parlance, this activity is referred to as "psychological operations".
Russia has denied any involvement in any of this cyber activity and conclusive proof is difficult to obtain. After all, the Russia will be conducting its information warfare campaign through proxy cyber groups who themselves will be using heavily disguised covert internet servers. However, according to US intelligence officials, Russian hackers made repeated attempts during 2016 to stage cyber break-ins into major US institutions, including the White House and the State Department.
Russia's clear long-term strategy is to use the internet to further its aims in information warfare. It has proved that this form of warfare is more potent than kinetic warfare and that it can reap the benefits quickly and without fear of a coordinated response from the US or NATO. Its use of criminal cyber rings ensures that it benefits from no (provable) direct links to the Russian government. A further downside is that China, North Korea and Iran seem to be copying this model and have already been active in attacks against other nation states.
The internet has changed mass communication in countless positive ways. But it is becoming an increasingly dangerous tool for subversive activity. A re-think and a re-boot are looking increasingly necessary.
This article was originally published on The Conversation website under a Creative Commons Attribution 4.0 International License. Read the original article here.
Read more:
Data Breach Preparation and Response: Breaches are Certain, Impact is Not is the first book to provide 360 degree visibility and guidance on how to proactively prepare for and manage a data breach and limit impact. Data breaches are inevitable incidents that can disrupt business operations and carry severe reputational and financial impact, making them one of the largest risks facing organizations today.
Alternatively, visit the Elsevier Store to view our extensive range and to purchase your own print copies of books on cybersecurity and National Security! Use discount code STC317at checkout and save up to 30% on your very own copies!
]]> When to Fold 'em: AI Beats World's Top Poker Players
08 Feb 2017 21:31:05 +0000 If you were about to start playing a game of online poker, you might want to think...
]]>Poker is a harder game for computers to master than chess or Go. Shutterstock
If you were about to start playing a game of online poker, you might want to think again. Humankind has just been beaten at yet another game, this time Heads-Up No-Limit Texas Hold'em poker. This is a milestone moment for artificial intelligence (AI).
The first game that humans lost to machines was backgammon. In 1979, the world backgammon champion was beaten by Hans Berliner's BKG 9.8 program.
In 1997, Gary Kasparov who was the reigning world chess champion lost to IBM's Deep Blue program. Kasparov remarked that he could "smell" a new form of intelligence across the table from him.
Most recently, the ancient Chinese board game of Go fell to the machines. In March last year, one of the leading Go players on the planet, Lee Sedol, was beaten 4-1 by Google's AlphaGo program.
And to rub our faces in it, over the Christmas break, AlphaGo anonymously played dozens of the world's leading Go players online and won convincingly.
Why poker?
Go has been described as the Mount Everest of board games. It is far more complex than chess or many other games. However, it is less of a challenge than poker.
Like the real world, poker is a game of uncertainty. Players don't know what cards the other players have. Or what cards will be dealt in the future. In a game like chess or Go, by comparison, all the players can see the board. Everyone has complete information. This makes Chess and Go much easier to program than poker.
Poker also requires understanding the psychology of the other players. Are they bluffing? Should you fold? Should you bluff?
Finally poker involves betting. When should you bet? What should you bet? This again adds to the challenge of writing a poker program that plays as well as or better than humans.
Over the last three weeks, four of the top poker players have been locked in an exhausting 120,000 game match at the Rivers Casino in Pittsburgh.
Libratus is set to win the tournament later today, finishing ahead of the humans with more than US$1 million (A$1.32m) of notional winnings. The pros can be consoled by sharing out the actual US$200,000 (A$265,000) prize pot.
In order to reduce the influence of sheer luck on the result, the tournament used duplicate hands. This means that two decks of identically shuffled cards are used to two separate tables. On one table, a human player is simultaneously dealt their hand, call it hand A, and the AI is dealt hand B. On the other table (situated in another room), the AI player is dealt hand A and human player dealt hand B.
This means that even if one player receives an unusual number of lucky hands, then this will be mirrored for the other player in the duplicate game.
This also explains why so many games have been played. The end result is that we can say with statistical confidence that Libratus is better than the human players.
Like IBM's Deep Blue in chess, Libratus used a lot of brute force calculation as to how to play best. We know it calls upon Pittsburgh's Supercomputing Centre to play out every end game.
And each night, Libratus uses this supercomputer to refine its strategy. In case you think this is unfair on the humans, the pros also get together at night after each match to compare performance and plan for the next day.
Libratus also takes advantage of game theory, the branch of mathematics made famous by the movie A Beautiful Mind about John Nash. Libratus looks to play strategic moves that cannot be bettered whatever its opponent does.
What next?
Poker is still not solved. Libratus only plays the two player version of Heads-Up No-Limit Texas Hold'em poker. Adding more players increases the complexity greatly. So it will be a few years yet before computers can play well against four or more players.
There were several limitations in the Oxford study. Ironically, one was that it automated the task of predicting which jobs were under risk. The study used machine learning and a small training set of 70 hand labelled jobs to predict which of over 700 professions was under risk.
This is where you can help. I am calling on the wisdom of the crowd to see if we can make a better prediction. Please take a few minutes to complete our survey. At the end, you can nominate a charity to receive a donation in recognition of your time and effort.
Even before the results of our survey are in, its clear that some jobs such as taxi driver, truck driver, radiographer and now poker pro are under threat. Of course, technology will also create other new jobs. But whether as many get created or destroyed remains an interesting open question.
To keep ahead of the bots, humans will need to play to their strengths like creativity and emotional intelligence. We also should look to augment rather than replace humans. Together humans and machines can outperform machines or humans alone. The best chess player today is a human working with a computer.
Together, we can be super-human.
This article was originally published in The Conversation under a Creative Commons Attribution No Derivatives license. Read the original article here.
Alternatively, visit the new Elsevier Store to purchase your copy of these titles or to view our extensive range of machine learning books! Use discount code STC317 at checkout and save up to 30% on your very own copy!
]]> You Might Want to Think Twice About Surrendering Online Privacy for the Sake of Convenience
25 Jan 2017 21:33:02 +0000 is inconvenient to guard one's privacy, and the better one protects it, the more inconvenience one must...
]]>Just a click away once you tick this too-long-to-read privacy agreement. Shutterstock
It is inconvenient to guard one's privacy, and the better one protects it, the more inconvenience one must endure. Enjoying privacy, at a minimum, demands installing software to block tracking online, using long and different passwords for online services, remembering to turn off the WiFi and Bluetooth signals on your mobile phone when leaving the house, using cash, and so on.
The more privacy conscious have to go through the trouble of using encryption for all their messages, covering the camera on their laptop with a sticker, suffering the slowness and limitations of using Tor (a software that enables anonymity online), and may even be willing to forgo the many advantages of having a mobile phone altogether.
Companies and institutions should not make it this hard for people to enjoy privacy – we shouldn't have to go through all this trouble to make good on a right. However, we live in a non-ideal world, where it is more and more a fact of the matter that governments and businesses exploit people's personal information for economic and political reasons.
So, individuals living in the real world are faced with the dilemma of either complying with the default option and surrendering their privacy, or trying to resist exposure through paying a high price in inconvenience. It makes sense to ask whether privacy is worth all the trouble.
Imagine going into a shop, picking out whatever you fancy, putting it in your bag, and simply walking out. No cash, no credit cards, no queues. Cameras using facial recognition have identified you and you will be billed automatically. You rarely go into shops, anyway. Only when you feel like going for a stroll, or when you wish to explore new products. Most of the time, everything in your house gets restocked automatically through sensors connected to the Internet of Things. That future may not be far away. Amazon just opened a checkout-free shop in Seattle, and may soon open more stores in the UK.
The inconvenience of convenience
The bright side of convenience is an attractive one: it promises us an easier life. Convenience, like pleasure, is an important component of a good life. If we didn't choose convenience every now and again our lives would be hopelessly uncomfortable and inefficient.
It is inconvenient to only buy from socially responsible businesses, to exercise, to find new things to do, to keep well informed, to vote and protest when governments commit injustices. A good life demands a reasonable degree of struggle – the right balance between the ease of convenience and the benefits of meaningful efforts. Like pleasure, convenience has to be weighed against the price we are paying for it, and the short- and long-term consequences that might ensue.
Weighing up the losses
Unfortunately, it is not easy to assess the weight of privacy losses. Typically, in the online world, no small privacy loss will create a catastrophe. One business tracking one click of yours is not a big deal. But privacy losses accumulate, and the entirety of what you have revealed online through browsing, clicking, buying and liking, can paint a frighteningly detailed portrait of you.
Privacy losses are like ecologic damages or health deterioration: no one act of littering, no one puff of a cigarette will bring about disaster, but the sum of them through time might.
What possible damage could come from giving up privacy online, you may wonder. If you ask for a job, it is likely that the company considering hiring you will buy a file on you from data brokers. Your file may contain information on browsing habits, credit history, health records, and more. The company may not hire you because of something you posted on social media, or because of some other kind of "stain" on your record, and you will never know why it was, nor will you ever be able to contest that decision.
Similarly, a bank may not grant you a loan from information they glean from you on the internet. The information on which they make their decision may be inaccurate, but again, you will never know. Hackers could turn on your camera and blackmail you with sensitive footage. Criminals may commit identity theft.
According to the Federal Trade Commission, identity theft complaints in the US increased by 47% between 2014 and 2015. Trolls may harass you online and offline. Insurance companies may charge you according to information about your habits. Products such as flights may become more expensive for you depending on how much you seem to want them. And the list goes on.
It is paramount that we demand businesses and government institutions enable us to enjoy privacy online more easily. In the meantime, however, you might want to think twice about surrendering your privacy for the sake of convenience.Cyberattackers pose many threats to a wide range of targets. Russia, for example, was accused of hacking Democratic Party computers throughout the year, interfering with the U.S. presidential election. Then there was the unknown attacker who, on a single October day, used thousands of internet-connected devices, such as digital video recorders and cameras compromised by Mirai malware, to take down several high-profile websites, including Twitter.
Deterrence focuses on making potential adversaries think twice about attacking, forcing them to consider the costs of doing so, as well as the consequences that might come from a counterattack. There are two main principles of deterrence. The first, denial, involves convincing would-be attackers that they won't succeed, at least without enormous effort and cost beyond what they are willing to invest. The second is punishment: Making sure the adversaries know there will be a strong response that might inflict more harm than they are willing to bear.
For decades, deterrence has effectively countered the threat of nuclear weapons. Can we achieve similar results against cyber weapons?
Cyber weapons are nothing like nuclear ones. They are readily developed and deployed by individuals and small groups as well as states. They are easily replicated and distributed across networks, rendering impossible the hope of anything that might be called "cyber nonproliferation." Cyber weapons are often deployed under a cloak of anonymity, making it difficult to figure out who is really responsible. And cyberattacks can achieve a broad range of effects, most of which are disruptive and costly, but not catastrophic.
This does not mean cyber deterrence is doomed to failure. The sheer scale of cyberattacks demands that we do better to defend against them.
There are three things we can do to strengthen cyber deterrence: Improve cybersecurity, employ active defenses and establish international norms for cyberspace. The first two of these measures will significantly improve our cyber defenses so that even if an attack is not deterred, it will not succeed.
Stepping up protection
Cybersecurity aids deterrence primarily through the principle of denial. It stops attacks before they can achieve their goals. This includes beefing up login security, encrypting data and communications, fighting viruses and other malware, and keeping software updated to patch weaknesses when they're found.
Cybersecurity guru Bruce Schneier aptly characterizes the prevalence of insecure Internet-of-Things devices as a market failure akin to pollution. Simply put, the market favors cheap insecure devices over ones that are more costly but secure. His solution? Regulation, either by imposing basic security standards on manufacturers, or by holding them liable when their products are used in attacks.
Active defenses
When it comes to taking action against attackers, there are many ways to monitor, identify and counter adversary cyberattacks. These active cyber defenses are similar to air defense systems that monitor the sky for hostile aircraft and shoot down incoming missiles. Network monitors that watch for and block ("shoot down") hostile packets are one example, as are honeypots that attract or deflect adversary packets into safe areas. There, they do not harm the targeted network, and can even be studied to reveal attackers' techniques.
Another set of active defenses involves collecting, analyzing and sharing information about potential threats so that network operators can respond to the latest developments. For example, operators could regularly scan their systems looking for devices vulnerable to or compromised by the Mirai botnet or other malware. If they found some, they could disconnect the devices from the network and alert the devices' owners to the danger.
Active cyber defense does more than just deny attackers opportunities. It can often unmask the people behind them, leading to punishment. Nongovernment attackers can be shut down, arrested and prosecuted; countries conducting or supporting cyberwarfare can be sanctioned by the international community.
Currently, however, the private sector is reluctant to employ many active defenses because of legal uncertainties. The Center for Cyber and Homeland Security at George Washington University recommends several actions that the government and the private sector could take to enable more widespread use of active defenses, including clarifying regulations.
Cyberspace will never be immune to attack – no more than our streets will be immune to crime. But with stronger cybersecurity, increased use of active cyber defenses, and international cyber norms, we can hope to at least keep a lid on the problem.
Handbook of System Safety and Security presents an update on the world's increasing adoption of computer-enabled products and the essential services they provide to our daily lives. The tailoring of these products and services to our personal preferences is expected and made possible by intelligence that is enabled by communication between them. Ensuring that the systems of these connected products operate safely, without creating hazards to us and those around us, is the focus of this book, which presents the central topics of current research and practice in systems safety and security as it relates to applications within transportation, energy, and the medical sciences.
]]> Migration
18 Jan 2017 11:30:34 +0000 have often talked about the process that might be applied to the selection of an embedded operating...]]> Intelligence: Computer Says YES (But Is it Right?)
08 Dec 2016 17:34:55 +0000 that learn for themselves are with us now. As they become more common in 'high-stakes' applications like...
Computers that learn for themselves are with us now. As they become more common in 'high-stakes' applications like robotic surgery, terrorism detection and driverless cars, researchers ask what can be done to make sure we can trust them.
As we see an escalation in what machines can do, they will challenge our notions of intelligence and make it all the more important that we have the means to trust what they tell us. – Zoubin Ghahramani
There would always be a first death in a driverless car and it happened in May 2016. Joshua Brown had engaged the autopilot system in his Tesla when a tractor-trailor drove across the road in front of him. It seems that neither he nor the sensors in the autopilot noticed the white-sided truck against a brightly lit sky, with tragic results.
Of course many people die in car crashes every day – in the USA there is one fatality every 94 million miles, and according to Tesla this was the first known fatality in over 130 million miles of driving with activated autopilot. In fact, given that most road fatalities are the result of human error, it has been said that autonomous cars should make travelling safer.
Even so, the tragedy raised a pertinent question: how much do we understand – and trust – the computers in an autonomous vehicle? Or, in fact, in any machine that has been taught to carry out an activity that a human would do?
We are now in the era of machine learning. Machines can be trained to recognise certain patterns in their environment and to respond appropriately. It happens every time your digital camera detects a face and throws a box around it to focus, or the personal assistant on your smartphone answers a question, or the adverts match your interests when you search online.
Machine learning is a way to program computers to learn from experience and improve their performance in a way that resembles how humans and animals learn tasks. As machine learning techniques become more common in everything from finance to healthcare, the issue of trust is becoming increasingly important, says Zoubin Ghahramani, Professor of Information Engineering in Cambridge's Department of Engineering.
Faced with a life or death decision, would a driverless car decide to hit pedestrians, or avoid them and risk the lives of its occupants? Providing a medical diagnosis, could a machine be wildly inaccurate because it has based its opinion on a too-small sample size? In making financial transactions, should a computer explain how robust is its assessment of the volatility of the stock markets?
"Machines can now achieve near-human abilities at many cognitive tasks even if confronted with a situation they have never seen before, or an incomplete set of data," says Ghahramani. "But what is going on inside the 'black box'? If the processes by which decisions were being made were more transparent, then trust would be less of an issue."
His team builds the algorithms that lie at the heart of these technologies (the "invisible bit" as he refers to it). Trust and transparency are important themes in their work: "We really view the whole mathematics of machine learning as sitting inside a framework of understanding uncertainty. Before you see data – whether you are a baby learning a language or a scientist analysing some data – you start with a lot of uncertainty and then as you have more and more data you have more and more certainty.
"When machines make decisions, we want them to be clear on what stage they have reached in this process. And when they are unsure, we want them to tell us."
One method is to build in an internal self-evaluation or calibration stage so that the machine can test its own certainty, and report back.
Two years ago, Ghahramani's group launched the Automatic Statistician with funding from Google. The tool helps scientists analyse datasets for statistically significant patterns and, crucially, it also provides a report to explain how sure it is about its predictions.
"The difficulty with machine learning systems is you don't really know what's going on inside – and the answers they provide are not contextualised, like a human would do. The Automatic Statistician explains what it's doing, in a human-understandable form."
Where transparency becomes especially relevant is in applications like medical diagnoses, where understanding the provenance of how a decision is made is necessary to trust it.
Dr Adrian Weller, who works with Ghahramani, highlights the difficulty: "A particular issue with new artificial intelligence (AI) systems that learn or evolve is that their processes do not clearly map to rational decision-making pathways that are easy for humans to understand." His research aims both at making these pathways more transparent, sometimes through visualisation, and at looking at what happens when systems are used in real-world scenarios that extend beyond their training environments – an increasingly common occurrence.
"We would like AI systems to monitor their situation dynamically, detect whether there has been a change in their environment and – if they can no longer work reliably – then provide an alert and perhaps shift to a safety mode." A driverless car, for instance, might decide that a foggy night in heavy traffic requires a human driver to take control.
Weller's theme of trust and transparency forms just one of the projects at the newly launched £10 million Leverhulme Centre for the Future of Intelligence (CFI). Ghahramani, who is Deputy Director of the Centre, explains: "It's important to understand how developing technologies can help rather than replace humans. Over the coming years, philosophers, social scientists, cognitive scientists and computer scientists will help guide the future of the technology and study its implications – both the concerns and the benefits to society."
CFI brings together four of the world's leading universities (Cambridge, Oxford, Berkeley and Imperial College, London) to explore the implications of AI for human civilisation. Together, an interdisciplinary community of researchers will work closely with policy-makers and industry investigating topics such as the regulation of autonomous weaponry, and the implications of AI for democracy.
Ghahramani describes the excitement felt across the machine learning field: "It's exploding in importance. It used to be an area of research that was very academic – but in the past five years people have realised these methods are incredibly useful across a wide range of societally important areas.
"We are awash with data, we have increasing computing power and we will see more and more applications that make predictions in real time. And as we see an escalation in what machines can do, they will challenge our notions of intelligence and make it all the more important that we have the means to trust what they tell us."
Artificial intelligence has the power to eradicate poverty and disease or hasten the end of human civilisation as we know it – according to a speech delivered by Professor Stephen Hawking 19 October 2016 at the launch of the Centre for the Future of Intelligence.
This article first appeared on the Conversation. Click here for the original article.
Visit the Elsevier Store to view our extensive range of books on machine learning and artificial intelligence! Below is a small selection of books that discuss some of the topics in the above article. Use discount code STC215 at checkout and save up to 30% on your very own copy!
Quantum Machine Learning captures a broad array of highly specialized content in an accessible and up-to-date review of the growing academic field of quantum machine learning and its applications in industry.
]]> Cybercrime When There's Plenty of Phish in the Sea
28 Nov 2016 21:19:43 +0000 more and more crime moves online, computer scientists, criminologists and legal academics have joined forces in Cambridge...
As more and more crime moves online, computer scientists, criminologists and legal academics have joined forces in Cambridge to improve our understanding and responses to cybercrime, helping governments, businesses and ordinary users construct better defences.
You don't actually have to be as clever as people once thought in order to fool a user
Richard Clayton
We've all received the emails, hundreds, maybe thousands of them. Warnings that our bank account will be closed tomorrow, and we've only got to click a link and send credit card information to stop it from happening. Promises of untold riches, and it will only cost a tiny fee to access them. Stories of people in desperate circumstances, who only need some kind soul to go to the nearest Western Union and send a money transfer to save them.
Tricking people into handing over sensitive information such as credit card details – known as 'phishing' – is one of the ways criminals scam people online. Most of us think we're smarter than these scams. Most of us think that we could probably con the con artist if we tried. But we would be wrong.
Across the world, cybercrime is booming. When the UK government included cybercrime in the national crime statistics for the first time in 2015, it doubled the crime rate overnight. Millions of people worldwide are victimised by online scams, whether it's blocking access to a website, stealing personal or credit card information, or attempting to extort money by remotely holding the contents of a personal computer hostage.
"Since 2005, the police have largely ignored cybercrime," says Professor Ross Anderson of Cambridge's Computer Laboratory. "Reported crime fell by as much as a half in some categories. Yet, now that online and electronic fraud are included, the number of reported crimes has more than doubled. Crime was not falling; it was just moving online."
