Windows 10Windows 10 is a major release of Microsoft's Windows NT operating system. It is the direct successor to Windows 8.1, which was released nearly two years earlier. It was released to manufacturing on July 15, 2015, and later to retail on July 29, 2015. Windows 10 was made available for download via MSDN and TechNet, as a free upgrade for retail copies of Windows 8 and Windows 8.1 users via the Windows Store, and to Windows 7 users via Windows Update.
Windows 10 editionsWindows 10 has several editions, all with varying feature sets, use cases, or intended devices. Certain editions are distributed only on devices directly from an original equipment manufacturer (OEM), while editions such as Enterprise and Education are only available through volume licensing channels. Microsoft also makes editions of Windows 10 available to device manufacturers for use on specific classes of devices, including IoT devices and previously marketed Windows 10 Mobile for smartphones.
Windows 10 MobileWindows 10 Mobile is a discontinued mobile operating system developed by Microsoft. First released in 2015, it is a successor to Windows Phone 8.1, but was marketed by Microsoft as being an edition of its PC operating system Windows 10. Windows 10 Mobile aimed to provide greater consistency with its counterpart for PCs, including more extensive synchronization of content, Universal Windows Platform apps, as well as the capability, on supported hardware, to connect devices to an external display and use a desktop interface with mouse and keyboard input support (reminiscent of Windows on PCs).
Algebraic number fieldIn mathematics, an algebraic number field (or simply number field) is an extension field of the field of rational numbers such that the field extension has finite degree (and hence is an algebraic field extension). Thus is a field that contains and has finite dimension when considered as a vector space over . The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
Microsoft OfficeMicrosoft Office, or simply Office, is a discontinued family of client software, server software, and services developed by Microsoft. It was first announced by Bill Gates on August 1, 1988, at COMDEX in Las Vegas. Initially a marketing term for an office suite (bundled set of productivity applications), the first version of Office contained Microsoft Word, Microsoft Excel, and Microsoft PowerPoint. Over the years, Office applications have grown substantially closer with shared features such as a common spell checker, Object Linking and Embedding data integration and Visual Basic for Applications scripting language.
OneDriveMicrosoft OneDrive (formerly SkyDrive) is a operated by Microsoft. First launched in August 2007, it enables registered users to share and synchronize their files. OneDrive also works as the storage backend of the web version of Microsoft Office. OneDrive offers 5 GB of storage space free of charge, with 100 GB, 1 TB, and 6 TB storage options available either separately or with Microsoft 365 subscriptions. The OneDrive client app adds and cloud backup features to its device.
Microsoft WindowsMicrosoft Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for servers, and Windows IoT for embedded systems. Defunct Windows families include Windows 9x, Windows Mobile, and Windows Phone. The first version of Windows was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs).
Windows 11Windows 11 is the latest major release of Microsoft's Windows NT operating system, released on October 5, 2021. It was a free upgrade to its predecessor, Windows 10 (2015), and is available for any Windows 10 devices that meet the new Windows 11 system requirements, but can also be installed on unsupported devices by bypassing the restrictions of system requirements.
Algebraic extensionIn mathematics, an algebraic extension is a field extension L/K such that every element of the larger field L is algebraic over the smaller field K; that is, every element of L is a root of a non-zero polynomial with coefficients in K. A field extension that is not algebraic, is said to be transcendental, and must contain transcendental elements, that is, elements that are not algebraic. The algebraic extensions of the field of the rational numbers are called algebraic number fields and are the main objects of study of algebraic number theory.
Microsoft Office 2007Microsoft Office 2007 (codenamed Office 12) is an office suite for Windows, developed and published by Microsoft. It was officially revealed on March 9, 2006 and was the 12th version of Microsoft Office. It was released to manufacturing on November 3, 2006; it was subsequently made available to volume license customers on November 30, 2006, and later to retail on January 30, 2007, shortly after the completion of Windows Vista. The ninth major release of Office for Windows, Office 2007 was preceded by Office 2003 and succeeded by Office 2010.
Microsoft Office 2010Microsoft Office 2010 (codenamed Office 14) is a version of Microsoft Office for Microsoft Windows unveiled by Microsoft on May 15, 2009, and released to manufacturing on April 15, 2010, with general availability on June 15, 2010, as the successor to Office 2007 and the predecessor to Office 2013. The macOS equivalent, Microsoft Office 2011 for Mac was released on October 26, 2010. Office 2010 introduces user interface enhancements including a Backstage view that consolidates document management tasks into a single location.
IsomorphismIn mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape". The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects).
Transcendental extensionIn mathematics, a transcendental extension is a field extension such that there exists an element in the field that is transcendental over the field ; that is, an element that is not a root of any univariate polynomial with coefficients in . In other words, a transcendental extension is a field extension that is not algebraic. For example, are both transcendental extensions of A transcendence basis of a field extension (or a transcendence basis of over ) is a maximal algebraically independent subset of over Transcendence bases share many properties with bases of vector spaces.
Algebraic numberAn algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x^2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number is algebraic because it is a root of x^4 + 4. All integers and rational numbers are algebraic, as are all roots of integers.
Start menuThe Start menu is a graphical user interface element that has been part of Microsoft Windows since Windows 95, providing a means of opening programs and performing other functions in the Windows shell. The Start menu, and the Taskbar on which it appears, were created and named in 1993 by Daniel Oran, a program manager at Microsoft who had previously collaborated on Great ape language research with the behavioral psychologist B.F. Skinner at Harvard. The Start menu was renamed Start screen in Windows 8, before returning to its original name with Windows 10.
Irrational numberIn mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers. When the ratio of lengths of two line segments is an irrational number, the line segments are also described as being incommensurable, meaning that they share no "measure" in common, that is, there is no length ("the measure"), no matter how short, that could be used to express the lengths of both of the two given segments as integer multiples of itself.
Function field of an algebraic varietyIn algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex algebraic geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions. In complex algebraic geometry the objects of study are complex analytic varieties, on which we have a local notion of complex analysis, through which we may define meromorphic functions.
Isomorphism theoremsIn mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and various other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences.
Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
Quadratic irrational numberIn mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers. Since fractions in the coefficients of a quadratic equation can be cleared by multiplying both sides by their least common denominator, a quadratic irrational is an irrational root of some quadratic equation with integer coefficients.
