Research about Automata theory

Research Findings:
1.  these real computers are quite complicated-too much so to allow us to set up a manageable mathematical theory of them directly. Instead we use an idealized computer called a computational model.

2.  This controller is a computer that has just a single bit of memory, capable of recording which of the two states the controller is in. Other common devices have controllers with somewhat larger memories. In an elevator controller a state may represent the floor the elevator is on and the inputs might be the signals received from the buttons.

3.  A Markov chain (discrete-time Markov chain or DTMC[1]), named after Andrey Markov, is a random process that undergoes transitions from one state to another on a state space.
4.  each diagram usually represents objects of a single class and track the different states of its objects through the system
5.  In automata theory and sequential logic, a state transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite semiautomaton or finite state machine will move to, based on the current state and other inputs.
6.  In automata theory, a finite state machine is called a deterministic finite automaton (DFA), if 1) each of its transitions is uniquely determined by its source state and input symbol, and 2) reading an input symbol is required for each state transition.
7.  A nondeterministic finite automaton (NFA), or nondeterministic finite state machine, does not need to obey these restrictions. In particular, every DFA is also an NFA.
8.  NFAs are used in the implementation of regular expressions: Thompson's construction is an algorithm for compiling a regular expression to an NFA that can efficiently perform pattern matching on strings.
9.  Unlike a DFA, it is non-deterministic, i.e., for some state and input symbol, the next state may be one of two or more possible states.
10.  In theoretical computer science and formal language theory, a regular expression (sometimes called a rational expression)[1][2] is a sequence of characters that define a search pattern, mainly for use in pattern matching with strings, or string matching, i.e. "find and replace"-like operations.
11.  In theoretical computer science and formal language theory, a regular language (also called a rational language[1][2]) is a formal language that can be expressed using a regular expression, in the strict sense of the latter notion used in theoretical computer science (as opposed to many regular expressions engines provided by modern programming languages, which are augmented with features that allow recognition of languages that cannot be expressed by a classic regular expression).
12.  Regular languages are very useful in input parsing and programming language design.
14.  Nondeterministic finite automata are useful in several respects. As we will show, every NFA can be converted into an equivalent DFA, and constructing NFAs is sometimes easier than directly constructing DFAs
15.  every NFA can be converted into an equivalent DFA, but sometimes that DFA may have many more states. The smallest DFA for A contains eight states. Furthermore, understanding the functioning of the NFA is much easier, as you may see by examining the following figure for the DFA.
16.   In the automata theory, a nondeterministic finite automaton with ε-moves (NFA-ε)(also known as NFA-λ) is an extension of nondeterministic finite automaton(NFA), which allows a transformation to a new state without consuming any input symbols.
17.   The transitions without consuming an input symbol are called ε-transitions or λ-transitions. In the state diagrams, they are usually labeled with the Greek letter ε or λ.
18.  NFA-εs are defined because certain properties can be more easily proved on them as compared to NFA. Since a NFA-ε can always be transformed into a NFA, the properties are also true for NFAs.
19.  In a DFA the transition function takes a state and an input symbol and produces the next state. In an NFA the transition function takes a state and an input symbol or the empty string and produces the set of possible next states.
20. a regular language has a DFA recognizing it and any DFA is also an NFA.
21. The value of the arithmetic expression is the number 32. The value of a regular expression is a language.
22.  In regular expressions, the star operation is done first, followed by concatenation, and finally union, unless parentheses are used to change the usual order.
23.  The expression E represents the language containing a single string-namely, the empty string-whereas 0 represents the language that doesn't contain any strings
24. any regular expression can be converted into a finite automaton that recognizes the language it describes, and vice versa. Recall that a regular language is one that is recognized by some finite automaton.
25.  A language is regular if and only if some regular expression describes it.
26.  Automata theory deals with the definitions and properties of mathematical models of computation. These models play a role in several applied areas of computer science. One model, called the finite automaton, is used in text processing, compilers, and hardware design. Another model, called the context-free grammar, is used in programming languages and artificial intelligence
27.  If A is the set of all strings that machine M accepts, we say that A is the language of machine M and write L(M) = A.We say that M recognizes A or that M accepts A. Because the term accept has different meanings when we refer to machines accepting strings and machines accepting languages, we prefer the term recognize for languages in order to avoid confusion.
28.  A machine may accept several strings, but it always recognizes only one language. If the machine accepts no strings, it still recognizes one languagenamely, the empty language 0.
29.  In the theory of computation the objects are languages and the tools include operations specifically designed for manipulating them. We define three operations on languages, called the regular operations, and use them to study properties of the regular languages
30.  计算机控制系统的控制程序具有有限状态自动机（FA）的特征，可以用有限状态机理论来描述。有限自动机（Finite Automata Machine）是计算机科学的重要基石，它在软件开发领域内通常被称作有限状态机（Finite State Machine），是一种应用非常广泛的软件设计模式。
31.  Generalized nondeterministic finite automata are simply nondeterministic finite automata wherein the transition arrows may have any regular expressions as labels, instead of only members of the alphabet or E.
32.  The property states that all strings in the language can be "pumped" if they are at least as long as a certain special value, called the pumping length. That means each such string contains a section that can be repeated any number of times with the resulting string remaining in the language.
33.  context-free grammars, a more powerful method of describing languages. Such grammars can describe certain features that have a recursive structure, which makes them useful in a variety of applications.
36.  pushdown automata, a class of machines recognizing the context-free languages. Pushdown automata are useful because they allow us to gain additional insight into the power of context-free grammars.
37.  All strings generated in this way constitute the language of the grammar. We write L(G 1) for the language of grammar G1 . Some experimentation with the grammar G1 shows us that L(G1 ) is {On#n1 j n > O}. Any language that can be generated by some context-free grammar is called a context-free language (CFL).
38.  A compiler translates code written in a programming language into another form, usually one more suitable for execution. To do so the compiler extracts the meaning of the code to be compiled in a process called parsing
39.  As with the design of finite automata, discussed in Section 1.1 (page 41), the design of context-free grammars requires creativity. Indeed, context-free grammars are even trickier to construct than finite automata because we are more accustomed to programming a machine for specific tasks than we are to describing languages with grammars
40,  Solving several simpler problems is often easier than solving one complicated problem.
41.  If a grammar generates the same string in several different ways, we say that the string is derived ambiguously in that grammar. If a grammar generates some string ambiguously we say that the grammar is ambiguous.
42.  Natural language processing (NLP) is a field of computer science, artificial intelligence, and computational linguistics concerned with the interactions between computers and human (natural) languages. As such, NLP is related to the area of human–computer interaction. Many challenges in NLP involve natural language understanding, that is, enabling computers to derive meaning from human or natural language input, and others involve natural language generation.
43.  When we say that a grammar generates a string ambiguously, we mean that the string has two different parse trees, not two different derivations.
44.  Pushdown Automata are like nondeterministic finite automata but have an extra component called a stack. The stack allows pushdown automata to recognize some nonregular languages.
45.  Pushdown automata are equivalent in power to context-free grammars. This equivalence is useful because it gives us two options for proving that a language is context free. We can give either a context-free grammar generating it or a pushdown automaton recognizing it. Certain languages are more easily described in terms of generators, whereas others are more easily described in terms of recognizers.
46.  Recognizer vs Generator
47.  A programmable logic device (PLD) is an electronic component used to build reconfigurable digital circuits.
48.  In digital circuit theory, combinational logic (sometimes also referred to as time-independent logic[1] ) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only
49.  Digital electronics or digital (electronic) circuits are electronics that handle digital signals - discrete bands of analog levels - rather than by continuous ranges (as used in analogue electronics).
50.  In most cases, the number of these states is two, and they are represented by two voltage bands: one near a reference value (typically termed as "ground" or zero volts), and the other a value near the supply voltage. These correspond to the "false" ("0") and "true" ("1") values of the Boolean domain respectively, named after its inventor, George Boole, yielding binary code.
60.  In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more logical inputs, and produces a single logical output.
61.  sequential logic has memory while combinational logic does not.
62.  In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
63.  Combinational logic is used in computer circuits to perform Boolean algebra on input signals and on stored data.
64.  Practical circuits will have a mix of combinational and sequential logic, with sequential logic making sure everything happens in order and combinational logic performing functions like arithmetic, logic, or conversion.
65.  Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages. Mainly the former are used in parser design.
66.  the unlimited nature of a stack allows the PDA to store numbers of unbounded size.
67.  The domain of the transition function is Q x SE x rF. Thus the current state, next input symbol read, and top symbol of the stack determine the next move of a pushdown automaton.
68.  A language is context free if and only if some pushdown automaton recognizes it.
69.  The point is, a computer scientist is not satisfied until they actually run an experiment on a computer.  In fact, they aren’t satisfied until they run a lot of experiments on a computer.  Whereas for a mathematician, the proof is enough.  The proof in fact, is the proof that something is true or not.  Whereas the computer scientist requires physical results.  This seems to me a curious fact.
70.  I think this is why computer scientists refer to themselves as scientists, because CS is an experimental science.  Mathematics is too, in the sense that both disciplines play with thought experiments.  Mathematicians simply choose to do their thought experiments on paper, where as computer scientists prefer screens.

