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MATHEMATICS Mathematics is the abstract study of structure, space, and change.There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.
Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. MORE |
PROBABILITY Probability (likelihood) is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
These concepts have been given an axiomatic mathematical derivation in probability theory (see probability axioms), which is used widely in such areas of study as mathematics, statistics, finance, gambling, science, artificial intelligence/machine learning and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems. MORE |
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STATISTICS Statistics is the study of the collection, organization, analysis, interpretation and presentation of data. It deals with all aspects of data, including the planning of data collection in terms of the design of surveys and experiments.
The word statistics, when referring to the scientific discipline, is singular, as in "Statistics is an art." This should not be confused with the word statistic, referring to a quantity (such as mean or median) calculated from a set of data, whose plural is statistics e.g.("this statistic seems wrong" or "these statistics are misleading"). MORE |
FINANCE Finance is the science of funds management, or the allocation of assets and liabilities over time under conditions of certainty and uncertainty. A key point in finance is the time value of money, which states that a unit of currency today is worth more than the same unit of currency tomorrow. Finance aims to price assets based on their risk level, and expected rate of return. Finance can be broken into three different sub categories: public finance, corporate finance and personal finance.MORE |
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ECONOMICS Economics is the social science that analyzes the production, distribution, and consumption of goods and services. Political economy was the earlier name for the subject, but economists in the late 19th century suggested "economics" as a shorter term for "economic science" that also avoided a narrow political-interest connotation and as similar in form to "mathematics", "ethics", and so forth.
A focus of the subject is how economic agents behave or interact and how economies work. Consistent with this, a primary textbook distinction is between microeconomics and macroeconomics. - Microeconomics examines the behavior of basic elements in the economy, including individual agents (such as households and firms or as buyers and sellers) and markets, and their interactions.
- Macroeconomics analyzes the entire economy and issues affecting it, including unemployment, inflation, economic growth, and monetary and fiscal policy.
Other broad distinctions include those between positive economics (describing "what is") and normative economics (advocating "what ought to be"); between economic theory and applied economics; between rational and behavioral economics; and between mainstream economics (more "orthodox" and dealing with the "rationality-individualism-equilibrium nexus") and heterodox economics (more "radical" and dealing with the "institutions-history-social structure nexus").
Economic analysis may be applied throughout society, as in business, finance, health care, and government, but also to such diverse subjects as crime, education, the family, law, politics, religion, social institutions, war, and science. At the turn of the 21st century, the expanding domain of economics in the social sciences has been described as economic imperialism. MORE |
COMPUTER PROGRAMMING Computer programming is the comprehensive process that leads from an original formulation of a computing problem to executable programs. It involves activities such as analysis, understanding, and generically solving such problems resulting in an algorithm, verification of requirements of the algorithm including its correctness and its resource consumption, implementation (or coding) of the algorithm in a target programming language, testing, debugging, and maintaining the source code, implementation of the build system and management of derived artefacts such as machine code of computer programs. The algorithm is often only represented in human-parseable form and reasoned about using logic. Source code is written in one or more programming languages (such as C++, C#, Java, Python, Smalltalk, etc.). The purpose of programming is to find a sequence of instructions that will automate performing a specific task or solve a given problem. The process of programming thus often requires expertise in many different subjects, including knowledge of the application domain, specialized algorithms and formal logic. The first step in most formal software development processes is requirements analysis, followed by testing to determine value modeling, implementation, and failure elimination (debugging). There exist a lot of differing approaches for each of those tasks. One approach popular for requirements analysis is Use Case analysis. Many programmers use forms of Agile software development where the various stages of formal software development are more integrated together into short cycles that take a few weeks rather than years. There are many approaches to the Software development process.
Popular modeling techniques include Object-Oriented Analysis and Design (OOAD) and Model-Driven Architecture (MDA). The Unified Modeling Language (UML) is a notation used for both the OOAD and MDA.
A similar technique used for database design is Entity-Relationship Modeling (ER Modeling).
Implementation techniques include imperative languages (object-oriented or procedural), functional languages, and logic language MORE |
