Philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.
Unconditional convergenceIn mathematics, specifically functional analysis, a series is unconditionally convergent if all reorderings of the series converge to the same value. In contrast, a series is conditionally convergent if it converges but different orderings do not all converge to that same value. Unconditional convergence is equivalent to absolute convergence in finite-dimensional vector spaces, but is a weaker property in infinite dimensions. Let be a topological vector space.
Function of several real variablesIn mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. This concept extends the idea of a function of a real variable to several variables. The "input" variables take real values, while the "output", also called the "value of the function", may be real or complex.
Nonstandard analysisThe history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using epsilon–delta procedures rather than infinitesimals. Nonstandard analysis instead reformulates the calculus using a logically rigorous notion of infinitesimal numbers. Nonstandard analysis originated in the early 1960s by the mathematician Abraham Robinson.
Function of a real variableIn mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subset of that contains an interval of positive length. Most real functions that are considered and studied are differentiable in some interval. The most widely considered such functions are the real functions, which are the real-valued functions of a real variable, that is, the functions of a real variable whose codomain is the set of real numbers.
Constructive proofIn mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object. This is in contrast to a non-constructive proof (also known as an existence proof or pure existence theorem), which proves the existence of a particular kind of object without providing an example. For avoiding confusion with the stronger concept that follows, such a constructive proof is sometimes called an effective proof.
Proof by exhaustionProof by exhaustion, also known as proof by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases, and where each type of case is checked to see if the proposition in question holds. This is a method of direct proof. A proof by exhaustion typically contains two stages: A proof that the set of cases is exhaustive; i.e.
Compact discThe compact disc (CD) is a digital optical disc data storage format that was co-developed by Philips and Sony to store and play digital audio recordings. In August 1982, the first compact disc was manufactured. It was then released in October 1982 in Japan and branded as Digital Audio Compact Disc. It was released on March 2, 1983 in North America and Europe. The format was later adapted (as CD-ROM) for general-purpose data storage.
MarchMarch is the third month of the year in both the Julian and Gregorian calendars. It is the second of seven months to have a length of 31 days. In the Northern Hemisphere, the meteorological beginning of spring occurs on the first day of March. The March equinox on the 20 or 21 marks the astronomical beginning of spring in the Northern Hemisphere and the beginning of autumn in the Southern Hemisphere, where September is the seasonal equivalent of the Northern Hemisphere's March.
MarsMars is the fourth planet and the furthest terrestrial planet from the Sun. The reddish color of its surface is due to finely grained iron(III) oxide dust in the soil, giving it the nickname "the Red Planet". Mars's radius is second smallest among the planets in the Solar System at . The Martian dichotomy is visible on the surface: on average, the terrain on Mars's northern hemisphere is flatter and lower than its southern hemisphere. Mars has a thin atmosphere made primarily of carbon dioxide and two irregularly shaped natural satellites: Phobos and Deimos.
Mars roverA Mars rover is a motor vehicle designed to travel on the surface of Mars. Rovers have several advantages over stationary landers: they examine more territory, they can be directed to interesting features, they can place themselves in sunny positions to weather winter months, and they can advance the knowledge of how to perform very remote robotic vehicle control. They serve a different purpose than orbital spacecraft like Mars Reconnaissance Orbiter. A more recent development is the Mars helicopter.
Trigonometric functionsIn mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
