MATH-1-LESSON-2-Students-copy
Page 1: Introduction
Title: Mathematics in the Modern World
Presented by: Jessa P. Real, MMATH
Institution: Misamis University Arts
Motto: Diversitas est Fortitudo
Page 2: Mathematical Language and Symbols
Course code: 904
Institution: Misamis University Arts
Page 3: Outline
Characteristics of Mathematical Language
Expression vs Sentence
Translating English Statements to Mathematical Expression or Sentence
Page 4: Learning Outcome
Perform operations on mathematical equations.
Institution: Misamis University Arts and OATS Milk
Page 5: Importance of Language
Language facilitates expressing and understanding ideas.
It systematically enables communication.
Page 6: Characteristics of Mathematical Language
Precise
Able to make very fine distinctions.
Concise
Capable of expressing ideas briefly.
Powerful
Can express complex thoughts with relative ease.
Page 7: Mathematical Symbols
Digits: The 10-digit Hindu-Arabic numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Operation Symbols: +, -, x, ÷
Variables: x, y, z, w, etc.
Page 8: Translating Statements
Symbol: R
Name: Real Number
Meaning: Any number found in the real world.
Page 9: Natural Numbers
Symbol: N = {1, 2, 3,...}
Name: Natural Number
Meaning: All positive counting numbers.
Page 10: Whole Numbers
Symbol: W = {0, 1, 2, 3,...}
Name: Whole Number
Meaning: Set of natural numbers including 0.
Page 11: Integers
Symbol: Z = {..., -3, -2, -1, 0, 1, 2, 3,...}
Name: Integers
Meaning: Positive and negative counting numbers including zero.
Page 12: Rational Numbers
Symbol: Q = {-3, 0, -6, 5/6, 3.23,...}
Name: Rational Number
Meaning: Numbers expressible as a fraction p/q (p and q integers, q ≠ 0).
Page 13: Irrational Numbers
Symbol: Q' = {...}
Name: Irrational Number
Meaning: Numbers such as square roots of positive rational numbers and cube roots of rational numbers.
Page 14: Additional Mathematical Symbols
Common Symbols: =, <, ≤, >, ≥, %, π, etc.
Set Theory Notations: { }, ε, ∪, ∩, etc.
Page 15: Element
Example: 1. 2 ∈ A
A = {2, 4, 6, 8}
Symbol: ∈
Name: Element
Meaning: An object contained in the set.
Page 16: Intersection
Example: 1. A ∩ B = {2, 4}
Symbol: ∩
Name: Intersection
Meaning: Objects common to both sets A and B.
Page 17: Union
Example: 1. A ∪ B = {2, 4, 6, 8}
Symbol: ∪
Name: Union
Meaning: Objects in either set A or B (or both sets).
Page 18: Empty Set
Example: B ∩ C = { }
Symbol: { }
Name: Empty Set
Meaning: A set with no elements.
Page 19: Subset
Example: A ⊂ B (A is a subset of B)
Symbol: ⊂
Name: Subset
Meaning: Every element of A is contained in B; B has more elements.
Page 20: Mathematical Translation
< (less than)
(greater than)
≤ (less than or equal to)
≥ (greater than or equal to)
Page 21: Quantifiers
Universal Quantifier:
“For all”; “For every”
Example: For every x ∈ N
Existential Quantifier:
“There exists”; “For some”
Example: There exists an x ∈ Z
Page 22: Expression vs Sentence
In English: Nouns name entities (people, places, things).
In Mathematics:
Expression: Arrangement of symbols representing a mathematical object.
Sentence: Arrangement expressing a complete thought.
Page 23: Sentence Definition
A correct arrangement of mathematical symbols that expresses a complete thought.
Page 24: Operations on Mathematical Equations
Focus on various operations and their applications.
Institution: Misamis University Arts
Page 25: Step 1
Clear fractions using the LCM.
If no fractions, simplify using PEMDAS.
Example: 4(x - 3) + 12 = 15 - 5(x + 6)
Simplifying steps leading to 4x = -5x - 15.
Page 26: Step 2
Transpose variables on one side; constants on the other.
Example: 4x + 5x = -15 - 0.
Reverse operations on operands when transposing.
Page 27: Step 3
Simplify both sides of the equation.
Example: Transition to 9x = -15.
Page 28: Step 5
Isolate the variable.
Example: 9x = -15 leads to x = -5/3.
Pages 29-32: Continuing Step-by-Step Operations
Continued examples following similar steps for clarity and practice.
Page 33: Conclusion
Thank you!
Institution: Misamis University Arts
Page 34: References
Hengania et al. (2023). Mathematics in the Modern World, MUTYA Publishing House Inc.
Aufmann et al. (2013). Mathematical Excursions 3rd ed., Belmont: Brooks/Cole, Cengage Learning.
Aufmann et al. (2018). Mathematics in the Modern World, Philippine ed., Manila: Rex Book Store, Inc.
The Fibonacci sequence: A brief introduction, plus.maths.org.