MATHEMATICS 17
EXERCISES
I. TRUE or FALSE. Write TRUE if the statement is correct, and write FALSE otherwise.
1. The set of imaginary numbers is closed under addition and multiplication.
2. For all a R, m, n N, n m n = mn a
m
3. For all a R, m, n N, a n =
THE GOLDEN
RATIO
A Report by Group 18
MATH 1 WFX
The Myth Of The Golden Ratio
Definition:
Phi- = a Greek term inspired by a Greek sculptor named Phidias
1.618
*It is the division of a length into a larger part and a smaller part, wherein the
smaller part
Math in Literature
GROUP 9
Francis Flores, Christian Paul Francisco,
Karl Angelo Francisco, Jasmine Gabbuat, Kathleen Gabriel,
Justine Maria Regina Galandines, Eira Chariz Galang
I. INTRODUCTION
II. STRUCTURE
Western Literary Structures
1. Basic Literary
MATH IN SOCIAL SCIENCES II
GRAPHS AND NETWORKS
Group
3
BRIDGES IN
KNIGSBERG
Problem:
Knigsberg is divided into four
parts by the river Pregel, and
connected by seven bridges. Is
it possible to tour Knigsberg
along a path that crosses
every bridge once, an
-the
wave of a single perfect musical
note of a specific frequency
-Standard
Frequency
- Guitar Tuning
Fundamental a.k.a. primary frequency;
the lowest sound (or harmonic) in the
harmonic series
Overtone/s any sound/s (or
harmonic/s) in the harmonic serie
Math in Social Sciences II
Group 21
Small World
Networks
Definition
A network where the typical
distance L between two
randomly chosen nodes (the
number of steps required)
grows proportionally to the
logarithm of the number of
nodes N in the network.
Smal
Mathematics in Art
GROUP 13
LIMPOT | LOGMAO | LONTOK | LUCINARIO | MACABODBOD | MADERAZO | MADRID
MATHEMATICS: the study of numbers, quantities,
shapes and the relations between them
ART: something that is created with imagination
and skill and that is be
DANCE
MATHEMATICS
Dance
a way of human
expression through
movement
Overview: Dance
Dance is a way of
communication and expression.
All societies use dance to
communicate through personal
and cultural levels that meets
needs, physically and
spiritually.
Da
MATHEMATICS IN THEATER
Theater in this case refers to the performing art in which actors and actresses act in a
play
BUDGETING
Some knowledge in mathematics is required in order to plan a realistic budget (and predict profit)
BUDGET
Production Cost
publ
MATH
IN
ECONOMICS
GROUP 14
Magalong Maglasang Main
Maago Maalac Marcelino
Martinez
Reasons behind having Math
in Economics
Why is there so much Math in Economics?
Economics wants to understand the behavior of
individuals
It aims to answer questions like
Mathematics in Medical and Life
Sciences
Life without Math is like living on Earth without land
The Field of Medicine
Ophthalmology
The measuring of the clarity of vision is an
obvious way in which Mathematics is
applied.
Pediatrics
Quantifying the nutrit
TOPIC: MATH IN ART I
(VISUAL ARTS AND DESIGN)
By: Group 13
RELATIONSHIP OF MATH AND ART
1. Mathematics and art are related in a variety of
ways. Mathematics has itself been described as an
art motivated by beauty.
2. Mathematics can be discerned in arts s
FRACTALS IN THE
HUMAN BODY
& NATURE
R I G O R , R O D U L F O, R O N DA I N , R O S A L E S ,
R O Y E C A , S A L A N D A N A N , S A LV A D O R
Fractals in the Human Body
Human Body: Lungs
The bronchial tubes in the
1 fractal
the first 7
human lung have
MATHEMATICS 17
EXERCISE 5
I. Linear Equations.
1. Find the general form of the equation of the line that is perpendicular to the line x + 2y = 3 and
passes through the midpoint of the points P (1, 3) and Q (5, 1).
