What are Patterns?
Patterns are sequences or designs that are orderly or that repeats |
Types of Patterns: |
Symmetry |
It is when different sides are alike. A reflection of a mirror is one of symmetry. |
Fractals |
These are 'never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale. |
Spirals |
A pattern that spirals, examples are seashells, hurricanes, and galaxies. |
Fibonacci Patterns |
The least understood pattern in nature, it is a pattern that increases its sequence exponentially. (i.e. 1,2,4,8,16,32,etc.) |
Tesselations |
A pattern formed of cubes or tiles, can occur in both living and non-living things. |
The Use of Mathematics
Technology |
This aspect depends on basic research to advance. Its value is determined on by math and experimentation using statistics |
| |
Examples: Predicting the Weather, Navigation, Computer Circuits. |
Engineering |
Math is used to design components and products, maintain operating components, model real-life situations for testing and learning purposes as well build and maintain structures. |
| |
Examples: Robotics, Construction, Microwaves, Rockets and Satellites, Automotive Design. |
Media |
Math can be found in Media. Using camera lens or convincing nature of numbers for advertising. |
| |
Examples: Digital Music, Movie Graphics, Polling and Voting. |
Medicine and Health |
Advanced medical studies rely on statistics . |
| |
Examples: Crowd People: Population Dynamics, Pharmacy and Medicine, MRI and Tomography. |
Finance and Business |
Businesses require skill in product making and providing service. Overseeing finances is key to survival and success. |
| |
Examples: Insurance, Loans and Mortgages, Fraud Detection, Pricing Strategies, Game Theory. |
|
|
Language of Mathematics
What is Language? |
It is a complex system of words and symbols, either spoken or written, used by a particular community as a means of communication. |
Characteristics of Language |
Precise |
Able to make very fine distinctions. |
Concise |
Able to say things briefly. |
Powerful |
Able to express complex thoughts with relative ease. |
English Language of Mathematics
| |
English |
Mathematics |
Name given to an object of interest: |
Noun. |
Expression. |
| |
Example: Carol, Manila, book |
Example: 5, 2+3, 1/2 |
A complete thought: |
Sentence. |
Sentence. |
| |
Example: Dash likes guinea pigs. |
Example: 3+4=7, 3+4=8 |
Sets, Functions, and Relations
The word "is" has three distinct meanings. |
Example: "5 is the square root of 25." "5 is less than 10." "5 is a prime number." |
Elementary Logic
Logical Connective |
It is a symbol or a word used to connect 2 or more sentences. Each logical connective can be expressed as a truth function. |
Negation "~" |
Opposite of the statement, usually employing the word not. |
Original Statement: |
Negation of Statement: |
"p" Today is Monday |
"~p" Today is not monday. |
Conjunction "∧" |
It is formed by using the word "and" to join two sentences. |
| |
"p∧q" Sister likes dogs and Mother likes cats. |
Disjunction "∨" |
It is formed by using the word "or" to join two simple sentences. |
| |
"p∨q" The clock is slow or the time is correct. |
Implication "⇒" |
It is a type of relationship between 2 statements or sentences. It is formed using the word "if" to create implication. |
| |
"p⇒q" If my heart stops, then I will die. |
|
|
|
