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Signals and Systems/Probability Basics

Probability
This section of the Signals and Systems book will be talking about probability, random signals, and noise. This book will not, however, attempt to teach the basics of probability, because there are dozens of resources (both on the internet at large, and on Wikipedia mathematics bookshelf) for probability and statistics. This book will assume a basic knowledge of probability, and will work to explain random phenomena in the context of an Electrical Engineering book on signals.

Random Variable
A random variable is a quantity whose value is not fixed but depends somehow on chance. Typically the value of a random variable may consist of a fixed part and a random component due to uncertainty or disturbance. Other types of random variables takes their values as a result of the outcome of a random experiment.

Random variables are usually denoted with a capital letter. For instance, a generic random variable that we will use often is X. The capital letter represents the random variable itself and the corresponding lower-case letter (in this case "x") will be used to denote the observed value of X. x is one particular value of the process X.

Mean
The mean or more precise the expected value of a random variable is the central value of the random value, or the average of the observed values in the long run. We denote the mean of a signal x as μx. We will discuss the precise definition of the mean in the next chapter.

Standard Deviation
The standard deviation of a signal x, denoted by the symbol σx serves as a measure of how much deviation from the mean the signal demonstrates. For instance, if the standard deviation is small, most values of x are close to the mean. If the standard deviation is large, the values are more spread out.

The standard deviation is an easy concept to understand, but in practice it's not a quantity that is easy to compute directly, nor is it useful in calculations. However, the standard deviation is related to a more useful quantity, the variance.

Variance
The variance is the square of the standard deviation and is more of theoretical importance. We denote the variance of a signal x as σx2. We will discuss the variance and how it is calculated in the next chapter.

Probability Function
The probability function P is the probability that a certain event will occur. It is calculated based on the probability density function and cumulative distribution function, described below.

We can use the P operator in a variety of ways:

 * $$P[\mbox{A coin is heads}] = \frac{1}{2}$$
 * $$P[\mbox{A dice shows a 3}] = \frac{1}{6}$$

Probability Density Function
The Probability Density Function (PDF) of a random variable is a description of the distribution of the values of the random variable. By integrating this function over a particular range, we can find the probability that the random variable takes on a value in that interval. The integral of this function over all possible values is 1.

We denote the density function of a signal x as fx. The probability of an event xi will occur is given as:

 * $$P[x_i] = f_x(x_i)$$

Cumulative Distribution Function
The Cumulative Distribution Function (CDF) of a random variable describes the probability of observing a value at or below a certain threshold. A CDF function will be nondecreasing with the properties that the value of the CDF at negative infinity is zero, and the value of the CDF at positive infinity is 1.

We denote the CDF of a function with a capital F. The CDF of a signal x will have the subscript fx.

We can say that the probability of an event occurring less then or equal to xi is defined in terms of the CDF as:

 * $$P[x \le x_i] = F_x(x_i)$$

Likewise, we can define the probability that an event occurs that is greater then xi as:

 * $$P[x > x_i] = 1 - F_x(x_i)$$

Or, the probability that an event occurs that is greater then or equal to xi:

 * $$P[x \ge x_i] = 1 - F_x(x_i) + f_x(x_i)$$

Relation with PDF
The CDF and PDF are related to one another by a simple integral relation:

 * $$F_x(x) = \int_{-\infty}^x f_x(\tau)d\tau$$
 * $$f_x(x) = \frac{d}{dx}F_x(x)$$

Terminology
Several book sources refer to the CDF as the "Probability Distribution Function", with the acronym PDF. To avoid the ambiguity of having both the distribution function and the density function with the same acronym (PDF), some books will refer to the density function as "pdf" (lower case) and the distribution function as "PDF" upper case. To avoid this ambiguity, this book will refer to the distribution function as the CDF, and the density function as the PDF.

title: Signals and Systems/Probability Basics


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Principles of Sociology/New Agers and Fundamentalism

“Social Perspectives on New Age Religion/Spirituality”

''It is difficult to have a productive discussion about religion and spirituality if the conversation doesn't get beyond what people consider the fundamental realm of faith, that is, the more unquestionable nature of religion. However, it is important to consider what social forces influence people's experience inside a specific religious context or organization and the consequences these behaviors have on shaping society at large. Discussing the emergence of “new age” religious practices helps us get beyond most people's hang ups regarding their religious commitments and provides us an interesting new arena to thoughtfully explore.''

What is the meaning of “New Age”? (ideas)

How does a person labeled “New Age” behave? (behaviors)

How many people actually engage in New Age activities? (statistics)

Is there a New Age social movement or just a trend? (ideology and growth dynamics)

Most monotheistic religions have mystical aspects, or sects within the larger body…

Judaism – Kabbalah Islam – Sufism and Whirling Dervishes Christianity – Chanting Monastic Meditation

More polytheistic faiths like Hinduism, Buddhism, and animism tend to incorporate mysticism throughout

The New Age turn in America is not part of a consolidated religious sect (like the Hare Krishnas) nor a more mainstream cult (like the Moonies). New Age is better described as a large and diverse subcultural realm.

New Age spirituality and religious philosophy as we conceive of it today should be considered a distinctly American phenomenon, perhaps even part of our larger ethnicity. Our country has a long history of religious experimentalism and fundamentalist revival stretching back to the 17 th century. The New Age has captivated people much like the Spiritualists, Transcendentalists, and Theosophists did in the past.

This large-scale, fragmented, decentralized religious subculture drew its principal inspiration from sources outside of the Judeo-Christian tradition, mostly eastern religions and philosophies. While it was in many respects a continuation of a preexisting occult-metaphysical tradition, the addition to its ranks of a sizable number of former counterculturists from the 1950s period onward meant that New Age was no longer a marginal phenomenon: by the eighties, it had become an integral part of a new, truly pluralistic mainstream.

