Matm.pdf

MATHEMATICS - formed system for Formula: recognizing, classifying, patterns. - Mathematics is partly invented. Much of Mathematics is discovered. - unravel the puzzle of nature, a useful way to and to think about nature. PATTERNS - regular, repeated or recurri...

MATHEMATICS - formed system for Formula: recognizing, classifying, patterns. - Mathematics is partly invented. Much of Mathematics is discovered. - unravel the puzzle of nature, a useful way to and to think about nature. PATTERNS - regular, repeated or recurring Ø = 1.618034 forms or designs. TESSELLATION - shape is repeated MATHEMATICAL LANGUAGE: over and over again covering a plane - language is a system of conventional spoken, manual without any gaps or overlaps. (signed), or written symbols. FRACTALS - are infinitely complex Mathematical Expression - does not patterns that are self-similar across convey complete thoughts. different scales. (never-ending Mathematical sentence - 2 types of pattern) message. Open message either True or False. Closed message known to be True SYMMETRY - nature's artwork that or False. creates harmony and balance. Set - collection of subject FIBONACCI SEQUENCE: Elements - member of set. It is - Leonardo Bonacci of Pisa. An Italian merchant. The most denoted ∈. If its not an element ∈ talented Western mathematician of the middle put ∉. ages.He is well-known as Roster Method - Just enumerating and Fibonacci which is the short separated by comma. term for filius Bonacci. Rule Method - describe specifically B = ( x in natural number ) - FIBONACCI numbers are an Subset - set in which all of its elements are integer in the infinite sequence. found in the other set. - It was believed that the concept Proper Subset Sign : A ⊂ B of Fibonacci sequence was derived from the story of the Subset : A ⊆ B reproduction of rabbits. Cardinality - refers to the number of elements. Denoted by n( ). Universal Set - contains all of the elements found in other sets. Denoted by U. Empty Set - set woth no element. Denoted by { }. Null set denoted by Ø. Composition of Function - denoted by ( f Equal Set - set with exactly the same °g ) ( x ) which means f(g(x)). evaluate from elements. inner to outer. Equivalent Set - set with the same ELEMENTARY LOGIC - set of rules that cardinality. Cardinality = same number. govern the structure | determine. Union - combine 2 sets A U B. Proposition - statement either true or false Intersection - elements that are common but not both | if no sufficient information determine it is not proposition. Denoted by to both sets. A∩B / n ( A∩B ). P, Q, R or p, q, r. Set Complement - set of elements x in U Types of Proposition: such that x is not A. A^1 Simple - single idea statement Symbolic: A^1 = { x ∈ U|x∉A} Compound - two or more ideas LOGICAL CONNECTIVES: Set Difference - difference of set A and B Denoted by A ~ B | A - B Symmetric Difference - set consisting of STATEM CONNE SYMBO TYPES all elements that belong to A or to B, but ENT CTIVES LIC OF FORMS STATEM not to both A and B. Denoted by A ⊕ B. ENT difference of two set-combine. Cartesian Product A x B - pair of each Not P Not –P Negatio element A in B | each element of B to A. n P and Q And P^Q Conjun RELATION AND FUNCTION: ction Relation - set up order pairs (x, y) Not all relation are function. P or Q Or PvQ Disjunct Function - Alicia, where value of X ion correspond to exact one value of Y. All If P, If… , P => Q Conditi function are relation. I. then Q then… , onal Domain - a set of all possible values of X. Range - a set of all possible , values of Y. P if and if and P⇔Q Bicondi Evolution of function - find F(x) for a given only if Q only if tional value of X is to evaluate the function F by substituting the value of X in the equation. 1. P - parentheses 2. E - exponent 3. M - multiply 4. D - division 5. A - addition 6. S - subtract Conditional Statement - statements which are in the form “If P, then Q”. P is the hypothesis where Q is the conclusion. Converse of P => Q to Q => P Conditional Inverse of P => Q to –P => Q conditional Contrapositive of P => Q to –Q => Conditional –P VISION : A premier inclusive university of choice aspiring to improve man as man by developing individuals through a legacy of excellent education and compassionate value formation. MISSION: The Our Lady of Fatima University, together with Fatima Medical Science Foundation, Inc. is dedicated to the improvement of man as man through the holistic formation of individuals imbued with knowledge, skills, and virtues.