MITMW 1

• Mathematics

  The study of relationships among numbers, quantities, and shapes. It includes arithmetic, algebra, trigonometry, geometry, statistics, and calculus.
• Fields of study

  • Chemistry
  • Humanities
  • Mathematics
  • Physics
• Patterns


  • Spirals, symmetries, mosaics, stripes, spots, etc. that can be modelled mathematically
• Types of patterns

  • Disorder
  • Disorganization
  • Patterns
  • Plainness
• Aristotle


  One Greek philosopher who studied patterns to explain order in nature which lead to the modern understanding of visible patterns
• Mathematical language


  The system commonly used to communicate mathematical ideas as it is more precise than any other language
• Characteristics of mathematical language

  • Non-temporal (no past, present or future)
  • Devoid of emotional content
  • Precise
• Process to solve a problem

  1. Modeling and formulating

  2. Transforming and manipulating

  3. Inferring

  4. Communicating
• Modeling and formulating

  • Urban planning: City planners use mathematical models to simulate traffic flow, pedestrian movement, and resource allocation
  • Epidemiology: Epidemiologists model the spread of diseases using differential equations
• Transforming and manipulating

  • Optimization in engineering design: Finding the dimensions of a cylindrical storage tank to meet volume requirement while minimizing material cost
• Inferring

  • Data collection and analysis: Gather data on various aspects, including the number of orders, total sales revenue, average order value, and customer demographics during the promotional period and a comparable non-promotional period
• Mathematical expression

  Can be classified as monomial, binomial, trinomial, or polynomial
• Mathematical sentence

  Combines two mathematical expressions using a comparison operator such as =, ≠, >, <, ≥, ≤
• Open sentence


  A mathematical sentence that is not known if it is true or false
• Closed sentence


  A mathematical sentence that is known to be either true or false
• Convention


  A technique used by mathematicians, engineers, scientists in which each particular symbol has a particular meaning
• Context

  The particular topics being studied, important to understand the context to understand mathematical symbols
• Set


  A well-defined collection of distinct objects known as the elements or members
• Symbol

  Particular meaning
• Symbols in Mathematics

  • Greek and Latin letters used for physical quantities, special functions, and conventions in representing the defined variable
• Greek letters


  • �� (pi) used to represent the constant value 3.14159...
  • �� (alpha), 𝛽 (beta), and �� (theta) used to represent angles
• Greek capital letter 𝚺 (sigma)


  • Commonly used to represent the summation
• It is a technique used by mathematicians, engineers, scientists in which each particular symbol has particular meaning
• Reasons for using symbols

  • context
  • convention
  • sets
  • functions
• Context

  Refers to the particular topics being studied and it is important to understand the context to understand mathematical symbols
• Set


  A well-defined collection of distinct objects known as the element/s or member/s of it
• Representing a set


  • S = {1, 2, 3, 4, 5}
  • F = {banana, mango, pineapple, orange}
• Two ways to describe a set

  • Roster/Tabular Method
  • Rule/Descriptive Method
• Finite Set

  A set is called a finite set if the elements in the set can be counted
• Finite Sets

  • S = {1, 2, 3, 4}
  • S = {x | x ∈ ℕ, x ≤ 9}
• Infinite Set


  A set is called a finite set if it has countless members
• Infinite Sets

  • The set ℕ of whole numbers
  • Y = {..., -4, -3, -2, -1, 0, 1}
• Empty Set

  A set which has no members, denoted by ∅ or {}
• Singleton Set

  A set which contains only one member
• Singleton Sets

  • A = {x | x is neither prime nor composite}
  • B = {x | x is an even prime number}
• Pair Set


  A set which contains only two members
• Pair Set


  • A = {x | x ∈ ℕ, x < 2}
• Universal Set


  The set of all objects under consideration, denoted by ⋃ or ��
• Universal Set


  • If the sets are some natural numbers, then the set of ℕ of all numbers may be regarded as the universal set
• Cardinal Number of a Set

  The number of distinct members of a finite set, denoted by n(A)