There are lots of interesting groups that have incorporated New Age beliefs and techniques into their repertoire. Before the dot com bubble burst, seminar spirituality had become widespread across the corporate landscape, encouraging creativity and personal growth in business management. Even the army has taken on some aspects: “Be All That You Can Be” and Delta Force uses New Age training exercises

Some people will tell you that the New Age movement has been siphoning off followers of mainstream Christian and Jewish denominations. People have been predicting the decline of traditional religious faiths for more than a century now, but statistics show it still hasn't come to pass. What is more likely to be happening is that while people continue to practice their inherited faith, they take on other New Age practices as well on the side and use them in a complementary fashion when their religion falls short…

Observers have noticed a general rise in spirituality over the last 50 years or so. This can be evidenced by the rise in New Age beliefs, the revival of ancient indigenous spiritualism, and the rebirth of Charismatic Christian churches across the churches constantly invoking the Holy Spirit in their congregation. Max Weber might insist that this “re-enchantment” of the world is a response to the increasing power of science and predicable rationality. Also, the sheer amount of choice people have in spirituality might also play a role

The baby boom generation is said to have taken on the New Age ideology most readily. Why might that be?

What might explain why so many Jews embrace New Age practices and their roots in eastern philosophy?

Can you see any links between the rise in New Age spirituality and the rise of more fundamentalist faiths?

Traits of the New Age:

• an attitude of "epistemological individualism," that is, a belief that the individual is the ultimate locus for the determination of truth.

• an attitude of "revelational indeterminacy," that is, a belief that the truth may be revealed in diverse ways and through diverse agents. No individual or organization possesses a monopoly on the truth.

• New Age is more about transformation than about prediction (astrology) – as such, it changes its focus constantly. It can only be defined by its primal experience of transformation. New Agers have either experienced or are diligently seeking a profound personal transformation from an old, unacceptable life to a new, exciting future....

• Those who have experienced a personal transformation project the possibility of the transformation not of just a number of additional individuals, but of the culture and of humanity itself.

• There is always an emphasis on healing, whether physical, mental, or spiritually oriented - it can come from within or from direct encounters with a guru

Similar Traits in Religious Fundamentalism:

• Personal transformation (salvation) and direct spiritual experience (communion) are at the heart of one's life project - private transformation must find its twin in the transformation of society.

• Fundamentalists hear voices more than see visions: their mysticism comes clad in a rhetoric of newness that is expressed as ongoing revelation in their day to day decision making.

• Fundamentalists stress healing, either through charismatic preachers (the anointed) or mass prayer.... physical health is a sign of blessing, part of the empowerment that comes through close contact with what is sacred. Another sign of blessing is material prosperity.

• Both tend to take texts and revelations quite literally (religious materialism)

• Both have a populist, non-elite, volunteer-oriented notion of "do-it-yourself" salvation

Some Ways to Identify These Types of Social Movements:

• Sense of belonging – A large number of persons unequivocally identifying with some group or idea

• Common values – values and practices that everyone must try to live up to in order to bring the vision to fruition in the world

• Goals of the movement – attempting to create an alternative society that they believe will eventually supplant mainstream society.

• Common Style— a way of appearing and behaving on a daily basis to give aesthetic continuity to the movement as a whole – in these groups it is often anti-materialistic simplicity.

• Jargon – there is a discourse within the movement that outsiders have difficulty understanding.

• Mass communication – there are a large number of alternative sources of information, such as newsletters and magazines, which circulate news within the movement and which rarely appeal to people outside of the movement.

Do people get the same kinds of things from New Age practices as they do from more mainstream religions?

What types of people do you think have a tendency to adopt New Age behaviors and ways of thinking?

How might the New Age movement and the bobo mentality we discussed earlier overlap? Why?

Healing = spiritual growth/learning

What does the term “new Age convey” – this debate is what spawned my interest in doing this presentation – it is the distinction between faddish caricatures and actual measurements of widespread behaviors. You can't just ask someone if they are new age.

Is New Age a social movement? Not in the traditional sense, but it is a number of groups and individuals that have a number of beliefs and orientations that have what the philosopher Ludwig Wittgenstein has called a 'family resemblance'—two members of the family may bear almost no resemblance to each other, although they both resemble a third member

Yoga, meditation, homeopathy, eastern religious philosophy, crystals, holistic medicine, natural food, eco-awareness

Because of its diverse and decentralized nature, new age practices have infiltrated many traditional people's lives –Jews, Christians, businessmen, and doctors alike

A significant proportion, if not a majority of those people embracing new age spirituality and philosophy are from the Baby Boom generation – those hippies and counterculturalists who embarked on various types of spiritual quests in the decades following the 1960s. This is associated with a relative turn inwards of American culture – brought on by the onset of vast individualistic consumerism, youth subcultures, and an overall breakdown in value congruency.

New age is largely an emphasis on the self with concomitant emphasis on novel experience.

How many people are “new agers” in one sense or another of holding alternative religious views?

This is very hard to tell and it certainly depends on what part of the country you look in… i.e. San Francisco has more new agers than Omaha for sure. It is difficult to get good numbers on the population mostly because quantitative sociologists aren't so interested in collecting statistics to study this group – qualitative researchers have more fun just talking to a select few of these folks.

