Ako, si , ay nangangakong magsisipag mag-aral hindi lang ... aking kontrata: Ako, si _____, ay nangangakong magsisipag mag-aral hindi lang para sa aking sarili kundi para rin sa aking pamilya, para sa

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  • Ang aking kontrata:

    Ako, si ______________, ay nangangakong magsisipag mag-aral hindi lang para sa aking sarili kundi para rin sa aking pamilya, para sa aking bayang Pilipinas at para sa ikauunlad ng mundo.

  • MATH 17: College Algebra and Trigonometry

    Lecturer: Jomar Fajardo Rabajante 1st Semester AY 2012-2013 Math Division, IMSP, UPLB

  • SOME PRINCIPLES OF LEARNING

    Law of Use and Disuse

    Law of Frequency and Recency

    Law of Intensity

    Law of Readiness / Law of Mindset

    Law of Belonging and Motivation

    Mathematics Division, IMSP, UPLB

  • MATHEMATICS

    MATHs (Sipnayan)

    Math is the study of patterns

    Math is a language

    Math is a tool for solving problems

    Mathematics Division, IMSP, UPLB

  • ALGEBRA

    ETYMOLOGY OF ALGEBRA

    From Arabic word al-jabr which literally means restoration

    Mathematics Division, IMSP, UPLB

  • ALGEBRA AND ARITHMETIC

    Mathematics Division, IMSP, UPLB

    Algebra is a generalization of Arithmetic.

    ARITHMETIC ALGEBRA

  • ALGEBRA AND ARITHMETIC

    ASSIGNMENT:

    1. What is the Fundamental Theorem of Arithmetic?

    2. What is the Fundamental Theorem of Algebra?

    Mathematics Division, IMSP, UPLB

  • ALGEBRA

    DISCIPLINES UNDER ALGEBRA

    Elementary Algebra (e.g. HS and College Algebra)

    Linear Algebra

    Modern (Abstract) Algebra

    Etc Mathematics Division, IMSP, UPLB

  • ABSTRACTION OF ALGEBRA

    ALGEBRA as the study of STRUCTURES

    - study of the structure of abstract mathematical systems

    Mathematics Division, IMSP, UPLB

  • ABSTRACTION OF ALGEBRA

    Mathematics Division, IMSP, UPLB

    Examples (you can also use < >)

    [Z2, +2] (binary arithmetic)

    [Z4, x4]

    [Z12, +12] (clock arithmetic)

    [DC, followed by]

    [R, +, ]

  • ABSTRACTION OF ALGEBRA

    Algebraic Structure/Algebraic System

    An algebraic structure is an abstract mathematical system involving

    1) sets of objects and

    2) some operations on those objects,

    usually satisfying certain axioms.

    Mathematics Division, IMSP, UPLB

  • ABSTRACTION OF ALGEBRA

    Mathematics Division, IMSP, UPLB

  • SETS (the basic ingredient

    of algebra)

    Mathematics Division, IMSP, UPLB

  • A SET is a well-defined collection of objects, real or imagined.

    Examples: Which of the following is a set?

    1. Collection of all cities in the Philippines

    2. Collection of good character actresses in Philippine movies

    3. Collection of beautiful flowers in the Botanical Garden

    4. Collection of all small positive numbers

    5. Collection of all letters in the Filipino alphabet

    Mathematics Division, IMSP, UPLB

    SETS

  • SETS

    WHY WELL-DEFINED?

    For us to be able to determine/describe the elements of a set without confusion!

    For us to be able to determine whether a given object belongs to the set or not.

    Mathematics Division, IMSP, UPLB

  • SETS

    Do we really need to know the notion of sets?

    Consider you are a bachelor looking for a girlfriend

    Consider you are a grade 1 student

    Mathematics Division, IMSP, UPLB

  • SETS

    To name a set, we usually use capital letters.

    The objects that make up a set are called elements.

    In symbols, we write a A, in case a belongs to set A.

    Otherwise, we write a A.

    Mathematics Division, IMSP, UPLB

  • METHODS FOR DESCRIBING A SET

    roster or enumeration method

    rule or set builder method

    Mathematics Division, IMSP, UPLB

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Roster or enumeration method:

    W={b,a,y,i,n}

    Mathematics Division, IMSP, UPLB

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Roster or enumeration method:

    W={b,a,y,i,n}

    Mathematics Division, IMSP, UPLB

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Rule or set builder method:

    W={x | x is a letter in the word baybayin}

    Mathematics Division, IMSP, UPLB

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Rule or set builder method:

    W={x | x is a letter in the word baybayin}

    Mathematics Division, IMSP, UPLB

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Rule or set builder method:

    W={x | x is a letter in the word baybayin}

    such that

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Rule or set builder method:

    W={x | x is a letter in the word baybayin}

    Variable that represents any element in the set

  • METHODS FOR DESCRIBING A SET

    Consider the set of all letters in the word baybayin. Let us name it as set W.

    Rule or set builder method:

    W={x | x is a letter in the word baybayin}

    Criteria for deciding whether an object belongs to the set

  • EXAMPLE

    Set of all possible outcomes when you throw a coin

    Set of all undergraduate subjects offered in UPLB

    Questions:

    When is the rule method more useful than the roster method?

    When is the roster method more useful than the rule method?

  • EXAMPLE

    Can you write D using the rule method? D={butter, bread, coffee, rice}

    Can you write P using the roster method? P={x | x is a point in a line}

  • EMPTY SET

    There are sets that are so special they are given specific names.

    One of them is the empty set, denoted by { } or .

    The empty set has no element.

    Examples are:

    1. The set of snakes that can fly

    2. The set of dogs that can talk

    Mathematics Division, IMSP, UPLB

  • TRIVIA

    Is this an empty set?

    {}

    Mathematics Division, IMSP, UPLB

  • UNIVERSAL SET

    Another special set is the universal set denoted by U.

    The universal set is a set that contains all objects under consideration.

  • UNIVERSAL SET

    Q, W, R, T, Y, P, S,

    D, F, G, H, J, K, L

    {x|x is a letter from the English alphabet}

    A, E, I, O, U

  • EXAMPLES

    Give a universal set from which the members of the following sets could be chosen:

    1. {4, 8, 12, 16}

    2. {Rizal, Bonifacio, Mabini}

  • QUESTIONS

    Can U={1,2,3,4,5} be a universal set of

    2. {1,2,3,4,5}?

    1. {1,2,3}?

    3. {1,2,3,4,5,6}?