NFAs have been generalized in multiple ways, e.g., 
nondeterministic finite automaton with ε-moves,
finite state transducers,
pushdown automata,
ω-automata,
and probabilistic automata.

Terms:
Finite State Machine
Finite Automation
State Diagram
State Transition Table
Deterministic Finite Automation
Non-Deterministic Finite Automation
NFA [Used for Regular Expression]
DFA
GNFA
NFA-εs
Formal Definition [With mathematics]
Regular
Regular Expression
Regular Language
Theorem
Corollary
Lemma
Pumping Lemma
pigeonhole principle
Grammar,
Parser
Pushdown Automata
Derivation
PDA

Context-Free Grammar:
Substitute Rules
Productions
Variable
Terminals
CFG
Parse Tree
Grammar
Syntax
Semantics
Context-Free Language
Chomsky Normal Form
Conversion

PDA:
Lemma
Circuits

Languages:
Context-Free Languages
Regular Languages


Conversion Tasks:
1. Convert NFA -> DFA
2. Convert DFA -> NFA -> GNFA
3. Convert GNFA -> Regular Expression
4. Convert Language -> CFG
5. DFA -> CFG

Computational Model:
DFA
NFA
GNFA
Regular Language
Non Regular Language
CFG
Pushdown Automata

You use a grammar to describe a language by generating each string of that language in the following manner:
1. Write down the start variable. It is the variable on the left-hand side of the top rule, unless specified otherwise.
2. Find a variable that is written down and a rule that starts with that variable. Replace the written down variable with the right-hand side of that rule.
3. Repeat step 2 until no variables remain

Questions:
1. Computer Science vs Mathematics

References:
https://en.wikipedia.org/wiki/Markov_chain
https://en.wikipedia.org/wiki/State_transition_table
https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton#Example
https://en.wikipedia.org/wiki/Regular_expression
https://en.wikipedia.org/wiki/Greek_alphabet
https://en.wikipedia.org/wiki/Nondeterministic_finite_automaton_with_%CE%B5-moves
http://baike.baidu.com/view/409351.htm
https://en.wikipedia.org/wiki/Parsing
https://en.wikipedia.org/wiki/Digital_electronics
https://en.wikipedia.org/wiki/Logic_gate
https://en.wikipedia.org/wiki/Boolean_algebra
http://faculty.etsu.edu/tarnoff/ntes2150/balgebra/balgebra.htm
http://www.scott-a-s.com/cs-is-not-math/
https://www.quora.com/Why-should-I-choose-computer-science-over-mathematics
http://cs.nyu.edu/acm/wordpress/?p=145

Research about Sharing Economy

Knowledge Overview:
1.  Peer-to-peer (P2P) computing or networking is a distributed application architecture that partitions tasks or work loads between peers. Peers are equally privileged, equipotent participants in the application. They are said to form a peer-to-peer network of nodes.
2.  Social peer-to-peer processes are interactions with a peer-to-peer dynamic, whether these peers are humans or computers
3.  Sharing economy can take a variety of forms, including using information technology to provide individuals, corporations, non-profits and governments with information that enables the optimization of resources[2] through the redistribution, sharing and reuse of excess capacity in goods and services.
4.  The consumer peer-to-peer rental market is valued at $26bn (£15bn), with new services and platforms popping up all the time.
5.  The sharing economy[8] encompasses a wide range of structures including for-profit, non-profit, barter and co-operative structures.
6.  Theory is driving the entrepreneurship and innovation.
7.  Open data is the idea that some data should be freely available to everyone to use and republish as they wish, without restrictions from copyright, patents or other mechanisms of control.
8.  Sharing economy organizations say they are committed to building and validating trusted relationships between members of their community, including producers, suppliers, customers or participants.
9.  Social media are computer-mediated tools that allow people to create, share, or exchange information, career interests,[1] ideas, and pictures/videos in virtual communities and networks
10.  An ideology is a body of ideas, and those who agree with the main idea of something take an ideological stand to support it.
11.  Web 2.0 describes World Wide Web sites that emphasize user-generated content, usability, and interoperability.
12.  A Web 2.0 site may allow users to interact and collaborate with each other in a social media dialogue as creators of user-generated content in a virtual community, in contrast to Web sites where people are limited to the passive viewing of content.
14.  In the social sciences, Social structure' is the patterned social arrangements in society that are both emergent from and determinant of the actions of the individuals.
15.  A virtual community is a social network of individuals who interact through specific social media, potentially crossing geographical and political boundaries in order to pursue mutual interests or goals.
16.  A folksonomy is a system in which users apply public tags to online items, typically to aid them in re-finding those items.
17.  A mashup, in web development, is a web page, or web application, that uses content from more than one source to create a single new service displayed in a single graphical interface.
18.  A social networking service (also social networking site or SNS) is a platform to build social networks or social relations among people who share similar interests, activities, backgrounds or real-life connections. A social network service consists of a representation of each user (often a profile), his or her social links, and a variety of additional services such as career services.
19.  An online community is a virtual community whose members interact with each other primarily via the Internet.
20.  The Semantic Web provides a common framework that allows data to be shared and reused across application, enterprise, and community boundaries
21.  User-generated content (UGC) is defined as "any form of content such as blogs, wikis, discussion forums, posts, chats, tweets, podcasting, pins, digital images, video, audio files, advertisements and other forms of media that was created by users of an online system or service, often made available via social media websites"
22.  the sharing economy "allows people to take idle capital and turn them into revenue sources.
23.  People are taking spare bedroom[s], cars, tools they are not using and becoming their own entrepreneurs.
24.  When “sharing” is market-mediated — when a company is an intermediary between consumers who don’t know each other — it is no longer sharing at all. Rather, consumers are paying to access someone else’s goods or services.
25.  sharing economy businesses "extract" profits from their given sector by "successfully [making] an end run around the existing costs of doing business" - taxes, regulations, and insurance.
26.  The so-called sharing economy is supposed to offer a new kind of capitalism, one where regular folks, enabled by efficient online platforms, can turn their fallow assets into cash machines ... But the reality is that these markets also tend to attract a class of well-heeled professional operators, who outperform the amateurs — just like the rest of the economy.
27.  In almost every case, what compels people to open up their homes and cars to complete strangers is money, not trust.
28.  Business Insider’s view is that since the Sharing Economy is in its infancy, this has been accepted. However, as the industry matures, this will need to change.
29.  Recent innovations in mobile and sensor technologies allow for creating a digital representation of almost any physical entity and its parameters over time at any place.
30.  Technology enables service providers to make the location of their customers the location of their business
31.  A PSS is pre-designed system of products, service, supporting infrastructures, and necessary networks that is a so-called dematerialized solution to consumer preferences and needs. It has also been defined as a "self-learning" system, one of whose goals is continual improvement.
32.  Cooking or cookery is the art, technology and craft of preparing food for consumption with the use of heat.
33.  The crowdfunding model is based on three types of actors: the project initiator who proposes the idea and/or project to be funded; individuals or groups who support the idea; and a moderating organization (the "platform") that brings the parties together to launch the idea .
34.  An Information filtering system is a system that removes redundant or unwanted information from an information stream using (semi)automated or computerized methods prior to presentation to a human user
35.  Recommender systems or recommendation systems (sometimes replacing "system" with a synonym such as platform or engine) are a subclass of information filtering system that seek to predict the 'rating' or 'preference' that a user would give to an item.
36.  In general, collaborative filtering is the process of filtering for information or patterns using techniques involving collaboration among multiple agents, viewpoints, data sources, etc.
37.