In 2015, computer scientists, criminologists and legal academics joined forces to form the Cambridge Cybercrime Centre, with funding from the Engineering and Physical Sciences Research Council. Their aim is to help governments, businesses and ordinary users to construct better defences.
To understand how the criminals operate, researchers use machine learning and other techniques to recognise bad websites, understand what kinds of brands tend to be attacked and how often, determine how many criminals are behind an attack by looking at the pattern of the creation of fake sites and how effective the various defence systems are at getting them taken down.
One way in which studying cybercrime differs from many other areas of research is that the datasets are difficult to come by. Most belong to private companies, and researchers need to work hard to negotiate access. This is generally done through nondisclosure agreements, even if the data is out of date. And once researchers complete their work, they cannot make the data public, since it would reduce the competitive advantage of corporate players, and it may also make it possible for criminals to reverse engineer what was detected (and what wasn't) and stay one step ahead of law enforcement.
One of the goals of the Cambridge Cybercrime Centre is to make it easier for cybercrime researchers from around the world to get access to data and share their results with colleagues.
To open up cybercrime research to colleagues across the globe, the team will leverage their existing relationships to collect and store cybercrime datasets, and then any bona fide researcher can sign a licence with the Centre and get to work without all the complexity of identifying and approaching the data holders themselves.
"Right now, getting access to data in this area is incredibly complicated," says Dr Richard Clayton of Cambridge's Computer Laboratory, who is also Director of the Centre. "But we think the framework we've set up will create a step change in the amount of work in cybercrime that uses real data. More people will be able to do research, and by allowing others to work on the same datasets more people will be able to do reproducible research and compare techniques, which is done extremely rarely at the moment."
One of the team helping to make this work is Dr Julia Powles, a legal researcher cross-appointed between the Computer Laboratory and Faculty of Law. "There are several hurdles to data sharing," says Powles. "Part of my job is to identify which ones are legitimate – for example, when there are genuine data protection and privacy concerns, or risks to commercial interests – and to work out when we are just dealing with paper tigers. We are striving to be as clear, principled and creative as possible in ratcheting up research in this essential field."
Better research will make for better defences for governments, businesses and ordinary users. Today, there are a lot more tools to help users defend themselves against cybercrime – browsers are getting better at recognising bad URLs, for example – but, at the same time, criminals are becoming ever more effective, and more and more people are getting caught in their traps.
"You don't actually have to be as clever as people once thought in order to fool a user," says Clayton when explaining how fake bank websites are used to 'phish' for user credentials. "It used to be that cybercriminals would register a new domain name, like Barclays with two Ls, for instance. But they generally don't do that for phishing attacks anymore, as end users aren't looking at the address bar, they're looking at whether the page looks right, whether the logos look right."
The Centre is also looking at issues around what motivates someone to commit cybercrime, and what makes them stop.
According to Dr Alice Hutchings, a criminologist specialising in cybercrime, cybercriminals tend to fall into two main categories. The first category is the opportunistic offender, who may be motivated by a major strain in their lives, such as financial pressures or problems with gambling or addiction, and who uses cybercrime as a way to meet their goals. The second type of offender typically comes from a more stable background, and is gradually exposed to techniques for committing cybercrime through associations with others.
Both groups will usually keep offending as long as cybercrime meets their particular needs, whether it's financial gratification, or supporting a drug habit, or giving them recognition within their community. What often makes offenders stop is the point at which the costs of continuing outweigh the benefits: for instance, when it takes a toll on their employment, other outside interests or personal relationships.
"Most offenders never get caught, so there's no reason to think that they won't go back to cybercrime," says Hutchings. "They can always start again if circumstances in their lives change.
"There is so much cybercrime happening out there. You can educate potential victims, but there will always be other potential victims, and new ways that criminals can come up with to social engineer somebody's details, for example. Proactive prevention against potential offenders is a good place to start."
Criminologist Professor Lawrence Sherman believes the collaboration between security engineering and criminology is long overdue, both at Cambridge and globally: "Cybercrime is the crime of this century, a challenge we are just beginning to understand and challenge with science."
"We're extremely grateful to the people giving us this data, who are doing it because they think academic research will make a difference," says Clayton. "Our key contribution is realising that there was a roadblock in terms of being able to distribute the data. It's not that other people couldn't get the data before, but it was very time-consuming, so only a limited number of people were doing research in this area – we want to change that."
"Our Cybercrime Centre will not only provide detailed technical information about what's going on, so that firms can construct better defences," says Anderson. "It will also provide strategic information, as a basis for making better policy."
Visit the Elsevier Store to view our extensive range of security books! Below are two titles that deal with the topic of this article. Use discount code STC215 at checkout and save up to 30% on your very own copy!The Basics of Cyber Safety presents modern tactics on how to secure computer and mobile devices, including what behaviors are safe while surfing, searching, and interacting with others in the virtual world. The book's author, Professor John Sammons, who teaches information security at Marshall University, introduces readers to the basic concepts of protecting their computer, mobile devices, and data during a time that is described as the most connected in history.
This article was originally published on the University of Cambridge website under a Creative Commons Attribution 4.0 International License. Read the original article here.
]]> an Embedded Operating System
15 Nov 2016 12:52:42 +0000 was recently approached for help by a Mentor Graphics customer, who was planning a new project and...
]]>I was recently approached for help by a Mentor Graphics customer, who was planning a new project and needed to select an operating system. They wanted guidance with that choice. Of course, one is tempted to say that it does not matter which of our products they chose (as, between them, Nucleus RTOS and Mentor Embedded Linux do cover most possibilities), but I felt they needed something more objective.
There is actually a huge choice. Given that it is decided to purchase an OS, instead of developing something in-house (an expensive option which rarely makes sense), there is the choice between the "heavyweight" OSes, like Windows CE and various flavors of Linux, and around 200 other, mostly real time (RTOS), products. What the customer was after was a simple decision driven process, like a flowchart …
I did not know of the existence of such a tool and thought about whether I could create one. However, I quickly realized that too many of the parameters were inter-connected for a straightforward flow-chart to handle. Instead, I thought it would be better to formulate a concise list of key questions, the aggregate answers to which would lead to a decision. This is a topic that I commonly address in web seminars, conference papers etc. Here, I can only give a taste of the kinds of questions to be asked:
Is your application real time? In other words, does it need to respond to external events in a very predictable fashion? If the answer is yes, then looking at a true RTOS may be your best option. Although real-time extensions may be available for other OSes, I might question the benefits of making such a choice.
Is memory size an issue? All embedded systems have some kind of limit to how much memory they can have, but if this is quite stringent, the choice of one of the heavyweight OSes may not be wise.
Do you have plenty of CPU power? Or is the processor you have only just about powerful enough for the application. Efficient CPU usage – low overhead, if you like – is a trademark of most RTOSes, which make them a good choice if you do not have power to spare.
Does your device have power consumption issues? Particularly, but not exclusively, with portable devices, power consumption is a key factor. The previous two parameters – memory and CPU power – are both significant here. You may also be looking for power management facilities within the OS.
Do you have a requirement to support obscure devices or unusual communications protocols? Although most RTOS products tend to have a wide range of middleware and drivers, Linux is likely to trump them when it comes to anything out of the ordinary. The validation of protocols should be checked, of course.
Does (or could) your target system have a memory management unit (MMU)? If not, the heavyweight OSes are unlikely to be an option, as they do require an MMU. Typically, RTOSes (with a few exceptions) are thread based (not process), so an MMU is not mandatory. However, in many cases, an available MMU can be used to provide inter-task protection.
What kind of security does your device need? How important is it to protect tasks from one another? If this is a requirement, then a process model OS may be a good choice. This includes all the heavyweights and a few RTOS products. Other RTOSes may, as I mentioned above, use an MMU to facilitate "thread protected mode", which offers some security, with a lower overhead than process model.
Do you need to apply for certification for your application? This is mandatory for certain types of product in particular industries, like aerospace and medical. The certification process tends to be complex and expensive. It requires the availability of source code. The cost is also very sensitive to the volume of code to be processed, which mitigates in favor of the leaner RTOS products.
Do you require interoperability with enterprise software systems? If so, this may imply that one of the Microsoft products may be a good choice, as they are strong in this area.
What is the sale price of your product and what volumes do you anticipate shipping? Cost models for OSes vary. They may be royalty based, perhaps with a sliding scale on volume. They may be royalty free, with just an up-front charge per device/project. They may be "free", requiring up-front tooling expenditure and perhaps an ongoing service/support charge. The OS cost must be factored into the overall cost of development and production. Furthermore, if the OS reduces memory and CPU power requirements, it helps minimize the bill of materials (BOM) of the product.
What is your past experience of embedded OSes? Do you have in-house expertise with specific APIs, like POSIX? If so, this can affect your choice. Linux uses POSIX, but this API is also available with many RTOSes. Your past experience with an OS company with support, documentation etc. is also well worth factoring in; I know that this is a strong driver for repeat business at Mentor Embedded.
This is a very broad guide, but I believe that if you methodically address the above questions, your OS choice will become, at least, clearer. | 677.169 | 1 |
The mathXpert Pre-Calculus Assistant is the second part of a 3-tier advanced Mathematics series. Each successive title in the series includes all the content of the previous title and is therefore higher priced.
Part 2: Pre-Calculus Assistant, the product described on this page — includes all the material of Algebra Assistant
Part 3: Calculus Assistant, includes all the material of Algebra Assistant and Pre-Calculus Assistant
MathXpert Series Overview
MathXpert is a system that allows a person to do mathematics on a computer screen in much the same way as it is done with pencil and paper, but with some important differences:
1. It is not possible to make a mistake. 2. If you do not know what to do, MathXpert can help you.
MathXpert is designed to provide a self-correcting way to learn mathematics. For example, suppose you think (incorrectly) that ln(x+y) = ln x + ln y. You will not be able to apply this incorrect rule in MathXpert, because only correct rules are offered as menu choices for you to choose. If you have in mind to use this incorrect rule, you will learn something from its unavailability. You may, of course, have to ask your teacher why it isn't there. MathXpert is meant to replace blackboards and homework (and graphing calculators), but not teachers and books.
The first and most important design principle of MathXpert is the "glass box" or "transparency" principle — show all the steps. Indeed, this principle combines with the idea that the user should be in control to dictate the basic design of MathXpert: the user chooses the steps and thus controls the development of the computation, while the computer carries out the low-level details.
Carrying out a calculation
To step through a problem, you use the mouse to select a term to work on, then you choose an operation from a short menu of possibly relevant operations. You do not have to type anything or memorize any commands. Since MathXpert carries out the operation for you, no mistake in the mechanics is possible. You can concentrate on choosing what to do. For example, to determine the value of x in the simple linear equation 3x + 2 = 11, when you use the mouse to highlight the 2, a menu pops up giving you a choice of operations that can be carried out, one of which is "subtract from both sides". When you select that, a new line is produced reading either 3x + 2 - 2 = 11 - 2 or 3x = 9, depending on your level (see below). If you didn't know what to do for that first step, clicking the Hint button would have popped up the suggestion, "Subtract something from both sides." If you still didn't know how to proceed, the Show Step button would have made MathXpert perform the correct task for you.
Working with a graph
You're never more than one click away from a graphical representation of any equation. The tools in the Graph Toolbar permit you to zoom out and zoom in (on the horizontal and vertical axes separately), to select a rectangle for the next drawing, to move a cursor (the Point and Slope tool) along the graph to display the numerical values of points on the graph and the slope at that point, and to change the values of parameters in the formula so that you can see how the graph changes if those values change. (Parameters are extra letters in the formula, for example b in y = x + b.) MathXpert, unlike any other software, uses its algebraic module and its prover to internally calculate the singularities of a function before graphing it. This makes it able to draw graphs that graphing calculators are incapable of drawing correctly.
Getting a problem to work with
You can select one of MathXpert's more than 1600 pre-stored problems, without having to type anything. Or, perhaps your teacher has prepared a homework file in MathXpert for you, so you can get your own homework without typing. Finally, if you want to enter your own problem, you can type it in. To start with, choose Edit on a similar problem provided by MathXpert, and you will see what form MathXpert expects you to type. Entering problems into MathXpert is easier than entering them into a scientific calculator. MathXpert never intervenes to provide help. You are free to "wander" by taking any mathematically correct steps at all, whether or not they are leading toward the "ideal" solution of the problem. Having reached an awkward solution, you may choose to compare it with MathXpert's automatic solution -- but that would be your choice. At no point will the program specifically tell you to do something different.
MathXpert's Algebra is correct
Many people think that computers would never make a mistake in algebra, but in fact this "correctness principle" is usually violated by computer algebra systems. For example, in most other computer algebra systems, you can start with the equation b = 0, and divide both sides by b. On the left you will get b/b = 1, and on the right you will get 0/b = 0. Thus you have derived the wrong equation 1=0. The problem here is that the other systems do not keep track of the assumptions and the side conditions. The side conditions of operations can be quite complicated. For example, if we try to integrate 1/x from -1 to 1, many computer algebra systems will simply form the indefinite integral 1/|x| and evaluate it from -1 to 1, producing the answer zero, failing to note that the integral is undefined due to the singularity at zero. The side condition that the function should be continuous on the (closed) interval of integration is not checked.
While scientists and engineers should be able to judge the correctness of answers they receive from computer algebra systems, that cannot be said for students. MathXpert satisfies the correctness principle by keeping track of assumptions and side conditions, and being able to infer side conditions from assumptions.
Instruction is tailored to the student's level
MathXpert contains a "user model" that consists of recording, for each of some 1600 mathematical operations, whether that operation is at the moment well-known, known, learning, or unknown. This controls the level of detail shown in the automode solution. For example, in the linear-equations example above, when subtracting something from both sides is learning, it does not simplify the result, but when it is known or well-known, it does simplify the result. Thus we got 11-2 in the first case and 9 in the second case. If this problem were entered under an advanced-algebra topic, it might have been solved in one step with the justification Solve linear equation. That one-step operation is not used in beginning algebra, because there it is classified as unknown. This illustrates how MathXpert tailors its output: it sets up an ideal user model based on the initial choice of topic. If the topic is elementary, the user model will set more operations to learning or unknown. If it is advanced, some powerful operations that are not used in elementary topics become available.
mathXpert Pre-Calculus Assistant features
As well as the ability to work through an unlimited number of your own problems, the mathXpert Pre-Calculus Assistant includes 5,000 pre-designed examples. They cover all the topics found in Algebra Assistant, plus the following:
Advanced Algebra
Sigma notation
Binomial theorem
Simplification review
Cubic equations (one real root)
Logs and Exponential Functions
Logarithmic functions
Changing base of logarithms
Exponents and logarithms
Equations with logarithms
Exponential equations
Simplify Logs and powers
Complex numbers
Complex arithmetic
Polar form of complex numbers
De Moivre's theorem
Complex quadratic equations
Complex trig and log functions
Cubic equations
Basic Trigonometry
Evaluating trig functions
Trig identities
Simplifying trig expressions
Simple trig equations
Addition formulae
Double angle formulae
Verifying trig identifies
Advanced Trigonometry
Half angle formulae
Trigonometric products
Trig factor identities
Inverse trig functions
Trig equations
Hyperbolic functions
Deriving hyperbolic function laws
Hyperbolic trigonometry
Matrices
Row operations on matrix equations
Gauss-Jordan elimination
Solving equations by matrix inverse
System Requirements
Win 98/ME/2K/NT/XP — can be run on a Mac using Virtual PC or on Linux using WINE.
HTML Browser required. (Internet Explorer 5.0 or later recommended.)
The software is available in different license versions:
Single User
Site License: A single-room lab up to 35 computers, plus a single teacher's copy.
This software is a web download. We will send you a unique serial number you can use to download and install the software.
Please select the license version you require from the drop-down menu below. The price increase over the single user edition is displayed next to the license version you select. | 677.169 | 1 |
Search Results (75)
This worksheet will allow you to visually see how slope changes using ...
This worksheet will allow you to visually see how slope changes using dynamic text and Sliders. By using Sliders students can see how the slope or the steepness of the line changes with respect to the values of x and y. Students will al
Elementary Algebra is a work text that covers the traditional topics studied ...
Elementary Algebra is a work text that covers the traditional topics studied in a modern elementary algebra course. It is intended for students who (1) have no exposure to elementary algebra, (2) have previously had an unpleasant experience with elementary algebra, or (3) need to review algebraic concepts and techniques. In F.LE Equal Differences over Equal Intervals 2, students prove the property in general (for equal intervals of any length).
In this task students observe using graphs and tables that a quantity ...
In this task students observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
In this task students have the opportunity to construct linear and exponential ...
In this task students have the opportunity to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This lesson is designed for students to gather and analyze data about ...
This lesson is designed for students to gather and analyze data about baseball figures. The student will use the Internet or other resources to collect statistical data on the top five home run hitters for the current season as well as their career home run totals. The students will graph the data and determine if it is linear or non-linear.
This problem provides an opportunity to experiment with modeling real data. Populations ...
This problem provides an opportunity to experiment with modeling real data. Populations are often modeled with exponential functions and in this particular case we see that, over the last 200 years, the rate of population growth accelerated rapidly, reaching a peak a little after the middle of the 20th century and now it is slowing down.
Partial differential equations (PDEs) describe the relationships among the derivatives of an ...
Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. Experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. Upon successful completion of this course, the student will be able to: State the heat, wave, Laplace, and Poisson equations and explain their physical origins; Define harmonic functions; State and justify the maximum principle for harmonic functions; State the mean value property for harmonic functions; Define linear operators and identify linear operations; Identify and classify linear PDEs; Identify homogeneous PDEs and evolution equations; Relate solving homogeneous linear PDEs to finding kernels of linear operators; Define boundary value problem and identify boundary conditions as periodic, Dirichlet, Neumann, or Robin (mixed); Explain physical significance of boundary conditions; Show uniqueness of solutions to the heat, wave, Laplace and Poisson equations with various boundary conditions; Define well-posedness; Define, characterize, and use inner products; Define the space of L2 functions, state its key properties, and identify L2 functions; Define orthogonality and orthonormal basis and show the orthogonality of certain trigonometric functions; Distinguish between pointwise, uniform, and L2 convergence and show convergence of Fourier series; Define Fourier series on [0,pi] and [0,L] and identify sufficient conditions for their convergence and uniqueness; Compute Fourier coefficients and construct Fourier series; Use the method of characteristics to solve linear and nonlinear first-order wave equations; Solve the one-dimensional wave equation using d'Alembert's formula; Use similarity methods to solve PDEs; Solve the heat, wave, Laplace, and Poisson equations using separation of variables and apply boundary conditions; Define the delta function and apply ideas from calculus and Fourier series to generalized functions; Derive Green's representation formula; Use Green's functions to solve the Poisson equation on the unit disk; Define the Fourier transform; Derive basic properties of the Fourier transform of a function, such as its relationship to the Fourier transform of the derivative; Show that the inverse Fourier transform of a product is a convolution; Compute Fourier transforms of functions; Use the Fourier transform to solve the heat and wave equations on unbounded domains. (Mathematics 222) | 677.169 | 1 |
Basic Mathematical Skills with Geometry
Basic Mathematical Skills with Geometry, 7/e by Baratto/Bergman is part of the latest offerings in the successful Streeter-Hutchison Series in Mathematics. The seventh edition continues the hallmark approach of encouraging the learning of mathematics by focusing its coverage on mastering math through practice. This worktext seeks to provide carefully detailed explanations and accessible pedagogy to introduce basic mathematical skills and put the content in context. The authors use a three-pronged approach (I. Communication, II. Pattern Recognition, and III. Problem Solving) to present the material and stimulate critical thinking skills. Items such as Math Anxiety boxes, Check Yourself exercises, and Activities represent this approach and the underlying philosophy of mastering math through practice. The exercise sets have been expanded, organized, and clearly labeled. Vocational and professional-technical exercises have been added throughout. Repeated exposure to this consistent structure should help advance the student's skills in relating to mathematics. The book is designed for a one-semester basic math course and is appropriate for lecture, learning center, laboratory, or self-paced courses. It is accompanied by numerous useful supplements, including McGraw-Hill's online homework management system, MathZone.
"synopsis" may belong to another edition of this title.
About the Author:
Don began teaching in a preschool while he was an undergraduate. He subsequently taught children with disabilities, adults with disabilities, high school mathematics, and college mathematics. Although each position offered different challenges, it was always breaking a challenging lesson into teachable components that he most enjoyed.
It was at Clackamas Community College that he found his professional niche. The community college allowed him to focus on teaching within a department that constantly challenged faculty and students to expect more. Under the guidance of Jim Streeter, Don learned to present his approach to teaching in the form of a textbook. Don has also been an active member of many professional organizations. He has been president of ORMATYC, AMATYC committee chair, and ACM curriculum committee member. He has presented at AMATYC, ORMATYC, AACC, MAA, ICTCM, and a variety of other conferences.
