
Popular Mobile Development Platforms
Gone are those days where mobile phones acted just as a communication device used to talk and write short messages. Smartphones are entering the enterprise through the back door. This is nothing new. Plenty of technologies (laptops, WiFi, thumb drives) first caught on in consumer markets and then sneaked their way into the enterprise. Mobile phones are more than complete communication and entertainment device. Therefore, mobile development has become one of the most competitive territories for the developers. Around the world, mobile developers use mobile platforms for the development of some amazing apps. Some of these platforms are exclusively limited to the firms, which produce products while others are available for thirdparty usage. There are offshore development centers around the world, which are using these platforms for the development and running of amazing applications, which run on these platforms. You can outsource custom development projects to such centers. Popular Development Platforms Symbian OS  Holding one of the largest shares in the market, Symbian OS is one of the favorites among mobile developers. It is an open source operating system (OS) and development platform designed for smartphones and maintained by Nokia. The Symbian kernel (EKA2) supports sufficiently fast realtime response to build a singlecore phone around it. Google Android – Mobile development was revolutionized ever since the launch of Android, which is based upon a modified version of the Linux kernel. This userfriendly platform's software stack consists of Java applications running on a Javabased, objectoriented application framework on top of Java core libraries. Android started as an OS from a small startup company and was later acquired by Google. Apple iOS – The igeneration's development platform, iOS is used by mobile developers to create applications for the iPhones, iPads and Apple TV. It is exclusively used for iPhone development, as Apple does not license its iOS for installation on thirdparty hardware. This platform is derived from Mac OS X and is therefore a Unixlike operating system by nature. BlackBerry OS – This is a proprietary development platform developed by Research In Motion for its BlackBerry devices. RIM allows thirdparty developers to write software using the available BlackBerry API (application programming interface) classes. There are more than 15,000 downloadable applications, which are developed using this platform. Windows Phone – This is the latest offering from the big daddy of computing Microsoft. This is the successor to the successful Windows Mobile, which was used for development purpose for many years. It is a closed proprietary mobile development platform. A new design language Metro allows mobile developers to integrate the operating system with third party and other Microsoft services. webOS– This is one of the oldest mobile development platforms in the world. webOS proprietary mobile operating system running on the Linux kernel and was owned by Palm before being taken over by HP. The platform allows the development of third party applications. These applications have to be certified by HP. Applications for it is written in JavaScript, HTML as well as C and C++.
Ñïåö³àëüí³ñòü: Ìàòåìàòèêà ( çà íàïðÿìàìè)
Analytic Geometry Analytic geometry or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning. In classical mathematics, analytic geometry, also known as coordinate geometry, or Cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis. This contrasts with the synthetic approach of Euclidean geometry, which treats certain geometric notions as primitive, and uses deductive reasoning based on axioms and theorems to derive truth. Analytic geometry is widely used in physics and engineering, and is the foundation of most modern fields of geometry, including algebraic, differential, discrete, and computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions of measurement. Geometrically, one studies the Euclidean plane (2 dimensions) and Euclidean space (3 dimensions). As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way and extracting numerical information from that representation. The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom. In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates. The most common coordinate system to use is the Cartesian coordinate system, where each point has an xcoordinate representing its horizontal position, and a ycoordinate representing its vertical position. These are typically written as an ordered pair (x, y). This system can also be used for threedimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates (x, y, z). Other coordinate systems are possible. On the plane the most common alternative is polar coordinates, where every point is represented by its radius r from the origin and its angle θ. In three dimensions, common alternative coordinate systems include cylindrical coordinates and spherical coordinates. In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation. For example, the equation y = x corresponds to the set of all the points on the plane whose xcoordinate and ycoordinate are equal. These points form a line, and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures. Usually, a single equation corresponds to a curve on the plane. This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x^{2} + y^{2} = 0 specifies only the single point (0, 0). In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces, or as a system of parametric equations. The equation x^{2} + y^{2} = r^{2} is the equation for any circle with a radius of r.