Driving Factors:
1.  Mobile Technology
2.  Smart Devices
3.  Connected Cars

Collaborative Consumptions:
Product Service Systems
Redistribution Market (swap.com)
Collaborative Lifestyles (TaskRabbit)

Terms:
Two-Sided Marketplace
Barter,
Swap

Foundation:
P2P Network

References:
https://en.wikipedia.org/wiki/Sharing_economy
https://en.wikipedia.org/wiki/Social_structure
https://en.wikipedia.org/wiki/Social_network
https://en.wikipedia.org/wiki/Virtual_community
https://en.wikipedia.org/wiki/Folksonomy
https://en.wikipedia.org/wiki/Web_2.0
https://en.wikipedia.org/wiki/Portal:Business_and_economics
https://en.wikipedia.org/wiki/Club_good
https://en.wikipedia.org/wiki/Smart_products
https://en.wikipedia.org/wiki/Crowdfunding

Research about Swapping Economy

Research Findings:
1.  An alternative currency (or private currency) is any currency used as an alternative to the dominant national or multinational currency systems.
2.  A local exchange trading system (also local employment and trading system or local energy transfer system; abbreviated to LETS or LETSystem) is a locally initiated, democratically organised, not-for-profit community enterprise that provides a community information service and records transactions of members exchanging goods and services by using the currency of locally created LETS Credits
3.  A complementary currency is used to supplement to a national currency.
4.  complementary currencies aim to protect, stimulate or orientate the economy.
5.  Mutual credit is a type of alternative currency in which the currency used in a transaction can be created at the time of the transaction.
6.  An IOU (abbreviated from the phrase "I owe you")[1][2] is usually an informal document acknowledging debt.
7.  In some cases, IOUs may be redeemable for a specific product or service rather than a quantity of currency,[3] constituting a form of scrip.
8.  Scrip (sometimes in India called chit) is a term for any substitute for legal tender and is often a form of credit.
9.  Monetary economics is a branch of economics that provides a framework for analyzing money in its functions as a medium of exchange, store of value, and unit of account.
10.  The availability of interest-free loans is a great advantage to members of the system.
11.  In finance, unsecured debt refers to any type of debt or general obligation that is not protected by a guarantor, or collateralized by a lien on specific assets of the borrower in the case of a bankruptcy or liquidation or failure to meet the terms for repayment.
12.  it is usually (but does not need to be) a local currency, and it can have a demurrage fee for the holding of balances.
14.  Barter is part of Sharing Economy
15.  Anarchism is a political philosophy that advocates self-governed societies with voluntary institutions.
16.  While there are reports that the system is growing, in 2011 the system handles only a tiny fraction of international world commercial activity
17.  A report in Time Magazine suggested that alternative forms of money are "growing in popularity" in places such as South Africa and elsewhere
18.  One estimate suggested that the total value of local exchange trading systems trades worldwide was one billion South African rands in 2004.
19.  A mutual savings bank is a financial institution chartered by a central or regional government, without capital stock, that is owned by its members who subscribe to a common fund.
20.  Mutualism is based on a labor theory of value that holds that when labor or its product is sold, in exchange, it ought to receive goods or services embodying "the amount of labor necessary to produce an article of exactly similar and equal utility"
31.  Exchange Economy is a part of Sharing Economy
32.  Economists since Adam Smith, looking at archaic societies, have used the inefficiency of barter to explain the emergence of money, the economy, and hence the discipline of economics itself.
33.  In economics, the invisible hand is a metaphor used by Adam Smith to describe unintended social benefits resulting from individual actions.
34.  The exact phrase is used just three times in Smith's writings, but has come to capture his notion that individuals' efforts to pursue their own interest may frequently benefit society more than if their actions were directly intending to benefit society.
35.  The idea of trade and market exchange automatically channeling self-interest toward socially desirable ends is a central justification for the laissez-faire economic philosophy, which lies behind neoclassical economics.
36.  Specialization depended on trade, but was hindered by the "double coincidence of wants" which barter requires, i.e., for the exchange to occur, each participant must want what the other has.
37.  Money, as a universally desired medium of exchange, allows each half of the transaction to be separated.
38.  For barter to occur between two parties, both parties need to have what the other wants.
39.  In a monetary economy, money plays the role of a measure of value of all goods, so their values can be assessed against each other; this role may be absent in a barter economy.
40.  If a person wants to buy a certain amount of another's goods, but only has for payment one indivisible unit of another good which is worth more than what the person wants to obtain, a barter transaction cannot occur.
41.  Direct barter doesn't require payment in money (when money is in short supply) hence will be utilized when there is little information about the credit worthiness of trade partners or there is a lack of trust.
42.  An anthropologist is a person with an extensive knowledge of anthropology who uses this knowledge in their work, typically to solve problems specific to humanity.
43.  Anthropology is the study of humanity.
44.  The exchange plays an important role because they provide the record-keeping, brokering expertise and monthly statements to each member. Commercial exchanges make money by charging a commission on each transaction either all on the buy side, all on the sell side, or a combination of both. Transaction fees typically run between 8 and 15%.
45.  There are two industry groups in the United States, the National Association of Trade Exchanges (NATE) and the International Reciprocal Trade Association (IRTA). Both offer training and promote high ethical standards among their members. Moreover, each has created its own currency through which its member barter companies can trade. NATE's currency is the known as the BANC and IRTA's currency is called Universal Currency (UC)
46.   However the IRS now requires barter exchanges to be reported as per the Tax Equity and Fiscal Responsibility Act of 1982.
47.   While most time-based exchange systems are service exchanges in that most exchange involves the provision of services that can be measured in a time unit, it is also possible to exchange goods by 'pricing' them in terms of the average national hourly wage rate
48.   Time Dollars are a tax-exempt complementary currency[7] used as a means of providing mutual credit in Time Banking.
49.   Time Bank members exchange services for Time Dollars.
50.  This "one-for-one" system that relies on an abundant resource is designed to both recognize and encourage reciprocal community service, resist inflation, avoid hoarding, enable trade, and encourage cooperation among participants.
51.  Time banking is a pattern of reciprocal service exchange that uses units of time as currency.
52.  A time bank, also known as a service exchange, is a community that practices time banking.
53.  Time banking is primarily used to provide incentives and rewards for work such as mentoring children, caring for the elderly, being neighborly—work usually done on a volunteer basis—which a pure market system devalues.
54.  As well as gaining credits, participating individuals, particularly those more used to being recipients in other parts of their lives, can potentially gain confidence, social contact and skills through giving to others.
55.  Time Banking is a community development tool and works by facilitating the exchange of skills and experience within a community.
56.  According to Edgar S. Cahn, time banking had its roots in a time when "money for social programs [had] dried up"[27] and no dominant approach to social service in the U.S. was coming up with creative ways to solve the problem.
57.  Americans face at least three interlocking sets of problems: growing inequality in access by those at the bottom to the most basic goods and services; increasing social problems stemming from the need to rebuild family, neighborhood and community; and a growing disillusion with public programs designed to address these problems
58.  one of the major failings of many social service organizations was their unwillingness to enroll the help of those people they were trying to help.
59.  He theorized that a system like time banking could "[rebuild] the infrastructure of trust and caring that can strengthen families and communities."[29] He hoped that the system "would enable individuals and communities to become more self-sufficient, to insulate themselves from the vagaries of politics and to tap the capacity of individuals who were in effect being relegated to the scrap heap and dismissed as freeloaders.
60.  Time Bank members earn credit in Time Dollars for each hour they spend helping other members of the community.
61.  Services offered by members in Time Banks include: Child Care, Legal Assistance, Language Lessons, Home Repair, and Respite Care for caregivers, among other things.
62.  Some Time Banks employ a paid coordinator to keep track of transactions and to match requests for services with those who can provide them
63.  It is precisely the non-commercial, not-for-profit, noncontractual, and non-monetary value of time dollars which exempts them from taxation in the United States; were they to be used as a substitute for money, they would simply be another form of exchange.
64.  there is no guarantee that every person's needs will be provided for by a Time Bank by dint of the fact that the supply of certain skills may be lacking in a community.
65.  Trade exists due to the specialization and division of labor, in which most people concentrate on a small aspect of production, trading for other products.
66.  Numismatics is the study or collection of currency, including coins, tokens, paper money, and related objects.
67.  A flea market (or swap meet) is a type of bazaar that rents space to people who want to sell or barter merchandise. Used goods, low quality items, and high quality items such as collectibles and antiques are commonly sold.
68.  Fractional ownership is a method in which several unrelated parties can share in, and mitigate the risk of, ownership of a high-value tangible asset, usually a jet, yacht or piece of resort real estate.
69.  Peer-to-peer renting refers to the process of an individual renting an owned good, service, or property to another individual.