Above all, he encourages you to be involved, whether as a teacher or as a learner. Whether discussing curricula at a professional meeting or homework in a cafeteria, it is the process of communicating an idea that helps one to clarify it.
Stefan began teaching math and science in New York City middle schools. He also taught math at the University of Oregon, Southeast Missouri State University, and York County Technical College. Currently, Stefan is a member of the mathematics faculty at Clackamas Community College where he has found a niche, delighting in the CCC faculty, staff, and students. Stefan's own education includes the University of Michigan (BGS, 1988), Brooklyn College (CUNY), and the University of Oregon (MS, 1996).
Stefan is currently serving on the AMATYC Executive Board as the organization's Northwest Vice President. He has also been involved with ORMATYC, NEMATYC, NCTM, and the State of Oregon Math Chairs group, as well as other local organizations. He has applied his knowledge of math to various fi elds, using statistics, technology, and web design. More personally, Stefan and his wife, Peggy, try to spend time enjoying the wonders of Oregon and the Pacifi c Northwest. Their activities include scuba diving, self-defense training, and hiking.
Barry has enjoyed teaching mathematics to a wide variety of students over the years. He began in the fi eld of adult basic education and moved into the teaching of high school mathematics in 1977. He taught high school math for 11 years, at which point he served as a K-12 mathematics specialist for his county. This work allowed him the opportunity to help promote the emerging NCTM standards in his region.
In 1990, Barry began the next portion of his career, having been hired to teach at Clackamas Community College. He maintains a strong interest in the appropriate use of technology and visual models in the learning of mathematics.
Throughout the past 32 years, Barry has played an active role in professional organizations. As a member of OCTM, he contributed several articles and activities to the group's journal. He has presented at AMATYC, OCTM, NCTM, ORMATYC, and ICTCM conferences. Barry also served 4 years as an offi cer of ORMATYC and participated on an AMATYC committee to provide feedback to revisions of NCTM's standards. | 677.169 | 1 |
Product Description:
Get a good grade in your precalculus course with Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH and it's accompanying CD-ROM! Written in a clear, student-friendly style and providing a graphical perspective so you can develop a visual understanding of college algebra and trigonometry, this text provides you with the tools you need to be successful in this course. Preparing for exams is made easy with iLrn, an online tutorial resource, that gives you access to text-specific tutorials, step-by-step explanations, exercises, quizzes, and one-on-one online help from a tutor. Examples, exercises, applications, and real-life data found throughout the text will help you become a successful mathematics student!
REVIEWS for Precal | 677.169 | 1 |
Algebra geometry
What 5 fictional heroines would wear on their first date Which Lord of the Flies character are you? Which Shakespearean villain are you. Geometry Geometry is all about shapes and their properties If you like playing with objects, or like drawing, then geometry is for you! Geometry can be divided into. Software for math teachers that creates exactly the worksheets you need in a matter of minutes Try for free Available for Pre-Algebra, Algebra 1, Geometry, Algebra.
Algebra Nation is a comprehensive online and mobile resource for students, teachers, and parents. The best multimedia instruction on the web to help you with your Algebra & Geometry homework and study.
JMAP offers New York teachers and other users of the Common Core State Standards free resources that simplify the integration of Regents exam questions into their. Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. A comprehensive and coherent set of mathematics standards for each and every student from prekindergarten through grade 12, Principles and Standards is the first. Holt McDougal Algebra 1, Geometry and Algebra 2 student editions are now streamlined to focus on a deeper understanding of math strategies and concepts.
Pre-algebra and algebra lessons, from negative numbers through pre-calculus Grouped by level of study Lessons are practical in nature informal in tone, and contain.
Free algebra lessons, games, videos, books, and online tutoring We can help you with middle school, high school, or even college algebra, and we have math lessons in. Purplemath Need help with math? Start browsing Purplemath's free resources below! Practial Algebra Lessons: Purplemath's algebra lessons are informal in their tone. | 677.169 | 1 |
Showing 1 to 3 of 5
I recommend it because every major will require Calc 2 and it is important for students to understand the basic fundamentals of differentiation and integration
Course highlights:
This course is more about integration and show how scientists had applied it in real life. I've learned a lot about integration techniques and knows how important it is in Physics and more advanced mathematics courses
This course was a necessary pre-requisite for the Mechanical Engineering degree I am working towards at the moment. I am taking this course online, and it is not bad, but there is definitely room for improvement. The exams are much harder than the homework and quizzes, and only some sections have online lectures. If there is not an online lecture, you will need to learn the material from a third party source, the homework examples, or carefully read the book. This is an online class, and typically online classes are taken to increase the convenience of returning to school. However, in this class, you are required to take the exams in a local testing center. This makes exams slightly inconvenient if you are working a full-time job while attending this class. I have also noticed any of the material which the work has to be graded, thus a grade is not returned immediately, the grade takes a long time to be returned.
Course highlights:
This course focused on basic calculus principles (ie. differentiation, integration, limits, etc.), but made them more difficult than Calculus I. This is to be expected, but the algebra involved to solve problems is also more in depth as well as very tedious.
Hours per week:
9-11 hours
Advice for students:
Be sure to do every homework assignment, and use any resources possible. The best resource is to find someone who has experience with this material, and have them help you if get stuck. One of the biggest issues with this class is the fact there is no professor to walk you through methods of doing things as well as why these problems are important or relative. | 677.169 | 1 |
Algebra Function Rule Review Coloring Sheet
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This is a fun review of functions that I use with my Algebra 1 and Pre-Algebra classes. The worksheet includes 25 function problems that increase in difficulty.
Working with function rules is all about reading and following directions. This worksheet forces students to pay attention to detail as the find function values and color their design.
To help students choose their colors, I instruct them to begin with their "favorite" color (color "A"). After this, they use a color wheel to locate a triad for colors "B" and "C." The students enjoy using the color wheel, and this helps to ensure that the colors they select will go well together.
As for the worksheet, students find each function value, locate their answers on the grid, and color that section of the grid according to the design listed on their worksheet.
The coloring aspect adds a fun touch to the review, allows students to self-check their work, and makes grading a snap | 677.169 | 1 |
New Problems in Euclidean Geometry
New Problems in Euclidean Geometry
15.00
This book should appeal to anyone 16+ who enjoys solving the kind of challenging and attractive geometry problems that have virtually vanished from the school curriculum, but which still play a central role in national and international mathematics competitions. It is a treasure trove of wonderful geometrical problems, with hints for their solution.
Quantity:
Add To Cart
ISBN 10: 1-906001-09-X
ISBN 13: 978-1-906001-09 | 677.169 | 1 |
Geometry workbook makes the fundamental concepts of geometry accessible and interesting for college students and incorporates a variety of basic algebra skills in order to show the connection between Geometry and Algebra.Alan Bass is the author of 'Geometry: Fundamental Concepts and Applications', published 2007 under ISBN 9780321473318 and ISBN 03214733 | 677.169 | 1 |
Introduction to Algebraic Equations Student Practice Pages
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PRODUCT DESCRIPTION
These student practice sheets were created to accompany the units in our Algebra 1 Interactive Notebook Bundle. They provide additional practice for the concepts introduced in each unit. Each student worksheet contains 15 problems and they can be used for homework assignments, work for early finishers, or review. They can also be used as guided practice problems when reteaching is necessary.
Worksheets are provided for the following topics:
The Addition Principle for Equations (Practice 1)
The Addition Principle for Equations (Practice 2)
The Addition Principle for Equations (Practice 3)
The Addition Principle for Equations (Practice 4)
The Multiplication Principle for Equations
The Division Principle for Equations | 677.169 | 1 |
Betty Hurley
Dr. Betty Hurley has a doctorate in math education from the University of Rochester. She has been at SUNY Empire State College for over 30 years and is currently a professor and area coordinator in mathematics, developing and teaching online math courses. She has co-authored a book, "Foundations of Learning," and has recently been experimenting with ePortfolios for learning. She has developed some open educational resources (OERs), including a course called, A Mathematical Journey, available through Wikieducator and a course on ePortfolios for STEM educators as an HP FellowIf you are in the business environment, you need to have basic quantitative skills, including a combination of algebra and statistics. If you've tried gaining these before in a traditional classroom environment and struggled, this course can help you. You may want to use it as a first step before taking a college course in quantitative methods | 677.169 | 1 |
The following is a list
of mathematics courses that require the completion of a summer assignment. It is expected that each student will complete the assignment by the end
of the summer to prepare for the school year. The teacher will check that the
entire assignment was completed on the first day of school. The students are
tested on the material shortly after the start of the school year. Specific
information for each course's summer assignment may be found on the expectations sheet for that course. Extra copies of all summer assignments are
available in guidance. Some necessary materials may also be available on this
website.
Algebra 1 (all levels) (Grades 8 and 9) - A set of practice problems are provided to
review concepts and skills necessary for success in Algebra, specifically,
solving linear equations and inequalities. The material is reviewed the first
two days in September and a quiz will be given following the review days. Rationale:
It enables all students entering Algebra 1 to strengthen solving processes
necessary for more rigorous content as well as ensures the delivery of all Common Core content throughout the school year.
Honors Geometry (Grade 9/10) - An assignment and set
of practice problems are provided for Chapter 1 of the Honors Geometry textbook
- essentially a review of familiar vocabulary and geometric concepts previously
learned. The material is reviewed for a few days in September and a test will
be given following the review days. Rationale: It enables
the class to begin more advanced Geometry topics earlier and eliminates the
tedium of review of vocabulary the students have learned in previous courses.
Algebra 2 and
Honors Algebra 2 (Grade 10, 11) - A set of practice problems are provided for concepts and skills
necessary for success in Algebra 2/Honors Algebra 2 - essentially a review of
Algebra 1 topics. The material is reviewed for the first two days of school and
a test will be given following the review days. Rationale:
It enables both level classes to begin Algebra 2 topics immediately so the
focus is on Algebra 2 throughout the school year.
Precalculus and Honors Precalculus (Grade 11, 12) - A set of practice problems are provided from the back of the textbook - essentially a skills review of concepts from Algebra 2. The material is reviewed for the first two days of school in September and a test is given on the third day of school. Rationale: It enables the class to begin Precalculus immediately without spending several weeks reviewing previously learned Algebra 2 topics.
AP
Calculus (Grade 12) -
A set of notes and practice problems with answers to the evens are provided
from the first chapter of the textbook, along with excerpts from
previous editions and a review of trigonometry - essentially a review
of all pertinent concepts from Precalculus. The material is reviewed for a few
days in September and a test will be given following the review days. Rationale:
It enables the class to complete all topics for the College Board AP curriculum
by April, in time to review thoroughly for the AP exam administered in May.
AP Statistics (Grades 10 - 12) - The assignment requires
students to review the basics of statistics, using the internet as a
resource. Selected answers are provided. The material is reviewed for a
few days in September and a test will be given following the review days. Rationale:
It enables the class to begin more advanced statistics topics earlier and
eliminates the tedium of review of vocabulary and basic data graphs the
students have learned in previous courses. It also enables the class to
complete all topics for the College Board AP curriculum by April, in time to
review thoroughly for the AP exam administered in May. | 677.169 | 1 |
PDF (Acrobat) Document File
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0.61 MB
PRODUCT DESCRIPTION
This booklet was created to be used as a review after teaching a system of equations unit. Included topics are:
* Determining if a point is a solution
* Solving a system by graphing
* Solving a system using substitution
* Solve a system using elimination
* Types of Solution (one, no solution, or infinitely many)
Great resource to be included in an interactive notebook. Algebra 1 TEKS A.3F and A.5C | 677.169 | 1 |
For a one-semester or one-quarter course covering calculus for students majoring in business, economics, social sciences, or life sciences.This text covers calculus with an emphasis on cross-discipline principles and practices. Designed to be both student-friendly and accessible, it develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on concepts and ideas, followed immediately by the development of computational skills, ideas, and problem-solving | 677.169 | 1 |
Puzzles in Mathematics and Logic by Aaron J. Friedland
Book Description
100 original problems in math and logic, featuring permutations, combinations, properties of numbers, algebra, solid and plane geometry, logic, and probability. Although only high school math is needed to solve these problems, even accomplished mathematicians are likely to find some surprises here. Complete and ingenious solutions provided for all problems. 31 drawings | 677.169 | 1 |
A complete training package lets you learn Adobe Illustrator CC at your own speed Adobe Illustrator is the leading drawing and illustration software used to create artwork for a variety of media. This book-and-DVD package provides 13 self-paced lessons that get you up to speed on the latest version of Illustrator (Creative Cloud). Step-by-step... more...
This book provides fundamental knowledge in the fields of attosecond science and free electron lasers, based on the insight that the further development of both disciplines can greatly benefit from mutual exposure and interaction between the two communities. With respect to the interaction of high intensity lasers with matter, it covers ultrafast... more...
Currently there is substantial exchange and communication between academic communities around the world as researchers endeavour to discover why so many children 'fail' at a subject that society deems crucial for future economic survival. This book charts current thinking and trends in teacher education around the world, and looks critically at the... more...
On the occasion of the celebration of ?Twenty Years of Didactique of Ma- ematics? in France, Jeremy Kilpatrick commented that though the works of Guy Brousseau are known through texts referring to them or mentioning their existence, the original texts are unknown, or known only with difficulty, in the non-Fren- speaking world. With very few exceptions,... more...
Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas... more...
This book focuses on aspects of mathematical beliefs, from a variety of different perspectives. Current knowledge of the field is synthesized and existing boundaries are extended. The volume is intended for researchers in the field, as well as for mathematics educators teaching the next generation of students. more...
Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology'... more...
A significantly revised and improved introduction to a critical aspect of scientific computation Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations... more...... more... | 677.169 | 1 |
Elementary Real Analysis
Elementary Real Analysis is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the "big picture" and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces. Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis. | 677.169 | 1 |
Giving students more detailed explanations, this resource supplements the brief answers found at the back of the book for selected exercises by providing fully worked-out solutions. It also contains problem-solving strategies, additional algebra steps, and review for selected problems | 677.169 | 1 |
Professor of mathematics and computer science, University of Iowa, Iowa City, Iowa. Author of An Introduction to Numerical Analysis, Elementary Numerical Analysis, The Numerical Solution of Integral Equations of the Second Kind, and (with Weimin Han) Theoretical Numerical Analysis.
area of mathematics and computer science that creates, analyzes, and implements algorithms for obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Since the mid 20th century, the growth in power and availability of digital computers has led to an increasing use of realistic mathematical models in science and engineering, and numerical analysis of increasing sophistication is needed to solve these more detailed models of the world. The formal academic area of numerical analysis ranges from quite theoretical mathematical studies to computer science issues. With the increasing availability of computers, the new discipline of scientific computing, or computational science, emerged during the 1980s and 1990s. The discipline combines numerical analysis, symbolic mathematical computations, computer graphics, and other areas of computer science to make it easier to... | 677.169 | 1 |
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About the Book
Author David Weltman's fourth edition of Intermediate Algebra offers students complete coverage of topics such as Linear Equations and Inequalities, Exponential and Radical Expressions, Relations and Functions and many more. This challenging algebra text requires students to comprehend information presented by providing over 7,000 problems for students to complete. Intermediate Algebra also assists students in associating the fundamental topics of algebra with real world data through its featured "internet connections" and encourages class participation and involvement through "group activities." | 677.169 | 1 |
Product Description:
Harold Jacobs's "Geometry" created a revolution in the approach to teaching this subject, one that gave rise to many ideas now seen in the NCTM Standards. Since its publication nearly one million students have used this legendary text. Suitable for either classroom use or self-paced study, it uses innovative discussions, cartoons, anecdotes, examples, and exercises that unfailingly capture and hold student interest. This edition is the Jacobs for a new generation. It has all the features that have kept the text in class by itself for nearly 3 decades, all in a thoroughly revised, full-color presentation that shows today's students how fun geometry can be. The text remains proof-based although the presentation is in the less formal paragraph format. The approach focuses on guided discovery to help students develop geometric intuition.
REVIEWS for Geometry | 677.169 | 1 |
Friday, April 20, 2012
Mathematics of Planet Earth 2013
MAA is a participating partner in Mathematics of Planet Earth 2013, a year-long program to publicize and promote the role of mathematics in developing a better understanding of dynamic processes affecting Planet Earth, ranging from geophysical systems governing climate to economic and financial activity.
The following titles are related to the Mathematics of Planet Earth theme and can be found in the MAA Store.
Based on the author's environmental and risk consulting experience with the firm of Arthur D. Little Inc., this book takes three key environmental issues and shows how mathematical modeling is used routinely in the real world to investigate them. These three issues are groundwater contamination, air pollution, and hazardous materials accidents. There is an elementary and an advanced chapter on each of these topics, readily separable to allow this book to be used with different audiences.
The book is heavily illustrated, and the problems reflect the kinds of issues encountered in practice. There is a highly interdisciplinary tone throughout with necessary background introduced as needed.
This book is intended as a text for a modeling course accessible to students who have mastered a one-year course in calculus. Mooney and Swift present a unique approach to modeling. It balances theoretical versus empirical models, analytic models versus simulation, deterministic versus stochastic models, and discrete versus continuous models.
Examples are drawn from real-world data or from models that have been used in various applied fields.
This collection of articles highlights the role of mathematics in solving and illuminating pressing environmental challenges. It does so at an elementary level, demonstrating a wide variety of significant environmental applications that can be explored without resorting to calculus.
Topics include ground-level ozone, pollution and water use, preservation of whales, mathematical economics, the movement of clouds over a mountain range, population models, the spread of infections, the survival of buffalo after the 19th century slaughter, groundwater dissipation, and the cleaning up of oil spills | 677.169 | 1 |
'Nation's Newspaper' Moves Into Math Texts
The newspaper that made colorful charts and numeric tidbits
commonplace in American journalism is now making its mark in U.S.
textbooks.
USA Today will be inserting its graphics and articles in a
new series of pre-algebra and algebra books published by
Glencoe/McGraw-Hill, one of the leading publishers of mathematics texts
for secondary schools.
The newspaper's content will help students see the practical
applications of the algebraic concepts they're learning, according to
officials with the publishing company, which is marketing the new
textbook series to schools for the start of the 2002-03 school
year.
"We were interested in getting more real-life content in our books,"
said Darlene R. Leshnock, the vice president of mathematics editorial
for the New York City-based publisher.
"It was fairly easy to find examples of how algebra applies to the
real world," she said, in USA Today's
Snapshots—stand-alone graphics that the McLean, Va.- based
newspaper has made a staple since its introduction in 1982.
In Glencoe/McGraw-Hill's new pre-algebra, Algebra 1, and Algebra 2
texts, USA Today articles and graphics will appear in the
introduction to each of the books' five units. The books also will
incorporate one or two examples from the 2.1 million-circulation
national newspaper.
Math or Marketing?
The newspaper, which is owned by the Gannett Co. and calls itself
"the nation's newspaper," has a contract similar to those signed by
other textbook authors, according to Ms. Leshnock. Neither she nor
Diane H. Barrett, the director of USA Today's national
educational programs, would disclose the financial arrangements.
In a lesson on ratios and proportions, the new Algebra 1 book
reproduces a Snapshot from the paper's sports section. The chart, which
is clearly marked with the newspaper's logo, lists the number of medals
won by seven countries in the history of the Summer Olympics.
Students are asked to write the ratios of gold medals to the total
number awarded each of the countries. A second question tells them to
find out if any of the ratios form a proportion, meaning that two of
the ratios would be equivalent.
The exercise gives students the chance to apply the skills they've
learned and to understand their importance, according to Alice B.
Foster, the marketing manager for Glencoe's mathematics books.
What's more, it gives students experience in interpreting data, a
skill that they will need in reading newspapers, business reports, and
a variety of documents in their adult lives, she added.
Critics, however, say the partnership between the two publishing
powerhouses has more to do with marketing than teaching algebra.
Glencoe/McGraw-Hill will try to sell textbooks by pushing a familiar
brand name in front of teachers and curriculum directors, according to
William J. Bennetta, the president of the Textbook League, a Sausalito,
Calif.-based nonprofit group that reviews textbooks. Meanwhile, USA
Today will have its logo prominently displayed in front of a legion
of potential readers, he added.
"This is all just advertising gimmickry," Mr. Bennetta contended.
"Most books could be cut in half without any loss of pedagogical value
to the student."
'Real-World Content'
The partnership marks the first time that the 20-year-old newspaper
has had any of its content published in a textbook. But the newspaper
has been active in K-12 schools since its founding, said Ms.
Barrett.
The newspaper distributes free copies to schools throughout the
country so that teachers can use them in lesson plans. Ms. Barrett
would not say how many copies of the paper are distributed through the
program.
