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A college degree may not be required, but classical composers generally hold a master's degree. If you have a specific career goal in mind before starting on your educational journey, it will help you select the master's in music program that best fits your budget, location, interests, lifestyle, and timeframe. Music master's programs take two to three years to complete for full-time students.

Your exact graduation timeline and the total cost of your program depends on your status as a student. Working professionals might opt to attend their courses part-time, though part-time students often take longer to finish their degrees, and may end up spending more money than full-time students.

Working professionals may also consider taking online classes, which tend to be cheaper since they don't require expenses for transportation, parking, or housing. In some circumstances, online programs reduce out-of-state tuition fees for students, whereas out-of-state students might otherwise pay twice the tuition of their in-state counterparts.

If your prospective school is out of state but located somewhere with better employment opportunities or a lower cost of living, it might be worthwhile to relocate. Students must weigh the pros and the cons before choosing to attend an out-of-state college. Finally, students should consider their prospective programs' course offerings.

Not every college offers specializations, and some colleges may not be accredited. Make sure to review the curriculum to ensure the offered courses serve your interests. Also confirm that your school and program of choice have been accredited. Read on to learn more about the different types of accreditation. Colleges and their programs must meet certain quality standards to receive accreditation, which lets students know that their institution or specific program has undergone a quality assurance review.

Programmatic accreditation means an independent body reviewed and approved of a specific program or department within a college. Approximately schools have NASM accreditation. This accreditation carries distinction, but it is not mandatory. Graduates from accredited music schools have an advantage on the job market and if they pursue a Ph.

Colleges may obtain either regional or national accreditation. Regional accreditation carries more prestige and is usually administered to four-year colleges, whereas for-profit and vocational schools tend to receive national accreditation. Seven accrediting bodies oversee regional accreditation in the United Highest Degree - Major Herrin - Highest Degree (Vinyl).

Credits from regionally accredited colleges transfer easily to most other institutions, but credits from nationally accredited schools may not. Applications for master's programs require a tremendous amount of time and effort, so students should only apply to programs for which they meet the admission requirements and have the adequate prerequisites.

Students should plan on applying to five to eight graduate schools. Standard admissions procedures apply for both on-campus and online programs, but online programs can be more competitive than on-campus programs, and they often have lower acceptance rates. Every admissions office provides detailed directions on how to apply to its master's in music program. Students can find admissions requirements, including the required supplemental materials, posted on each college's website.

Below, find some of the common prerequisites for music master's degree. Music master's curricula vary between institutions, but most programs have similar structures, with many of the same core course offerings and concentration options.

Most master's music programs take about the same time to complete. The cost of each program varies widely. For more information about the specifics of master's in music programs, read on. No two master's in music programs have identical coursework. Students must research each program's curriculum to see if it suits their career goals. One program may focus on teaching students to become music educators, while another might train them to become composers.

Generally, all core courses in music master's programs include in-depth research, music theory, history, and music criticism. Below you will find a few sample courses, but bear in mind, exact classes vary depending on the college. This class covers the principles of the advanced-level music research methodologies required of all master's students.

Students build on their undergraduate skills and learn to analyze Highest Degree - Major Herrin - Highest Degree (Vinyl) works and gather quantitative and qualitative data. Students typically write and present a final research paper. This course prepares students for academic research music jobs and teaching positions.

Students work in labs to become proficient in music technologies, such as MIDI. The course covers techniques in music recording, editing, mixing, sequencing, and notation. This course prepares students to work as composers and directors in studios, using computer-based technology tools.

This in-depth course overlaps with other disciplines, including sociology, philosophy, and psychology. Students learn complex compositional techniques. Many students become teachers, film and theater composers, or go on to earn a Ph.

The final project may be a research paper or a composition recital. This course explores the historic overview of ethnomusicology. Students learn to critically examine music through a cultural lens, and objectively study the cultural music contributions from across the globe.

Students may have to write a major research paper and possibly do fieldwork. Prospective music teachers will find this class useful in their career. Students study the structural arrangements of selected tonal compositions and analyze those works from an objective standpoint. The class usually requires students to do multiple research papers, including a final paper and presentation analyzing a chosen musical work. This class prepares students for careers in music composition and teaching.

Students should expect to invest two and a half years toward a master's in music program. Many different factors affect the length of your master's program, including required credits. Master's in music programs require students to complete 33 to 50 credits, plus additional credits if the program requires a thesis project.

Working professionals who cannot take a full course load may consider part-time studies, which may take longer and cost more. To complete a degree faster, students may want to look into online programs, which tend to offer more rigorous coursework on an accelerated path.