One downside of mutual credit, 
as with any form of credit, especially if it is run with unsecured debt, is the possibility of people exploiting the system by running up a large negative balance and not repaying it.

Solutions:
1. This problem can be addressed by caps on negative balance that can be raised as balances are paid off.
2. The problem can also be addressed by a using a well-worded membership agreement with clauses that specify members remain fully liable for all negative balances and reasonable time limits for calling in stagnant negative balances.
3.  Another solution is limiting the system to a small, close-knit community based on trust, where the community holds people accountable. Perhaps for this reason,[citation needed] most mutual credit systems are small, under 2000 members

Free Market:


Topics:
Barter
Gift Economy
LETS, Mutual Credit
Time Banking
Complementary Currency
CES
Mutulism

Currencies:
IOU

Mutual Credit

Alternative Currency

Theories:
Labor Theory of Value
Equity Theory

Copying:
From Senior Care to Pet Care

People:
Adam Smith (16 June 1723 NS (5 June 1723 OS) – 17 July 1790) was a Scottish moral philosopher, pioneer of political economy, and a key figure in the Scottish Enlightenment.

Examples:
Cincinnati Time Store
Echo business trading network (Economy of Hours)
International Monetary Systems

Books:
Wealth of Nations

References:
https://en.wikipedia.org/wiki/Time-based_currency
https://en.wikipedia.org/wiki/Complementary_currency
https://en.wikipedia.org/wiki/Mutual_credit
https://en.wikipedia.org/wiki/Mutualism_(economic_theory)
https://en.wikipedia.org/wiki/Free_market
https://en.wikipedia.org/wiki/Mutual_savings_bank
https://en.wikipedia.org/wiki/Local_exchange_trading_system
https://en.wikipedia.org/wiki/Anthropology
https://en.wikipedia.org/wiki/Social_capital
https://en.wikipedia.org/wiki/Time-based_currency
https://en.wikipedia.org/wiki/Trade
https://en.wikipedia.org/wiki/Book_swapping

Research about theoretical computer science

Knowledge Overview:
1.  Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
2.  In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm.
3.  The field is divided into three major branches: automata theory and language, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?"
4.  In computability theory and computational complexity theory, a model of computation is the definition of the set of allowable operations used in computation and their respective costs.
5.  It is used for measuring the complexity of an algorithm in execution time and or memory space: by assuming a certain model of computation, it is possible to analyze the computational resources required or to discuss the limitations of algorithms or computers.
6.  So in principle, any problem that can be solved (decided) by a Turing machine can be solved by a computer that has a finite amount of memory.
7.  A finite-state machine (FSM) or finite-state automaton (plural: automata), or simply a state machine, is a mathematical model of computation used to design both computer programs and sequential logic circuits. It is conceived as an abstract machine that can be in one of a finite number of states.
8.  An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory. Abstraction of computing processes is used in both the computer science and computer engineering disciplines and usually assumes a discrete time paradigm
9.  One popular model more similar to real modern machines is the RAM model, which allows random access to indexed memory locations.
10.  In computer science and automata theory, the state of a digital logic circuit or computer program is a technical term for all the stored information, at a given instant in time, to which the circuit or program has access
11.  In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more logical inputs, and produces a single logical output.
12.  Digital logic circuits can be divided into two types: combinational logic, whose output signals are dependent only on its present input signals, and sequential logic, whose outputs are a function of both the current inputs and the past history of inputs.
14.  a computer program stores data in variables, which represent storage locations in the computer's memory. The contents of these memory locations, at any given point in the program's execution, is called the program's state.
15.  The term is often used in contrast to declarative programming, which focuses on what the program should accomplish without specifying how the program should achieve the result.
16.  In some of these programs, information about previous data characters or packets received is stored in variables and used to affect the processing of the current character or packet. This is called a "stateful protocol" and the data carried over from the previous processing cycle is called the "state". In others, the program has no information about the previous data stream and starts "fresh" with each data input; this is called a "stateless protocol".
17.  In computability theory and computational complexity theory, a model of computation is the definition of the set of allowable operations used in computation and their respective costs.
18.  A Turing machine is an abstract machine[1] that manipulates symbols on a strip of tape according to a table of rules; to be more exact, it is a mathematical model that defines such a device.
19.  An automaton is supposed to run on some given sequence of inputs in discrete time steps.
20.  In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols that may be constrained by rules that are specific to it.
21.  The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed; frequently it is required to be finite.
22.  A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, also called its formation rule.
23.  In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power.
24.  Automata theory is the study of abstract machines (or more appropriately, abstract 'mathematical' machines or systems) and the computational problems that can be solved using these machines.2
25.  Language theory is a branch of mathematics concerned with describing languages as a set of operations over an alphabet.
26.  Because automata are used as models for computation, formal languages are the preferred mode of specification for any problem that must be computed.
27.  The statement that the halting problem cannot be solved by a Turing machine[7] is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine.
28.  Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
29.  In order to analyze how much time and space a given algorithm requires, computer scientists express the time or space required to solve the problem as a function of the size of the input problem.
30.  The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000.
31.  Hamilton's mathematical contributions are primarily in the field of differential geometry and more specifically geometric analysis. He is best known for having discovered the Ricci flow and starting a research program that ultimately led to the proof, by Grigori Perelman, of the Thurston geometrization conjecture and the solution of the Poincaré conjecture. In August 2006, Perelman was awarded, but declined, the Fields Medal for his proof, in part citing Hamilton's work as being foundational.
32.  An algorithm is said to be of polynomial time if its running time is upper bounded by a polynomial expression in the size of the input for the algorithm, i.e., T(n) = O(nk) for some constant k.
33.  Problems for which a deterministic polynomial time algorithm exists belong to the complexity class P, which is central in the field of computational complexity theory.
34.  Cobham's thesis states that polynomial time is a synonym for "tractable", "feasible", "efficient", or "fast".
35.  P is the smallest time-complexity class on a deterministic machine which is robust in terms of machine model changes.
36.  the set of problems that can be solved by an abstract machine M using O(f(n)) of resource R, where n is the size of the input.
37.  complexity classes can be defined based on function problems (an example is FP), counting problems (e.g. #P), optimization problems, promise problems, etc.
38.  Logic (from the Ancient Greek: λογική, logike)[1] is the branch of philosophy concerned with the use and study of valid reasoning.
39.  Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.
40.  An algorithm is an effective method expressed as a finite list[4] of well-defined instructions[5] for calculating a function.
41.  Determinism is the philosophical position that for every event, including human interactions, there exist conditions that could cause no other event.
42.  Usually, efficient data structures are key to designing efficient algorithms.
43.  A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.
44.  Three significant characteristics of distributed systems are: concurrency of components, lack of a global clock, and independent failure of components.
45.  Machine learning is a scientific discipline that deals with the construction and study of algorithms that can learn from data. Such algorithms operate by building a model based on inputs[21]:2 and using that to make predictions or decisions, rather than following only explicitly programmed instructions.
46.  Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in practice by any adversary.
47.  performing appropriate mathematical analysis can contribute to the reliability and robustness of a design

