midterm for gned03

• • language - is a systematic way of communication with other people of sounds or convention symbols.
• • mathematical language - the system used to communicate mathematical ideas
• • according jamison (2000) the use of language in mathematics differ from the language of ordinary speech in three important ways.
• define three mathematical language - non-temporal, devoid of emotional content and precise.
• variable - a quantity that may change within the context or like it represent the letter by x and y
• • mathemaitcal expression - it consist of term and separated with other term with either plus or minus (literal, numerial and constant)
• • mathematical sentences - combines two mathematical expressions using a comparison operator.
• • open sentence - mathematical sentences that is not known to be either true or false.
• • closed sentence - mathematical sentence that is known to be either true or false.
• • set - is said to be well-defined collections of a distinct objects, usually represented by capital letters, the object of sets are separated by a comma the object that belong in a sets are the elements, or members of the sets
• elements - B= {2,4,6,8...} called?
• • roster or tabular method - a method which the elements are enumerated, listed and separated by comma.
• • rule or descriptive method - a method which is common characteristic are being defined.
• • two ways on describing a set - roster/tabular method and rule/descriptive method.
• finite sets - the number of the elements is countable
• infinite - the numbers of elements cannot be counted
• empty sets - the sets that contains no element.
• universal sets - refer to the set of all elements.
• kind of sets - finite sets , infinite sets, empty sets and universal sets
• equal sets - are set with exactly same elements and cardinality.
• equivalent sets - are set with the same number of element or cardinality.
• joint sets - are set with least one common element.
• disjoint set - are set with no common elements.
• subsets - if A and B sets, then A is called a subset of B.
• proper subsets - is a subset of the set except a set itself

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• power set - the set containing all the subsets of a given set with no elements.
• improper subsets - the first set is equal to the first set itself and null set.
• three characteristics of mathematical language - precise, concise and powerful
• union of sets - elements are found in both set.
• intersection of a set - set whose elements are common to both set.
• differences of a set - set whose elements are found in set a but not in set b.
• complement of a set - set whose elements are found in universal set but not in a.
• Venn diagram - pictorial representation of relation and operation of sets.
• Mathematics - The study of the relationship among numbers, quantities and shapes. Nurtures human characteristic like power of creativity, reasoning, critical thinking, and spatial thinking.
• • Mathematics - is the study of pattern and structure. It is fundamental to the physical and biological sciences, engineering and information technology, to economics and increasingly to the social sciences
• Plato, Pythagoras and Empedocles - studied patterns to explain order in nature which lead to the modern understanding of visible patterns.
• In the 19th Century Joseph Plateau - Belgian Physicist, examined soap films. leading him to formulate the concept of a minimal surface.
• Ernst Haeckel - German Biologist and Artist, painted a hundred of marine organisms to emphasize their symmetry.
• D’Arcy Thompson - Scottish Biologist, pioneered the study of growth patterns in both plants and animal showing that simple equations could explain spiral growth
• In 20th Century Alan Turing - British Mathematician, Predicted mechanisms of morphogenesis which give rise to patterns of spots and stripes.