math

42問 • 1年前

問題一覧

Are two fundamental forms of reasoning for mathematicians

inductive and deductive reasoning

Is the logical process in which multiple premises, all believed to be true or found true most of the time are combined to obtain a specific conclusion

inductive reasoning

The process of reaching conclusions based on previously known facts

deductive reasoning

The conclusions reached by this type of reasoning are not always valid

inductive reasoning

The conclusions reached by this type of reasoning are valid and can be relied on

deductive reasoning

Is an evidence; some may call it an argument that establishes a fact or the veracity of something holds

proof

This definition tells us that in order to claim that the statement are argument is true or valid, there has to be some evidences verified by science

proof

It gives validation of something that is assumed to be true or false

proof

Polya's four stop approach to problem solving

understand the problem devise a plan carry out the plan look back/review the solution

The process of reasoning to a general conclusion through observations of specific cases

inductive reasoning

Inductive reasoning is also called

induction

Often used by mathematicians and scientists to predict answers to complicated problems

inductive reasoning

Is a part of the scientific method

inductive reasoning

When we make a prediction based on specific observations, it is called ______

hypothesis or conjecture

_____ (1564 to 1642) used INDUCTIVE REASONING to discover that the time required for a pendulum to complete one swing, called THE PERIOD OF A PENDULUM, depends on the length of the pendulum

GALILEO GALILEI

GALILEO GALILEI (_____) used INDUCTIVE REASONING to discover that the time required for a pendulum to complete one swing, called THE PERIOD OF A PENDULUM, depends on the length of the pendulum

1564 to 1642

GALILEO GALILEI (1564 to 1642) used _______ to discover that the time required for a pendulum to complete one swing, called THE PERIOD OF A PENDULUM, depends on the length of the pendulum

INDUCTIVE REASONING

GALILEO GALILEI (1564 to 1642) used INDUCTIVE REASONING to discover that the time required for a pendulum to complete one swing, called ______, depends on the length of the pendulum

THE PERIOD OF A PENDULUM

Is the time it takes for the pendulum to swing from left to right and back to its original position

the period of a pendulum

In testing a conjecture, if a special case is found that satisfies the conditions of the conjecture but produces a different result, that case is called a

counter example

If a counter example cannot be found, the conjecture is neither _______

proven nor disproven

Is the process of reasoning to a specific conclusion from a general statement

deductive reasoning

Deductive reasoning is also called

deduction

It applies general assumptions, procedures, or principles to reach a conclusion

deductive reasoning

General to specific

deductive

Specific to general

inductive

A question that motivates you to search for a solution

problem

This implies, first, what you want or need to solve the; and second, that you have to search for a way to find a solution

problem

Whether a question is a problem or an exercise depends on the prior knowledge of the problem solver

problem

About finding a solution not just answers to questions

problem solving

One of the foremost recent mathematicians to make a study of problem solving was _______

GEORGE POLYA (1887 TO 1985)

GEORGE POLYA (1887 to 1985) was born in _____ and moved to the UNITED STATES in 1940

HUNGARY

GEORGE POLYA (1887 to 1985) was born in HUNGARY and moved to the ____ in ____

UNITED STATES 1940

Know what is asked, what are given, etc

understand the problem

Techniques to solve the problem

devise a plan

Check or verify the result

look back or review the solution

Characteristics of the mathematics language

precise concise powerful

Able to make very fine distinctions or definitions

precise

Able to say things briefly

concise

Able to express complex thoughts with relative ease

powerful

Structural rules governing the use of symbols representing mathematical objects

grammar of mathematics

The word "_____" could mean equality, inequality, or membership in a set

Business Finance

Sab Sescon · 46問 · 2年前

Business Finance