Areas:
Algorithms
Data Structures
Computational Complexity Theory
Distributed Computation
Parallel Computation
Machine Learning
Cryptography
Information Theory
Computational Number Theory
Automata Theory
Coding Theory

Computational Learning Theory
Formal Methods
Program Semantics
Symbolic Computation
Computational Geometry
Very-Large-Scale Integration
Computational Biology
Quantum Computation


Terms:
Halting Problems

Theory:
Automata Theory
Formal Language
Computability Theory/Theory of Computation
Computational Complexity Theory

Programming:
Imperative Programming
Declarative Programming

Machines:
Abstract Machine
RAM Model
Finite State Machine
Turing Machine [Critical]

Time Complexity:
Constant Time
Logarithmic Time
linear Time
Quadratic Time
Polynomial Time
Exponential Time
Factorial Time

Model of Computation:
Turing machines,
finite state machines,
recursive functions,
lambda calculus,
combinatory logic,
cellular automaton,
abstract rewriting systems.

People:
Grigori Yakovlevich Perelman is a Russian mathematician who made landmark contributions to Riemannian geometry and geometric topology before apparently withdrawing from mathematics.

Categories about Model of Computation:
1. abstract machine and models equivalent to it (e.g. lambda calculus is equivalent to the Turing machine) used in proofs of computability and upper bounds on computational complexity of algorithms,
2. decision tree models, used in proofs of lower bounds on computational complexity of algorithmic problems.

Fields:
NP-Hardness
NP-Complete

Examples for FSM:
Vending Machine
Traffic Lights

References:
https://en.wikipedia.org/wiki/Theoretical_computer_science
https://en.wikipedia.org/wiki/Theory_of_computation
https://en.wikipedia.org/wiki/Abstract_machine
https://en.wikipedia.org/wiki/State_(computer_science)
https://en.wikipedia.org/wiki/Model_of_computation
https://en.wikipedia.org/wiki/Finite-state_machine
https://en.wikipedia.org/wiki/Formal_language
https://en.wikipedia.org/wiki/Automata_theory
https://en.wikipedia.org/wiki/Millennium_Prize_Problems
https://en.wikipedia.org/wiki/Time_complexity#Polynomial_time
https://en.wikipedia.org/wiki/Theoretical_computer_science
https://en.wikipedia.org/wiki/Logic
https://en.wikipedia.org/wiki/Amdahl%27s_law

Research about Knowledge

Knowledge Sharing:
1.  Knowledge is a familiarity, awareness or understanding of someone or something, such as facts, information, descriptions, or skills, which is acquired through experience or education by perceiving, discovering, or learning.
2.  A skill is the learned ability to carry out a task with pre-determined results often within a given amount of time, energy, or both.
3.  Human capital is the stock of knowledge, habits, social and personality attributes, including creativity, embodied in the ability to perform labor so as to produce economic value.
4.  Human capital is a collection of resources—all the knowledge, talents, skills, abilities, experience, intelligence, training, judgment, and wisdom possessed individually and collectively by individuals in a population. These resources are the total capacity of the people that represents a form of wealth which can be directed to accomplish the goals of the nation or state or a portion thereof.
5.  Skills can often be divided into domain-general and domain-specific skills.
6.  To reach mastery, authors Malcolm Gladwell and Robert Greene claim that 10,000 hours of work will have to be put into training.
7.  Experience is the knowledge or mastery of an event or subject gained through involvement in or exposure to it
8.  The concept of experience generally refers to know-how or procedural knowledge, rather than propositional knowledge: on-the-job training rather than book-learning.
9.  A habit (or wont) is a routine of behavior that is repeated regularly and tends to occur unconsciously.
10.  A habit, from the standpoint of psychology, is a more or less fixed way of thinking, willing, or feeling acquired through previous repetition of a mental experience
11.  The process by which new behaviours become automatic is habit formation. Old habits are hard to break and new habits are hard to form because the behavioural patterns we repeat are imprinted in our neural pathways,[6] but it is possible to form new habits through repetition.
12.  Features of an automatic behavior are all or some of: efficiency, lack of awareness, unintentionality, uncontrollability.
14.  Lally et al. (2010) found the average time for participants to reach the asymptote of automaticity was 66 days with a range of 18–254 days.
15.  As the habit is forming, it can be analysed in three parts: the cue, the behavior, and the reward.
16.  Wisdom is the ability to think and act using knowledge, experience, understanding, common sense, and insight.
17.  The difference in knowledge is knowing it; wisdom is doing it.
18.  Insight is the understanding of a specific cause and effect in a specific context.
19.

Key Terms:
Knowledge
Talents
Skills
Abilities
Experience
Intelligence
Training
Judgment
Wisdom
Understanding
Common Sense
Insight

References:
https://en.wikipedia.org/wiki/Skill
https://en.wikipedia.org/wiki/Ability
https://en.wikipedia.org/wiki/Experience
https://en.wikipedia.org/wiki/Habit
https://en.wikipedia.org/wiki/Wisdom
https://en.wikipedia.org/wiki/Insight

Research about Mathematics Model and Game Theory

Knowledge Sharing:
1.  A mathematical model is a description of a system using mathematical concepts and language.
2.  Mathematical models are used in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (such as computer science, artificial intelligence), as well as in the social sciences (such as economics, psychology, sociology, political science).
3.  Physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively.
4.  A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.
5.  In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments.
6.  Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed.
7.  Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models.
8.  Mathematical models are usually composed of relationships and variables. Relationships can be described by operators, such as algebraic operators, functions, differential operators, etc. Variables are abstractions of system parameters of interest, that can be quantified.
9.  In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.
10.  optimization includes finding "best available" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.
11.  In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, then the model is regarded as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.
12.  A dynamic model accounts for time-dependent changes in the state of the system, while a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are represented by differential equations.
14.  A discrete model treats objects as discrete, such as the particles in a molecular model or the states in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a point charge.
15.  A deductive model is a logical structure based on a theory. An inductive model arises from empirical findings and generalization from them. The floating model rests on neither theory nor observation, but is merely the invocation of expected structure.
16.  Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics.
17.  Much of economic theory is currently presented in terms of mathematical economic models, a set of stylized and simplified mathematical relationships asserted to clarify assumptions and implications.
18.

About Game Theory:
1.  Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, biology and Poker
2.  To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome.
3.  These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability.
4.

People:
John von Neumann /vɒn ˈnɔɪmən/ (Hungarian: Neumann János (Hungarian pronunciation: [ˈnɒjmɒn ˈjaːnoʃ ˈlɒjoʃ]); December 28, 1903 – February 8, 1957) was a Hungarian-American pure and applied mathematician, physicist, inventor, and polymath.

Types:
dynamical systems,
statistical models,
differential equations,
game theoretic models.