Labeling problems and recognizing shortcomings and needlessness of labels. In a recent edition of Body Mind Spirit, one of the more widely distributed New Age magazines, the editor, Paul Zuromski, raises the question, "Is 'New Age' Dead?" This question is asked in the context of a short piece on the editor's page which explains why the magazine has dropped its banner "Your New Age Information Resource" in favor of "Tools for Creating a Richer, More Fulfilling Life." After asserting that he never cared much for the New Age label anyway, the editor proceeds to cite Gallup Poll findings, as well as certain other evidence, which indicate that the label has acquired negative connotations in the mind of the general public. Partially because of this negative press, even book publishers are abandoning the new age category for a series of "more accurate labels like self-help, new science, metaphysics, Eastern religions, philosophy, natural living," and so forth

Link between Christian fundamentalism and New Age - In viewing the New Age as an expression of American culture, Bednaroski is drawing on Catherine Albanese's work on the New Age. Albanese puts forward a broad interpretation of the significance of the New Age in "Religion and the American Experience." 17 In this article, she argues that

Think about how Max Weber's notions of disenchantment and reenchantment line up with new age ideas about energy, animism, also see new Christian revivals and the emphasis on the spirit

Think about the ever presence of charlatans, pop-mysticism, and disingenuous or counterfeit spirituality

Think about the role of the charismatic leader/teacher in these movements – the oracle, seer, shaman, prophet

There are reportedly 300,000 witches and neopagans worldwide

Why do Jews overrepresent themselves in New Age organizations as compared to their portion of the population?

What kind of people adopt New Age practices and spiritual beliefs?

How do people become New Age? hint – it isn't TV

Are New Agers accepting of other social outcasts – gays, awkward teenage girls, etc?

What is the overt connection between mysticism and the New Age movement?

What is their stance on environmental issues and how might it be related to animism and belief in reviving tribal religions?

Think about the difference between New Age groups and formal religious organizations (like churches) in the way of social services provided, and community in the spatial sense of a meeting house

Here is an example of New Age discourse at a corporate training session:

"We look within to find our own individual self and universal source. That source has been called the Inner Self, the hidden mind, the divine spark, the Divine Ego, the Great I Am, God, and Essence. Some say that the very purpose of human existence is to get acquainted with your own essential qualities and express them in your daily activities. Whether it is the purpose of life or not, it is a fine definition of personal creativity: living every moment from your essence."

The above passage is not quoted from a book on metaphysics, Eastern philosophy, or one authored by Shirley MacLaine. It is from Creativity in Business, written by Michael Ray, a professor at Stanford Business School 1 Ray has taught a course of the same name for several years. Its purpose is to teach students how to use New Age metaphysical teachings to increase their creativity in a business setting. The contents of the book include meditation techniques, yoga exercises, and even specific instructions on how to contact a personal "Spirit Guide."2 “human potential” seminars

Creativity in Business is a clear example of how the American business community is becoming more and more receptive to New Age practices when used to increase productivity and efficiency. In July of 1986 officials from IBM, AT&T, and General Motors met in New Mexico to discuss how metaphysics, the occult, and Hindu mysticism could possibly aid businessmen in an increasingly competitive marketplace.3

Even the U.S. Army has joined in. The slogan "Be All You Can Be" is a direct result of a commission established to explore the possibility of creating a "New Age Army."4 Interest in New Age training methods became so significant in the armed services that in 1984 a project was undertaken by the National Research Council which would investigate these phenomena in detail. Their final report, published in 1988, concluded

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Principles of Sociology/Radical Center Initiatives

The discussion below is based on The Radical Center: the Future of American Politics by Ted Halstead and Michael Lind, both fellows at the New America Foundation (www.newamerica.net), an influential non-partisan public policy institute

''For the first time in American history, a majority of the eligible voting population identify as independents, aligning with neither of the two major parties or any of the other available partisan options. Even in an election that is as controversial and allegedly historically significant as this one, most voters seem disgusted with both the Democratic and Republican parties and the candidates they have nominated for our highest political office. Only around half of this population regularly turns out to vote in presidential elections. This electoral “de-alignment” shows that no political entity in our nation has had the capacity to unite a majority of citizens in a lasting coalition for quite some time now. Instead, we have a “duopoly” of two antiquated, constantly feuding, and largely un-compelling giants. These two beasts have been captured by extreme special interest groups within their party ranks and thus are unable to articulate a vision that might motivate the majority of citizens to take an active part in the political process; not just to vote for the “lesser evil”. Between infighting and constant skirmishing with the other big party, neither has the ability to carry out necessary information age reforms of our antique social contracts. In such a climate, what direction do politics in America need to move in order to address the search for new, innovative solutions to our most pressing and seemingly intractable social problems''?

Domestic Problems Facing America Today : Social Security insecurity, disproportionate aging of the population, immigration-induced economic effects, health insurance, poor public education in primary and secondary schools, income inequality, two-party stagnation

Broad Ideas of the Radical Centrist Agenda :

• Information Age America is distinctly different from our last great historical era, New Deal America, though most of our social institutions remain holdovers from that period and its predecessors (like Reconstruction America)

• Our public philosophy hasn't changed much - freedom to enrich oneself through hard work, freedom from oppression and destitution, freedom of public/private association - but our material realities have, so we must change our social infrastructure

• New technologies have brought us the potential of yet greater freedoms, but we must have both expanded choice and security to fully explore them, thus we must give our citizens greater choice – in voting, education, medicine, and their careers – however, a society will resist innovation so long as it is unable to implement means to mitigate the painful transition period

Economic Innovation Demands Social Innovation :

• Creative destruction is increasing at a startling pace because our economic productivity requires constant innovation

• Workers need to be able to change jobs without devastating lapses in income or insurance; without a security net to ensure these basic needs, voters will pressure politicians to safeguard outmoded jobs and industries, thus stagnating innovation

• An Information Age social contract must link all benefits to individuals rather than to employers or intermediate institutions

• More jobs are short-term because less employers want to offer insurance benefits, which are fiscal and administrative hassles

• Less and less of the population has adequate health insurance, this is especially concentrated amongst lower income groups

• A single-payer universal health care system like all other industrialized nations use has some disadvantages as an alternative – necessary rationing, killing the private insurance industry, and the lack of a private medicine market would retard innovation

• Instead, like we do with automobiles, make a basic private insurance plan mandatory for all who can afford it and provide government subsidization for the most needy who cannot – rich citizens could still purchase private “luxury” insurance plans

Social Security Reforms:

• Demographic forces in the baby-boom generation and medical technology (contraception/longevity) threaten social security

• The existing pay-as-you-go intergenerational transfer model is unsustainable in a slowly growing population

• Why would we want to continue to risk a trade-off between fiscally burdening our working generation and endangering the health and overall well-being of our aging citizens?