2. Find the ordinate of the point whose a
MATHEMATICS 17
EXERCISE 9
I. Variations.
1. If a function f (x) varies inversely as the cube of x, nd the value of
f (2)
.
f (3)
2. The volume of a cone varies jointly as the square of the radius of the base and the height. If the radius of
the base of th
MATHEMATICS 17
EXERCISE 8
I. Polynomial Functions.
1. Which among the following: 1, 2, 2, 1, 3 is a zero of the function
f (x) = x4 4x3 7x2 + 22x + 24.
2. Show that 3 is a zero of multiplicity two of the polynomial function dened by
P (x) = x4 3x3 11x2 +
MATHEMATICS 17
EXERCISE 13
I. Determine the amplitude, period, phase shift and vertical shift of the following then draw one cyle of the
graph.
1. f (x) = 4 sin(2x ) + 1
IV. Do as indicated.
1. Show that tan1 2 + cot1 (3) =
2. Show that sin1 x + cos1 x =
MATHEMATICS 17
EXERCISE 14
I. Evaluate the following and express your answers in
rectangular form.
1.
3
2
1i
2
8cis120
2. (2cis60 )2
3.
1
cis60
2
4.
III. Determine how many triangles can be formed given
the following conditions. If exactly one exists, s
GROUP 2
FIBONACCI SEQUENCE
W H AT I S T H E
FIBONACCI SEQUENCE?
W H AT I S T H E F I B O N A C C I S E Q U E N C E ?
It is the series of numbers wherein the next number is
found by adding the 2 numbers before it.
0, 1, 1, 2, 3, 5, 8. . .
0+1=1
(Its that
FRACTALS
What are FRACTALS?
- An object or quantity that forms a never ending
pattern which repeats at different scales (selfsimilarity)
- Complex but made by a simple repeating process
- can be mathematical or natural
formed by calculating a simple
equat
GOLDEN
MEAN IN
FILM
The Golden Mean (1.618)
Golden Ratio
Pythagoras
*Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, )
5/8=0.625
55/89=0.61797753
Ali Shirazi's Visual Essay on P.T. Anderson's
There Will Be Blood
the use of:
> the Golden Rat
Math in
Engineering
Group 17
Without math,
there would be no
engineering.
Civil Engineering
The second-oldest engineering discipline that deals
with infrastructures and the maintenance of a
physical and naturally built environment.
The Triangle Theory
Eng
MATH IN
SCIENCE AND
TECHNOLOGY
II
Group 8 Esteban, Encinas, Faller, Esguerra, Empleo, Fernandez & Dungo
HISTORY
Prehistoric
Beginning of the Christian Era Black Magic
1700 BC: King Hammurabis reign over Babylon
All known metals were listed in conjunction
1. Mathematical
Statements
and
Logic
The following are NOT mathematical
statements
!
x+y
!
Happy Birthday!
!
Tweet me.
!
Can we be friends?
`
1
Marian P. Roque
Math 1
Institute of Mathematics
UP Diliman
Thursday, June 21, 2012
1.1 Mathematical Statements
Cardinality of innite sets
The cardinality |A| of a nite set A is simply the number of elements in it. When it
comes to innite sets, we no longer can speak of the number of elements in such a
set. We can, however, try to match up the elements of two innit
The correct answer is underlined or enclosed in a box. I have discussed 1 4 in class.
1. If A B, which of the following is always true?
(a) A B = B
(c) A \ B =
(b) A B = A
(d) n(A) < n(B)
Use a Venn Diagram to verify that (a), (b) are not true. (d) is no
NATIONAL INSTITUTE OF PHYSICS
College of Science
University of the Philippines
Diliman, Quezon City 1101 Metro-Manila
Course
PHYSICS 73 (ELEMENTARY PHYSICS III)
Credit Units
4 units
Course Description
Thermal physics, relativity, quantum physics
Prereq, C
INSTITUTE OF MATHEMATICS
College of Science
University of the Philippines Diliman
COURSE POLICIES AND SYLLABUS
Course Number/Title:
Mathematics 53 (Elementary Analysis I)
Prerequisite:
Mathematics 17
Course Credit: 5 units
References:
1.
2.
3.
4.
5.
Insti