Mat41 Prelim Exam

Richard Courant

Who said this - “As an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.”

Paul Dirac

Who says this - “Mathematics is the tool especially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field.”

Classification

Within logical-mathematical knowledge is the process of __ which represents the first step towards learning more complex mathematical concepts.

Logical Sequence

Ideas in mathematics need to flow in order that make sense. The __ can naturally match what occurs in a text ( main idea) and what reader needs to understand.

Structure

In mathematics a ___ on a set is an additional mathematical object that is related to that given set in some particular characteristic or manner , and attaches ( or relates) to that set to endow it with additional meaning or significance.

Accuracy

__ is how close a measured value is to the actual ( true) value. It is the degree to which a given quantity is correct and free from error.

Precision

Is how close the measured values are to each other

Abstractness

__ is the process of extracting the underlying essence of a mathematical concept by taking away any dependence on real-world objects.

Symbolism

A mathematical __ is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other __ that occur in a formula.

Applicability

The __ of mathematics can lie everywhere on a spectrum from the completely simple to the utterly complex . Mathematics can be used in all fields of human endeavors

Generalization

Making __ is the fundamentals of mathematics. It is a skill that must be developed among students. It is important in functioning society.

A science of measure, Intellectual game, The art of drawing conclusion, A tool subject, and A system of logical procedure

list the nature of mathematics

A Science of Measures

Measurement is an integral part of modern science as well as of engineering, commerce, and daily life. It is an activity that involves interaction with concrete system with the aim of representing aspects of that system in abstract terms if concrete implies real. It often involves representation of ideal systems

Intellectual game

___ are games of skill that require significant intelligence and cognitive effort. These games may be largely based on a wide or deep knowledge, where the major test is the person’s ability is to remember and to recall.

The Art of Drawing Conclusion

Making sense of this world is natural characteristic that everyone must develop . Making sense of mathematics using logical thinking is the foundation of reasoning and proof standard.

A Tool Subject

In many field human activity, mathematics is undeniably a highly powerful instrument of investigation. Mathematics is applied in all fields

A System of Logical Procedure

Problem solving is an important component of mathematics. It is more than a vehicle for teaching and reinforcing mathematical knowledge and helping to meet everyday challenges. Problem- solving is also a skill which can enhance our logical reasoning

symmetry, fractals, spirals, fibonacci patterns, and tessellations

list the patterns and numbers in nature and the world

Symmetry

these reflection may be mirror images with only two sides like the two side of our bodies.

Fractals

The "never-ending" patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale.

Spirals

Common pattern in nature that we see more often in living things.

Fibonacci Patterns

Sequence of numbers that goes 1,1,2,3,5,8,13,21... and so on. Each number is the sum the two numbers before it

Tessellations

Patterns that are formed by repeated cubes or tiles

Language

A complex system of words and symbols, either spoken or written, used by a particular community as a means of communication.

precise, concise, and powerful

characteristics of the language of mathematics

precise

able to make very fine distinctions

Concise

able to say things briefly

Powerful

able to express complex thoughts with relative ease.

Logical Connective

A symbol which is used to connect two or more propositional or predicate logics in such a manner that resultant logic depends only on the input logics and the meaning of the connective used.

negation, conjunction, and disjunction

Common Logical connectives operator

Negation

In Mathematics, the ___ of a statement is the opposite of the given mathematical statement.

Conjunction

Is a statement formed by adding two statements with the connector AND. If both the combining statements are true, then this statement will be true; otherwise, it is false.

Disjunction

Is a compound statement formed by joining two statements with the connector OR. A __ is false if and only if both statements are false; otherwise it is true.

Inductive Reasoning

the process of reaching a general conclusion by examining specific examples.

Deductive Reasoning

the process of reaching a conclusion by applying general assumptions, procedures, or principles.

George Polya

He was born in hungary and moved to the United States 1940

classification, logical sequence, structure, precision and accuracy, abstractness, symbolism, applicability, and generalization

list the characteristic of mathematics