Some online master's in music degrees take a year and a half to complete. Students may also be able to transfer graduate level college credits earned at another college. Students must also account for the cost of housing, transportation, technology fees, photocopies, books, and other college-related expenses.

Advanced degrees also have additional costs you must consider, such as thesis reading fees. Tuition becomes even more expensive for out-of-state students. If you do not meet residency requirements -- which is typically one year of in-state residency before beginning school -- then you may pay double or more for out-of-state tuition. However, online programs sometimes provide in-state tuition to out-of-state residents.

Moreover, tuition increases for part-time students, since they usually take longer to complete their degrees. Finally, tuition varies between college types. Public four-year colleges almost always cost less than private four-year colleges. You may be able to offset the increased costs of attending a private college or an out-of-state college through scholarships or grants -- which are essentially "free money" that you do not have to pay back.

Founded in by Oscar Sonneck, the Musical Quarterly features academic articles by composers and musicologists. The publication's website features a link to music jobs posted on the Oxford University Press Journals Career Network. JSTOR features more than 2, academic journals, which students and faculty can access online or download for an annual or monthly fee.

The app keeps track of college classes and syncs everything on multiple devices. A grade-tracking feature also lets students track their GPA. The app costs a fee to use. When you cannot make it to the on-campus writing center, use the online grammar checker Grammarly for free.

Grammarly proofreads your writing for grammatical and spelling errors. You can add the Grammarly extension to your web browser, or download the app. Graduate students studying music may join a professional music organization to make connections with like-minded individuals at events and conferences.

Professional music organizations also offer their members access to scholarships, fellowships, and grant opportunities. Many also offer free access to music job boards.

In particular, if a is a polynomial then P a is also a polynomial. More specifically, when a is the indeterminate xthen the image of x by this function is the polynomial P itself substituting x for x does not change anything. In other words. A polynomial is an expression that can be built from constants and symbols called indeterminates or variables by means of additionmultiplication and exponentiation to a non-negative integer power. Two such expressions that may be transformed, one to the other, by applying the usual properties of commutativityassociativity and distributivity of addition and multiplication are considered as defining the same polynomial.

The mapping that associates the result of this substitution to the substituted value is a functioncalled a polynomial function. This can be expressed more concisely by using summation notation :. That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms.

The exponent on an indeterminate in a term is called the degree of that indeterminate in that term; the degree of the term is the sum of the degrees of the indeterminates in that term, and the degree of a polynomial is the largest degree of any one term with nonzero coefficient.

A term with no indeterminates and a polynomial with no indeterminates are called, respectively, a constant term and a constant polynomial. The degree of the zero polynomial, 0, which has no terms at all is generally treated as not defined but see below.

Forming a sum of several terms produces a polynomial. For example, the following is a polynomial:. It consists of three terms: the first is degree two, the second is degree one, and the third is degree zero.

Polynomials of small degree have been given specific names. A polynomial of degree zero is a constant polynomial or simply a constant. Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. For higher degrees the specific names are not commonly used, although quartic polynomial for degree four and quintic polynomial for degree five are sometimes used.

The names for the degrees may be applied to the polynomial or to its terms. The polynomial 0, which may be considered to have no terms at all, is called the zero polynomial.

Unlike other constant polynomials, its degree is not zero. The zero polynomial is also unique in that it is the only polynomial in one indeterminate having an infinite number of roots. In the case of polynomials in more than one indeterminate, a polynomial is called homogeneous of degree n if all its non-zero terms have degree n.

The zero polynomial is homogeneous, and, as homogeneous polynomial, its degree is undefined. For more details, see homogeneous polynomial. The commutative law of addition can be used to rearrange terms into any preferred order. In polynomials with one indeterminate, the terms are usually ordered according to degree, either in "descending powers of x ", with the term of largest degree first, or in "ascending powers of x ". The polynomial in the example above is written in descending powers of x.

The first term has coefficient 3indeterminate xand exponent 2. The third term is a constant. Because the degree of a non-zero polynomial is the largest degree of any one term, this polynomial has degree two.

Two terms with the same indeterminates raised to the same powers are called "similar terms" or "like terms", and they can be combined, using the distributive lawinto a single term whose coefficient is the sum of the coefficients of the terms that were combined.

It may happen that this makes the coefficient 0. The term "quadrinomial" is occasionally used for a four-term polynomial. A real polynomial is a polynomial with real coefficients. When it is used to define a functionthe domain is not so restricted.