• So, like the newly proposed citizen-based insurance savings model, perhaps we should make similar moves in social security

• This is also a compelling idea because for the first time since the Great Depression, we have a negative national savings rate.

• Our politicians have been encouraging consumption (through the tax code and social security) for the past 60 years to buoy our manufacturing economy and trade relationships, but this occurred in an era of increasing media encouragement as well

• Unless a cultural shift occurs in fiscal responsibility, a large number of future retirees will be dependent of the public purse

• Since it seems Americans need help to accumulate adequate retirement funds, perhaps we should institute a mandatory 5% savings rate as well… social security already takes out 6% and employers match that for 12% total… if the mandatory retirement and insurance payments were taken out of this portion, it would still leave more to subsidize low-income earners

• Furthermore, people would be able to play around with how to invest this money, so long as it isn't too risky

• Finally, it wouldn't be a bad idea to move back the retirement/payout ages to compensate for increased longevity patterns

Enfranchising All Citizens in the New Economy :

• The United States has had many historical programs to broaden capital ownership – the Homestead Act after the Civil War and the GI Bill after WWII for example – but it has been a while since the last manifestation

• People are likely to become better citizens the more they have a stake in different social institutions – economic, political, etc.

• Still, our society maintains privileged groups in both these interconnected spheres… “Capitalism isn't designed to create capitalists, but to finance capital. Absent political will, these dramatically different goals will not be reconciled.”

• Perhaps we should make a point of giving children a financial nest egg at birth to give them a chance to finance a trial of their own innovative ideas in the marketplace. Call it “universal capitalism”. $5000 at birth would yield about $20000 at maturity.

• Even if most children don't use this money to capitalize an idea, it would give children with not a whole lot else going for them a better shot of catching up with the larger trust fund babies – at only about $20 billion cost to the public

• Furthermore, the money need not go to people who are already advantaged, it would be “means-tested” to avoid such waste.

Maximizing Choice at the Ballot Box :

• Our election system limits races to two main parties by design, not by tradition or any kind of will by the people.

• Plurality voting is the main reason that Clinton won in 1992 and Bush won in 2000 - Perot in 1992 siphoned off enough third-party but otherwise conservative votes to cause Bush Sr. to lose - Nader did the same thing to Gore in 2000 with liberal votes

• This is a perversion of the public will (all half of it) in deciding elected offices, but is also a reinforcer for the two party system, because any time you vote for another party or candidate, you're more likely to be a spoiler than to effect change

• Instant runoff or rank order voting consists of listing one's preferences in order (say 1 to 5) as to which candidates you favor more than others – thus, if no candidate wins a first choice majority of the votes, the secondary votes would be counted until one candidate achieves a majority by this route. However, you can see how the electoral college interferes in the presidency.

• This would encourage the emergence of serious third parties and candidates to run and voters to take them fully into account at the ballot box, while ensuring that no fringe or extremist parties could win with only a small percentage of the vote.

• Also, it would ensure that parties are represented in the government more in proportion to their actual strength in the electorate. It wouldn't cause the instability of multiparty parliaments in other countries because our executive branch is independent of the legislature and our representatives are elected by different shapes and sizes of constituencies.

• Furthermore, like Maine and Nebraska, at least the electoral votes allotted to the state could be divided by the popular vote

The Simple Consumption Tax :

• Information age tax systems should be as simple, equitable, transparent, and efficient as possible. Our national tax code is 10,000 pages long and trained professionals have trouble fully comprehending it. State sales taxes are even more complicated and regressive, people earning $750,000 pay 1% of their income sales tax annually, people making $15,000 pay 7%.

• E-commerce is proving the state sales tax system even more arcane, as products bought in other states are often exempted, the current moratorium on Internet taxes is already hurting state incomes (much of which goes education), but will only get worse

• Instead, instituting a national consumption tax whose proceeds are rebated to the states on a per capita basis could simplify the entire process and help poorer people simply by exempting $15,000 worth of essentials - housing, food, transportation

• After income taxes, say you make $50,000 annually, if you saved $10,000 and subtracted the $15,000 basic allotment, your taxable consumption would be $25,000, at 10%, it would be $2,500 you end up paying in consumption tax

• This progressive tax system would raise the same amount of money as the current patchwork of complex state and local taxes

• The rich would pay more, and education since it is considered a public virtue in the information economy, would be exempted

• While we're at it, we might as well move the same direction with the income tax code, eliminating most of the possible deductions from the income tax code that disproportionately benefit the well-to-do and salvage just middle class necessities

• Furthermore, corporate taxes should be eliminated in order to not encourage companies to look for overseas tax-shelters to move their headquarters and to not to force states to compete amongst themselves to offer the best tax breaks. Instead of corporate taxes, the burden should be shifted to the wealthy individuals themselves and their passive, high-profit assets

Education Finance Reform :

• Schools are still financed the same way as they were in the agricultural era – through local property taxes and state sales tax. This means that schools in districts with lower valued properties overall have less money to work with – the same is true of inner city schools which additionally often have lots of government-owned tax-exempt properties in their vicinity.