Counting To count a group of objects means to assign a natural number to each one of the objects, as if it were a label for that object, such that a natural number is never assigned to an object unless its predecessor was already assigned to another object, with the exception that zero is not assigned to any object: the smallest natural number to be assigned is one, and the largest natural number assigned depends on the size of the group. It is called the count and it is equal to the number of objects in that group. The process of counting a group is the following: Step 1: Let "the count" be equal to zero. "The count" is a variable quantity, which though beginning with a value of zero, will soon have its value changed several times. Step 2: Find at least one object in the group which has not been labelled with a natural number. If no such object can be found (if they have all been labelled) then the counting is finished. Otherwise choose one of the unlabelled objects. Step 3: Increase the count by one. That is, replace the value of the count by its successor. Step 4: Assign the new value of the count, as a label, to the unlabelled object chosen in Step 2. Step 5: Go back to Step 2. When the counting is finished, the last value of the count will be the final count. This count is equal to the number of objects in the group. Often, when counting objects, one does not keep track of what numerical label corresponds to which object: one only keeps track of the subgroup of objects which have already been labelled, so as to be able to identify unlabelled objects necessary for Step 2. However, if one is counting persons, then one can ask the persons who are being counted to each keep track of the number which the person's self has been assigned. After the count has finished it is possible to ask the group of persons to file up in a line, in order of increasing numerical label. What the persons would do during the process of lining up would be something like this: each pair of persons who are unsure of their positions in the line ask each other what their numbers are: the person whose number is smaller should stand on the left side and the one with the larger number on the right side of the other person. Thus, pairs of persons compare their numbers and their positions, and commute their positions as necessary, and through repetition of such conditional commutations they become ordered.
Elementary arithmetic Elementary arithmetic is the simplified portion of arithmetic , which is considered necessary and appropriate during primary education. It includes the operations of addition, subtraction, multiplication, and division. It is taught in elementary school. Elementary arithmetic starts with the natural numbers and the written symbols (digits) which represent them. The process for combining a pair of these numbers with the four basic operations usually relies on memorized results for small values of numbers, including the contents of a multiplication table to assist with multiplication and division. Elementary arithmetic also includes fractions and negative numbers, which can be represented on a number line. The abacus is an early mechanical device for performing elementary arithmetic, which is still used in many parts of Asia. Modern calculating tools, which perform elementary arithmetic operations, include cash registers, electronic calculators, and computers. Local standards usually define the educational methods and content included in the elementary level of instruction. In the United States and Canada, controversial subjects include the amount of calculator usage compared to manual computation and the broader debate between traditional mathematics and reform mathematics. Digits are the entire set of symbols used to represent numbers. In a particular numeral system, a single digit represents a different amount than any other digit, although the symbols in the same numeral system might vary between cultures. In modern usage, the Arabic numerals are the most common set of symbols, and the most frequently used form of these digits is the Western style. Each single digit matches the following amounts: 0 , zero. Used in the absence of objects to be counted. 1 , one. Applied to a single item. 2 , two. Applied to a pair of items. 3 , three. Applied to three items. 4 , four. Applied to four items. 5 , five. Applied to five items. 6 , six. Applied to six items. 7 , seven. Applied to seven items. 8 , eight. Applied to eight items. 9 , nine. Applied to nine items. Any numeral system defines the value of all numbers which contain more than one digit, most often by addition of the value for adjacent digits. The Hindu–Arabic numeral system includes positional notation to determine the value for any numeral. In this type of system, the increase in value for an additional digit includes one or more multiplications with the radix value and the result is added to the value of an adjacent digit. With Arabic numerals, the radix value of ten produces a value of twentyone (equal to 2×10 + 1) for the numeral "21". An additional multiplication with the radix value occurs for each additional digit, so the numeral "201" represents a value of twohundredandone (equal to 2×10×10 + 0×10 + 1). The elementary level of study typically includes understanding the value of individual whole numbers using Arabic numerals with a maximum of seven digits, and performing the four basic operations using Arabic numerals with a maximum of four digits each.
