chapter 1

• Mathematics


  A formal system of thought for recognizing, classifying, and exploiting patterns
• Where is Mathematics?


  • In every people's daily task or activity
  • In nature, arts, music, medicine, and other disciplines
  • In communities
  • IT IS EVERYWHERE
• What is Mathematics for?

  • Useful in making conclusions and/or predictions of the events of the world
  • Use to describe the natural order and occurrences of the universe
  • Use to organize patterns and regularities as well as irregularities
  • Help to control weather, epidemics
  • Provide tools for calculations
  • Provide new questions to think about
• What is Mathematics all about?

  • Numbers
  • Symbols
  • Equations
  • Operations
  • Functions
  • Calculations
  • Abstractions
  • Devising proofs
• How is Mathematics is done?

  • With curiosity
  • With a penchant for seeking patterns and generalities
  • With the desire to know the truth
  • With trial and error
  • Without fear of facing more questions and problems to solve
• Who uses Mathematics?


  • Mathematicians (pure and applied)
  • Scientists (natural and social)
  • Everyone
• Why is mathematics important to know / learn?

  • It puts order in disorder
  • It helps us become better persons
  • It helps make a world a better place to live in
• Pattern


  A term used to describe repeating objects or events
• Nature's patterns are not just there to be admired, they are vital clues to the rules that govern natural processes
• Self-Organized Patterns


  Patterns formed without external intervention
• Invoked Organized Patterns


  Patterns formed with external intervention
• Fibonacci sequence


  A sequence of numbers in which terms are obtained by adding the two previous terms in the sequence
• Leonardo Fibonacci


  An Italian mathematician who discovered the Fibonacci sequence
• The original problem that Fibonacci investigated (in the year 1202) was about how fast rabbits could breed in ideal circumstances
• The discovery of Fibonacci numbers opened many other discoveries from different fields in science
• How mathematics helps


  • Organize Patterns and Regularities in the World
  • Predict the Behavior of Nature and Phenomena in the World
  • Control Nature and Occurrences in the World for our Own Ends
  • Has Numerous Applications in Making it Indispensable
• Applications of Math in everyone's everyday life

  • Calculating money and finance
  • Counting number of students in a class
  • Time taken for your travel
  • Building construction
  • Measuring Quantity of liquid, food etc.
• Some Scientific Applications of Mathematics

  • Finding time and position of objects
  • Finding paths or trajectories
  • Explaining theories in Physics and Chemistry
  • Oscillating of currents, string, vibrations, LCR circuits
  • Finding area, perimeter, and volumes
  • Calculating work, potential, torque, momentum
  • Population growth of a city or a country
  • Decay of nuclei, chemical reactions
  • Calculating minimum and maximum values of function
  • Solving and analyzing real-life situations