Module 1: The Nature of Mathematics

• Module One is an introduction to the nature of mathematics as an exploration of patterns
• Unit Lessons

  • Lesson 1.1 Mathematics of Our World
  • Lesson 1.2 Mathematics in Our World
  • Lesson 1.3 Mathematics of Sequence
• Mathematics

  A tool that is immensely useful, practical, and powerful
• Mathematics


  A formal system of thought that was gradually developed in the human mind and evolved in human culture
• Mathematics is present in everything we do; it is all around us and it is the building block of our daily activities
• Mathematics as a tool


  It allows us to perceive realities in different contexts that would otherwise be intangible to us
• Mathematics is a powerful tool in decision-making and it is a way of life
• Mathematics helps us to take the complex processes that are naturally occurring in the world and represents them by utilizing logic
• Mathematics has countless hidden uses and applications
• Mathematics plays an important role in many sciences
• Applied mathematics


  A useful tool in biological sciences, for instance, predicting and controlling the spread of various diseases
• Mathematics provides tools for calculations
• Mathematics


  It provides new questions to think about
• Mathematics

  • It is a study of patterns
  • It involves reasoning, which can be inductive or deductive
  • It applies methods of proof both in conventional and unconventional fashion
• Mathematics builds upon itself
• Doing mathematics


  It is done with curiosity, a penchant for seeking patterns, and a desire to know the truth
• Mathematics is for everyone
• Mathematics applications

  • Mathematics for engineers
  • Mathematics for commerce and finance
  • Mathematics for weather forecasting
  • Mathematics related to health
  • Mathematics to harness energy for utilization
• Everyone uses mathematics in different degrees and levels
• Humanity needs, beyond rudiment of mathematics, to safeguard our existence
• Types of mathematics

  • Pure
  • Applied
• Fields that use mathematics

  • Engineering
  • Commerce
  • Finance
  • Weather forecasting
  • Health
  • Energy
• Mathematics puts order amidst disorder
• Mathematics helps us become better persons and helps make the world a better place to live in
• Patterns


  Structures, forms, or designs that are regular, consistent, or recurring
• Mathematical training is vital to decipher the clues provided by nature
• The role of mathematics goes beyond prediction
• Understanding how the system works allows us to control it
• Mathematics helps us understand the mathematical pattern of a storm to avoid or prevent catastrophes
• Mathematics helps us understand the contagion of the virus to control its spread
• Mathematics helps us understand the unpredictability of cancer cells to combat it before it even exists
• Mathematics is a useful way to think about nature
• Stewart: '“Whatever the reasons, mathematics is a useful way to think about nature. What does it want to tell us about the patterns we observe? There are many answers. We want to understand how they happen; to understand why they happen, which is different; to organize the underlying patterns and regularities in the most satisfying way; to predict how nature will behave; to control nature for our own ends; to make practical use of what we have learned about our world. Mathematics helps us to do all these things, and often, it is indispensable.”'
• Patterns are all around us
• Finding and understanding patterns give us great power to play like god
• Visual patterns

  Often unpredictable, never quite repeatable, and often contain fractals
• Flow patterns

  Usually found in water, stone, and the growth of trees
• Movement patterns


  Exhibit regular rhythm in locomotion
• Rhythm


  The most basic pattern in nature
• Texture


  A quality of a certain object that we sense through touch