However, a real polynomial function is a function from the reals to the reals that is defined by a real polynomial. Similarly, an integer polynomial is a polynomial with integer coefficients, and a complex polynomial is a polynomial with complex coefficients. A polynomial in one indeterminate is called a univariate polynomiala polynomial in more than one indeterminate is called a multivariate polynomial.

A polynomial with two indeterminates is called a bivariate polynomial. These notions refer more to the kind of polynomials one is generally working with than to individual polynomials; for instance when working with univariate polynomials one does not exclude constant polynomials which may result, for instance, from the subtraction of non-constant polynomialsalthough strictly speaking constant polynomials do not contain any indeterminates at all.

It is possible to further classify multivariate polynomials as bivariatetrivariateand so on, according to the maximum number of indeterminates allowed. Again, so that the set of objects under consideration be closed under subtraction, a study of trivariate polynomials usually allows bivariate polynomials, and so on.

It is common, also, to say simply "polynomials in xyand z ", listing the indeterminates allowed. The evaluation of a polynomial consists of substituting a numerical value to each indeterminate and carrying out the indicated multiplications and additions. For polynomials in one indeterminate, the evaluation is usually more efficient lower number of arithmetic operations to perform using Horner's method :. Polynomials can be added using the associative law of addition grouping all their terms together into a single sumpossibly followed by reordering, and combining of like terms.

To work out the product of two polynomials into a sum Highest Degree - Major Herrin - Highest Degree (Vinyl) terms, the distributive law is repeatedly applied, which results in each term of one polynomial being multiplied by every term of the other.

This is more efficient than the usual algorithm of division when the quotient is not needed. As for the integers, two kinds of divisions are considered for the polynomials. The Euclidean division of polynomials generalizes the Euclidean division of the integers. By hand as well as with a computer, this division can be computed by the polynomial long division algorithm.

All polynomials with coefficients in a unique factorization domain for example, the integers or a field also have a factored form in which the polynomial is written as a product of irreducible polynomials and a constant. This factored form is unique up to the order of the factors and their multiplication by an invertible constant. In the case of the field of complex numbersthe irreducible factors are linear. Over the real numbersthey have the degree either one or two.

Over the integers and the rational numbers the irreducible factors may have any degree. The computation of the factored form, called factorization is, in general, too difficult to be done by hand-written computation. However, efficient polynomial factorization algorithms are available in most computer algebra systems.

A formal quotient of polynomials, that is, an algebraic fraction wherein the numerator and denominator are polynomials, is called a " rational expression " or "rational fraction" and is not, in general, a polynomial. Division of a polynomial by a number, however, yields another polynomial. Because subtraction can be replaced by addition of the opposite quantity, and because positive integer exponents can be replaced by repeated multiplication, all polynomials can be constructed from constants and indeterminates using only addition and multiplication.

A polynomial function is a function that can be defined by evaluating a polynomial. More precisely, a function f of one argument from a given domain is a polynomial function if there exists a polynomial. Generally, unless otherwise specified, polynomial functions have complex coefficients, arguments, and values. In particular, a polynomial, restricted to have real coefficients, defines a function from the complex numbers to the complex numbers. If the domain of this function is also restricted to the reals, the resulting function maps reals to reals.

Polynomial functions of several variables are similarly defined, using polynomials in more than one indeterminate, as in. According to the definition of polynomial functions, there may be expressions that obviously are not polynomials but nevertheless define polynomial functions.

Every polynomial function is continuoussmoothand entire. A polynomial function in one real variable can be represented by a graph. A non-constant polynomial function tends to infinity when the variable increases indefinitely in absolute value. If the degree is higher than one, the graph does not have any asymptote. It has two parabolic branches with vertical direction one branch for positive x and one for negative x.

Polynomial graphs are analyzed in calculus using intercepts, slopes, concavity, and end behavior. A polynomial equationalso called an algebraic equationis an equation of the form [14]. When considering equations, the indeterminates variables of polynomials are also called unknownsand the solutions are the possible values of the unknowns for which the equality is true in general more than one solution may exist.

In elementary algebramethods such as Highest Degree - Major Herrin - Highest Degree (Vinyl) quadratic formula are taught for solving all first degree and second degree polynomial equations in one variable. There are also formulas for the cubic and quartic equations, Highest Degree - Major Herrin - Highest Degree (Vinyl). For higher degrees, the Abel—Ruffini theorem asserts that there can not exist a general formula in radicals. However, root-finding algorithms may be used to find numerical approximations of the roots of a polynomial expression of any degree.

The number of solutions of a polynomial equation with real coefficients may not exceed the degree, and equals the degree when the complex solutions are counted with their multiplicity. This fact is called the fundamental theorem of algebra.