USA Today also posts daily lesson plans on its Web site based
on articles in every issue.
"It's relevant, real-world content that engages young people in
learning," Ms. Barrett said.
Glencoe/McGraw-Hill officials proposed the partnership with USA
Today, Ms. Foster said, because they saw many teachers clipping
charts from the newspaper to use as classroom resources.
This year, Glencoe/McGraw-Hill will submit the textbooks to
officials in Kentucky, Oregon, and South Carolina for review in their
textbook-adoption processes, Ms. Leshnock said. It will also apply for
adoption in California next year when the state reviews materials for
its list of approved textbooks.
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We encourage lively debate, but please be respectful of others. Profanity and personal attacks are prohibited. By commenting, you are agreeing to abide by our user agreement.
All comments are public. | 677.169 | 1 |
Discrete Mathematics
Description
Discrete mathematics is the study of mathematical structures that are discrete, separated or distinct; in contrast with calculus which deals with continuous change. It is an important area of pure and applied mathematics, as well as providing the mathematical basis for the understanding of computers and modern computation. Discrete Mathematics is important in the sciences, where it has increasing application in many areas, an exemplar of which is the understanding of DNA sequences in molecular biology. The Discrete Mathematics course introduces first year students to the basic concepts of discrete mathematics, covering topics such as sets, logic, enumeration methods, probability, recurrence relations, induction and graph theory. The course provides important background for students pursuing a BMath degree. It covers much of the mathematics essential for students majoring in Computer Science or Software Engineering, and is a compulsory course in those degree programs Be able to read, interpret and write some basic mathematical notation
2. Be able to recognise and/or construct examples of mathematical objects introduced during the course, such as sets and functions
3. Have been introduced to several mathematical models, (e.g. propositional logic, trees) including some of those underlying computing and information technology
4. Have had the opportunity to develop capacity in knowing what constitutes a valid argument, and in constructing valid arguments/proofs
5. Have had opportunity to develop problem solving skills; and been introduced to ways of thinking useful for simplifying complex situations | 677.169 | 1 |
Maths for adults by Graham Lawler(
Book
)
3
editions published
in
2005
in
English
and held by
145
libraries
worldwide
This text is designed for adults who need to brush up on their basic maths skills - whether for a job, a course or simply to help with their children's homework - and who are looking for clear, non-patronising explanations. Fractions, percentages, averages, decimals, data presentation, geometry and algebra are all set out in a clear way
Algebra : basic algebra explained by Graham Lawler(
Book
)
4
editions published
between
2004
and
2005
in
English
and held by
125
libraries
worldwide
Covers the essential information needed to understand the basic concepts in algebra and explains how to use algebraic techniques to solve problems
Maths by Graham Lawler(
Book
)
1
edition published
in
2002
in
English
and held by
79
libraries
worldwide
Maths by Graham Lawler(
Book
)
3
editions published
between
2004
and
2005
in
English
and held by
63
libraries
worldwide
Genetics : the science of genetics revealed by Edwin Oxlade(
Book
)
1
edition published
in
2007
in
English
and held by
58
libraries
worldwide
Examines the field of genetics, discussing DNA research, heredity, cloning, genetic engineering, and the possibility of gene therapy
Maths foundation by Rob Kearsley Bullen(
Book
)
2
editions published
in
2010
in
English
and held by
49
libraries
worldwide | 677.169 | 1 |
Sidebar
Weekly schedule
Math 225
You are required to watch 1-3 videos before each class unless stated otherwise for that day in the schedule below.
The videos are titled by section numbers from the text. The section covered in each class are the videos you need to watch before each class. | 677.169 | 1 |
Computational Geometry
Overview
This overview introduces a set of problems from the field of computational geometry. Many of these problems were first investigated by mathematicians over the past few centuries. Since the 1970s, computational geometry has been recognized as the systematic study of geometric algorithms and data structures that enable their efficient execution. These algorithms solve numerous real-world problems, some of which we will present in this chapter. Too often, the data structures and algorithms presented in this chapter have been considered "too advanced" for the undergraduate curriculum. Software professionals, however, will readily be able to learn these structures and the principles behind the algorithms and apply them to the challenging problems they must face.
Classifying Problems
A computational geometry problem inherently involves geometric objects, such as points, lines, and polygons. More precisely, a computational geometry problem is defined by (a) the type of input data to be processed, (b) the computation to be performed, and (c) whether the task is static or dynamic. These classifications help identify the techniques that can improve efficiency across families of related problems.
Input data
A computational geometry problem must define the input data. The following are the most common types of input data to be processed:
A set of points in the two-dimensional plane
A set of line segments in the plane
A set of rectangles in the plane
A set ...
Find the exact information you need to solve a problem on the fly, or go deeper to master
the technologies and skills you need to succeed | 677.169 | 1 |
This book is suitable for both students and a general audience interested in learning what pure mathematics is all about. Pure mathematics is presented in a friendly, accessible, and nonetheless rigorous style. Definitions, theorems, and proofs are accompanied by creative analogies and illustrations to convey the meaning and intuition behind the abstract math.
Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting; develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples; develop the ability to read and understand written mathematical proofs; develop talents for creative thinking and problem solving; improve their quality of communication in mathematics | 677.169 | 1 |
Pages
Wednesday, September 8, 2010
Math: Phobia or Fun?
It's OFFICIALLY Back-to-School at Long Leaf Academy! It is always fun to pull out new notebooks and pencils and paper and start learning anew. After a sweet summer break, the McBlessings were excited to begin new subjects and revisit old ones this week.
Much to the dismay of my MainMost (a former high school math teacher), both of our high school daughters have a phobia of math. Luckily, though, they were able to do a "refresher" course before jumping right back into math this year. We received two math DVDs from –The Pre-Algebra Tutor, Volume 1 and The Texas Instruments TI-83/TI-84 Calculator Tutor.
The Pre-Algebra Tutor, Volume 1 is a 5-hour video tutorial that breaks down the basic concepts of Pre-Algebra and makes them less intimidating. Instructor Jason Gibson works multiple example problems step-by-step so that students can actually "see" math come to life. Excellent for visual learners, The Pre-Algebra Tutor, Volume 1 covers the following algebraic concepts:
Real Numbers
The Number Line
Greater Than, Less Than, Equal To
Absolute Value and Adding Integers
Subtracting Integers
Multiplying Integers
Dividing Integers
Powers and Exponents
Order of Operation
I appreciate the positive encouragement Mr. Gibson entwines throughout the video reminding students that they CAN do math!
The Texas Instruments TI-83/TI-84 Calculator Tutor is an 8-hour video tutorial designed to help you achieve maximize benefit from your TI-83/TI-84 Calculator. This 3 DVD set teaches you how to use all of the bells and whistles available on your graphing calculator. The 37 lessons range in topics as simple as basic arithmetic to more complex topics such as calculating the definite integral by graphing. Although my daughters were not yet ready to use the TI Calculator in their math studies, the MainMost found the videos most interesting. A lover of all things math, he enjoyed watching the videos and was excited to get his graphing calculator out again. Beginning with a very good overview of the TI Calculator and ending with working with complex numbers, Professor Gibson does an excellent job of demonstrating each function of this very capable calculator. Anyone who has ever wanted to master a graphing calculator will find this DVD series most beneficial.
Both of these DVD sets sell for $26.95 each and come with a money-back guarantee! They are available at along with a multitude of other math resources for all age levels—from beginning counting videos to differential equations and physics. Also worth checking out on the website are free interactive math references and articles. A great tool to turn math phobias into math fun!
Please visit the crew blog to see what my crew mates are saying about Math Tutor DVD!
~~I was given the opportunity to use and review these two math videos by Math Tutor | 677.169 | 1 |
A.2.c factoring completely first- and second-degree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorizations.
A.EI Equations and Inequalities
A.4 Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions. The student will solve multistep linear and quadratic equations in two variables, including
A.5.c solving real-world problems involving inequalities; and
A.5.d solving systems of inequalities.
A.6 The student will graph linear equations and linear inequalities in two variables, including
A.6.a determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined; and
A.8 The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.
A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions.
9-12.MA Mathematical Analysis
9-12.MA.1 The student will investigate and identify the characteristics of polynomial and rational functions and use these to sketch the graphs of the functions. This will include determining zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Graphing utilities will be used to investigate and verify these characteristics.
9-12.MA.2 The student will apply compositions of functions and inverses of functions to real-world situations. Analytical methods and graphing utilities will be used to investigate and verify the domain and range of resulting functions.
9-12.MA.3 The student will investigate and describe the continuity of functions, using graphs and algebraic methods.
9-12.MA.6 The student will use mathematical induction to prove formulas and mathematical statements.
9-12.MA.7 The student will find the limit of an algebraic function, if it exists, as the variable approaches either a finite number or infinity. A graphing utility will be used to verify intuitive reasoning, algebraic methods, and numerical substitution.
9-12.MA.8 The student will investigate and identify the characteristics of conic section equations in (h, k) and standard forms. Transformations in the coordinate plane will be used to graph conic sections.
9-12.MA.9 The student will investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and real-world problems. This will include the role of e, natural and common logarithms, laws of exponents and logarithms, and the solution of logarithmic and exponential equations.
9-12.MA.10 The student will investigate and identify the characteristics of the graphs of polar equations, using graphing utilities. This will include classification of polar equations, the effects of changes in the parameters in polar equations, conversion of complex numbers from rectangular form to polar form and vice versa, and the intersection of the graphs of polar equations.
9-12.MA.11 The student will perform operations with vectors in the coordinate plane and solve real-world problems, using vectors. This will include the following topics: operations of addition, subtraction, scalar multiplication, and inner (dot) product; norm of a vector; unit vector; graphing; properties; simple proofs; complex numbers (as vectors); and perpendicular components.
9-12.MA.12 The student will use parametric equations to model and solve application problems.
9-12.MA.13 The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines. | 677.169 | 1 |
There's a world of data out there, and this series of modules helps you integrate it into your high-school mathematics courses. Using the major data analysis concepts to provide realistic situations for the development of mathematical kwledge and opportunities for practice, the material reinforces concepts taught in current texts. Extensive use of real data provides opportunities for students to engage in meaningful mathematics, and motivates them to apply what they learn. Future modules include: -- Mathematics in a World of Data -- Introduction to Probability -- Exploring Systems of Inequalities -- Projects: Planning and Conducting Surveys and Experiments -- Probability Models -- Exploring Least Squares Regression -- Mathematical Modeling Using Data and Logarithms -- Exploring Centers -- Advanced Modeling Using Matrices -- Exploring Symbols
Key Features
Author(s)
Gail F Burrill, Patrick Hopfensperger
Publisher
Pearson Education
Date of Publication
01/02/1997
Language
English
Format
Paperback / softback
ISBN-10
1572322101
ISBN-13
9781572322103
Subject
Education & Teaching
Publication Data
Country of Publication
United States
Imprint
Pearson Education
Dimensions
Weight
413 g
Width
216 mm
Height
274 mm
Spine
10 | 677.169 | 1 |
Steps in Commutative Algebra by Rodney Y. Sharp
Book Description
This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen-Macaulay rings, have been added. This book is ideal as a route into commutative algebra | 677.169 | 1 |
PDF (Acrobat) Document File
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0.7 MB | 9 pages
PRODUCT DESCRIPTION
Assess your math students' proficiency in solving multistep equations, including solving literal equations and word problems. There are 20 cards in total. The answers are included 20 task cards (unless you have a class of 40:
Algebra: Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning. A.REI.1
Solve equations and inequalities in one variable. Literal that are linear in the variables being solved for. A.REI.3, 4a, 4b | 677.169 | 1 |
BUYER OFFERS: We are a retail store with set pricing and unfortunately we can't fulfil any requests to sell items for less than the listed price.
Description: David Poole's innovative LINEAR ALGEBRA: A MODERN INTRODUCTION, 4e emphasizes a vectors approach and better prepares students to make the transition from computational to theoretical mathematics. Balancing theory and applications, the book is written in a conversational style and combines a traditional presentation with a focus on student-centered learning. Theoretical, computational, and applied topics are presented in a flexible yet integrated way. Stressing geometric understanding before computational techniques, vectors and vector geometry are introduced early to help students visualize concepts and develop mathematical maturity for abstract thinking. Additionally, the book includes ample applications drawn from a variety of disciplines, which reinforce the fact that linear algebra is a valuable tool for modeling real-life | 677.169 | 1 |
algebraic geometry
Definition of algebraic geometry
: a branch of mathematics concerned with describing the properties of geometric structures by algebraic expressions and especially those properties that are invariant under changes of coordinate systems <Anthropologist Clifford Geertz speaks of new "blurred genres" in scholarship, fields like cognitive science, molecular biology, bioethics, and algebraic geometry … — Daniel McNeill et al.>; especially: the study of sets of points in space of n dimensions that satisfy systems of polynomial equations in which each equation contains n variables
1821
First Known Use of algebraic geometry
1821
Seen and Heard
What made you want to look up algebraic geometry? Please tell us where you read or heard it (including the quote, if possible). | 677.169 | 1 |
Summary and Info
Get the confidence and the math skills you need to get started with calculus! Are you preparing for calculus? This easy-to-follow, hands-on workbook helps you master basic pre-calculus concepts and practice the types of problems you'll encounter in your cour sework. You get valuable exercises, problem-solving shortcuts, plenty of workspace, and step-by-step solutions to every problem. You'll also memorize the most frequently used equations, see how to avoid common mistakes, understand tricky trig proofs, and much more. 100s of Problems! | 677.169 | 1 |
An Introduction to Ordinary Differential Equations
Introduction to Ordinary Differential Equations by Ravi P. Agarwal
Book Description
Ordinary differential equations serve as mathematical models for many exciting real world problems. Rapid growth in the theory and applications of differential equations has resulted in a continued interest in their study by students in many disciplines. This textbook organizes material around theorems and proofs, comprising of 42 class-tested lectures that effectively convey the subject in easily manageable sections. The presentation is driven by detailed examples that illustrate how the subject works. Numerous exercise sets, with an "answers and hints" section, are included. The book further provides a background and history of the subject.
This collection of 24 papers, which encompasses the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm, delay, impulse integral and integro-differential equations in various spaces on bounded as well as unbounded intervals, is designed to conduce and spur further research in this | 677.169 | 1 |
ONLINE -CRASH COURSE-10TH CBSE BOARD - 2 MONTHS
About the
Course
• This class will be fully ONLINE via WIZIQ.com to share white board.
• Real feel as in physical class room. so no any problem in interaction.
• This class is dedicated for all the students going to appear in coming CBSE Board examination.
• Concept will be taught in easy way so that weak students can also understand and remember.
• Important formulae and trick will be focused more and way that how to remember easily.
• All the doubts will be cleared
• Question paper will be provided to practice
• To help in continuous study by giving the enough HomeWork.
Topics
Covered
ALGEBRA
1. QUADRATIC EQUATIONS
Standard form of a quadratic equation ax2 + bx + c = 0, (a1 0). Solution of the quadratic equations (only real roots) by factorization and by completing the square, i.e. by using quadratic formula. Relationship between discriminate and nature of roots. Problems related today to day activities to be incorporated.
2. ARITHMETIC PROGRESSIONS
Motivation for studying AP. Derivation of standard results of finding the nth term and sum of first n terms.
TRIGONOMETRY
1. HEIGHTS AND DISTANCES
Simple and believable problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation / depression should be only 30o, 45o, 60o.
GEOMETRY
1. CIRCLES
Tangents to a circle motivated by chords drawn from points coming closer and closer and closer to the point.
(Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
(Prove) The lengths of tangents drawn from an external point to circle are equal.
COORDINATE GEOMETRY
Review the concepts of coordinate geometry done earlier including graphs of linear equations. Awareness of geometrical representation of quadratic polynomials. Distance between two points and section formula (internal). Area of a triangle.
CONSTRUCTIONS
1. Division of a line segment in a given ratio (internally)
2. Tangent to a circle from a point outside it.
3. Construction of a triangle similar to a given triangle.
MENSURATION
AREAS RELATED TO CIRCLES
Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter / circumference of the above said plane figures. (In calculating area of segment of a circle, problems should be restricted to central angle of 60o, 90o & 120o only. Plane figures involving triangles, simple quadrilaterals and circle should be taken.)
SURFACE AREAS AND VOLUMES
(i) Problem on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinder/cones. Frustum of a cone.
(ii) Problems involving converting one type of metallic solid into another and other mixed problem.(Problems with combination of not more than two different solids be taken.)
PROBABILITY
Classical definition of probability. Connection with probability as given in class IX. Simple problem on single events, not using set notation.
Who
should attend
1. One who is going to attend CBSE Board Exam and looking for best math preparation
1. He wants to Score Centum (100%)
2. He can do excellent but need someone to assist
3. He has quality to be a great mathematician or programmer or scientist
4. He feels poor in math but willing to learn math in simple way with a patient teacher and get confidence.
Pre-requisites
What
you need to bring
Maths Book of NCERT, R S AGRAWAL and RD Sharma for 10th
Note Book
pen
""""
Key
Takeaways
? Easy Concept to Solve the question yourself of any kind of question related to topic taught
Short cut tricks to do multiplication and division and more for faster calculations
? Confidence and Enthusiasm
? Motivation and Direction to go to right path for solving maths and getting high score like 100% or centum
? Career guideline ( if you want)
Reviews
Recommendations & reviews from previous Customers:
Calvin Lu
attended ONLINE -CRASH COURSE-10TH CBSE BOARD - 2 MONTHS
Questions and Comments
Thousands of experts Tutors, Trainers & other Professionals are available to answer your questions | 677.169 | 1 |
Introduction to Analysis' is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this book the student is givenMore...
'Introduction to Analysis' is designed to bridge the gap between the intuitive calculus usually offered at the undergraduate level and the sophisticated analysis courses the student encounters at the graduate level. In this book the student is given the vocabulary and facts necessary for further study in analysis | 677.169 | 1 |
Mathematics
Mathematics is one of the core subjects and contributes to the school curriculum by developing pupils' ability to calculate; to reason logically, algebraically and geometrically; to solve problems and handle data.
Mathematics is taught because:
of its use in everyday life
it can be enjoyable
of its value as subject in its own right
of its application to other subjects
The aims of the Mathematics Department are:
to build confidence in pupils so that they can deal with the Mathematics of everyday life
to encourage a sense of success in their Mathematical ability
to make pupils aware that Mathematics is an ally that can help in the study of other subjects
to develop each pupils potential so that those who wish to proceed to higher education may do so
Examinati
KEY STAGE 3
In Year 8 a system of setting is used to allocate pupils to Mathematics classes. Results from Tracking Tests are used to identify pupils whose progress would merit moving to a higher class.
In Years 9 and 10 classes follow 2 schemes of work according to their ability level. Those pupils following Scheme A will begin to experience some of the Mathematical concepts and topics needed at GCSE level.
GCSE
In Year 11 and 12 GCSE Maths is taught to the majority of pupils and the full range of grades are available to pupils. Those unable to attain a grade at GCSE will follow a suitable examination (Entry Level).
GCSE Further Maths is available as an option choice for those pupils studying Higher Tier Maths who are considering studying 'A' Level Maths in Sixth year.
A LEVEL
AS and A2 courses are available for those students who have performed particularly well at GCSE Level. Ideally a grade B or better at GCSE is recommended and completion of the GCSE Further Maths course is desirable. | 677.169 | 1 |
Number Theory by Don Redmond
Book Description
This text provides a detailed introduction to number theory, demonstrating how other areas of mathematics enter into the study of the properties of natural numbers. It contains problem sets within each section and at the end of each chapter to reinforce essential concepts, and includes up-to-date information on divisibility problems, polynomial congruence, the sums of squares and trigonometric sums.;Five or more copies may be ordered by college or university bookstores at a special price, available on application.
Buy Number Theory book by Don Redmond | 677.169 | 1 |
Essential GCSE Mathematics is a computer based training course covering all the topics examined in the General Certificate of Secondary Education, following the new, two-tier GCSE specifications which comprise both Foundation and Higher Levels. | 677.169 | 1 |
Course description & Objectives
College Algebra MATH 1111
3-0-3. Prerequisite: Satisfactory placement scores/MATH 0099
This course is a functional approach to algebra that incorporates the use of appropriate
technology. Emphasis will be placed on the study of functions and their graphs; inequalities; and
linear, quadratic, piece-wise defined, rational, polynomial, exponential and logarithmic
functions. Appropriate applications will be included. Students receive credit toward graduation
for only one of the following courses: MATH 1001, MATH 1111.
