MATHEMATICS IN MODERN WORLD MODULE 1-6

• Mathematics


  Comes from greek word means that which is LEARNT or LESSON
• Patterns


  • Are regular, repeated or recurring forms or design
• Pythagoras


  The father of numbers
• Plato


  Pioneered the study of the onthology of mathematics objects
• Aristotle


  Studied logic and issues related to infinity
• Realism


  Math exist objectively and independent of human thought
• Idealism


  Holds that mathematics is a product of human imagination
• Applied Mathematics


  Is the branch of mathematics that are involved in the study of the physical, biological, or sociological world
• Pure Mathematics


  Is driven by abstract problems, rather than real world problems
• Universal Turing Machine


  Which began as an abstract idea later laid the groundwork for the development of the modern computer
• Asymmetric


  If an object is not symmetrical
• Line or Bilateral


  Left and right portion are exactly the same
• Radial or Rotational


  Rotate the object by several degrees and you can still achieve the same appearance as the original position
• Angle of Rotation


  The smallest angle that a figure can be rotated while still preserving the original formation
• Spherical Geometry


  Generate two identical halves when you cut it along its center
• Leonardo of Pisa


  Also known as Fibonacci
• Recursive Definition


  for a sequence is one in which each successive term of the sequence is defined by using some of the preceding terms
• Logarithmic or Equiangular Spiral


  Follows the rule that as distance from the spiral center increase
• Golden Ratio


  The ratios of successive Fibonacci numbers approach the number phi, ration between two numbers
• Phi


  a/b = phi ≈ 1.61803
• Language


  May be a system of words or codes used within a discipline
• Components of Language


  • Vocabulary
  • Meaning
  • Grammar
  • Syntax
  • Narrative
• Language must be


  • Precise
  • Concise
  • Powerful
• Mathematical Expression


  Mathematical analogue of a noun
• Mathematical Expressions


  Is a name given to some mathematical object of interest
• Real Numbers


  Are usually named with lower case letters
• Sets


  Are usually named with capital letters
• Mathematical Sentence


  Is the analogue of english sentence,it is a correct arrangement of mathematical symbols that states a complete thought
• Open Sentences


  Some statement are true depending upon the number that is chosen for the variable
• Paradoxes


  Some sentences that are impossible to determine their truthfulness because they present a contradiction
• Variables


  Are symbols or letters that may have one or more possible value
• Constant


  Are number with fixed value
• Mathematical Constant


  Speacial symbols that have exact numerical value
• Mathematical Verb


  Are symbols that show the relationship of at least expression
• Set


  Undefined terms in mathematics and is described as a well defined collection of objects
• Well Defined


  Means that a given object can be categorically identified to belong to the collection or not
• Set Notation


  Are methods of representing sets
• Axom of Extension


  Says that a set is completely determined by what is elements are not the order in which they might be listed or the fact that some elements might be used more than once
• Set Roster Notation


  Writing of all its elements between braces
• Set Builder Notation


  A description of the elements of the set is specifically written