Keys:
Linear vs Nonlinear
Static vs Dynamic
Explicit vs Implicit
Discrete vs Continuous
Deterministic vs Probabilistic
Deductive, Inductive, or Floating

References:
https://en.wikipedia.org/wiki/Mathematical_model

Research about Macroeconomy

Knowledge Overview:
1.  Classical economics asserts that markets function best without government interference
2.  A consumer price index (CPI) measures changes in the price level of a market basket of consumer goods and services purchased by households.
3.  Wholesaling, jobbing, or distributing is the sale of goods or merchandise to retailers; to industrial, commercial, institutional, or other professional business users; or to other wholesalers and related subordinated services.
4.  In economics, the GDP deflator (implicit price deflator) is a measure of the level of prices of all new, domestically produced, final goods and services in an economy.
5.  Technical progress (or technological progress) is an economic measure of innovation.
6.  The primary sector of the economy is the sector of an economy making direct use of natural resources.
7.  Forestry is the science and craft of creating, managing, using, conserving, and repairing forests and associated resources to meet desired goals, needs, and values for human benefit.
8.  The primary sector of the economy is the sector of an economy making direct use of natural resources. This includes agriculture, forestry, fishing and mining.
9.  the secondary sector produces manufactured goods, and the tertiary sector produces services.
10.  The primary sector is usually most important in less-developed countries, and typically less important in industrial countries.
11.  A developed country, industrialized country, or "more economically developed country" (MEDC), is a sovereign state that has a highly developed economy and advanced technological infrastructure relative to other less industrialized nations.
12.  Gross national product (GNP) is the market value of all the products and services produced in one year by labour and property supplied by the citizens of a country.
14.  Gross domestic product (GDP) is a monetary measure of the value of all final goods and services produced in a period of time (quarterly or yearly).
15.  GNP is an economic statistic that is equal to GDP plus any income earned by residents from overseas investments minus income earned within the domestic economy by overseas residents.
16.  Per capita income or average income measures the average income earned per person in a given area (city, region, country, etc.) in a specified year.
17.  Per capita income is the mean money income received in the past 12 months computed for every man, woman, and child in a geographic area."[3] (Children are counted if they are at least 15 years old.)
18.  Developed countries have post-industrial economies, meaning the service sector provides more wealth than the industrial sector.
19.  The secondary sector of the economy includes those economic sectors that produce a finished, usable product: production and construction.
20.  Nations that export manufactured products tend to generate higher marginal GDP growth which supports higher incomes and marginal tax revenue needed to fund the quality of life initiatives such as health care and infrastructure in the economy.
21.  Among developed countries, it is an important source of well paying jobs for the middle class to facilitate greater social mobility for successive generations on the economy
22.  Developed countries have post-industrial economies, meaning the service sector provides more wealth than the industrial sector. They are contrasted with developing countries, which are in the process of industrialization, or undeveloped countries, which are pre-industrial and almost entirely agrarian.
23.  The Human Development Index (HDI) is a composite statistic of life expectancy, education, and income per capita indicators, which are used to rank countries into four tiers of human development.
24.  In contrast, a change in consumer tastes or preferences would be an exogenous change on the demand curve.
25.  The economics of a depression were the spur for the creation of "macroeconomics" as a separate discipline field of study.
26.  The business cycle or economic cycle is the downward and upward movement of gross domestic product (GDP) around its long-term growth trend.
27.  The IS–LM model, or Hicks–Hansen model, is a macroeconomic tool that shows the relationship between interest rates and real output, in the goods and services market and the money market (also known as the assets market).
28.  Keynesian economics (/ˈkeɪnziən/ kayn-zee-ən; or Keynesianism) are the various theories about how in the short run, and especially during recessions, economic output is strongly influenced by aggregate demand (total spending in the economy).
29.  Real business-cycle theory (RBC theory) are a class of New classical macroeconomics models in which business-cycle fluctuations to a large extent can be accounted for by real (in contrast to nominal) shocks.
30.  The labour force only includes workers actively looking for jobs.
31.  Frictional unemployment is the time period between jobs when a worker is searching for, or transitioning from one job to another. It is sometimes called search unemployment and can be based on the circumstances of the unemployed individual.
32.  Structural unemployment is a form of unemployment caused by a mismatch between the skills that workers in the economy can offer, and the skills demanded of workers by employers (also known as the skills gap).
33.  A factor of overall unemployment that relates to the cyclical trends in growth and production that occur within the business cycle.
34.  According to International Labour Organization report, more than 200 million people globally or 6% of the world's workforce were without a job in 2012
35.  These theories argue against interventions imposed on the labor market from the outside, such as unionization, bureaucratic work rules, minimum wage laws, taxes, and other regulations that they claim discourage the hiring of workers.
36.  Structural arguments emphasize causes and solutions related to disruptive technologies and globalization.
37.  In economics, Okun's law (named after Arthur Melvin Okun, who proposed the relationship in 1962[1]) is an empirically observed relationship between unemployment and losses in a country's production.
38.  Money has a general acceptability, a relative consistency in value, divisibility, durability, portability, elastic in supply and survives with mass public confidence.
39.  As a medium of exchange, money facilitates trade.
40.  Its economic function can be contrasted with barter (non-monetary exchange).
41.  Barter is a system of exchange where goods or services are directly exchanged for other goods or services without using a medium of exchange, such as money.
42.  A gift economy, gift culture, or gift exchange is a mode of exchange where valuables are not traded or sold, but rather given without an explicit agreement for immediate or future rewards.
43.  Gift economies are said, by some,[7] to build communities, and that the market serves as an acid on those relationships
44.  In cultural anthropology, reciprocity refers to the non-market exchange of goods or labour ranging from direct barter (immediate exchange) to forms of gift exchange where a return is eventually expected (delayed exchange) as in the exchange of birthday gifts.
45.  Some forms of reciprocity are thus closely related to redistribution, where goods and services are collected by a central figure for eventual distribution to followers
46.  It is distinguishable from gift economies in many ways; one of them is that the reciprocal exchange is immediate and not delayed in time. It is usually bilateral, but may be multilateral (i.e., mediated through barter organizations)
47.  Barter, as a replacement for money as the method of exchange, is used in times of monetary crisis, such as when the currency may be either unstable (e.g., hyperinflation or deflationary spiral) or simply unavailable for conducting commerce.
48.  The labor theory of value (LTV) is a heterodox economic theory of value that argues that the economic value of a good or service is determined by the total amount of socially necessary labor required to produce it, rather than by the use or pleasure its owner gets from it.
49.  Marxian economics, particularly in academia, is distinguished from Marxism as a political ideology as well as the normative aspects of Marxist thought
50.  The coincidence of wants problem (often "double coincidence of wants"[verification needed]) is an important category of transaction costs that impose severe limitations on economies lacking a medium of exchange (such as money), which have to rely on barter or other in-kind transactions.
51.  The problem is caused by the improbability of the wants, needs, or events that cause or motivate a transaction occurring at the same time and the same place.
52.  In-kind transactions have several limitations, most notably timing constraints.
53.  Money can reduce the transaction cost of exchange because of its ready acceptability. Then it is less costly for the seller to accept money in exchange, rather than what the buyer produces.
54.  Governments increase spending and cut taxes to boost aggregate demand. Resources that have been idled can be used by the government.
55.  For example, unemployed home builders can be hired to expand highways. Tax cuts allow consumers to increase their spending, which boosts aggregate demand.
56.  In economics, crowding out is argued by some economists to be a phenomenon that occurs when increased government involvement in a sector of the market economy substantially affects the remainder of the market, either on the supply or demand side of the market.
57.  Other commentators and other economists sometimes use the term "crowding out" to refer the government spending using up financial and other resources that would otherwise be used by private enterprise.
58.  The Ricardian equivalence proposition (also known as the Ricardo–De Viti–Barro equivalence theorem[1]) is an economic hypothesis holding that consumers are forward looking and so internalize the government's budget constraint when making their consumption decisions.
59.  Governments can finance their expenditures either through taxes or by issuing bonds. Since bonds are loans, they must eventually be repaid—presumably by raising taxes in the future. The choice is therefore "tax now or tax later."
60.  A tariff is a tax on imports or exports (an international trade tariff).
61.  Often division of labour and division of work are both part of the economic activity within an industrial nation or organisation.
62.  A comprehensive world view or worldview is the fundamental cognitive orientation of an individual or society encompassing the entirety of the individual or society's knowledge and point of view.
63.  In 2000, the International Monetary Fund (IMF) identified four basic aspects of globalization: trade and transactions, capital and investment movements, migration and movement of people, and the dissemination of knowledge.
64.  A planned economy is an economic system in which inputs are based on direct allocation.
65.  Capitalism is an economic system based on private ownership of the means of production and the creation of goods and services for profit.
66.  Political economy is a term used for studying production and trade, and their relations with law, custom, and government, as well as with the distribution of national income and wealth.
67.  With the fall of Communism, attention shifted to problems of transition economies.
68.  Contemporary economics uses mathematics. Economists draw on the tools of calculus, linear algebra, statistics, game theory, and computer science.[84] Professional economists are expected to be familiar with these tools, while a minority specialize in econometrics and mathematical methods.
69.