As a result of taking this course, students will be able to
Solve equations
Solve inequalities
(a) graph functions
(b) interpret functions
Model problem contexts mathematically to arrive at solutions
Use technology appropriately
Use logical, mathematical reasoning
(a) appropriately express numbers in a variety of ways in given contexts
(b) appropriately express algebraic expressions in a variety of ways in given contexts | 677.169 | 1 |
Oakwood, CA AlgebraThe Algebra section was recently expanded to include basic College Algebra. Pre-algebra: 14 questions on basic numeric properties, operations and arithmetic. Algebra: 19 questions on solving equations (both regular and quadratic), inequalities and systems of equations in 2 variables, dealing with polynomials and factoring, and some stuff like complex numbers, exponent operations, etc | 677.169 | 1 |
Synopsis
Following the successful format of the GCSE: Revision and Practice series Intermediate 11-14 Mathematics is targeted at eh 3-5 tier of entry. * Aimed at specific tier of entry to ensure that students are focused on the mathematical concepts they need to know * Key learning points at the beginning of each section so students can see what they need to know * Worked examples showing the key techniques of how to tackle problems and approach questions effectively * Graded exercises presented in two sections allow students to revisit and practise an area twice to consolidate understanding * Regular revision sections including past National Tests paper questions so students can check their understanding and test long-term memory * National Test style practice papers at the end of each book allow students to spend valuable time familiarising themselves with the tests while testing knowledge | 677.169 | 1 |
MYTUTOR SUBJECT ANSWERS
What's the point of Maths?
Every subject has a paticular career path. Maths is an exception which is at the forfront of most things. Anytime you saw data, results, surveys, polls, predictions, forecasts, returns & any others that was maths.
When your exam results they are sometimes created by combining marks to create a spread of data. Then the grades are given from the percentage levels in the data.
Still stuck? Get one-to-one help from a personally interviewed subject specialist
252 SUBJECT SPECIALISTS | 677.169 | 1 |
MAT 264 FALL 2012 UM
Unied Calculus and Analytic Geometry IV
Review topics for the nal exam
1. Find the domain and range of a function of several variables; sketch the level curves.
2. Show that a limit does not exist. Find points of discontinuity of a fu | 677.169 | 1 |
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Unformatted text preview: Math 205, Spring 2008 B. Dodson Text - Peterson-Sochacki Office hours: M,W: 10:20-11:20, Tu: 11:30 - 12:30 and by appt. email: bad0@lehigh.edu - 1. Course Info 2. Homework 1: 1.1: 1-6, 17, 18, 21 Due Friday - An m n matrix A is an array with m horizontal rows; n vertical columns i, j th entry a i,j in the i th row, and j th column. row vector or row n-vector, a, is a 1 n matrix, just one row. column vector or column n-vector, b, is a n 1 matrix, just one column. - Example 1. Give the rows and columns of A = 2 10 6 5- 1 3 . What are the entries a 1 , 2 , a 2 , 1 , a 3 , 1 , a 1 , 3 ? The matrix sum, A + B, is defined only when A and B have the same shape; and then the i, j th entry of A + B is a i,j + b i,j , the sum of the i, j th entries of A and B. 2 The scalar multiple of the matrix A by the scalar (number!) c is the matrix with the same shape as A, but with i, j th entry of ca i,j . Matrix multiplication: 1. row n-vector by column m-vector, only when n = m, is the number a 1 b 1 + a 2 b 2 + + a n b n , where the a i are the entries of a and the b i are the entries of b. 2. m n matrix A by p-column vector b, only when n = p, is the m-column vector with i th entry ( i th row of A ) b. Problem 2. Multiply A = - 1 2 4 7 5- 4 by c = 5- 1 ....
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This note was uploaded on 02/29/2008 for the course MATH 205 taught by Professor Zhang during the Spring '08 term at Lehigh University . | 677.169 | 1 |
STEM Function Notation Crime Scene Lab
Compressed Zip File
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6.5 MB | 30 pages
PRODUCT DESCRIPTION
Comes with: Power Point Presentation, Lesson in PDF format.
Students will apply function notation to solve a missing persons case. The teacher will set up a crime scene in their classroom of six buried bodies. Students will identify if the body is male or female and apply the correct equation to calculate the persons height. They will also use the same equations to calculate the length of their humerus, tibia and radius bone! This assignment will surly impress both students and administration. This usually takes two 90 min periods to complete | 677.169 | 1 |
Product details
ISBN-13: 9780521294928
ISBN: 0521294924
Publication Date: 1979
Publisher: Cambridge University Press
AUTHOR
Page, E. S., Wilson, Leslie B.
SUMMARY
Written by the same authors as the highly successful Information Representation and Manipulation in a Computer, this book describes algorithms of mathematical methods and illustrates their application with examples. The mathematical background needed is elementary algebra and calculus. Numerous exercises are provided, with hints to their solutions.Page, E. S. is the author of 'Introduction to Computational Combinatorics', published 1979 under ISBN 9780521294928 and ISBN 05212949 | 677.169 | 1 |
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Calculus Essentials For Dummies Author: Mark Ryan
ISBN: 9780470618356 Format: Paperback Number Of Pages: 192 Published: 21 May 2010 Country of Publication: GB Dimensions (cm): 21.8 x 14.3 x 1.3 Description: Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides explanations of key concepts for students who may have taken calculus in high school and want to review the most important concepts as they gear up for a faster-paced college course. Free of review and ramp-up material, Calculus Essentials For Dummies sticks to the point with content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical two-semester high school calculus class or a college level Calculus I course, from limits and differentiation to integration and infinite series. This guide is also a perfect reference for parents who need to review critical calculus concepts as they help high school students with homework assignments, as well as for adult learners headed back into the classroom who just need a refresher of the core concepts.
The Essentials For Dummies Series
Dummies is proud to present our new series, The Essentials For Dummies. Now students who are prepping for exams | 677.169 | 1 |
edition features the exact same content as the traditional book in a convenient, three-hole- punched, loose-leaf version. Books a la Carte also offer a great value--this format costs significantly less than a new textbook. More than 350,000 students have prepared for teaching mathematics with A Problem Solving Approach to Mathematics for Elementary School Teachers since its first edition, and it remains the gold standard today. This book not only helps students learn the material by promoting active learning and developing skills and concepts-it also provides an invaluable reference to future teachers by including professional development features and discussions of today's standards. The Eleventh Edition is streamlined to keep students focused on what is most important. The Common Core State Standards (CCSS) have been integrated into the book to keep current with educational developments. To see available supplements that will enliven your course with activities, classroom videos, and professional development for future teachers, visit This package contains:
Books a la Carte for A Problem Solving Approach to Mathematics for Elementary School Teachers, Eleventh Edition | 677.169 | 1 |
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CCSS.Math.Content.HSA-SSE.A.1b: Common Core State Standards for Mathematics
Interpret complicated expressions by viewing one or more of their parts as a single entity.
CCSS.Math.Content.HSA-APR.D.7: Common Core State Standards for Mathematics
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
CCSS.Math.Content.HSA-CED.A.1: Common Core State Standards for Mathematics
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. | 677.169 | 1 |
Our students learn to analytical thinking while they explore concepts in Statistics, Probability, Algebra and Geometry.
Pre Algebra 11th Grade First Semester
This course prepares the students for Algebra A. The emphasis is on sharpening computational skills and then applying these skills to algebra. Solving simple equations and graphing of linear equations are included.
Algebra A 11th Grade Second Semester
Student begin by solving increasingly complex equations. They learn ratios, exponents, rational expressions and equations, polynomials and the use of rational numbers to solve real life problems.
Algebra B 12th Grade First Semester
This course continues to develop the mathematical ability of our students in the areas of graphs, square roots and quadratic equations by focusing on real life situations.
Geometry A 12th Grade Second Semester
This college preparatory course covers the essential introductory components of Geometry. The use of computers and graphing calculators are required. The problems are designed to stress logical reasoning in mathematics. | 677.169 | 1 |
Schaum's Outline of Laplace Transforms by Murray R. Spiegel
Book Description
Master Laplace transforms with "Schaum's" - the high-performance study guide. It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love "Schaum's Outlines" because they produce results. Each year, hundreds of thousands of students improve their test scores and final grades with these indispensable study guides. Get the edge on your classmates. Use "Schaum's"! If you don't have a lot of time but want to excel in class, this book helps you: brush up before tests; find answers fast; study quickly and more effectively; get the big picture without spending hours poring over lengthy textbooks."Schaum's Outlines" give you the information your teachers expect you to know in a handy and succinct format - without overwhelming you with unnecessary details. You get a complete overview of the subject. Plus, you get plenty of practice exercises to test your skill. Compatible with any classroom text, "Schaum's" let you study at your own pace and remind you of all the important facts you need to remember - fast! And "Schaum's" are so complete, they're perfect for preparing for graduate or professional exams.
Inside, you will find: 450 problems, including step-by-step solutions; hundreds of additional practice problems, with answers supplied; clear explanations of applications of Laplace transforms; understandable coverage of Fourier series and the complex inversion theory. If you want top grades and a thorough understanding of Laplace transforms, this powerful study tool is the best tutor you can have!
Tough Test Questions? Missed Lectures? Not Enough Time? In this book, each outline presents all the essential course information in an easy-to-follow, topic-by-topic format. It covers elementary to advanced math topics. It is arranged by topics for easy reference.
Author Biography - Murray R. Spiegel
The Late MURRAY R. SPIEGEl received the M.S degree in Physics and the Ph.D. in Mathematics from Cornell University. He had positions at Harvard University, Columbia University, Oak Ridge and Rensselaer Polytechnic Insitute, and served as a mathematical consultant at several large Companies. His last Position was professor and Chairman of mathematics at the Rensselaer Polytechnic Institute Hartford Graduate Center. He was interested in most branches of mathematics at the Rensselaer polytechnic Institute, Hartford Graduate Center. He was interested in most branches of mathematics, especially those which involve applications to physics and engineering problems. He was the author of numerous journal articles and 14 books on various topics in | 677.169 | 1 |
A Historian Looks Back: The Calculus as Algebra and Selected Writings (Spectrum)
Description
Judith Grabiner has written extensively on the history of mathematics, principally for mathematicians rather than historians. This collection of her work highlights the benefits of studying the development of mathematical ideas and the relationship between culture and mathematics. She also considers the struggles and successes of famous mathematicians with the aim of inspiring students and teachers alike. A large part of this book is the author's The Calculus as Algebra: J.-L. Lagrange, 1736-1813 which focuses on Lagrange's pioneering attempt to reduce the calculus to algebra. The nine other articles are on a broad range of other topics such as some widely held myths about the history of mathematics and the work of heavyweight mathematicians such as Descartes, Newton, Maclaurin and Lagrange. Six of these articles have won awards from the MAA for expository excellence. This collection is an inspiring resource for history of mathematics courses.
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Contents
Introduction; Part I. The Calculus as Algebra: Introduction; 1. The development of Lagrange's ideas on the calculus: 1754-1797; 2. The algebraic background of the theory of analytic functions; 3. The contents of the functions; 4. From proof-technique to definition: the pre-history of Delta-Epsilon methods; Conclusion; Appendix; Bibliography; Bibliography: 1966-present; Part II. Selected Writings: 5. The mathematician, the historian, and the history of mathematics; 6. Who gave you the Epsilon? Cauchy and the origins of rigorous calculus; 7. The changing concept of change: the derivative from Fermat to Weierstrass; 8. The centrality of mathematics in the history of Western thought; 9. Descartes and problem-solving; 10. The calculus as algebra, the calculus as geometry: Lagrange, Maclaurin, and their legacy; 11. Was Newton's calculus a dead end? The continental influence of Maclaurin's Treatise of Fluxions; 12. Newton, Maclaurin, and the authority of mathematics; 13. Why should historical truth matter to mathematicians? Dispelling myths while promoting maths; 14. Why did Lagrange 'prove' the parallel postulate?; Index; About the author. | 677.169 | 1 |
This text takes a right angle approach to trigonometry and is designed for use in a one or two term course in college algebra with trigonometry or precalculus. College Algebra with Trigonometry 6/E has been written to maximize student comprehension and great care has been taken to produce a text that is mathematically correct and accessible to students. Emphasis is on computational skills, ideas, and problem solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed. The single most crucial topic is function. The function concept is introduced and developed from several points of view and is substantially motivated through many illustrations and examples. One of the primary objectives of this book is to give the student substantial experience in modeling and solving real world problems. Enough applications are included to convince even the most skeptical student that mathematics really is useful.
"synopsis" may belong to another edition of this title.
Product Description:
This fifth edition of an algebra text has a new open format and expanded graphics which enforce concepts. Through an informal, active writing style and the use of numerous pedagogical aids, such as examples with matched problems, annotations, think boxes, chapter summaries and cumulative reviews, the text guides students of varied disciplines to success in college algebra and trigonometry. In this edition, greater emphasis is placed on graphing, by including a new section on graphing rational functions, and by the inclusion of new optional graphing calculator exercises. Other new features include many illustrative examples, new and varied problems, and new and updated applications.
About the Author:
Barnett-Emeritus, Merritt College
Raymond A. Barnett, a native of California, received his B.A. in mathematical statistics from the University of California at Berkeley and his M.A. in mathematics from the University of Southern California. He has been a member of the Merritt College Mathematics Department, and was chairman of the department for four years. Raymond Barnett has authored or co-authored eighteen textbooks in mathematics, most of which are still in use. In addition to international English editions, a number of books have been translated into Spanish. Co-authors include Michael Ziegler, Marquette University; Thomas Kearns, Northern University; Charles Burke, City College of San Francisco; John Fuji, Merritt College; and Karl Byleen, Marquette University. Michael R. Ziegler received his B.S. from Shippensburg StateCollege and his M.S. and Ph.D. from the University of Delaware. After completing post doctoral work at the University of Kentucky, he was appointed to the faculty of Marquette University where he currently holds the rank of Professor in the Department of Mathematics, Statistics, and Computer Science. Dr. Ziegler has published over a dozen research articles in complex analysis and has co-authored eleven undergraduate mathematics textbooks with Raymond A. Barnett, and more recently, Karl E. Byleen. Karl E. Byleen received the B.S., M.A. and Ph.D. degrees in mathematics from the University of Nebraska. He is currently an Associate Professor in the Department of Mathematics, Statistics and Computer Science of Marquette University. He has published a dozen research articles on the algebraic theory of semigroups. Why We wrote This Book: This text is written for student comprehension. Great care has beentaken to write a book that is mathematically correct and accessible. We emphasize computational skills, ideas, and problem solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed. Graphing calculators and computers are playing an increasing role in mathematics education and in real-world applications of mathematics. This books deals with the mathematics that is required to use modern technology effectively as an OPTIONAL feature. In appropriate places in the text, there are clearly identified examples and exercises related to graphing calculators and computers, illustrations of applications of spreadsheets, and sample computer output. All of these may be omitted without loss of continuity.
McGraw-Hill authors represent the leading experts in their fields and are dedicated to improving the lives, careers, and interests of readers worldwide
Book Description McGraw-Hill Inc.,US. Hardcover. Book Condition: GOOD. Good clean copy with no missing pages might be an ex library copy; Possibly may have minor marginal notes and or highlighting. Bookseller Inventory # 2511592057 | 677.169 | 1 |
Product Description:This new edition brings the fascinating and intriguing history of mathematics to life
The Second Edition of this internationally acclaimed text has been thoroughly revised, updated, and reorganized to give readers a fresh perspective on the evolution of mathematics. Written by one of the world's leading experts on the history of mathematics, the book details the key historical developments in the field, providing an understanding and appreciation of how mathematics influences today's science, art, music, literature, and society.
In the first edition, each chapter was devoted to a single culture. This Second Edition is organized by subject matter: a general survey of mathematics in many cultures, arithmetic, geometry, algebra, analysis, and mathematical inference. This new organization enables students to focus on one complete topic and, at the same time, compare how different cultures approached each topic. Many new photographs and diagrams have been added to this edition to enhance the presentation.
The text is divided into seven parts:
The World of Mathematics and the Mathematics of the World, including the origin and prehistory of mathematics, cultural surveys, and women mathematicians
Numbers, including counting, calculation, ancient number theory, and numbers and number theory in modern mathematics
Color Plates, illustrating the impact of mathematics on civilizations from Egypt to Japan to Mexico to modern Europe
Space, including measurement, Euclidean geometry, post-Euclidean geometry, and modern geometrics
Algebra, including problems leading to algebra, equations and methods, and modern algebra
Analysis, including the calculus, real, and complex analysis
Mathematical Inference, including probability and statistics, and logic and set theory
As readers progress through the text, they learn about the evolution of each topic, how different cultures devised their own solutions, and how these solutions enabled the cultures to develop and progress. In addition, readers will meet some of the greatest mathematicians of the ages, who helped lay the groundwork for today's science and technology.
The book's lively approach makes it appropriate for anyone interested in learning how the field of mathematics came to be what it is today. It can also serve as a textbook for undergraduate or graduate-level courses. An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
REVIEWS for The History of | 677.169 | 1 |
Calculus Know-it-all by Stan Gibilisco
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Calculus Know-It-ALL features: Checkpoints to help you track your knowledge and skill level Problem/solution pairs and chapter-ending quizzes to reinforce learning Fully explained answers to all practice exercises A multiple-choice exam to prepare you for standardized tests "Extra Credit" and "Challenge" problems to stretch your mind Stan's expert guidance gives you the know-how to: Understand mappings, relations, and functions Calculate limits and determine continuity Differentiate and integrate functions Analyze graphs using first and second derivatives Define and evaluate inverse functions Use specialized integration techniques Determine arc lengths, surface areas, and solid volumes Work with multivariable functions Take college entrance examinations with confidence And much more!
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The major revision of this classic boasts completely new drawings and more than 50% brand-new information - making it the most up-to-date and best resource on reading AND designing schematics available | 677.169 | 1 |
Designed as a text for a three-semester course in numerical analysis, this highly regarded work presents a broad overview of computer-oriented numerical algorithms for solving various types of mathematical problems. The book is intended not only to impart a working knowledge of practical techniques for solving real problems but to prepare the student for advanced studies at the graduate level. Topics include: Evaluation of elementary functions Solution of a single nonlinear equation with specific reference to polynomial equations Interpolation and approximation Numerical differentiation and quadrature Ordinary differential equations Computational problems in linear algebra Numerical solution of elliptic and parabolic partial differential equations by finite difference methods Solution of large linear systems by iterative methods In addition to thorough coverage of the fundamentals, these wide-ranging volumes contain such special features as an introduction to computer arithmetic, including an error analysis of a system of linear algebraic equations with rational coefficients, and an emphasis on computations as well as mathematical aspects of various problems. Geared toward senior-level undergraduates and first-year graduate students, the book assumes some knowledge of advanced calculus, elementary complex analysis, matrix theory, and ordinary and partial differential equations. However, the work is largely self-contained, with basic material summarized in an appendix, making it a perfect resource for self-study. Ideal as a course text in numerical analysis or as a supplementary text in numerical methods, A Survey of Numerical Mathematics judiciously blends mathematics, numerical analysis, and computation. The result is an unusually valuable reference and learning tool for modern mathematicians, computer scientists, programmers, engineers, and physical scientists.
REVIEWS for A Survey of Numerical | 677.169 | 1 |
According to an independent survey commissioned by Microsoft Corporation, 77% of teachers and 73% of parents claim math and science are the most difficult homework subjects for students, yet only 36% of parents feel capable to help their children. For this reason, Microsoft has developed a low-cost, software solution designed to help students in middle school, high school and entry-level college students: Microsoft Math 3.0.
Microsoft Math 3.0 features an extensive collection of capabilities to help students tackle complicated problems in pre-algebra, algebra, trigonometry, calculus, physics and chemistry, and puts them all in one convenient place on the home PC. Microsoft Math 3.0 is designed to help deepen students" overall understanding of these subjects by invoking a full-featured graphing calculator and step-by-step instructions on how to solve difficult problems. Microsoft Math is scheduled to be available for download in early May 2007 for an estimated retail price of $19.95* (U.S.).
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Circuit Training - Linear, Quadratic and Exponential Regression
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Give your students engaging practice with the circuit format! Students will need to use technology (graphing calculator, on-line software) to calculate regression equations to advance in the circuit. At first students will be told what kind of regression, but towards the end of the circuit students need to try several regressions and compare the r-value to see which is the best fit. 16 equations total. Can be turned into task cards or even a scavenger hunt | 677.169 | 1 |
(CC BY) This is an introduction to linear algebra. The main part of the book features row operations and everything is done in terms of the row reduced echelon form and specific algorithms. At the end, the more abstract notions of vector spaces and linear transformations on vector spaces are presented. However, this is intended to be a first course in linear algebra for students who are sophomores or juniors who have had a course in one variable calculus and a reasonable background in college algebra. | 677.169 | 1 |
Mastering GCSE Maths: Substitution into Formula (Higher Plus)
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This free 30-minute revision webinar on Substitution into Formula is part of a series of free webinars for GCSE Maths students. Topics have been selected based on what you find difficult… "I can't do simultaneous equations… How do you rearrange formula? … Negative numbers do my head in?…" If any of these quotes sound familiar, register to join us to help boost your performance in the new, tougher GCSE Maths exams in summer 2017.