• We hear a lot of debate about federal initiatives to reform our struggling K-12 schools in this countries (top notch politicians bank on this), but to a large extent this is totally disingenuous because of the tiny role the federal government actually plays in bringing about greater financial parity between vastly unequally funded schools (about 7% of school funding is federal)

• To get serious about this problem, it seems we must talk about ways to equalize per capita student funding brought about on a national basis – not at a state level – Mississippi spends $4,000 per student while New Jersey spends $10,000, even after adjusting for standard of living disparities are controlled for – not at a county level – disparities are sometimes even larger

• These differences translate into lower teacher salary (lower quality instructors), larger class sizes, and inferior facilities

• Some state supreme courts like California and Vermont have stated that this funding system violates the equal protection clause, “The distribution of a resource as precious as educational opportunity should not have as its determining force the mere fortuity of a child's residence.” Almost all states have been sued on this basis and this has led to some picking up more of the funding ticket than the local school districts themselves, but has not fully addressed the issue by any means.

• Worse still, it is often that affluent home owners or older residents without children refuse to increase property taxes

• How can we apply national standards to education or assessing all students on standardized tests with these gross disparities?

• Proceeds from a national consumption tax should be allotted to states on a per pupil basis, adjusting for different cost of living

Our Greatest National Challenges:

• Spatial and geographic divides based on race, class, and age

• We have become increasingly segregated in each of these respects

• The cultural and political difference between these groups have become wider as well

• It seems that these different groups have increasingly oppositional agendas and identities

• A successful vision for improving the nation must address how to bring these social factions together

• Finally, watch out for the capacity of expanded technological power to change our society further; namely genetics


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Template:Bartending:region

 Field Research

This entry is based on the input of several bartenders from the  region Region

title: Template:Bartending:region


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User talk:Telamon~enwikibooks/Japanese

Thanks for the info. Gmcfoley 22:45, 31 October 2005 (UTC)

title: User talk:Telamon~enwikibooks/Japanese


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Blender 3D: Noob to Pro/Advanced Tutorials/Advanced Animation/Guided tour/index

Here I'll show you all the stuff you need to know about the interface when animating. Where is it? How does it work? Why use it?

We are going to talk about:
 * Armature Object
 * Mesh Object
 * Constraints
 * Timeline Window
 * IPO Window
 * Action Window
 * NLA Window


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Talk:LaTeX/Mathematics

Various talk
Instead of images to illustrate math you can use some wikitex. It is not perfect, but is good enough for an illustration. If somebody wants to revert they are free to do so.Juliusross 23:43, 31 October 2005 (UTC)

 * wikitex looks better (the primary reason for using latex) than .png's but if .png must be used, make sure that final size and the original size are the same. MPR

Any good introduction to latex will tell you *not* to use $$...$$ for displayed maths

 * why do you say this? Juliusross 12:42, 30 November 2005 (UTC)

 * according to this website the reason is that if an error was to occur while using the $ sign, it would give an incomprehensible message. (TKelly 23:22, 6 March 2006 (UTC))

 * and many people recommend not to use $$...$$ because it interferes with other functions. See for example.

Refering to subequations
Could someone write in the subequations section of the article how it is possible to refer to subequations, please? 128.214.205.5 (talk) 10:36, 20 March 2008 (UTC)
 * Check out LaTeX/Labels and Cross-referencing, where it describes this and shows examples. It doesn't show examples specifically to subequations, but the rules don't change. Using the existing example:

 * +[[User:Mwtoews|mt] ] 00:55, 24 March 2008 (UTC)

Math Symbol Index
An index or table(s) of math symbols such as would be a nice addition.
 * I tend to use w:Help:Displaying a formula for this. Perhaps it should be forked and included here. +mt  01:03, 24 February 2008 (UTC)

describing ams-math
Is it really a good idea to describe ams-math on it's own in a separate section or would it be more appropriate to describe the relevant features as the text goes along? I've added the multiline stuff about ams to the multiline equation environments already (not so much as an example but because I didn't notice the ams-math specific section). As a reference guide, were I to want to remember what I should use for multiline equations, I would look under multiline equations and not think of the ams-math section at first. This could push me to quickly get the wrong result. Thoughts? Basenga 05:59, 29 June 2006 (UTC)

AMS-math section
After teaching how LaTeX works, I think we should give some good guidelines about using it properly. As an example, I don't think there is any point in using {math} and {displaymath} environments if you are using the amsmath package, since you should use the {equation*}, it is more consistent with any other way of displaying math you should use. It wouldn't make sense to say "{displaymath} exists but don't use it", so I suggest: we could write a "Basic Mathematics" page teaching all that LaTeX can do without amsmath, then we make another page titled "Advanced Mathematics" teaching how to use all the features of amsmath and saying all the commands that is better to use when writing a document with a lot of Maths. I'm referring to \begin{equation*} instead of \begin{displaymath}, or \text{...} instead of \mbox{...}, etc. What do you think about it?? Alejo2083 19:19, 22 September 2006 (UTC)

Removed TODO points

 * introduce eqnarray from ?

all the environments discussed to insert formulas are enough, I think I have considered any possible situation. eqnarray is redundant if you use flalign and all the other environments.

 * show how to create large matrix from and

AMS matrix environments are enough, there is no difference between big or small matrix, LaTeX takes care of it. Andy Roberts used the array anvironment, but it is pointless if you can use the ones of AMS.