Logic Logic is the science of formal principles of reasoning or correct inference. Historically, logic originated with the ancient Greek philosopher Aristotle. Logic was further developed and systematized by the Stoics and by the medieval scholastic philosophers. In the late 19th and 20th centuries, logic saw explosive growth, which has continued up to the present. One may ask whether logic is part of philosophy or independent of it. According to Bochenski, this issue is nowhere explicitly raised in the writings of Aristotle. However, Aristotle did go to great pains to formulate the basic concepts of logic (terms, premises, syllogisms, etc.) in a neutral way, independent of any particular philosophical orientation. Thus Aristotle seems to have viewed logic not as part of philosophy but rather as a tool or instrument to be used by philosophers and scientists alike. This attitude about logic is in agreement with the modern view, according to which the predicate calculus is a general method or framework not only for philosophical reasoning but also for reasoning about any subject matter whatsoever. Logic is the science of correct reasoning. What then is reasoning? According to Aristotle, reasoning is any argument in which certain assumptions or premises are laid down and then something other than these necessarily follows. Thus logic is the science of necessary inference. However, when logic is applied to specific subject matter, it is important to note that not all logical inference constitutes a scientifically valid demonstration. This is because a piece of formally correct reasoning is not scientifically valid unless it is based on a true and primary starting point. Furthermore, any decisions about what is true and primary do not pertain to logic but rather to the specific subject matter under consideration. In this way we limit the scope of logic, maintaining a sharp distinction between logic and the other sciences. All reasoning, both scientific and nonscientific, must take place within the logical framework, but it is only a framework, nothing more. This is what is meant by saying that logic is a formal science. For example, consider the following inference:
This inference is logically correct, because the conclusion ``some real estate is a good investment'' necessarily follows once we accept the premises ``some real estate will increase in value'' and ``anything that will increase in value is a good investment''. Yet this same inference may not be a demonstration of its conclusion, because one or both of the premises may be faulty. Thus logic can help us to clarify our reasoning, but it can only go so far. The real issue in this particular inference is ultimately one of finance and economics, not logic.
Probability theory Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of nondeterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. If an individual coin toss or the roll of a die is considered to be a random event, then if repeated many times the sequence of random events will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. A great discovery of twentieth century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics. Initially, probability theory mainly considered discrete events, and its methods were mainly combinatorial. Eventually, analytical considerations compelled the incorporation of continuous variables into the theory. This culminated in modern probability theory, on foundations laid by Andrey Nikolaevich Kolmogorov. Kolmogorov combined the notion of sample space presented his axiom system for probability theory in 1933. Fairly quickly this became the mostly undisputed axiomatic basis for modern probability theory but alternatives exist, in particular the adoption of finite rather than countable additivity by Bruno de Finetti. Most introductions to probability theory treat discrete probability distributions and continuous probability distributions separately. The more mathematically advanced measure theory based treatment of probability covers both the discrete, the continuous, any mix of these two and more. Consider an experiment that can produce a number of outcomes. The collection of all results is called the sample space of the experiment. The power set of the sample space is formed by considering all different collections of possible results. For example, rolling a die produces one of six possible results. One collection of possible results produce an odd number. Thus, the subset {1,3,5} is an element of the power set of the sample space of die rolls. These collections are called events. In this case, {1,3,5} is the event that the die falls on some odd number. If the results that actually occur fall in a given event, that event is said to have occurred. Probability is a way of assigning every "event" a value between zero and one, with the requirement that the event made up of all possible results (in our example, the event {1,2,3,4,5,6}) be assigned a value of one. To qualify as a probability distribution, the assignment of values must satisfy the requirement that if you look at a collection of mutually exclusive events (events that contain no common results, e.g., the events {1,6}, {3}, and {2,4} are all mutually exclusive), the probability that at least one of the events will occur is given by the sum of the probabilities of all the individual events.
²íæåíåðíîòåõíîëîã³÷íèé ôàêóëüòåò 

