Introduction to GAME THEORY

Game Theory Definitions

Any time we have a situation with two or more players that involves known payouts or quantifiable consequences, we can use game theory to help determine the most likely outcomes. Let's start out by defining a few terms commonly used in the study of game theory:

• Game: Any set of circumstances that has a result dependent on the actions of two or more decision-makers (players)
• Players: A strategic decision-maker within the context of the game
• Strategy: A complete plan of action a player will take given the set of circumstances that might arise within the game
• Payoff: The payout a player receives from arriving at a particular outcome (The payout can be in any quantifiable form, from dollars to utility.)
• Information set: The information available at a given point in the game (The term information set is most usually applied when the game has a sequential component.)
• Equilibrium: The point in a game where both players have made their decisions and an outcome is reached

Some important laws

1. LAW OF CONSERVATION OF ELECTRIC CHARGE: Electric charges can neither be created nor be destroyed. The total charge in an isolated system is always constant.

2. COULOMB'S LAW: The force of attraction or repulsion between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The direction of the force is along the line joining the two charges.

3. OHM'S LAW: A constant temperature the current through a conductor is directly proportional to the potential difference between the two ends of the conductor.

4. JOULE'S LAW: The heat produced in current carrying conductor is (a) directly proportional to the square of the current (b) directly proportional to its resistance and (c) directly proportional to the time of passage of current.

5. GRASSMAN'S LAW:  The eye perceives the new colour depending on the algebraic sum of the red, green and blue light fluxes. This forms the basis for the colour signal generation and is known as Grassman's law

6. BREWSTER'S LAW: The tangent of the polarizing angle is numerically equal to the refractive index of the medium.

7. LENZ'S LAW: The induced current produced in a circuit always flow in such a direction that it opposes the change or cause that produces it.

Why Should Primary School Have A Maths Club?

     Maths clubs come in all shapes and sizes and there is no one model that works for every school. however, every school should have one.

This is because they help raise the profile of maths within the school, increase the engagement of children in maths and help show that maths is a playful and diverse subject full of surprises.

A maths club can also:

• develop children’s knowledge and understanding of maths  

• strengthen the links between maths and other subjects

• provide children with opportunities to try new things

• help children apply their maths skills to other ‘real-life’ situations

• celebrate the achievement of children

• fuel a can-do approach to maths

• show children that maths is multidimensional

• develop children’s maths thinking

• promote collaborative learning between different year groups

• develop maths resilience

• boost self-confidence  

• cultivate creativity  

• help to raise standards

• increase parental engagement with the subject

Basic introduction to GROUP in abstract algebra

The definition of a group. Let G be a non-empty set and let ⋆ be a binary operation on G:
(bop) ⋆: G × G → G, (a, b) → a ⋆ b.
Then (G; ⋆) is a group if the following axioms are satisfied:
(G1) associativity: a ⋆ (b ⋆ c) = (a ⋆ b) ⋆ c for all a, b, c ∈ G
(G2) identity element: there exists e ∈ G such that a ⋆ e = e ⋆ a = a for all a ∈ G.
(G3) inverses: for any a ∈ G there exists a −1 (a inverse) ∈ G such that a ⋆ a−1 = a −1 ⋆ a = e.
If in addition the following holds
(G4) commutativity: a ⋆ b = b ⋆ a for all a, b ∈ G then (G; ⋆) is called an abelian group, or simply a commutative group.

Remarks: Note that (bop) is an essential part of the definition. and that (G2) must precede (G3) because (G3) refers back to the element e.

 Fact: if (G; ⋆) is a group then the identity e is unique and the inverse of any a in G is uniquely determined by a.

Importance of Statistics in Different Fields

Statistics plays a vital role in every field of human activity. Statistics helps in determining the existing position of per capita income, unemployment, population growth rates, housing, schooling medical facilities, etc., in a country.