Economy Systems:
Planned Economy
Capitalism
Comparative Economic System

Theories:
General Equilibrium Theory
Endogenous Growth Theory
Real Business Cycle Theory
Labor Theory of Value

Barter:
Coincidence of Wants

Measurements:
Consumer Price Index / CPI
Producer Price Index / Wholesale Price Index / PPI
GDP Deflator

Sectors:
Primary Sector ()

Terms:
Inflation, Deflation

Economics:
Classical Economics
New Classical Economics/NeoEconomics
Keynesian Economics
Gift Economy
Barter Economy
Market Economy
Marxian Economics

Unemployment Causes: 
Structural unemployment
Frictional unemployment


People:

Historical Events:
Great Depression
     https://en.wikipedia.org/wiki/Great_Depression
Great Recessions
     https://en.wikipedia.org/wiki/Great_Recession

Tools:
IS-LM Model
    -this tool is sometimes used not only to analyse the fluctuations of the economy but also to find appropriate stabilisation policies.


References:
https://en.wikipedia.org/wiki/General_equilibrium_theory
https://en.wikipedia.org/wiki/Partial_equilibrium
https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(PPP)
https://en.wikipedia.org/wiki/Consumer_price_index
https://en.wikipedia.org/wiki/Technical_progress_(economics)
https://en.wikipedia.org/wiki/Workforce
https://en.wikipedia.org/wiki/Exogeny
https://en.wikipedia.org/wiki/Unemployment#Classical_unemployment
https://en.wikipedia.org/wiki/Gift_economy
https://en.wikipedia.org/wiki/Labor_theory_of_value
https://en.wikipedia.org/wiki/Coincidence_of_wants
https://en.wikipedia.org/wiki/Crowding_out_(economics)
https://en.wikipedia.org/wiki/Globalization
https://en.wikipedia.org/wiki/Economic_model

Research about Microeconomy

Knowledge Sharing:
1.  The income approach, which is sometimes referred to as GDP(I), is calculated by adding up total compensation to employees, gross profits for incorporated and non incorporated firms, and taxes less any subsidies. The expenditure method is the more common approach and is calculated by adding total consumption, investment, government spending and net exports.
2.  The gross domestic product (GDP) is one of the primary indicators used to gauge the health of a country's economy.
3.  It represents the total dollar value of all goods and services produced over a specific time period; you can think of it as the size of the economy.
4.  Measuring GDP is complicated (which is why we leave it to the economists), but at its most basic, the calculation can be done in one of two ways: either by adding up what everyone earned in a year (income approach), or by adding up what everyone spent (expenditure method). Logically, both measures should arrive at roughly the same total.
5. The income approach, which is sometimes referred to as GDP(I), is calculated by adding up total compensation to employees, gross profits for incorporated and non incorporated firms, and taxes less any subsidies. The expenditure method is the more common approach and is calculated by adding total consumption, investment, government spending and net exports.
6.  The European Union (EU) is a politico-economic union of 28 member states that are located primarily in Europe
7.  The EU has developed a single market through a standardised system of laws that apply in all member states.
8.  EU policies aim to ensure the free movement of people, goods, services, and capital,[17] enact legislation in justice and home affairs, and maintain common policies on trade,[18] agriculture,[19] fisheries, and regional development.
9. Economics is the social science that describes the factors that determine the production, distribution and consumption of goods and services.
10. Microeconomics examines the behavior of basic elements in the economy, including individual agents and markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers.
11. Macroeconomics analyzes the entire economy (meaning aggregated production, consumption, savings, and investment) and issues affecting it, including unemployment of resources (labor, capital, and land), inflation, economic growth, and the public policies that address these issues (monetary, fiscal, and other policies).
12. The ultimate goal of economics is to improve the living conditions of people in their everyday life.
14.  Forms include monopoly (in which there is only one seller of a good), duopoly (in which there are only two sellers of a good), oligopoly (in which there are few sellers of a good), monopolistic competition (in which there are many sellers producing highly differentiated goods), monopsony (in which there is only one buyer of a good), and oligopsony (in which there are few buyers of a good). Unlike perfect competition, imperfect competition invariably means market power is unequally distributed.
15.  Microeconomics studies individual markets by simplifying the economic system by assuming that activity in the market being analysed does not affect other markets. This method of analysis is known as partial-equilibrium analysis (supply and demand). This method aggregates (the sum of all activity) in only one market.
16.  Production is a flow and thus a rate of output per period of time.
17.  Opportunity cost refers to the economic cost of production: the value of the next best opportunity foregone.
18.  Efficiency is improved if more output is generated without changing inputs, or in other words, the amount of "waste" is reduced.
19.  In economics, a production–possibility frontier (PPF), sometimes called a production–possibility curve, production-possibility boundary or product transformation curve, is a graph representing production tradeoffs of an economy given fixed resources.
20.  It is a graphical representation of the maximal mix of outputs that an economy can achieve using its existing resources to full extent and in the most efficient way.
21.  In economics, factors of production, resources, or inputs are what is used in the production process to produce output—that is, finished goods and services.
22.  There are three basic resources or factors of production: land, labour, and capital.
23.  Materials and energy are considered secondary factors in classical economics because they are obtained from land, labour and capital.
24.  Recent usage has distinguished human capital (the stock of knowledge in the labor force) from labor.
25.  Entrepreneurship is also sometimes considered a factor of production.
26.  Examples cited of such inefficiency include high unemployment during a business-cycle recession or economic organization of a country that discourages full use of resources.
27.  Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off.
28.  An economist is a professional in the social science discipline of economics.
29.  A generally accepted interpretation in academia is that an economist is one who has attained a Ph.D. in economics, teaches economic science, and has published literature in a field of economics.
30.  Social science is a major category of academic disciplines, concerned with society and the relationships among individuals within a society.
31.  The theory of supply and demand is an organizing principle for explaining how prices coordinate the amounts produced and consumed.
32.  Any business model innovation shall comply with Economics Theories.
33.  The law of demand states that, in general, price and quantity demanded in a given market are inversely related.
34.  Supply is the relation between the price of a good and the quantity available for sale at that price.
35.  Business Model is built on top of Economics. Economics is the Environment of any business.
36.  The goal is to chase supply and demand Equilibrium, not Free Price with high demand and low supply.
37.  with income and wealth as the constraints on demand
38.  The "Law of Supply" states that, in general, a rise in price leads to an expansion in supply and a fall in price leads to a contraction in supply.
39.  The law of demand states that, in general, price and quantity demanded in a given market are inversely related. That is, the higher the price of a product, the less of it people would be prepared to buy (other things unchanged). As the price of a commodity falls, consumers move toward it from relatively more expensive goods (the substitution effect).
40.  If there is a true value, people are willing to buy by exchanging the value with Money.
41.  Marginalist theory, such as above, describes the consumers as attempting to reach most-preferred positions, subject to income and wealth constraints while producers attempt to maximize profits subject to their own constraints, including demand for goods produced, technology, and the price of inputs.
42.  At the point where marginal profit reaches zero, further increases in production of the good stop.
43.  Firms combine labour and capital, and can achieve far greater economies of scale (when the average cost per unit declines as more units are produced) than individual market trading.
44.  Uncertainty in economics is an unknown prospect of gain or loss, whether quantifiable as risk or not.
45.  Game theory is a branch of applied mathematics that considers strategic interactions between agents, one kind of uncertainty.
46.  Game theory is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."
47.  Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics
48.  The mathematization of economics began in earnest in the 19th century
49.  In contract theory and economics, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other.
50.  In mathematical economics, the Arrow–Debreu model suggests that under certain economic assumptions (convex preferences, perfect competition, and demand independence) there must be a set of prices such that aggregate supplies will equal aggregate demands for every commodity in the economy.
51.  In economic theory, perfect competition (sometimes called pure competition) describes markets such that no participants are large enough to have the market power to set the price of a homogeneous product.
52.  If economic allocation in any system is not Pareto efficient, there is potential for a Pareto improvement—an increase in Pareto efficiency: through reallocation, improvements can be made to at least one participant's well-being without reducing any other participant's well-being.In economics, industrial organization is a field that builds on the theory of the firm by examining the structure of (and, therefore, the boundaries between) firms and markets.
53.  In economics and particularly in industrial organization, market power is the ability of a firm to profitably raise the market price of a good or service over marginal cost
54.  A firm with total market power can raise prices without losing any customers to competitors.
55.  Market participants that have market power are therefore sometimes referred to as "price makers" or "price setters", while those without are sometimes called "price takers".
56.  Significant market power occurs when prices exceed marginal cost and long run average cost, so the firm makes economic profits
57.  Neoclassical economics is a set of solutions to economics focusing on the determination of goods, outputs, and income distributions in markets through supply and demand.
58.  Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior.
59.  In economic theory a frictionless market is a financial market without transaction costs.

