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WESTERN INSTITUTE OF TECHNOLOGY
LUNA ST., LA PAZ, ILOILO CITY P.O. Box 258 ILOILO CITY
PHILIPPINES 5000 PHILIPPINES 5000
TELEPHONE Nos.: 3200259 3201475 3200902 3209767 3209853 3209456
FAX No. +6333 3201484 Globe-Islacom No. 5087151
Website: www.wit.edu.ph E-mail: wit@wit.edu.ph
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COLLEGE OF ARTS AND SCIENCES
DEPARTMENT OF MATHEMATICS
MATHEMATICS IN THE
MODERN WORLD
MODULE 3
________________________
Name of Student
_______________________________________
Course and Year
WESTERN INSTITUTE OF TECHNOLOGY
LUNA ST., LA PAZ, ILOILO CITY P.O. Box 258 ILOILO CITY
PHILIPPINES 5000 PHILIPPINES 5000
TELEPHONE Nos.: 3200259 3201475 3200902 3209767 3209853 3209456
FAX No. +6333 3201484 Globe-Islacom No. 5087151
Website: www.wit.edu.ph E-mail: wit@wit.edu.ph
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Course Number : Math 1
Course Title : Mathematics in the Modern World
Course Description : This course deals with the nature of mathematics, appreciation of its practical
and intellectual and aesthetic dimensions, and application of mathematical tools in
daily life.
The course begins with an introduction to the nature of mathematics as an
exploration of pattern (in nature and the environment) and as an application of
inductive and deductive reasoning. By exploring these topics, students are
encouraged to go beyond the typical understanding of mathematics as merely a set
of formulas but as a source of aesthetics in patterns of nature, for example, and a
rich language in itself (and of science) governed by logic and reasoning.
The course then proceeds to survey ways in which mathematics provide a tool for
understanding and dealing with various aspects of present – day living, such as
managing personal finances, making social choices, appreciating geometric designs,
understanding codes used in data transmission and security, and dividing limited
resources fairly. These aspects will provide opportunities for actually doing
mathematics in a broad range of exercses
Pre-requisite: None
Credit Units: 3 Units
Course Outline
Section I. The Nature of Mathematics
- Mathematical Language and Symbols
- Characteristics of mathematical language: precise, concise, powerful
- Expressions vs. sentences
- Conventions in the mathematical language
- Four basic concepts: sets, functions, relations, binary operations
References:
CHED Memorandum Order No. 20, series of 2013. (4 July 2013). General Education Curriculum:
Holistic understandings, intellectual and civic competencies
Nocon R. et al. (2018). Essential Mathematics for the Modern World. Quezon City: C & E Publishing,
Inc.
ABOUT THE COURSE
WESTERN INSTITUTE OF TECHNOLOGY
LUNA ST., LA PAZ, ILOILO CITY P.O. Box 258 ILOILO CITY
PHILIPPINES 5000 PHILIPPINES 5000
TELEPHONE Nos.: 3200259 3201475 3200902 3209767 3209853 3209456
FAX No. +6333 3201484 Globe-Islacom No. 5087151
Website: www.wit.edu.ph E-mail: wit@wit.edu.ph
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Date: November 24, 2014
Mathematics uses many symbols. There are ten digits (0, 1, 2, …, 9), symbols for operations (+ ,–
, x, ÷), symbols that represent values, (x, y, z, etc.), and many other special symbols (+. <, ≤, 𝜋, etc.).
Letters often (but not always) have special uses as follows:
Start of the alphabet a, b, c For constants (fixed values)
From I to n i, j, k, n Positive integers (for counting)
End of the alphabet x, y, z For variables (unknown)
Like in normal languages, the correspondence between symbols and their meaning are
conventions rather than rules.
Illustration:
In the equation y = ax + b, it is assumed that a and b are constants and x is a variable whose
values changes, which in turn makes the variable y change its value as well.