I agree about inserting the Mathematical symbols (the only point left in the TODO list), but we'd better add them in a different page, this one is long enough. Alessio Damato 18:13, 19 January 2007 (UTC)

 * By "large" matrix I ment a matrix with dots meaning omitted columns/rows. It's not obvious how to make these dots and you use them very often. --Derbeth talk 19:35, 19 January 2007 (UTC)

 * ah, you meant that. Well, there isn't any particular formatting for it, you just have to use the right symbols in the right places (such as \cdots). Anyway, if it's not clear from the context, I will add an example as soon as I have some time. Alessio Damato 13:40, 21 January 2007 (UTC)

 * The point is that \vdots (I don't remember exact code) hasn't been introduced in this tutorial). --Derbeth talk 13:51, 21 January 2007 (UTC)

 * I added something about it. It is already better than the original version by Andy Roberts, but I can think I can add few things more. Any suggestion is welcome :-) Alessio Damato 14:09, 22 January 2007 (UTC)

properly scaled integral
I don't know if this is an issue in the latex wikipedia uses, but regular latex on Linux doesn't scale the \int symbol to fit the equation it refers to. If anyone knows how to do this, please add it to the article. Thanks. --64.81.59.211 (talk) 22:05, 6 December 2007 (UTC)

 * it's not meant to. Moreover, \int is just a symbol with no argument, so it doesn't refer to anything and couldn't be scaled according to anything. I know that other programs do scale the integral symbol to fit the argument, but it's not such a good idea: if you write several formulae, the scaled integral would look different on each formula, that's definitely not elegant. If LaTeX does it by default, it might be the best choice (otherwise it would have been implemented differently). If you want to scale the integral, you can use modifiers such as \big and \huge to do it by hand. Alessio Damato (talk) 10:39, 9 December 2007 (UTC)

 * The \big and \huge commands don't work on a \int sign. If you want to force an \int to take on it's normally larger size (for example whilst in-line or within an array in an equation) then place \displaystyle before the \int

 * You can use, e.g., \mathlarger{\int}, which would make the symbol larger than its usual size.

set symbols
Just letting whoever edits this page, the \mathbb didn't work here without amssymb loaded

but still, thanks for the great docs :) --75.34.28.161 (talk) 02:32, 25 January 2008 (UTC)

 * I'll point it out in the document, thanks Alessio Damato (talk) 16:32, 26 January 2008 (UTC)

Negative space
While I'm pretty sure that negative space is there to do something, the example concerning binomial is a bit overstretched. There is a "\binom" macro. Are there not a proper example for negative space? --213.229.135.66 (talk) 15:06, 10 March 2008 (UTC) \pmod, try it and see for yourself 94.208.111.0 (talk) 20:07, 30 October 2008 (UTC)

Position of the Mathematical Symbols
Should the symbols be included in the text chapter or as an appendix? --ElectroKid (talk) 16:27, 11 April 2008 (UTC)

align or flalign
Other webpages suggest using align for multiline math. What exactly is the difference between flalign and align? The documentation doesn't say, but my testing seems to indicate that flaalign forces multicolumn displays (i.e. where more than two & symbols are used per line) to be the far-left and far-right of the screen. Is that correct? If so, I think it would be more appropriate to use align as the recommended environment.-3mta3 (talk) 16:47, 18 April 2008 (UTC)

Also, I think the extended detail should be moved to a subpage. It is rather repetitive at the moment -3mta3 (talk) 17:38, 18 April 2008 (UTC)

I think there is a typo in the flalign examples in the sections with names that start with "Several formulas, any alignment". They read like this: foo = bar = = baz = = quux

But, shouldn't the equal sign either come at the end of the line or start of the next line instead of both?

mathit
We should mention   somewhere.

Split page
This page is becoming unwieldy, and I have created a new page called LaTeX/Advanced Mathematics, and started to move some of the content over there. Any ideas on what should be kept on each page? -3mta3 (talk) 15:56, 9 November 2008 (UTC)

Array Example
The begin array {l l} looks a lot like {1 1}. Can this be fixed somehow? —Preceding unsigned comment added by 66.167.250.209 (discuss • contribs) 00:53, 1 March 2009

 * It looks all right in my browser (Opera on Linux). Probably just a question of fonts. You can always be bold and add or reference a note on alignment options. --Swift (talk) 04:13, 1 March 2009 (UTC)

Partial derivative symbol
I think   should be included on this page.

Discussion of integrals is problematic
The d before the integration variable is usually (most physics texts) italicized like the rest of the equation. One could use units (e.g. km) to illustrate the usage of \mathrm... Boeremoer (talk) 20:04, 23 November 2009 (UTC)

Indeed---my math texts also use normal math-mode text. --Lucasreddinger (talk) 07:04, 8 December 2009 (UTC)

Agreed. Although I know of some publications that do the \mathrm{d}, the 'house style' of the mathematics research journal that I am an editor for (and, for example, the American Math Soc journals) do not do this.

Extend closing root
The closing root does not work correctly when specifying a magnitude. While this is explained in the text, the following code allows the magnitude to be specified and displayed correctly:

This is a slightly refined version of the code presented in the roots section and adds a small space after the closing tick, which helps especially when there is a closing parenthesis touching the sqrt. If the community agrees that this version works, then it ought to replace the code currently in the roots section.

\Alpha, \Beta ...
I do believe the greek letters whitch are equal to our characters aren't made in LaTeX. If you want to use the \Alpha command, you get an error, you have to use A. I saw this by translating the page to dutch. --Sanderd17 (talk) 16:01, 18 January 2010 (UTC)

 * This is already mentioned on the page: LaTeX/Mathematics. --Swift (talk) 17:35, 18 January 2010 (UTC)

 * I think he refers to section LaTeX/Mathematics. It confused me as well. It is good that it is mentioned in LaTeX/Mathematics, but should still be corrected in section LaTeX/Mathematics. -- Matthias

 * I agree, this is an important error that should be corrected both in Greek Letters and in the List of Mathematical Symbols. For a reference, see ftp://ftp.di.uminho.pt/pub/ctan/info/symbols/comprehensive/symbols-a4.pdf, page 50.

