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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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Flashcards
Language
Language
A systematic way to communicate ideas or feelings using symbols, sounds, or marks with agreed-upon meanings.
Language of Mathematics
Language of Mathematics
The specialized system for communicating mathematical ideas, using natural language with specific terms and symbols.
Precision in Mathematical Language
Precision in Mathematical Language
The ability to make very fine distinctions, resulting in clear and precise meaning.
Conciseness in Mathematical Language
Conciseness in Mathematical Language
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Power of Mathematical Language
Power of Mathematical Language
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Mathematical Expression
Mathematical Expression
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Set (in Mathematics)
Set (in Mathematics)
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Function
Function
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Mathematical Sentence
Mathematical Sentence
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Order of Operations
Order of Operations
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Mathematical Convention
Mathematical Convention
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PEMDAS/BODMAS/MDAS
PEMDAS/BODMAS/MDAS
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Simplifying Expressions
Simplifying Expressions
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Sentence (Mathematical Sentence)
Sentence (Mathematical Sentence)
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Evaluating Expressions
Evaluating Expressions
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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.
