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MMW - L1 & L2
NATURE OF MATHEMATICS & MATHEMATICAL LANGUAGE AND SYMBOLS
| Term | Definition |
|---|---|
| Mathematics | - Study of Numbers and Arithmetic Operations - Set of tools that can be applied to question of “how many” or “how much” - A study of pattern - A language - A process of thinking - A set of problem solving tools - An Art |
| Pattern | - Is an arrangement which helps observes anticipate what they might see or what happens next. - Also shows what may have come before - Organizes information so that it becomes more useful. - Are studies because they are everywhere |
| - Logic Patterns - Number Patterns - Geometric Patterns - Word Patters | Various Types of Pattern |
| Logic Patterns | - Are Usually the first to be observed Comes before numeration - Being able to tell which things are blocks and which are not precedes learning to count blocks |
| Number Patterns | - Are familiar to students since they are among the first patterns encountered in school - Mathematics is useful especially when it helps predict events |
| Geometric Patterns | - Is a motif or design that depicts abstract shapes like lines, polygons, and circles, and typically repeats like a wallpaper. |
| Visual patterns | are observed in nature and in art. |
| Universal Constant | Da Vinci saw mathematics as a __________, with proportions repeating themselves across the universe |
| Line or Bilateral Symmetry | The left and right proportions are exactly the same called __________ or __________ |
| starfish | a five-fold symmetry |
| spiderwort | three-fold symmetry |
| snowflake | six-fold symmetry |
| - starfish - spiderwort - snowflake | Symmetries in Nature |
| Leonardo of Pisa | Fibonacci Sequence named after Italian mathematician __________ with nickname “Fibonacci” |
| Fibonacci Sequence | - Discover the sequence as he look at hypothesized group of rabbits bred and reproduced - Pine cone showing clockwise and counterclockwise spiral |
| Golden Ratio | Ratios of successive Fibonacci number approach the number Phi, known as __________ |
| Golden Ratio | - Approximately equal to 1.619 - Can be expressed as the ratio between two numbers |
| Language | - It is a systematic means of communicating by the use of sound or conventional symbols - The code humans use as a form of expressing themselves and communicating with others - May also be defined as a system of words used in a particular discipline |
| - A vocabulary of symbols or words - A grammar consisting of rules on the use of these symbols - A community of people who use and understand these symbols - A range of meaning that can be communicated with these symbols | Language Components |
| Mathematics | - A system of communication about objects like numbers, variables, sets, operations, functions, and equations - A collection of both symbols and their meaning shared by a global community of people who have an interest in the subject |
| sentence | A __________must contain a complete thought. In the English language, an ordinary sentence must contain a subject and a predicate |
| Precise | it can make very fine distinctions or definitions among a set of mathematical symbols |
| Concise | it can express otherwise long exposition or sentences briefly using the language of mathematics |
| Powerful | one can express complex thoughts with relative case |
| - Precise - Concise - Powerful | Characteristics of Mathematical Language |
| Logic | allows us to determine the validity of arguments in and out of mathematics |
| Proposition | is a declarative sentence that can be classified as true or false, but not both |
| paradox | A self-contradictory proposition like this is called a __________ |
| Simple Proposition | that conveys one thought with no connecting words |
| Compound Proposition | contains two or more simple propositions that are put together using connective words |
| Conjunction | - AND - ∧ |
| Disjunction | ∨ |
| Inclusive Disjunction | OR |
| Exclusive Disjunction | XOR |
| Conditional | - IF & THEN - → |
| Biconditional | - IF AND ONLY IF - ⇿ - The antecedent/premise and consequent/conclusion of the first statement have been switched in the second statement |
| Negation | - NOT - ~ - Is a statement that is false whenever the given statement is true, and thru whenever the given is false |
Created by:
KYUMM1E
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