\mathrm vs. \text
This suggests using \text to put text in equations. But the examples I have seen of actual math in Wikipedia (i.e., when editing the article) use \mathrm. Are these equivalent, or if not, which should be used when? Asmeurer (talk) 04:20, 12 December 2010 (UTC)
 * It's a mess. \mathrm changes the typeface and stays in mathmode and so normally should not be used in order to set text, for example it treats "-" as minus instead of hyphen. \text is the Latex solution, but does not work correctly in mediawiki, as it cannot display umlauts, whereas umlauts can be emulated in mathmode via the \ddot notation. \mbox works with umlauts, but for sure also has issues.
 * \mu\mathrm{-fast\;\ddot uberall} $$\quad\leftrightarrow\quad\mu\mathrm{-fast\;\ddot uberall} $$
 * \mu\mbox{-fast überall} $$\quad\leftrightarrow\quad\mu\mbox{-fast überall}$$
 * \mu\text{-fast ueberall} $$\quad\leftrightarrow\quad\mu\text{-fast ueberall} $$
 * --Erzbischof (talk) 11:16, 5 January 2011 (UTC)

"closed" roots
The trick to make square root signs "close" over their contents (http://en.wikibooks.org/wiki/LaTeX/Mathematics#Roots) _can_ be made to work with multiple roots. See: http://tex.stackexchange.com/questions/29834/closed-square-root-symbol Maybe this can be updated?

\mathrm vs. \textup
Many times I read that "symbol xyz should be typeset upright to make clear it's not an ordinary variable" (e.g., for the differential d), and then the example goes on to use \mathrm. A better approach would be to use \textup which expresses exactly what you want to have, namely upright text. In addition to clarity, the added advantage is that -- unlike \mathrm -- it doesn't change other properties of the font and would work properly in, e.g., sans-serif texts.

Unfortunately, Mediawiki doesn't seem to support \textup now (2012-06-07).

Spacing in simple slanted fractions
I'd suggest adding a negative space after a numenator in a slanted fraction. That would be

versus

The former one seems to me somewhat nicer (even that sfrac/nicefrac). 78.109.185.204 (discuss) 01:46, 28 August 2012 (UTC)

Isn't the equation environment different from equation*?
The article barely mentions the equation environment, which I believe is a Latex environment. Yet the equation* environment is prominent even though it's an amsmath exclusive. The article should clearly distinguish between them. 71.163.58.61 (discuss) 23:16, 28 September 2012 (UTC)

Colors
I added the color section to this, but couldn't add my parts on fixing the spacing around parts of equations, because it looks like Wikibooks doesn't support things like \mathbin. Any ideas on improving this section would be helpful. Ntypanski (discuss • contribs) 23:49, 30 October 2012 (UTC)

Limits example doesn't render as shown here on my MikTeX 2.9
Under LaTeX/Mathematics an example is given for using \lim:

but I get something like

unless I do

I'm happy to correct/update this, but just wanted to check that it's not a quirk of my setup (some unusual package perhaps). The behvaiour is the same with and without the amsmath package, which is the only explicitly maths-related package I call.

Also this post as stackexchange implies that what I need to do is right:

--ChrisHodgesUK (discuss • contribs) 15:25, 8 August 2013 (UTC)

The answer to this might be you are in an inline formula, where the subscript is placed as subscript. To get the maths, are you using \(…\) or $…$, or \[…\] or $$…$$? If you are using one of the first two, see if \displaystyle before \lim has the same effect as \limits after it. If it does, the answer is you are using inline math, which is not displayed, and has no default underscripts but only subscripts. \limits forces the underscript. \displaystyle forces the math to be displayed rather than inline. $$…$$ \[…\] mean displayed math, so see if \lim with neither \limits nor \displaystyle in there gets the expected output. If everything goes as I predicted, your question is answered. Otherwise, try asking it on stack exchange. Btw \limits is obligatory with integrals even in displayed math. MGorrone (discuss • contribs) 14:11, 28 December 2013 (UTC)

\nexists isn't in mathtools anymore
At least on my PC, latex complains that \nexists is an undefined control sequence. --Zilti (discuss • contribs) 17:05, 29 September 2013 (UTC)

\mathscr
The \mathscr command from the mathrsfs package covers only uppercase letters. For lowercase letters, you must define a math font, otherwise the letters will not get typesetted, but just completely vanish from the output pdf. For example, you can add

\usepackage{unicode-math}

\setmathfont{XITS Math}

\setmathfont[version=setB,StylisticSet=1]{XITS Math}

to the preamble. Of course, supposing you have XITS Math installed on you computer. MGorrone (discuss • contribs) 15:00, 28 December 2013 (UTC)

Reference to Text Formatting (\textbf)
Section LaTeX/Mathematics refers to in LaTeX/Text Formatting, which is not explained there (anymore?) --Azaël (discuss • contribs) 19:13, 3 February 2015 (UTC)

Typesetting intervals
As far as I notice there is absolutely no difference between the examples in 'Typesetting intervals'. Is this a wiki issue or did I miss anything?--129.69.61.80 (discuss) 11:27, 3 March 2015 (UTC)
 * Partially confirmed. I downloaded the three images and diff'ed them.    and   are byte-by-byte-identical.    is indeed different, with the comma slightly offset to the right.  I haven't tried with DVI/PDF, but I think we can say this is not important for PNG output.  Anyways, I doubt whether this make a difference for average users.  If we end up deciding to keep it, at least we should move it to Advanced Mathematics section(chapter?).  sheep0x (discuss • contribs) 19:04, 23 February 2016 (UTC)