The solutions of this equation are called the roots of the polynomial, or the zeros of the associated function they correspond to the points where the graph of the function meets the x -axis. When P is the zero polynomial, the corresponding polynomial equation is trivial, and this case is usually excluded when considering roots, as, with the above definitions, every number is a root of the zero polynomial, with an undefined multiplicity.

With this exception made, the number of roots of Peven counted with their respective multiplicities, cannot exceed the degree of P. If, however, the set of accepted solutions is expanded to the complex numbersevery non-constant polynomial has at least one root; this is the fundamental theorem of algebra. There may be several meanings of "solving an equation". For quadratic equationsthe quadratic formula provides such expressions of the solutions.

Since the 16th century, similar formulas using cube roots in addition to square rootsbut much more complicated are known for equations of degree three and four see cubic equation and quartic equation.

But formulas for degree 5 and higher eluded researchers for several centuries. InNiels Henrik Abel proved the striking result that there are equations of degree 5 whose solutions cannot be expressed by a finite formula, involving only arithmetic operations and radicals see Abel—Ruffini theorem.

This result marked the start of Galois theory and group theorytwo important branches of modern algebra. Galois himself noted that the computations implied by his method were impracticable.

Nevertheless, formulas for solvable equations of degrees 5 and 6 have been published see quintic function and sextic equation. When there is no algebraic expression for the roots, and when such an algebraic expression exists but is too complicated to be useful, the unique way of solving is to compute numerical approximations of the solutions.

The most efficient algorithms allow solving easily on a computer polynomial equations of degree higher than 1, see Root-finding algorithm. For polynomials in more than one indeterminate, the combinations of values for the variables for which the polynomial function takes the value zero are generally called zeros instead of "roots". The study of the sets of zeros of polynomials is the object of algebraic geometry.

For a set of polynomial equations in several unknowns, there are algorithms to decide whether they have a finite number of complex solutions, and, if this number is finite, for computing the solutions. See System of polynomial equations. The special case where all the polynomials are of degree one is called a system of linear equationsfor which another range of different solution methods exist, including the classical Gaussian elimination.

A polynomial equation for which one is interested only in the solutions which are integers is called a Diophantine equation. Solving Diophantine equations is generally a very hard task.

It has been proved that there cannot be any general algorithm for solving them, and even for deciding whether the set of solutions is empty see Hilbert's tenth problem. Some of the most famous problems that have been solved during the fifty last years are related to Diophantine equations, such as Fermat's Last Theorem. There are several generalizations of the concept of polynomials. A trigonometric polynomial is a finite linear combination of functions sin nx and cos nx with n taking on the values of one or more natural numbers.

If sin nx and cos nx are expanded in terms of sin x and cos xa trigonometric polynomial becomes a polynomial in the two variables sin x and cos x using List of trigonometric identities Multiple-angle formulae. Conversely, every polynomial in sin x and cos x may be converted, with Product-to-sum identitiesinto a linear combination of functions sin nx and cos nx.

This equivalence explains why linear combinations are called polynomials. For complex coefficientsthere is no difference between such a function and a finite Fourier series. Trigonometric polynomials are widely used, for example in trigonometric interpolation applied to the interpolation of periodic functions. They are used also in the discrete Fourier transform. A matrix polynomial is a polynomial with square matrices as variables.

A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question. A matrix polynomial identity is a matrix polynomial equation which holds for all matrices A in a specified matrix ring M n R. Laurent polynomials are like polynomials, but allow negative powers of the variable s to occur. A rational fraction is the quotient algebraic fraction of two polynomials. Any algebraic expression that can be rewritten as a rational fraction is a rational function.

While polynomial functions are defined for all values of the variables, a rational function is defined only for the values of the variables for which the denominator is not zero. The rational fractions include the Laurent polynomials, but do not limit denominators to powers of an indeterminate.

Formal power series are like polynomials, but allow infinitely many non-zero terms to occur, so that they do not have finite degree. Unlike polynomials they cannot in general be explicitly and fully written down just like irrational numbers cannotbut the rules for manipulating their terms are the same as for polynomials.

Non-formal power series also generalize polynomials, but the multiplication of two power series may not converge. The simple structure of polynomial functions makes them quite useful in analyzing general functions using polynomial approximations.

An important example in calculus is Taylor's theoremwhich roughly states that every differentiable function locally looks like a polynomial function, and the Stone—Weierstrass theoremwhich states that every continuous function defined on a compact interval of the real axis can be approximated on the whole interval as closely as desired by a polynomial function.

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