Even though the words “noun,” “verb,” or “pronoun” are not used in mathematics, the similarities
with the English language can be observed:
- Nouns could be constants, such as numbers or expressions with numbers:
1
3
- A verb could be the equal sign = , or inequality symbols like > or ≤.
- Pronouns could be variables like x or y:
5x – 8, 2xy, −
4
𝑥
- Sentences could be form by putting together these parts;
3x + 7 = 24, 2x + 2y = 7
The mathematical analogue of a “noun” will be called an expression. Thus an expression is a
name given to a mathematical object of interest. Whereas in English we need to talk about people,
places, and things, we’ll see that mathematics has much different ‘objects of interest’.
The mathematical analogue of a ‘sentence’ will also be called a sentence. A mathematical
sentence, just as an English sentence, must take a complete thought. The table below summarizes
the analogy
English Mathematics
Name given to an object of
interest:
NOUN
(person, place, thing)
Examples: Carol, Idaho, book
EXPRESSION
Examples:
a complete thought SENTENCE
Examples:
The capital of Idaho is Boise.
The capital of Idaho is Pocatello.
SENTENCE
Examples:
Languages have conventions. In English, it is conventional to capitalize proper nouns (like ‘Carol’
and ‘Idaho’). This convention makes it easy for a reader to distinguish between a common noun (like
‘carol’, a Christmas song) and a proper noun (like ‘Carol’). Mathematics has its conventions, which
help readers distinguish between different types of mathematical expressions.
Exercise Set 3.
Classify the entries in the list below as
- An English noun, or a mathematical expression
- An English sentence, or a mathematical sentence
- Cat _______________
2. 2 _______________
- The word ‘’cat’ begins with the letter ‘k’ _______________
4. 1 + 2 = 4 _______________
5. 5 – 3 _______________
6. 5 – 3 = 2 _______________
- The cat is black. _______________
WESTERN INSTITUTE OF TECHNOLOGY
LUNA ST., LA PAZ, ILOILO CITY P.O. Box 258 ILOILO CITY
PHILIPPINES 5000 PHILIPPINES 5000
TELEPHONE Nos.: 3200259 3201475 3200902 3209767 3209853 3209456
FAX No. +6333 3201484 Globe-Islacom No. 5087151
Website: www.wit.edu.ph E-mail: wit@wit.edu.ph
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Prof. Ninfa Sua-Sotomil
Issue: 2
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Approved: President
Date: November 24, 2014
Four Basic Concepts
- x _______________
- x = 1 _______________
- x – 1 = 0 _______________
- t + 3 _______________
- t + 3 = 3 + t _______________
- This sentence is false _______________
- x + 0 = x _______________
- 1 ∙ x = x _______________ 1. Sets
A collection of objects, and in mathematical discourse these objects are mathematical ones
such as numbers, points in space or other sets.
The members of a set are usually called its elements, and the symbol ∈ is usually read “is an
element of”.
Three common ways to denote a specific set, which will be discussed further later:
a. List its elements inside braces: { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 }.
b. Use dots to imply a list that is too long to write down”
c. Define a set via property;
2. Functions
Function – is a set of ordered pairs of number (x, y) in which no two distinct ordered pairs
have the same first number.
A function f from a set A to a set B is a correspondence, or rule, which assigns to each element
a of A exactly one element b of B****.
The set of all admissible values of x is called the domain of the function, and the set of all resulting
values of y is called the range of the function.
Bijection , bijective function or one – to – one correspondence – is a function between the
elements of two sets, where each element of one set is paired with exactly one element of the other
set, and each element of the other set is paired with exactly one element of the first set.
In this definition, the restriction that no two distinct ordered pairs can have the same first number
ensures that y is unique for a specific value of x. The symbols x and y denote variables. Because
the value of y is dependent on the choice of x , x denotes the independent variable and y denotes
the dependent variable.
f(x) – read as “ f of x ”
- called as a function value
- due to Swiss Mathematician and Physicist Leonhard Euler (1707 – 1783).