Typesettings intervals with forthcoming SimpleMathAjax extension or \mathop malfunctionning with Math extension
It seems that the following command

should render as {{LaTeX/Example|code= \mathop{\iiint\limits_{\Pi-\varpi} u(y){\partial a(y) \over \partial y_i}\,\mathrm{d} y_i $$\iiint\limits_{\Pi-\varpi} u(y){\partial a(y) \over \partial y_i}\,\mathrm{d} y_i$$ }} and it doesn't. The mathop operand is not taken into account in current Math extension, but it seems that it will work with the next SimpleMathAjax extension (as far as I have tested it successfully on more updated wiki).--Nbrouard (discuss • contribs) 18:00, 27 April 2016 (UTC)
 * render=

Math coding (Hyperbolic function)
Can someone finish the job and code  ? יהודה שמחה ולדמן (discuss • contribs) 14:41, 9 November 2016 (UTC)

Laplace Operator vs Delta
The symbols for Delta and for the laplace operator both look like a triangle pointing up, but should look different when both are used in the same text. There are some solutions to this problem posted over on stackexchange: https://tex.stackexchange.com/questions/76553/correct-symbol-for-the-laplace-operator-delta

Simultaneous equation symbol {
How can I use a simultaneous equation symbol, {? Ljyfree1004 (discuss • contribs) 12:58, 2 January 2021 (UTC)

Power (superscript) and indices (subscript): always use curly braces with commands?
LaTeX/Mathematics currently says that can be used as an exponent without curly braces:

But even though there are no errors, shouldn't this be strongly discouraged due to potential breakage in the future, just like what has been done with by beamer? See this discussion in the tex-live list. — Vincent Lefèvre (discuss • contribs) 10:46, 18 February 2022 (UTC)

title: Talk:LaTeX/Mathematics


text:
Cookbook:Chicken Alfredo

Chicken alfredo works with all types of pasta and noodles and can be modified for use with a variety of sauces. It is great for family dinners and recommended to serve with garlic bread.

Ingredients

 * 1 pound (450 g) boneless chicken breasts
 * 1 cup cream or half and half
 * 2 tablespoons white flour
 * ¼ cup chopped onion or shallot
 * 1 teaspoon thyme
 * ¼ teaspoon oregano
 * ½ teaspoon garlic powder
 * 1 tablespoon parsley, chopped
 * ½ teaspoon red pepper
 * ½ cup grated Parmesan cheese
 * 1 tablespoon cooking oil
 * ½ cup lemon juice
 * 1 tablespoon butter
 * 2 cups fettuccini pasta

Procedure

 * 1) Heat up oil slightly in a frying pan over a medium flame.
 * 2) Sauté chicken breasts and shallots in hot oil for 5 minutes or until golden brown. Add lemon juice to chicken and cook for an additional 10 minutes. Remove chicken from flame. Reserve juices. Transfer chicken into a casserole dish.
 * 3) Melt butter in clean frying pan. Add flour to butter and stir for about 3 minutes.
 * 4) Slowly add half and half, stirring continuously. Add all spices and seasonings to sauce.
 * 5) Stir in reserved juices and keep stirring. Reduce heat and slowly stir in Parmesan cheese.
 * 6) Keep stirring until a smooth consistency is achieved. Pour sauce over chicken in casserole dish.
 * 7) Cover and bake for 20 minutes at 350°F (175°C).
 * 8) While chicken is cooking, prepare pasta. When chicken is done, serve immediately.

Notes, tips, and variations

 * The thyme and oregano can be replaced by 1 teaspoon zaatar.

title: Cookbook:Chicken Alfredo


text:
Cookbook talk:Chicken Alfredo

Chicken broccoli alfredo authors and history
= From Wikipedia:Talk:Chicken broccoli alfredo =
 * 2005-10-31 23:39:33 User:Wcquidditch m (oops)
 * 2005-10-31 23:39:00 User:Wcquidditch (afd)
 * 2005-10-31 23:32:21 User:143.109.59.20

No broccoli?
There isn't any mention of broccoli as an ingredient in this recipe.

title: Cookbook talk:Chicken Alfredo


text:
Blender 3D: Noob to Pro/Advanced Tutorials/Advanced Animation/Guided tour/Armature/index

The Armature Object in itself is a tool for the animator to move an object or group of vertices in a reliable way. An armature is made of bones, which can be parented to each other, or connected to each other. It was built with the idea of a skeleton in mind. And in fact, in the 3D world with animation inclusive, its considered to be the skeleton.

You can add it using the SPACEKEY in 3Dview and selecting Armature. You'll then enter into Edit Mode where you can add or move bones to build your default rig. An armature has 3 states. You can switch using the dropdown menu in the header of the 3Dview or use the TABKEY to switch between Editmode <-> [Objectmode|Posemode] and CTRL-TABKEY to switch between Objectmode <-->Posemode:
 * Object Mode: Your armature is like any other Object, you can move it around the scene, scale it, rotate it and edit options in the button window.
 * Edit Mode: Your armature is in what we call rest position, you can modify the bones it contains.
 * Pose Mode: Your armature is ready to be animated, each bone can be moved, scaled or rotated, constraints get applied, you can pose your character and animate the bones' behavior over time. Take note that Pose mode is now a state of the armature you can switch on/off using CTRL-TABKEY. So when in Pose, you are still in object mode (you can select another object, contrary to the edit-mode)

Note: The following 3 pages of this tutorial contain screenshots and discuss techniques that are only available in Blender 2.40a and later. Refer to the Blender 2.40a release notes on Armature draw types and Armature envelopes.