60.  Information asymmetries and incomplete markets may result in economic inefficiency but also a possibility of improving efficiency through market, legal, and regulatory remedies,

61.  In microeconomics, economies of scale are the cost advantages that enterprises obtain due to size, output, or scale of operation, with cost per unit of output generally decreasing with increasing scale as fixed costs are spread out over more units of output.
62.  A business, also known as an enterprise or a firm, is an organization involved in the provision of goods, services, or both to consumers.
63.  Capitalism is an economic system based on private ownership of the means of production and the creation of goods and services for profit.
64.  Analysts divide the stock market itself into market sectors so that shares of companies that are in direct competition are listed alongside each other.
65.  The defining features are that people can consume public goods without having to pay for them and that more than one person can consume the good at the same time.
66.  In economics, income distribution is how a nation’s total GDP is distributed amongst its population
67.  Economic inequality, also known as income inequality, wealth inequality, or the gap between rich and poor is the disparity of any of various measures of economic well-being among individuals in a group, among groups in a population, or among countries
68.  In economics, utility is a measure of preferences over some set of goods and services. The concept is an important underpinning of rational choice theory.

Categories:
Microeconomics
Macroeconomics
Mathematical Economics
Behavioral Economics
Corporate Finance
Neoclassical Economics

Markets:
Incomplete Market
Complete Market
Frictionless Market
Capitalist Market

Theories:
1.  Theory of Supply and Demand
2.  Marginalism Thoery
3.  Economies of Scale
4.  Pareto Efficiency
5.  Rational Choice Theory

Imperfect Competition:
Oligopoly
Monopolistic Competition
Monopsony, Oligopsony

People:
Vilfredo Federico Damaso Pareto (born Wilfried Fritz Pareto; Italian: [vilˈfreːdo paˈreːto]; 15 July 1848 – 19 August 1923) was an Italian engineer, sociologist, economist, political scientist, and philosopher.
Kenneth Joseph "Ken" Arrow (born August 23, 1921) is an American economist, writer, and political theorist. He is the joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972.
Gary Stanley Becker (December 2, 1930 – May 3, 2014)[1] was an American economist.  Nobel Prize winner.

Key: Economist

References:
http://www.investopedia.com/ask/answers/199.asp
https://en.wikipedia.org/wiki/List_of_countries_by_GDP_(nominal)
http://knoema.com/sijweyg/gdp-per-capita-ranking-2015-data-and-charts
http://www.thetoptens.com/high-tech-countries/
https://en.wikipedia.org/wiki/Economics#Theory
https://en.wikipedia.org/wiki/Production%E2%80%93possibility_frontier
https://en.wikipedia.org/wiki/Factors_of_production
https://en.wikipedia.org/wiki/Marginalism
https://en.wikipedia.org/wiki/Industrial_organization
https://en.wikipedia.org/wiki/Rational_choice_theory
https://en.wikipedia.org/wiki/Capitalism
https://en.wikipedia.org/wiki/Business
https://en.wikipedia.org/wiki/Market_sector
https://en.wikipedia.org/wiki/Lorenz_curve
https://en.wikipedia.org/wiki/Utility

Research about Mathematical Proof

Knowledge Sharing:
1. Mathematics is all about proving that certain statements, such as Pythagoras' theorem, are true everywhere and for eternity.
2. Mathematics is perhaps the only field in which absolute certainty is possible, which is why mathematicians hold proofs so dearly.
3. A theorem is a proven statement that was constructed using previously proven statements, such as theorems, or constructed using axioms. Some theorems are very complicated and involved, so we will discuss their different parts.
4. A constructive proof is the most basic kind of proof there is. It is a proof that starts with a hypothesis, and a person uses a series of logical steps and a list of axioms, to arrive at a conclusion.
5. The method of proof by contradiction is to assume that a statement is not true and then to show that that assumption leads to a contradiction.
6. The beauty of induction is that it allows a theorem to be proven true where an infinite number of cases exist without exploring each case individually.
7. Mathematical induction is a mathematical proof technique, most commonly used to establish a given statement for all natural numbers, although it can be used to prove statements about any well-ordered set. It is a form of direct proof, and it is done in two steps. The first step, known as the base case, is to prove the given statement for the first natural number. The second step, known as the inductive step, is to prove that the given statement for any one natural number implies the given statement for the next natural number. From these two steps, mathematical induction is the rule from which we infer that the given statement is established for all natural numbers.
8.  Mathematical induction in this extended sense is closely related to recursion. Mathematical induction, in some form, is the foundation of all correctness proofs for computer programs.
9. Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other, the nested images that occur are a form of infinite recursion.
10.  Recursively defined mathematical objects include functions, sets, and especially fractals.
11.  Induction is a way of proving mathematical theorems. Like proof by contradiction or direct proof, this method is used to prove a variety of statements. Simplistic in nature, this method makes use of the fact that if a statement is true for some starting condition, and then it can be shown that the statement is true for a general subsequent condition, then, it is true in general. Formally, if we show that a statement is true for an integer n>4, and then we show that it is true for some integer k+1 if it is true for the integer k(k is greater than or equal to 4), then we have shown that it is true for all integers greater than 4.

Proof:
1. Constructive Proof
2. Proof by Contrapositive
3. Proof by Contradiction
4. Proof by Induction - Mathematical Induction
5. Counterexample
6. Proof by Exhaustion

Process:
1. Proof Idea
2. Proof Steps with simple condition
3. Proof Steps with complex condition

Foundations:
1. Recursions
2. Mathematical Induction

Reasoning:
1. Inductive Reasoning, Deductive Reasoning, etc.
2. Axioms -> Theorems

Questions?
1. What is the difference between Mathematical Induction and Recursion?

References:
http://algs4.cs.princeton.edu/42digraph/
https://en.wikibooks.org/wiki/Mathematical_Proof/Methods_of_Proof/Other_Proof_Types
https://en.wikipedia.org/wiki/Mathematical_induction
https://en.wikipedia.org/wiki/Recursion
https://en.wikipedia.org/wiki/Mathematical_proof#History_and_etymology