Upcoming Dates
Who should attend
This webinar is most suitable for Higher tier students who are up for a challenge, aiming for a Grade 8 or 9. A prior understanding of BODMAS and solving equations will be assumed.
About this event
This webinar will cover substituting values into formula, how you create expressions from given information, and how you solve problems involving formulae. This is a challenging webinar aimed at students who are aiming for a Grade 8 or 9. When you take part in the webinar, please make sure you have pen and paper ready to answer questions | 677.169 | 1 |
This eBook introduces the topic of proportionality, from developing the relationship between mathematical expressions and word sentences, describing mathematical relationships and exploring direct and inverse proportionality through expressions and graphical illustrations. | 677.169 | 1 |
Algebra
A-SSE.1. Interpret expressions
that represent a quantity in terms of its context.
a.Interpret parts of an expression, such as terms,
factors, and coefficients.
b.Interpret complicated expressions by viewing one
or more of their parts as a single entity.
A-SEE.2. Use the structure of an
expression to identify ways to rewrite it.
Write expressions in equivalent forms to solve problems
A-SEE.3. Choose and produce an
equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression
a.Factor a quadratic expression to reveal the
zeros of the function it defines.
b.Complete the square in a quadratic expression to
reveal the maximum or minimum value of the function it defines.
c.Use the properties of exponents to transform
expressions for exponential functions.
A-SEE.4. Derive the formula for
the sum of a finite geometric series (when the common ratio is not 1), and use
the formula to solve problems.
Arithmetic with
Polynomials and Rational Expressions
Perform arithmetic operations on
polynomials
A-APR.1. Understand that
polynomials form a system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and multiplication; add,
subtract, and multiply polynomials.
Understand the relationship between zeros
and factors of polynomials
A-APR.2.
Know and apply the Remainder Theorem.
A-APR.3. Identify zeros of
polynomials when suitable factorizations are available, and use the zeros to
construct a rough graph of the function defined by the polynomial.
Use polynomial identities to solve problems
A-APR.4. Prove polynomial
identities and use them to describe numerical relationships.
A-APR.5. Know and apply the
Binomial Theorem for the expansion of (x + y)n in posers of x and y
for a positive integer n, where x and y are any numbers, with coefficients
determined for example by Pascal's Triangle.
Rewrite Simple Rational Expressions
A-APR.6. Rewrite simple rational
expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
where a(z), b(x), q(x), and r(x) are polynomials with the degree of r(x) less
than the degree of b(x), using inspection, long division, or, for the more
complicated examples, a computer algebra system.
A-APR.7. Understand that rational expressions form a
system analogous to the rational numbers, closed under addition, subtraction,
multiplication, and division by a nonzero rational expression; add, subtract,
multiply, and divide rational expressions.
Creating Equations
Create Equations that Describe
Numbers or Relationships
A-CED.1. Create equations and
inequalities in one variable and use them to solve problems.
A-CED.2. Create equations in two
or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
A-CED.3. Represent constraints by
equations or inequalities, and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a modeling context.
A-CED.4. Rearrange formulas to
highlight a quantity of interest, using the same reasoning as in solving
equations.
Reasoning with
Equations and Inequalities
Understand Solving Equations as a Process of Reasoning and Explain the
Reasoning
A-REI.1. Explain each step in
solving a simple equation as following from the equality of numbers asserted at
the previous step, starting from the assumption that the original equation.
A-REI.2. Solve simple rational and
radical equations in one variable, and give examples showing how extraneous
solutions may arise.
Solve Equations and Inequalities in One
Variable
A-REI.3. Solve linear equations
and inequalities in one variable, including equations with coefficients
represented by letters.
A-REI.4. Solve quadratic equations
in one variable.
a.Use the method of completing the square to
transform any quadratic equation in x into an equation of the form (x-p)2
= q that has the same solutions. Derive the quadratic formula from this form.
b.Solve quadratic equations by inspection (e.g.
for x2 = 49), taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula fives complex solutions and
write them as a bi
for real numbers a and b.
Solve Systems of Equations
A-REI.5. Prove that, given a
system of two equations in two variables, replacing one question by the sum of
that equation and a multiple of the other produces a system with the same
solutions.
A-REI.6. Solve systems of linear
equations exactly and approximately (e.g. with graphs), focusing on pairs of
linear equations in two variables.
A-REI.7. Solve a simple system consisting of a linear
equation and a quadratic equation in two variables algebraically and
graphically.
A-REI.8. Represent a system of
linear equations as a single matrix equation in a vector variable.
A-REI.9. Find the inverse of a
matrix if it exists and use it to solve systems of linear equations (using
technology for matrices of dimension 3 x 3 or greater).
Represent and Solve Equations and
Inequalities Graphically
A-REI.10. Understand that the
graph of an equation in two variables is the set of all its solutions plotted
in the coordinate plane, often forming a curve (which could be a line).
A-REI.11. Explain why the
x-coordinates for the points where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f)x) = g(x); find the
solutions approximately, e.g. using technology to graph the functions, make
tales of values, or find successive approximations, Include cases where f(x) and/or
g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions.
A-REI.12. Graph the solutions to a
linear inequality in two variables as a half-plane (excluding the boundary in
the case of a strict inequality), and graph the solution set to a system of
linear inequalities in two variables as the intersection of the corresponding
half-planes. | 677.169 | 1 |
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Unformatted text preview: Review and Examples (Spr. 2006) Due Thursday 6th April These are examples of questions with the degree of difficulty that you will encounter in the lab-exam. Make sure that you can do them! Use Mathematica to solve all parts of the problems Vectors Problem 1. Show that for any vectors ~a , ~ b , ~ c that, (i) ~a. ( ~a ~ b ) = 0 (ii) ~a. ( ~ b ~ c ) = ( ~a ~ b ) .~ c Lists and Matrices Problem 2. Display the following matrix in matrixform. matrix = {{ . 2 ,- . 4 , . 1 } , { . 4 , . 2 ,- . 3 } , { . 6 ,- . 3 ,- . 1 }} We havent found the eigenvalues and vectors of symmetric matrices be- fore; however, this illustrates the power of mathematica. Look up Eigenvalue in the help manual. You wont fully appreciate the power of this until you have to solve eigenvalue problems by hand in advanced mechanics and quan- tum mechanics. Find the determinant, eigenvalues and eigenvectors of the matrix matrix ....
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This note was uploaded on 07/25/2008 for the course PHY 102 taught by Professor Duxbury during the Spring '08 term at Michigan State University. | 677.169 | 1 |
Video-lecture, Calculus
Description: Professor Adrian Banner,explains the basic concepts of Trignometry the sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations through the year.Lecture 20 of 24 | 677.169 | 1 |
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This is a 23-lecture series on Image Processing that I have created over the past 17 years (1999-2015) for my course, EECE 4353 / 5353, at the Vanderbilt University School of Engineering. The files are all in Adobe Acrobat (.pdf) format and MS Powerpoint (.ppt) format. They are quite large because of the images in them. The topics covered include: Image Enhancement by Point Operations, Color Correction, The 2-D Fourier Transform and Convolution, Linear Spatial Filtering, Image Sampling and... favoritefavoritefavoritefavorite ( 23 reviews ) Topics: image processing, image enhancement, image noise reduction, Fourier transforms, convolution,...
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A basic introduction to the Calculus and Linear Algebra. The goal is to make students mathematically literate in preparation for studying a scientific/engineering discipline. The first week covers differential calculus: graphing functions, limits, derivatives, and applying differentiation to real-world problems, such as maximization and rates of change. The second week covers integral calculus: sums, integration, areas under curves and computing volumes. This is not meant to be a comprehensive... Topics: ars digita, calculus, linear algebra
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A theoretical treatment of what can be computed and how fast it can be done. Applications to compilers, string searching, and control circuit design will be discussed. The hierarchy of finite state machines, pushdown machines, context free grammars and Turing machines will be analyzed, along with their variations. The notions of decidability, complexity theory and a complete discussion of NP-Complete problems round out the course. Text: Introduction to the Theory of Computation, Michael Sipser.... favoritefavoritefavoritefavoritefavorite ( 8 reviews ) Topic: computation
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Learn about the first Americans, the voyage of Christopher Columbus, and Cortez' defeat of the Aztecs. To watch the interactive media files (see left-hand column) first click the link to open it, then right-click anywhere on the page and select "play". favoritefavorite ( 4 reviews ) Topics: American History, Advanced Placement | 677.169 | 1 |
Solving Single and Multi-Step Equations and Inequalities
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Solving single and multi-step equations and inequalities is an essential skill for students in many levels of math. These guided notes provide room for students to show their work next to the explicit steps in the process.
Note: I used these notes on the first day of my Algebra 2 classes. It took very little class time and was great for reinforcing what the students learned in Algebra | 677.169 | 1 |
Free Home Delivery for Lucknow City*. Pan-India Delivery Rs. 60/- per book. Buy More than One Book and get reduced delivery charges.
Magical Book On Quicker Maths is a book that helps its readers tackle the mathematics sections in all competitive exams with minimum effort.
In Magical Book On Quicker Maths, M. Tyra provides a new and speedier approach to problem solving, one that is simple to understand and easy to apply. It is aimed at aspirants of all competitive exams conducted by banks, the Union Public Service Commission (UPSC), the Staff Selection Commission (SSC), LIC, CPO, UTI, GIC, and similar organizations.
With this book, M. Tyra aims to fulfil the need for faster and more effective methods of solving mathematical problems. The book begins with an introduction on tips for preparing for mathematics examinations, followed by chapters on various mathematical concepts. Some of the topics covered include fractions, surds, profit and loss, ratio and proportion, time and work, simple and compound interest, trigonometry, and data analysis.
The book is meant to help students from all streams, including science, commerce and arts.
The concepts involved are explained clearly and concisely so that students will find them easier to understand, regardless of whether or not they have good prior grounding in mathematics. The book also contains several illustrations, lending visual clarity to the concepts explained. It covers all the possible types and variations of problems that have appeared in competitive exams in recent times.
The author has put in two years of rigorous effort and research to come up with this book. He has derived many of the ideas from Vedic mathematics, number theory, and also through suggestions from his readers and other study resources on the subject.
About M. Tyra
M. Tyra or Manoj Tyra is an instructor of mathematics. He writes books on problem solving and quantitative aptitude, with a special focus on Vedic mathematics.
He has written Magical Book On Quicker Maths. Also, he has co-authored the book, Practice Book On Quicker Maths, with K. Kundan. This book can be used for practicing problem solving and strengthening one's understanding of the concepts from Magical Book On Quicker Maths. He started his own publication with Banking Services Chronicle, a monthly magazine. He has also developed study material for correspondence courses for IIT, CAT, and banking examinations.
He graduated in 1990, with a degree in Mathematics from Delhi University. He has taught and mentored several students, helping them prepare for various competitive exams. Learn More
Free Home Delivery for Lucknow City*. Pan-India Delivery Rs. 60/- per book. Buy More than One Book and get reduced delivery charges.
Quicker Maths (Hindi) : Magical Book Series
(9788190458931)
K. Kundan and M. Tyra's Quicker Math (Hindi) 2nd Edition is apt for grasping concepts quickly. The book is divided into several chapters so as to give you a better understanding of the subject. The book covers important mathematical concepts.
About the Authors
K. Kundan is an Indian author. He has penned down books like Data Interpretation And Data Sufficiency For MBA, General English and Language Comprehension for MBA Entrance Tests and Practice Book On Analytical Reasoning.
M. Tyra is an Indian author and has penned down books like Magical Book On Quicker Maths 3rd Edition and Practice Book on Quicker Maths 1st Edition. Learn More
Free Home Delivery for Lucknow City*. Pan-India Delivery Rs. 60/- per book. Buy More than One Book and get reduced delivery charges.
Contemporary Abstract Algebra is a great tool for teachers and researchers of the subject as it provides detailed explanations of important concepts related to the subject.
Summary Of The Book
The study of algebraic structures like modules, groups, fields and rings is known as abstract algebra.
Contemporary Abstract Algebra is well-structured and divided into five sections. The first section deals with Integers and Equivalence Relations, and makes readers aware of the basic features of the concepts. The book then goes on to describe different types of groups such as permutation, finite, and cyclic groups. It also provides thorough explanations of theorems.
The concept of rings is presented to readers. It covers all the important aspects like factorization of polynomials, integral domains, divisibility in integral domains, and ring homomorphisms. An abstract algebra manual would be incomplete without discussing fields. Comprehensive descriptions of finite and extension fields, geometric constructions, and vector spaces are included.
Important algebraic theories and concepts such as Galois theory, Sylow theorem, and cyclotomic extensions are presented in Contemporary Abstract Algebra. The group of orthogonal transformations of R' is thoroughly explained along with Jordan's classification of its finite subgroups.
Apart from theory, the book focuses on training students on how to apply these theorems. It features several exercises and examples which deal with the roots of algebra in number theory. These useful exercises also lay an emphasis on theory of equations and geometry. The accurate solutions to certain questions are also part of the book.
This edition even has another unique feature. It contains an index of famous mathematicians from history, which becomes a rich source of information for students.
Learn More
Free Home Delivery for Lucknow City*. Pan-India Delivery Rs. 40/- per book. Buy More than One Book and get reduced delivery charges.
Introduction to Topology and Modern Analysis 1st Edition is a comprehensive book for undergraduate and postgraduate students studying a course in mathematics. It covers both the basic and advanced theory and is one of the most recommended books in the field. The book is divided into: Topology, Operators and Algebra of Operators. It is an indispensable resource for anyone working with mathematics.
Table of Contents
Part I: TOPOLOGY
Chapter 1. Sets and Functions
Chapter 2. Metrics Spaces
Chapter 3. Topological Spaces
Chapter 4. Compactness
Chapter 5. Separation
Chapter 6. Connectedness
Chapter 7. Approximation
Part II: OPERATORS
Chapter 8. Algebraic Systems
Chapter 9. Banach Spaces
Chapter 10. Hilbert Spaces
Chapter 11. Finite-Dimensional Spectral Theory
Part III: ALGEBRAS OF OPERATORS
Chapter 12. General Preliminaries on Banach Algebras
Chapter 13. The Structure of Commutative Banach Algebras
Chapter 14. Some Special Commutive Banch Algebras
Appendices Learn More
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New Age JEE (Main) Plus ! Mathematics
(9788122440621)
This book is written with the object to enable the students to prepare and compete at the highest level for JEE+ Mathematics (Joint Entrance Examination) conducted jointly by thirteen Indian Institutes of Technology. A background of concepts required is given as synopsis at the beginning of each chapter. The questions put forward are designed to test comprehension, reasoning and analytical ability of the aspirants. Tips are given at appropriate places to solve difficult problems using special tricks to save time. The material is given in a manner so as to infuse step-by-step confidence in the students to tackle JEE Mathematics. The authors earnestly believe that students following this book will get through their entrance examination with higher ranks.
About the Author:
Nikhil Saxena has done MSc. (Mathematics) from Lucknow University. He is having 10 years of teaching experience with Career Point, Kota; Resonance Institute, Kota; Pinnacle Classes, Gwalior and other reputed institutes.
Contents:
Sets and Relations
Quadratic Equations
Complex Number
Matrices and Determinants
Sequences and Series
Mathematical Induction
Permutations and Combinations
Binomial Theorem
Logarithm
Function
Limits
Continuity and Differentiability
Differentiation
Application of Derivatives
Indefinite Integral
Definite Integral
Areas Bounded by Curves
Differential Equations
Straight Line
Circle
Conic Section (Parabola, Ellipse, Hyperbola)
Vector Algebra
Three Dimensional Geometry
Statistics
Probability
Trigonometric Function and Equation
Inverse Trigonometric Functions
Properties of Triangle and Heights & Distances
Linear Programming
Mathematical Reasoning
IIT-JEE (Mains) Solved Paper 2013
IIT-JEE (Mains) Solved Paper 2014
IIT-JEE (Mains) Solved Paper 2015
Learn More
Free Home Delivery for Lucknow City.* Pan-India Delivery Rs. 80/- per book. Buy More than One Book and get reduced delivery charges.
About the Author:
Mr. Sharat Chandra Gupta, B.Sc., B.Tech. (Hons), LL.B., FIE, FICA, PG (DIP), E.Q. Engg. Tokyo, is Advisor, Indian Buildings Congress and former Chief Engineer, CPWD. He has 37 years of professional experience in structural designs, field execution, construction management and training. He has attended around 40 national/international conferences and training courses, and published equal number of papers in journals and conferences. He has been member of several BIS and IRC Committees, Research Councils of CBRI, Roorkee, and NCCBM, Ballabhgarh, Board of Directors of U.P.Bridge Corporation and Hindustan Pre-fab Ltd. He has the credit of establishing the design and training organisations of the Delhi Development Authority.
The CPWD has brought out his three publications including one on Fire Damage Assessment and Renovation of Vigyan Bhawan. This is his first publication after superannuation and embodies what he experienced while being responsible for structural design of several raft foundations.
Contents:
PHYSICS
Syllabus
IIT-JEE 2004 to IIT-JEE 2014
IIT-JEE Sample Paper
CHEMISTRY
IIT-JEE 2004 to IIT-JEE 2014
IIT-JEE Sample Paper
MATHEMATICS
IIT-JEE 2004 to IIT-JEE 2014
IIT-JEE Sample Paper
IIT-JEE 2015 (Solved Paper)
IIT-JEE (Main & Advanced) Physics 2015
IIT-JEE (Main & Advanced) Chemistry 2015
IIT-JEE (Main & Advanced) Mathematics 2015 | 677.169 | 1 |
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Microsoft Releases Math 4.0 Free
Microsoft has released a new version of its math education software Mathematics 4.0, making it available as a free download for the first time.
By Dian Schaffhauser
03/10/11
Microsoft said the new version of its math program has been downloaded 250,000 times since its quiet January 2011 release.
Microsoft Mathematics 4.0, designed for students in middle school, high school, and early college, is intended to teach users how to solve equations while bolstering their understanding of fundamental math and science concepts. Although the company charged for its last version, this latest edition is free.
The new program works on computers running Windows XP, Vista, and 7, as well as Windows Server 2003 and 2008. The software includes a graphing calculator capable of plotting in 2D and 3D, a formulas and equations library, a triangle solver, a unit conversion tool, and ink handwriting support for tablet or ultra-mobile PC use. One new feature enables a user to create a custom movie where a 3D graphed image shifts among multiple shapes as variables change.
An 18-page step-by-step guide provides basic documentation to use the program's functions.
Microsoft Mathematics 4.0 is available now. Further information | 677.169 | 1 |
Interactive Mathematics Program
Welcome to our Interactive Mathematics Program (IMP) curriculum page.Here you will find information regarding the new IMP curriculum being implemented at the Seaman Freshman Center and Seaman High School. Starting with the class of 2018, all SHS students will begin with Math 1 their freshman year.
The flowchart below illustrates the progression of math courses following the completion of Math 1. Through each semester of this progression, students will have the opportunity to complete additional coursework for honors credit.
Please utilize the resources on this page to reach a greater understanding of Interactive Mathematics.
You can also visit the official IMP website by clicking on the link below: | 677.169 | 1 |
Featured Products
Help students make the transition from arithmetic to algebra and geometry! Perfect for use as full units of study, as supplements to the curriculum, or as tutorial resources at home. Each book includes step-by-step instructions with examples, practice problems using the concepts, real-life applications, a list of symbols and terms, tips, and answer keys. 128 pages.
Guide students toward a healthy lifestyle, both physically and financially! This revised and expanded edition adds much more information on work ethic, nutrition, and exercise; updates the sections on sexually transmitted diseases and drugs; and includes completely new sections on preparing financially for the future. Graphic organizers, self inventories, puzzles, real-life situations, and cloze activities provide creative opportunities for students to assess their own lifestyles and make good choices for the future. 128 pages.
Present basic information about the complex human body without overwhelming students with medical jargon! Make the study of the human body even more fascinating with Far Out Facts, fun tidbits of information that will keep students on their toes. Also included are a number of Webwise websites that provide students the opportunity to further explore various body systems or concepts presented in the activities. 80 pages.