(1) Business
Statistics helps businessmen to plan production according to the taste of the customers, and the quality of the products can also be checked more efficiently by using statistical methods. Thus, it can be seen that all business activities are based on statistical information.

(2) Economics

 Economics largely depends upon statistics. National income accounts are multipurpose indicators for economists and administrators, and statistical methods are used to prepare these accounts. In economics research, statistical methods are used to collect and analyze the data and test hypotheses.

(3) Mathematics

Statistics helps in describing these measurements more precisely. Statistics is a branch of applied mathematics. A large number of statistical methods like probability averages, dispersions, estimation, etc., is used in mathematics, and different techniques of pure mathematics like integration, differentiation and algebra are used in statistics.

(4) Banking

Statistics plays an important role in banking. Banks make use of statistics for a number of purposes. They work on the principle that everyone who deposits their money with the banks does not withdraw it at the same time. The bank earns profits out of these deposits by lending it to others on interest. Bankers use statistical approaches based on probability to estimate the number of deposits and their claims for a certain day.

(5) State Management (Administration)

Statistics is essential to a country. Different governmental policies are based on statistics. Statistical data are now widely used in making all administrative decisions.

(6) Accounting and Auditing

In auditing, sampling techniques are commonly used. An auditor determines the sample size to be audited on the basis of error.

(7) Natural and Social Sciences

Statistics plays a vital role in almost all the natural and social sciences. Statistical methods are commonly used for analyzing experiments results, and testing their significance in biology, physics, chemistry, mathematics, meteorology, research, chambers of commerce, sociology, business, public administration, communications and information technology, etc.

(8) Astronomy

Example: This distance of the moon from the earth is measured. Since history, astronomers have been using statistical methods like method of least squares to find the movements of stars.

Interesting things on pi

TNTET for mathematics

TNTET Exam Pattern 2019

Teachers Recruitment Board conducts TNTET exam for determining the eligibility of candidates for the post of Primary and Elementary level teachers only for schools in the state of Tamil Nadu. Given below is a detailed paper pattern for the exam:

Mode of Exam

• Offline i.e. Pen-paper based test.
• Each candidate will be allocated their own OMR sheet.
• Make sure to check that the seal of the sheet is not broken before starting the exam. 

Nature of Questions

• The questions in both the papers will be objective in nature.
• This means, all the questions in TNTET 2019 will be of Multiple Choice type (MCQs), having 4 choices.
• Candidates must select the most appropriate answer.
• The duration of Paper 1 and 2 is 3 hours each.

Total Questions | Sections

• Both the papers will have 150 questions each.
• Paper 1 will have 5 sections while Paper 2 will have 4 sections
• No restriction to move to and fro among the sections.
• All the questions are compulsory to attempt.

TNTET Marking Scheme 2019

• A uniform marking system is followed in the exam i.e. for Paper 1 and 2, each correct answer carries + 1 mark.
• As per the revised exam pattern of TNTET exam, there is no negative marking for any unanswered or incorrect answer.
• Hence, instead of skipping a question, one can use their calculated guess and mark the answer. 

TNTET Paper1 marking scheme:

                     Subjects                                       Questions       Marks

Child Development and Pedagogy
(relevant to the age group of 6 – 11 years)          30                  30

Language I 

(Tamil/Telugu/Malayalam/Kannada/Urdu)            30                  30

Language II – English                                            30                  30

Mathematics                                                           30                  30

Environmental Studies                                          30                  30

Total                                                                        150                150

TNTET Paper II Marking Scheme:

Subjects                                                               

Child Development and Pedagogy
(relevant to the age group of 11-14 years)        
Compulsory

Language
(Tamil/Telugu/Malayalam/Kannada/ Urdu)         
Compulsory

Language II - English                                                               
Compulsory

For Mathematics and Science Teacher:                

 Mathematics and Science

Above each sections carries 30 questions and 30 marks Totally 150 questions and 150 marks