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Questions and Answers
What characterizes the mathematical language as being precise?
What characterizes the mathematical language as being precise?
Which of the following is an example of a mathematical expression?
Which of the following is an example of a mathematical expression?
What is NOT a characteristic of mathematical language?
What is NOT a characteristic of mathematical language?
How does the mathematical language express complex thoughts?
How does the mathematical language express complex thoughts?
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Which of the following is true about mathematical expressions?
Which of the following is true about mathematical expressions?
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What defines a mathematical sentence?
What defines a mathematical sentence?
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What is an example of a linear polynomial expression?
What is an example of a linear polynomial expression?
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In the order of operations, what is the correct first step?
In the order of operations, what is the correct first step?
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Which of the following options illustrates the use of mathematical symbols for convenience?
Which of the following options illustrates the use of mathematical symbols for convenience?
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Which statement best explains the nature of mathematics as a language?
Which statement best explains the nature of mathematics as a language?
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Which terminology refers to the agreed-upon symbols and notations in mathematics?
Which terminology refers to the agreed-upon symbols and notations in mathematics?
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Which of the following options is classified as a mathematical sentence?
Which of the following options is classified as a mathematical sentence?
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What phrase corresponds to the mathematical operation of subtraction in English?
What phrase corresponds to the mathematical operation of subtraction in English?
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Which one of these is NOT a part of the order of operations?
Which one of these is NOT a part of the order of operations?
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Study Notes
NU LiPa Mathematics in the Modern World
- This course covers mathematics in the modern world
- Topics include Mathematical Language and Symbols, and the Four Basic Concepts of Mathematics
- Learning outcomes include discussing the language, symbols, and conventions of mathematics
- Explaining the nature of mathematics as a language
- Performing operations on mathematical expressions correctly
- Acknowledging that mathematics is a useful language
Mathematical Language
- Language is a system for communicating ideas or feelings using symbols, sounds, or marks
- Mathematical language uses technical terms and conventions peculiar to mathematical discourse
- Mathematical language employs a highly specialized symbolic notation for formulas
Characteristics of Mathematical Language
- Precise: Able to make very fine distinctions. Mathematical symbols are used based on their meaning and purpose
- Concise: Able to say things briefly. Complex English sentences can be shortened using mathematical symbols
- Powerful: Able to express complex thoughts with relative ease. Mathematical language facilitates critical thinking, analysis, and reasoning
Examples of commonly used symbols
- Hindu-Arabic numerals (0-9)
- Symbols for operations (+, -, ×, ÷)
- Symbols representing values (w, x, y, z, etc.)
- Other special symbols (=, <, >)
Expression versus Sentences
- Expression (mathematical expression): A finite combination of symbols that's well-formed according to context-dependent rules
- Expression (mathematical expression): Does not state a complete thought; cannot be deemed true or false
- Sentence (mathematical sentence): An analogue of an English sentence, a correct arrangement of mathematical symbols expressing a complete thought
- A mathematical sentence can be evaluated as true, false, or sometimes true/false
Parts of an Expression
- Terms: Expressions are built from terms
- Coefficient: The numerical factor in a term
- Variable: Symbols representing unknown quantities
- Constant: Numerical values in a term that do not change
Examples of Expressions
- Simple (e.g., 8x – 5) → linear polynomial
- More complex (e.g., 7x² + 4x – 10) → quadratic polynomial
- Complex (e.g., x²⁄4 –12 ) → rational fraction
- Complex (e.g. ∫𝑥^2 𝑑𝑥 )
Common Words and Phrases in Math
- Addition (+): plus, sum, more than, increased by, added to, greater than, total
- Subtraction (-): difference, subtract, less than, take away, decreased by
- Multiplication (×): product of, times, twice, thrice, factor, multiplied by
- Division (÷): divided by, quotient, split, share, distribute
Binary Operations for Functions
- Sum: f(x) + g(x)
- Difference: f(x) - g(x)
- Product: f(x) * g(x)
- Quotient: f(x) / g(x)
Types of Sets
- Empty/Null Set: A set with no elements (Ø or {})
- Finite Set: A set with a limited or countable number of elements
- Infinite Set: A set with an unlimited or uncountable number of elements
- Unit/Singleton Set: A set containing only one element
- Equal Sets: Sets containing precisely the same elements
- Equivalent Sets: Sets containing the same number of elements
- Universal Set: The set containing all the elements under consideration (denoted by U)
- Subsets: A set is considered a subset of another set if all its elements are also contained within the latter; denoted by ⊂
- Power Set: The collection of all possible subsets of a set; denoted by P(A) or Power(A)
Set Operations
- **Union (∪)$: A ∪ B$ - Includes elements from both sets $A$ and $B$
- **Difference (-): A-B$ – Includes elements from $A$ that are not in $B$
- **Intersection (∩): A ∩ B$ – Includes only elements that are in both sets$A$ and $B$
- **Complement (')$: A' $ - Includes elements from the universal set $U$ that are not in $A$
Order of Operations (PEMDAS/BODMAS)
- Parentheses/Brackets first
- Exponents/Orders next
- Multiplication and Division (left-to-right)
- Addition and Subtraction (left-to-right)
Relations and Functions
-
Relation: A rule that pairs elements of one set (domain) to one or more elements in another set (range) forming ordered pairs
-
Function: A specific type of relation where each element in the domain maps to precisely one element in the range.
- Types of Functions: One-to-one, one-to-many, many-to-one, many-to-many
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Description
Explore the key concepts of mathematics as a language in the modern world. This quiz will cover mathematical symbols, language, and the four basic mathematical operations. Discover how mathematics serves as a precise and concise means of communication.