Designed to meet the challenges set forth by Common Core State Standards. Each page contains two workouts—one for skills practice and one for applying those skills to solve a problem. Topics covered include geometry, ratio and proportional relationships, the number system, functions, expressions and equations, as well as statistics and probability. With a little time each day, your students will become better problem solvers and will acquire the skills they need to meet the mathematical expectations for their grade level. 64 pages. | 677.169 | 1 |
strong emphasis on skill-building, applications in the real world, and preparation for further math courses, this text unites the concepts of Elementary Algebra and Intermediate Algebra in one convenient and economical volume | 677.169 | 1 |
Mathematics for High School Teachers by Zalman Usiskin
Book Description
For algebra or geometry courses for teachers; courses in topics of mathematics; capstone courses for teachers or other students of mathematics; graduate courses for practicing teachers; or students who want a better understanding of mathematics. Filling a wide gap in the market, this text provides current and prospective high school teachers with an advanced treatment of mathematics that will help them understand the connections between the mathematics they will be teaching and the mathematics learned in college. It presents in-depth coverage of the most important concepts in high school mathematics: real numbers, functions, congruence, similarity, and more.
Buy Mathematics for High School Teachers book by Zalman Usisk | 677.169 | 1 |
Math Graphing Book for Students
739 Downloads
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PRODUCT DESCRIPTION
A great book for students who are learning about pictographs and bar graphs. The students are able to circle, underline, or highlight the components of the graphs as well as have the definitions of the components | 677.169 | 1 |
About
Our Adaptive Mathematics Learning Platform is an AI-powered platform that adaptively generates unlimited number of mathematics problems and helps middle school and high school students learn mathematical concepts rigorously, prepare for competitive exams (like SAT, JEE) and get detailed feedback on their performance. Our AI engine identifies the students' strengths and weaknesses and guides them to improve their performance with step-by-step interactive solutions and bite-sized lessons. Thousands of students and instructors from all over the world use our platform daily. | 677.169 | 1 |
Equations, Formulae and Expressions - Expanding Brackets Lesson 2
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PRODUCT DESCRIPTION
This is a interactive powerpoint lesson with differentiated activities teaching students how to expand and simplify single and double algebraic brackets. All the activities are differentiated and answers are provided allowing for effective self and peer assessment. This powerpoint works well as a part of the Equations, Formulae and Expressions lesson slides series, so if you like this one please look at the others I have | 677.169 | 1 |
Essentials of Engineering Mathematics: Worked Examples and Problems, 2e
Written for first-year undergraduate engineering courses, this book presents the fundamentals of mathematical techniques with numerous worked examples. Topics covered include complex numbers, differentiation and integration, matrices, Fourier series, and the Laplace transform. MATLAB and the Symbolic Math Toolbox are introduced in a chapter on symbolic algebra. | 677.169 | 1 |
Description
Calculus II is the second volume of the three-volume calculus sequence by Tunc Geveci. The series is designed for the usual three-semester calculus sequence that the majority of science and engineering majors in the United States are required to take.
The distinguishing features of the book are the focus on the concepts, essential functions and formulas of calculus and the effective use of graphics as an integral part of the exposition. Formulas that are not significant and exercises that involve artificial algebraic difficulties are avoided. The book uses Mathematica mainly for the graphics. Contents
Techniques of Integration | Application of Integration | Differential Equations | Infinite Series | Parametrized Curves and Polar Coordinates | Taylor's Formula for the Remainder | Answers to Some Problems | Basic Differentiation and Integration Formulas Related TopicsCalculus and Analysis, Engineering | 677.169 | 1 |
Assessment is a key driver in mathematics education. This book examines computer aided assessment (CAA) of mathematics in which computer algebra systems (CAS) are used to establish the mathematical properties of expressions provided by students in response to questions. In order to automate such assessment, the relevant criteria must be encoded and, in articulating precisely the desired criteria, the teacher needs to think very carefully about the goals of the task.Hence CAA acts as a vehicle to examine assessment and mathematics education in detail and from a fresh perspective. One example is how it is natural for busy teachers to set only those questions that can be marked by hand in a straightforward way, even though the constraints of paper-based formats restrict what they do and why. There are other kinds of questions, such as those with non-unique correct answers, or where assessing the properties requires the marker themselves to undertake a significant computation. It is simply not sensible for a person to set these to large groups of students when marking byhand. However, such questions have their place and value in provoking thought and learning. This book, aimed at teachers in both schools and universities, explores how, in certain cases, different question types can be automatically assessed. Case studies of existing systems have been included to illustrate this in a concrete and practical | 677.169 | 1 |
You
should know the basics of algebra and analysis: matrix manipulations,
determinants, vector spaces, derivatives, integrals, differential equations;
at least to the point of understanding what they are.
A basic general physics course of the kind served to most undergraduate
science students in first and second year would be rather helpful too,
as most of our examples will assume a certain understanding of the
world around us (not too much though: it's OK not to remember the value
of Planck constant). To this extent you should brush up on introductory
classical and quantum mechanics and introductory classical field theory
(electromagnetism).
Regarding
programming and general computing skills, a certain degree
of experience is expected. You should have been exposed to POSIX and
some basic POSIX tools: you should know how to manipulate POSIX
files and
directories and how to edit and compile programs. If you are a
Windows-NT
user, you can obtain GNU tools from - these provide
a fairly adequate level of POSIX compatibility and cost nothing.
If you are a Linux user, your computing skills are high enough.
If you have only ever used a Macintosh or Windows-95, do not despair.
You can learn
all that you need in one afternoon. If you are a fast learner. It's
not that hard.
Familiarity with, even a mastery of, GNU Emacs
will serve you well
in this course. | 677.169 | 1 |
Lectures on Discrete Geometry
Beschreibung
Beschreibung
The main topics in this introductory text to discrete geometry include basics on convex sets, convex polytopes and hyperplane arrangements, combinatorial complexity of geometric configurations, intersection patterns and transversals of convex sets, geometric Ramsey-type results, and embeddings of finite metric spaces into normed spaces. In each area, the text explains several key results and methods.
Pressestimmen
From the reviews: "Discrete geometry is not quite a newcomer on the stage of mathematics. ... The book under review covers ... a gap in the pedagogical literature, providing an expository treatment of a wide range of topics in discrete geometry, without assuming too many prerequisites from the reader. ... it will be ideal to be used both as a textbook and for self-study. ... In fact ... this book can be used as a 'mathematical companion' to a textbook on computational geometry ... ." (Paul A. Blaga, Studia Universitatis Babes-Bolyai Mathematica, Vol. XLVIII (1), March, 2004) "MatouSek's excellent new book concerns discrete geometry. ... The style is clear and pleasant; things are streamlined and collected in one place, and are explained on simple, concrete examples. ... a final chapter on 'What was it about? An informal summary' was an innovation that I found to be an excellent idea. Lectures on discrete geometry is a splendid book. I recommend it both to students and researchers in the field, as well as to those who like mathematics for its own inherent beauty." (Imre Bárány, Bulletin of the London Mathematical Society, Issue 35, 2003) "This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections, and thus, it can serve as a collection of surveys in several narrower subfields." (L'ENSEIGNEMENT MATHEMATIQUE, Vol. 48 (3-4), 2002) "This is an introduction to the field of discrete geometry understood as the investigation of combinatorial properties of configurations of (usually finitely many) geometric objects ... . The book is written in a lively and stimulating but very precise style and contains many figures. It gives a good impression of the richness and the relevance of the field." (Johann Linhart, Zentralblatt Math, Vol. 999 (24), 2002) | 677.169 | 1 |
common mistakes with examiner tips - A revision grid allows students to revise by topic
National 5 Mathematics Practice Papers for SQA Exams will help you to prepare for the look and feel of the exam. All the papers will provide extensive practice and reflect the type and level of questions students are likely to meet; the formats of different question papers and assessment methods; and the type of marking schemes used by the SQA.
Teach lessons that suit the individual needs of your students with this SQA endorsed and flexibly structured resource that provides a suggested approach through all three units. This textbook completely covers the latest National 4 syllabus. Each chapter includes summaries of key points and worked examples with explanatory notes showing how skills are applied. Section Reviews presented in non-calculator and calculator formats provide students with the opportunity to consolidate skills acquired over a number of chapters. There are plenty of exercises and invaluable exam practice throughout to help build confidence and knowledge. Although core answers are provided int he textbook, a corresponding teacher's 'Answers and Assessment' book is also available, including expanded answers plus sample assessmernt material for practice. - Covers the new specification with all the new topics in the SQA examinations - Provides thorough exam preparation, with graded Practice Exercises - Organised to make it easy to plan, manage and monitor student progress
A full course textbook for the new National 5 Physics syllabus, endorsed by SQA! This book is designed to act as a valuable resource for pupils studying National 5 Physics. It provides a core text which adheres closely to the SQA syllabus, with each section of the book matching a unit of the syllabus, and each chapter corresponding to a content area. It is an ideal - and comprehensive - teaching and learning resource for National 5 Physics. In addition to the core text, the book contains a variety of special features: For Interest, Research Tasks, Activities, Questions, Worked Examples, and Consolidation Questions. - The only textbook for the National 5 Physics syllabus offered by SQA, as examined 2014 onwards - Bestselling author, with extremely high reputation for Scottish Physics titles - Full colour presentation and motivating text design to encourage student enthusiasm
Ensure your students are prepared for every aspect of their assessment with the only textbook endorsed by SQA and that offers fully comprehensive coverage of the new syllabus requirements. - Written by a highly experienced author - Covers the new specification with all the new topics in the SQA examinations - Provides thorough exam preparation, with graded Practice Exercises - Organised to make it easy to plan, manage and monitor student progress | 677.169 | 1 |
like this course. It provided lots of information, but AoPS didn't present it like other math teachers who just shove worksheets under your nose. We took our time, and I understood everything. | 677.169 | 1 |
Compressed Zip File
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0.12 MB | 2 pages
PRODUCT DESCRIPTION
This r squared creation document is a review of the topics that will be covered on the Chapter 8 Test. The materials covered in the review are standards based and are aligned to Chapter 8 "Factoring Polynomials" of the Holt Algebra textbook. Concepts covered are how to find the prime factorization, how to find the GCF of polynomials, how to factor by taking out the GCF, how to factor a quadratic expression where the "a" term does not equal one, how to factor a quadratic expression where the "a" term equals one, how to factor a special quadratic expression, and how to factor out the GCF first, and then factor the remaining quadratic expression.
The zip file contains the worksheet in both .doc format as well as in .pdf. If you would like to make any changes, you may need to download MathType for free | 677.169 | 1 |
ACAD 08-006 Crosswalk with CRC identified NUCP Material
This comprehensive crosswalk links the objectives of ACAD 08-006 with GP Strategies ABC Material,
NUCP Surveyed Material, NANTeL resources, EPRI resources, web resources, and published material
available to all RCNET partners. Each field links to teaching materials that can be downloaded for use
in your classroom.
1.1.1.5 Apply scientific and engineering notation in calculations including conversion of numbers
MA-11-5, 6, 7, 8
MA-11-6, 7
1.1.1.6 Demonstrate the ability to apply the concept of dimensional analysis and to perform unit conversions, unit modifiers, and metric measurements such as conversion between metric and the U.S. customary system.
PH-01-2, 3, 4, 5, 6, 7, 11, 12, 13
PH-01-2
1.1.1.7 Perform basic algebraic operations, including calculations of area and volume. NOTE: Geometry concepts of area and volume are now included in the algebra statement.
1.1.1.9 Create and interpret graphs and control charts, including graphing data, obtaining information from graphs and control charts and nomograms, rectangular coordinate systems, and logarithmic coordinate systems.
1.1.3.3 Explain basic electronic theory, including semiconductors, diodes, and transistors. NOTE: This section of National Academy ACAD documents is out of date and does not reflect current technology; it is considered plant specific.
1.1.10 COMPUTERS (Plant specific) Explain and perform basic computer commands (NOTE: This section of the National Academy ACAD documents is out of date and does not reflect current techology; it is considered plant specific.
1.3.1.3 Pumps, ejectors, and eductors such as for pumps (centrifugal, positive displacement) - Include centrifugal pump laws, series, and parallel operation; net positive suction head; requirements of minimum flow and effects of dead-heading pump; and causes and indications of cavitation and how to prevent it.
Non-Licensed Operators
ACADs
GP Stratagies Matris
Lesson - Chapter - Objectives
Gap Materials from RCNET & Academic Partners
Textbooks & Other Published Materials
2.0 DISCIPLINE-SPECIFIC CURRICULUM FOR NON-LICENSED OPERATORS
2.1 Plant systems and Components Knowledge: Power Plant FundamentalsThis section provides the knowledge and skills necessary to operate and monitor systems and components for which the nonlicensed operator is responsible. Actual course/training content should consider personnel entry-level knowledge, skills and experience as well as job and task analysis results. Some systems and components would apply only to certain reactor types. Explain the principles and describe the components associated with various plant systems. (These topics build on the gneral system and component knowledge that is part of the Basic Systems Knowledge curriculum and focus on the in-depth knowledge required for the nonlicensed operator discipline.
3.1 Plant Systems and Components Knowledge: Systems Explain the principles and describe the components associated with various systems. (These topics build on the general system and component knowledge that is part of the Basic Systems Knowledge curriculum and focus on the in-depth knowledge required for the radiological protection technician discipline.)
3.1.1 Explain the importance of the following systems to plant safety and radioactivity containment and identify any radiological hazards and precautions associated with maintenance tasks for each
3.2.1.2 Identify those tools and equipment that may not be taken into radiologically controlled environments without specific controls in place.
3.2.1.3 Identify power sources that may be connected to tools and test equipment.
3.2.1.4 Explain the requirements for instruments and test equipment calibration.
3.2.1.5 Explain how to determine tool and equipment calibration status.
3.2.1.6 Describe proper methods of protecting tools and test equipment for the following:
3.2.1.6.1 In a radiologically controlled area
3.2.1.6.2 In a confined space
3.2.1.6.3 When working from heights
3.2.1.6.4 When working near open systems
3.2.2 Radiation Detection and Measurement Principles Discuss the basic theory of operation and operating characteristics of detectors, to include instrument efficiency, the factors that affect instrument efficiency, and the calculation of efficiency from given information; the effects of background radiation; and differentiation between the operating characteristics of a radiation field survey instrument and a radioactive contamination survey instrument.
3.2.3.4 Identify the instruments available for performing radiation surveys and demonstrate proficiency in using the instruments (plant specific)
3.2.3.5 Describe plant requirements for documentation of radiation surveys, including the use of survey maps, the review of completed surveys, the retention of records and the updating of area maps and postings (plant specific)
3.2.3.6 Explain actions to be taken if radiation levels are off scale on the instrument in use (plant specific)
3.2.3.7 Select the appropriate instrument for performance of radiation surveys under various conditions, based on expected radiation types, expected dose rate and environmental conditions (plant specific)
3.2.3.8 Identify the instruments available for performing contamination surveys such as the following:
3.2.3.14 Describe plant requirements for documentation of contamination surveys, including the use of survey maps, the review of completed surveys, the retention of records and the updating of area maps and postings (plant specific)
3.2.3.20 Identify factors that affect the statistical accuracy of radioactivity measurements, including count rate, background, count time, equipment efficiency, sample volume and sample geometry. Explain how the statistical accuracy of measurements can be improved
3.3.3.2 Describe the processes and characteristics of heavy charged particle (alpha particles, protons) interaction with matter, to include energy transfer by ionization and excitation; range-energy relationship; range of alpha particles in air, water, and tissue; and specific ionization as a function of distance.
NS-01-1, 2, 5
NS-03-1, 2, 3, 4, 5 NS-04-1, 2
PPT Interactions with Matter
3.3.3.3 Describe the processes and characteristics of beta particle interactions with matter, including range-energy relationship; energy transfer by ionization, excitation, and bremsstrahlung; irregular track due to scattering; bremsstrahlung production using high atomic number absorber; and range of beta particles in air, water and tissue (content added: density thickness).
3.3.6.1 Describe the principles of operation and characteristics of the types of dosimetry used at the plant (thermo luminescent dosimeters, film badge, alarming dosimeters, pocket ion chamber, teledosimetry, (content added: optical-luminescent dosimeters), including the range(s) of each device, the effects of fading and drift, the advantages of each type of device, the limitations of each type of device, and radio frequency interference.
3.3.6.3 Describe the plant calibration program for dosimetry. (plant specific)
3.3.6.4 Describe the types of dosimetry required for various work situations, (plant specific) such as entry into the restricted area; entry into the radiologically restricted area; entry into posted radiation areas, high radiation areas, or very high radiation areas; visitors; entry into areas with neutron radiation; entry into areas of non-uniform radiation fields; and planned special exposures. (Plant specific).
3.3.6.5 Describe the method and equipment used at the plant to determine doses from various types of radiation, including gamma whole-body dose, gamma extremity dose, beta skin dose, and neutron dose (plant specific).
3.3.6.6 Demonstrate the proper method for wearing dosimetry under various conditions, including determining the proper location of dosimetry.
3.3.6.8 Describe when a planned special exposure is allowed and the detailed requirements of the planned special exposure.
PPT Personnel Monitoring
KEEP
3.3.6.10 Explain the plant requirements for the use of extremity dosimetry, including conditions under which extremity dosimetry is required, (plant specific) administrative procedures for issuing and collecting extremity dosimetry, and types of extremity dosimeters (plant specific) .
3.3.6.11 Describe the plant criteria for performance of investigations of discrepancies in dosimetry readings (plant specific).
3.3.6.12 Explain actions to take in the event of abnormal situations (plant specific) such as:
3.3.8.3 Define and state the posting requirements for the the controlled area, radiologically restricted area, radiation area, high radiation area, locked high radiation area, very high radiation area, and (plant specific) hot spots.
PPT Radiation Protection Postings
PPT Protection Against Radiation
3.3.8.4 Describe techniques for controlling individual exposures during radiological work, such as the use of pocket ion chambers or alarming dosimeters to allow workers to monitor dose received, assignment of stay times, use of radiation work permits (RWP), radiological protection technician job coverage (local or video monitor), use of low does waiting areas, and use of remote electronic dosimeters.
PPT Radiological Controls
KEEP
3.3.8.5 Describe the access controls required for entry into each level of controlled area (as applicable) (plant specific) including the following:
3.3.8.5.1 radiation work permit requirements
3.3.8.5.2 dosimetry
3.3.8.5.3 notification to Radiological Protection Department
3.3.8.5.4 instrument or alarming dosimeter
3.3.8.5.5 locked barriers
3.3.8.5.6 warning signs and lights and key controls
3.3.8.6 Perform a radiation survey and (plant specific describe plant procedures) for performance of routine radiation surveys, including the frequency of surveys, instruments to be used, areas to be surveyed, survey techniques, and documentation of results.
3.3.8.7 Describe precautions and survey techniques for entering an area where radiation levels are unknown.
3.3.9.10 Describe plant requirements for monitoring tools and equipment for radioactive contamination when leaving the radiologically restricted area, for unrestricted use in the radiologically restricted area, for storeage or reuse within the radioloigally restricted area, and for release from the plant (plant specific).
3.3.9.11 Perform an area contamination survey, and (plant specificdescribe plant procedures for performing routine area contamination surveys), including, including (plant specific frequency of surveys), instruments to be used, areas to be surveyed, survey techniques, and (plant spedific documentation of results.)
3.3.9.12 Describe plant procedures for performing special contamination surveys (plant specific), including radioactive particles on personnel or equipment; radioactive particles in areas; small volumes of liquid leaving the radiologically controlled area; and loose material, such as sand, leaving the raiologically controlled area (Plant specific)
3.3.9.15 Define a full set of protective clothing under normal circumstances (plant specific)
3.3.9.16 Describe other types of protective clothing available, including conditions under which each is used, procedures for donning and removing protective clothing and inspections of clothing prior to use
3.3.9.17 Describe the devices used for containment of contamination during radiological work, such as drapes, glove bags, tents, drain bottles, berms, absorbents to contain liquid and catch containments
3.3.9.19 Identify the conditions in which the use of each type of containment device is to be considered
PPT Contamination Control, Decontamination, Respiratory Protection
3.3.9.20 Explain the inspections that are to be performed prior to the use of containment devices
PPT Contamination Control, Decontamination, Respiratory Protection
3.3.9.21 Describe techniques to minimize the spread of contamination, including protective clothing requirements and precautions during use, removal of contaminated equipment, and postjob removal or decontamination of the containment device.
3.3.9.22 Identify methods by which a work site can be prepared for the performance of highly contaminated work such as using disposable plastic; covering the work area with launderable, reusable sheeting; covering the work area with strippable paint; and painting concrete surfaces for ease in decontamination.
PPT Contamination Control, Decontamination, Respiratory Protection
3.3.9.23 Define cross-contamination and describe how it can result in the uncontrolled spread of contamination
PPT Contamination Control, Decontamination, Respiratory Protection
3.3.9.24 Describe techniques to minimize the spread of contamination when contaminated materials are brought out of posted areas
PPT Contamination Control, Decontamination, Respiratory Protection
3.3.9.25 Describe the purpose and use of a stepoff pad in controlling the spread of contamination
3.3.9.26 Discuss the generic plant requirements for entering and working in areas with contamination above plant limits, such as radiation work permits, protective clothing, use of tools for a hot tool room, step off pads, and notification of the Radiological Protection Department.
3.3.10.9 Identify work situations and work practices that could produce airborne radioactivity, such as opening a contaminated system; working in highly contaminated areas; grinding, cutting or welding radioactive or contaminated materials; and leaks from contaminated systems.
3.3.10.10 Describe controls that can be used to reduce exposure to airborne radioactivity, such as the use of filtered ventilation, decontamination of areas or equipment to eliminate the source of airborne radioactivity, use of containment devices (such as tents, glove bags), and repair of leaks in contaminated systems, the performance of work under water or keeping contaminated materials wet, and use of a respirator (last resort).
3.3.10.11 Identify the primary ventilation and filtration systems in the plant. (plant specific)
3.3.10.12 Identify plant requirements that must be met before an individual is issued a respirator such as training the individual in the proper use of equipment, medical evaluation, and quantitative fit test.
3.3.10.17 Demonstrate proper procedure for donning and removing each type of respiratory protection equipment used at the station. (plant specific)
3.3.10.18 Discuss the difference between paper filters and charcoal filters and when each is used.
PPT Radioactive Material Handling and Interpersonal Skills
KEEP
3.3.10.19 Discuss plant procedures for tracking exposure to airborne radioactivity, including levels at which tracking is required, sampling requirements, use of protection factors, documentation of exposures, timekeeping, and reporting and summing exposures. (Plant Specific)
3.3.10.20 Discuss plant requirements for entering and working in airborne radioactivity areas (plant specific), such as radiation work permit, respiratory protection equipment, and notification of the Radiological Protection Department. (Plant specific).
3.3.11 CONDUCT AND MONITORING OF RADIOLOGICAL WORK Perform and/or monitor radiological work operations.
3.3.11.1 Perform and/or monitor work in radiation areas, high radiation areas, and very high radiation areas (plant specific)
3.3.11.2 Perform and/or monitor work in areas where the potential exists for rapidly changing dose rates (plant specific), such as the spent fuel pool, during incore detector evolutions, and during radiography. (Plant specific)
3.3.11.5 Perform and/or monitor work in areas with airborne radioactivity or the potential for airborne radioactivity (plant specific)
3.3.11.6 Perform and/or monitor work in areas with high dose gradients (plant specific)
3.3.11.7 Describe the methods that can be used to invoke radiological protection requirements such as steps in written procedures, radiation work permits, verbal instructions from the supervisor, and verbal instructions from radiological protection personnel.:
3.3.11.20 Identify the pre-job radiological survey requirements for the work operation to be performed. Based on the results of the pre-job surveys and the scope of work, identify or evaluate the need for the following:
3.3.11.22 Describe how the results of ALARA reviews are implemented (plant specific), including the documentation required, mandatory versus suggested techniques, technician and worker authority and procedure for modifying requirements, and responsibility for implementation. (Plant specific):
3.3.11.23 Discuss generic plant procedures for conducting pre-job briefings for radiological work, including when briefings are required, the frequency of briefings for continuing jobs, personnel required to attend briefings, items to be discussed in briefings, and the importance of resolving all questions in briefings.
3.3.11.24 Explain how the type and location of whole-body dosimetry is determined for body position and dose rate gradient.
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.25 Identify the criteria used to determine the need for multiple badging or for extremity monitoring.
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.26 Identify measures to take when protective clothing is used in conditions that could result in heat stress.
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.27 Identify and explain factors that determine the need for and type of protective clothing to be used during radiological work such as level of contamination, position of the workers, presence of airborne radioactivity, presence of liquid, type of work being performed, environmental conditions, and total risk concept.
3.3.11.29 Describe special precautions that should be used when practical to control or reduce exposures during certain radiological conditions, such as assignment of stay times and timekeepers, continuous radiological protection technician coverage, use of alarming dosimeters or dose rate meters, use of temporary shielding, availability of low dose rate waiting areas, and removal of high dose rate sources.
3.3.11.30 Describe precautions to be used when practical to control spread of radioactive contamination during radiological work, such as the use of containment devices, special protective clothing requirements, and the use of disposable coverings during job-site preparation.
3.3.11.31 Describe precautions to be used, when practical, to control airborne radioactivity, such as special ventilation, containment devices, and work areas decontamination, as well as performing work under water or dampening the work area.
3.3.11.34 Describe the in-process radiological surveys that should be performed under various radiological conditions, including radiation surveys, contamination surveys, and airborne radioactivity surveys.
3.3.11.36 Identify generic locations that should be included in process radiation surveys, such as component being worked on, nearby piping and components, location where workers are positioned, path to and from the work site, low dose areas, hot spots, and potentially transient dose rate areas (resin lines, drain lines, movement of sources).
3.3.11.37 Discuss plant procedures for conducting in-progress airborne radioactivity samples, including when samples are to be taken, and define the following: breathing xone and the appropriate breathing zone for varous work situations, the method of sampling (for example, low volume, high volume, lapel, or continuous air monitor), the type of sampling (for example, particulate, iodine, noble gas, or trituim), and the documentation of the results (plant specific).
3.3.11.38 Explain actions that should be taken if surveys show radiological conditions significantly different from expected, such as high contact dose rates, high general area dose rates, unexpected low dose rates, high beta dose rates, very high contamination levels, very high airborne radioactivity, and unexpected lack of airborne radioactivity.
3.3.11.39 Discuss plant access control procedures for entry into the following for performance of work:
3.3.11.39.1 controlled area
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.39.2 radiological restricted area
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.39.3 restricted area
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.39.4 radiation area
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.39.5 high radiation area
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.39.6 very high radiation area
PPT Radioactive Material Handling and Interpersonal Skills
3.3.11.39.7 contaminated area
PPT Radioactive Material Handling and Interpersonal Skills
KEEP
3.3.11.39.8 airborne radioactivity area (plant specific)
3.3.11.40 Describe actions required when leaving a work site upon completion of radiological work, such as packaging, marking, and transferring contaminated tools, equipment, and trash; removing protective clothing; monitoring for contamination; returning special dosimetry; signing out of the RWP; and notifying radiological protection personnel of job completion.
3.3.11.42 Demonstrate the interpersonal and human relations skills that are used to perform job coverage effectively in conditions such as the following: main control point, satellite control point, job coverage during worker performance problems, and exit point control.
PPT Radioactive Material Handling & Interpersonal Skills
KEEP
3.3.12 RADIOLOGICAL INCIDENT EVALUATION AND CONTROL Explain the recognition of and appropriate responses to radiological events.
3.3.12.1 Describe, in general terms, the expected response to radiological incidents, including precedence given to treating injuries, mitigation and minimization of exposure to plant personnel and the public, mitigation and minimization of damage to equipment, and notification of appropriate personnel.
3.3.12.2 Discuss the role of various plant personnel in responding to radiological incidents (plant specific), including personnel directly involved in the incident and immediately affected by it (regardless of work group), other personnel nearby but not affected, control room personnel, radiological protection technicians, radiological protection supervisors, fire brigade, auxiliary operators, and plant managers. (Plant specific).
3.3.12.3 Identify the radiological consequence that may result from various incidents, such as a sudden increase in dose rate, the uncontrolled spread of contamination, a leak or spill of contaminated liquid, an injury to an individual performing radiological work, a fire in the radiologically restricted area, the loss of a high-activity radiation source, a degraded core, and uncontrolled or unsecured high radiation areas.:
3.3.13.6 Describe the procedure to be followed when an individual is contaminated, including performing a contamination survey (whole-body) by radiological protection personnel; recording contamination levels, location, date, and time on personnel contamination report; (Plant specific) direct decontamination of areas above the plant limit; identifying when nasal smears and/or a whole-body count are required; documenting the final results of decontamination; and interviewing the individual to identify the source of contamination.
3.3.13.9 Explain why hot water, cold water and abrasive cleaners are not used for personnel decontamination:
PPT Contamination Control, Decontamination, Respiratory Protection
3.3.13.10 Identify conditions in which skin dose calculations should be performed as a result of skin contamination.
PPT Personnel Monitoring
DOC Skin Dose
3.3.13.11 Describe why some areas of the plant should not be decontaminated, such as filter galleries, high radiation areas, and hallways between contaminated areas frequently traveled by operations personnel.
PPT Off-Normal and Emergency Response
3.3.13.12 Identify situations in which personnel decontamination is to be referred to other appropriate personnel: contaminated wounds; contaminated eyes, ears, nose, or throat; and contamination that cannot be removed through the use of approved techniques.
PPT Biological Effects of Radiation
PPT Radcon Emergency Response
3.3.13.13 Describe special procedures for decontamination of radioiodines.
3.3.14.16 Explain the radiological protection requirements associated with processing liquid wastes using techniques such as operation of evaporators, solidification of evaporate bottoms, transfer of demineralizer resin to shipping casks, and dewatering and solidification of resins.
4.3.5 Describe proper methods of protecting tools and test equipment including the following:
4.3.5.1 in a radiologically controlled area
4.3.5.2 in a confined space
4.3.5.3 when working from heights
4.3.5.4 when working near open systems
4.4 RADIATION DETECTION AND MEASUREMENT PRINCIPLES Discuss the basic theory of operation and the operating characteristics of detectors, including instrument efficiency, the factors that affect instrument efficiency, and the calculation of efficiency from given information, effects of background radiation, and differentiation between the operating characteristics of a radiation field survey instrument and a radioactive contamination survey instrument.
4.4.1 Explain the functions of an ion chamber, proportional counter and Geiger-Mueller counter
4.7.5 Determine specific sample collection equipment to be included in chemistry technician training based on job requirements. The following are examples of sample collection equipment to consider for inclusion in the chemistry technician training program.
4.9.8 Identify and use radiological quantities and their units including activity (curies and becquerels, disintegrations per second, disintegrations per minute), exposure (roentgens), dose (rads and grays), and dose equivalent (rems and sieverts).
4.14.4 Discuss the philosophy of radiation protection limits, to include the prevention of nostochastic effects, minimization of stochastic effect, concept of acceptable risk or comparable risk, and concepts of cost versus benefit and ALARA.
4.16.3 Identify the isotopes of primary concern for airborne radioactivity at the plant such as H-3, Co-58, Co-60, CS-134, CS-137,. I-131
PPT Air Sampling
4.16.4 Explain the characteristic difference between particulate, iodine, tritium and noble gases and how they affect the method of detecting and controlling airborne radioactivity
PPT Air Sampling
4.16.5 Identify the main ventilation and filtration systems in the plant (plant specific)
4.16.6 Discuss the purpose of using a continuous air monitor and identify situations in which continuous air monitors should be used
PPT Radiological Environmental Monitoring Program
4.16.7 Describe controls that can be used to reduce exposure to airborne radioactivity, such as using filtered ventilation, decontaminating areas or equipment to eliminate the source of airborne radioactivity, using containment devices (such as tents, glove bags), repairing leaks in contaminated systems, performing work under water or keeping contaminated materials wet, and using a respirator (last resort).
5.1.2.1.9 Describe the proper methods for adjustments and calibrations on components or systems
DOC Primary Systems
PPT Measurement System
5.1.2.1.10 Describe the methods to test (for example, leakage test, component operation, loop functional test, valve operation) a component when maintenance work is completed, and describe the administrative controls for performing local and manual operation of components during maintenance activities.
IC-06-7
PPT Loop Tuning
PPT Loop Calibration, Control & Troubleshooting
5.1.2.1.11 Explain the limitations of and requirements for maintenance activities associated with environmentally qualified and safety-related components and equipment
PPT Plant Status
5.1.2.1.12 Explain acceptable cleaning and inspection techniques for system components; and explain the lubrication principles associated with components such as valves, pumps, motors, and valve actuators, including the problems associated with improper lubrication.
5.1.2.16 Identify when components have been removed properly from service before maintenance activities are performed
IC-01-2
5.1.2.17 Identify system cleanliness requirements and describe the methods used to prevent foreign material from entering systems and components
PPT Foreign Material Exclusion
5.1.2.18 Identify industrial safety measures necessary for work in the vicinity of specific operating equipment including job aspects related to identifying, diagnosing and repairing system and component problems and using plant procedures and drawings
5.1.2.19 Identify proper rigging and lifting techniques for major components such as pumps and motors
PPT Hoists and Cranes
PPT Initial Rigging
5.1.2.20 Identify where the use of special tools or equipment (for example, cranes, scaffolding, breaker grounding devices) will be required and describe how they will be used during work on various components
5.1.2.2.10 human factors problems associated with plant equipment such as inadequate component labeling and working on components from difficult orientations
5.1.2.2.11 influences of harsh environmental conditions such as low lighting and tight working clearances
5.1.2.2.12 instrumentation and processors
5.1.2.2.12a control systems (level, pressure and temperature)
5.1.2.2.13 medium-sized pump and motor packages similar to component cooling or charging water pump assemblies
5.1.2.2.13a seal, bearing and coupling components
5.1.2.2.13b bolt torquing and foreign material exclusion
5.1.2.2.14 oral communications with station personnel involved with maintenance activities
5.1.2.2.15 packing replacement and adjustment
5.1.2.2.16 rotating and processing conditioning equipment
5.1.2.2.17 signal processing equipment
5.1.2.2.17a nuclear instrument cabinets
5.1.2.2.17b radiation monitoring components
5.1.2.2.17c reactor protection system panels
5.1.2.2.18 use of operating experience information
5.1.2.2.19 valves and valve actuators
5.1.2.2.20 valve mockups
5.1.2.2.20a ball, butterfly, gate, globe, check and relief valves
5.1.2.2.20b disassembly and assembly
5.1.2.2.20c cleaning
5.1.2.2.20d lubricating
5.1.2.2.20e inspecting
5.1.2.2.20f seat machining
5.1.2.2.21 valve actuators repair and testing
5.1.2.2.21a motor
5.1.2.2.21b pneumatic
5.1.2.2.21c solenoid
5.1.2.2.22 verification of important safety and status control functions such as checking the tagged boundary and performing an independent verification
k
5.2 DISCIPLINE-SPECIFIC CURRICULUM FOR MAINTENANCE PERSONNEL: MECHANICAL MAINTENANCE TECHNICIANS Describe the component types and characteristics, common failure mechanisms, and operating principles of plant components (generic training on power plant machinery/equipment will be followed by plant-specific-training and qualification).
5.2.2.11 other systems important to plant operations, such as those covered by technical specifications
PPT Chemistry and Radcon
PPT Plant Status
k
5.2.3 Perform the following specialized tasks (plant specific)
5.2.3.1 close tolerance machining
5.2.3.2 disassembling and reassembling the reactor vessel head and internals
5.2.3.3 establishing freeze seals
5.2.3.4 installing and removing reactor cavity seal
5.2.3.5 installing and using reactor pressure vessel stud tensioners
5.2.3.6 overhauling and repairing the control rod drive mechanism
5.2.3.7 overhauling the emergency diesel
5.2.3.8 plugging steam generator tubes (PWR)
5.2.3.9 removing and replacing control rod drive mechanism seals
5.2.3.10 replacing reactor coolant pump mechanical seal (PWR)
5.2.3.11 replacing reactor recirculation pump mechanical seal (BWR)
5.2.3.12 reactor internal pump maintenance (ABWR)
5.2.3.13 reduction gear and gear drive work
5.2.3.14 handling specialized rigging operations for jobs such as reactor vessel disassembly or main turbine maintenance
5.2.3.15 installing, inspecting and removing scaffolding
5.2.3.16 silverplating, electroplating
5.2.3.17 steam generator tube plug welding (PWR)
5.2.3.18 tempering and annealing
5.2.3.19 overhauling and aligning the turbine
5.2.3.20 welding (electric arc, gas, inert gas, metal spray)
k
5.3 DISCIPLINE-SPECIFIC CURRICULUM FOR MAINTENANCE PERSONNEL: ELECTRICAL TECHNICIANS Describe and explain electrical equipment, common failure mechanisms, and operating principles of plant components and be able to apply this knowledge. Generic training on power plant machinery/equipment will be followed by plant-specific training and qualification.
k
5.3.1 Diagnose problems and perform maintenance on the following equipment (plant specific)
5.3.1.1 electrical supply components
5.3.1.1a switchgear, load centers and motor control centers
5.3.1.1b transformers
5.3.1.1c inverters and uninterruptible power supplies
5.3.1.1d circuit breakers
5.3.1.1e batteries and chargers
5.3.1.2 electrical control components
5.3.1.2a relays
5.3.1.2b meters
5.3.1.2c control circuits
5.3.1.2d cables
5.3.1.3 resistive electrical equipment
5.3.1.3a heaters
5.3.1.3b heat tracing
5.3.1.4 rotating equipment
5.3.1.4a motors
5.3.1.4b generators
5.3.1.4c motor-generators
5.3.1.5 structural and auxiliary equipment
5.3.1.5a hoists and cranes
5.3.1.5b fire barriers
5.3.1.5c electric boilers
5.3.1.5d elevators
5.3.1.6 valve actuators
5.3.1.6a manual operation
5.3.1.6b testing
5.3.1.6c position indication
5.3.1.6d environmental impact
5.3.2 Explain detailed construction and use of the following:
5.3.2.1 battery systems
ES-07-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
5.3.2.2 cathodic protection systems
PPT Cathodic Protection Systems
5.3.2.3 electrical distribution, including alternating and direct current systems
5.3.2.11 other systems import to plant operations such as those covered by technical specifications
PPT Chemistry and Radcon
PPT Plant Status
k
5.3.3 Perform the following specialized tasks (plant specific)
5.3.3.1 breaker operation, setting, adjustment and repair
5.3.3.2 motor-operated valve diagnostic testing
5.3.3.3 motor overhauls
5.3.3.4 high potential (hi-pot) tests
5.3.3.5 stress relief of major components
5.3.3.6 high voltage connection preparation
5.3.3.7 relay setting, adjustment, calibration and repair
5.3.3.8 special soldering
5.3.3.9 tempering and annealing
5.3.3.10 battery load testing
5.3.3.11 switchgear testing
k
5.4 DISCIPLINE-SPECIFIC CURRICULUM FOR MAINTENANCE PERSONNEL: INSTRUMENT & CONTROL TECHNICIANS Describe general systems and components, focusing on the in-depth knowledge required for specific jobs tailored to the individual maintenance discipline. Building on the general system and component knowledge, describe the in-depth requirements for specific jobs tailored to the instrument and control maintenance discipline. Plant generic training on power plant machinery/equipment will be followed by plant-specific training and qualification. | 677.169 | 1 |
...
Show More the famous dilemmas that well-known mathematicians have attempted to solve. Helpful hints and detailed discussions of solutions are included, making this book a valuable resource for schools, student teachers, and college mathematics courses, as well as for anyone fascinated by mathematical | 677.169 | 1 |
Description
Forgot a formula?This formulary is clear, comprehensive, logical and designed in an attractive design. A very cool tool to study!!! trust me!!! pqMaths includes the following math topics: Algebra,Trigonometry,Geometry,Analytic Geometry, Integration, | 677.169 | 1 |
Mathematica is recognized as an important tool for advanced financial analysis but for introductory finance courses, financial calculators and spreadsheet programs are generally deemed sufficient. Given Mathematica's reputed difficulty for new users, it might seem that for an introductory course, the learning costs would outweigh the benefits. In this presentation, I aim to show the opposite is true.
Through drawing on some courseware that I'm developing, I first demonstrate that students do not need extensive knowledge of Mathematica to decipher and modify the simple code that can capture most of the basic financial functions.
Next, I argue that the Mathematica code has a transparency that one loses with a financial calculator or the built-in financial functions of a spreadsheet program. Finance educators often argue about the extent to which beginning students should be using financial calculators. One side argues that the computer tools allow students to work more rapidly through many different problems without doing the type of tedious calculations that they will never encounter in the work world. But traditionalists argue that students will be deprived of a level of understanding that can be gained when the calculations are done by writing out mathematical formulas. They argue that advanced courses will require a deeper understanding of the mechanics of the calculations. I show that with Mathematica both sides can be appeased: the code reveals as much as mathematical formulas, but the computations can be performed quickly and without tedium.
Finally, I show how Mathematica's graphical capability can be used to reinforce the students' understanding of various concepts. Even something quite complicated like the pattern of cash flows from mortgage-backed securities at different rates of prepayment can be made accessible with the use of an animated graphic. | 677.169 | 1 |
Simplifying Algebraic Expressions
PDF (Acrobat) Document File
Be sure that you have an application to open this file type before downloading and/or purchasing.
1.9 MB | 12 pages
PRODUCT DESCRIPTION
This lesson plan consists of definitions (variable, exponent, coefficient, simplify), how to use PEMDAS for the order of operations, and word problems. This could be used in either an Algebra 1 or Algebra 2 class and includes a detailed answer key | 677.169 | 1 |
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