Thinking
Critically
Chapter 1
Unit 1A
Living in the Media Age
Living in the Media Age
Logic is the study of the methods and principles of
reasoning.
An argument uses a set of facts or assumptions, called
premises, to support a conclusion.
A fallacy is
Math 824
Professor J. A. Paulos
Wachman 542, x-5003
paulos@temple.edu
Beury 160 Tuesdays and Thursdays from 11:40 to 1:20
plus individual recitation sections
Text: Using and Understanding
Mathematics,
A Quantitative Reasoning Approach (6th
Ed.)
The course
Notions of Central Tendency
The average or mean of a set of numbers is their
sum divided by how many there are.
The median of a set of numbers is the middle
number if the set is arranged in increasing order.
The mode of a set of numbers is the most
freque
Probability
Sample space - list or set of everything that might
happen.
Examples
Toss a coin two times.
Toss a coin three times.
S=cfw_ HH , HT ,TH , TT
S=cfw_ HHH , HHT , HTH , HTT ,
THH , THT ,TTH ,TTT
The set of all possible poker hands is another
sa
Probability of Many Events
Independent events
Events are independent if the occurence of any
one of them does not affect the probability of the
others. If events A, B, C, are independent then
P( A , B ,C all occur)=P (A ) P(B) P(C)
That is, if you are int
Conditional probability
P(someone is over 6 feet tall) = 0.05
P(someone is over 6 feet tall | person weighs more
than 300lbs) = 0.45
Read | as given that; that is P(someone is over
6 feet tall | person weighs more than 300 lbs)
means the probability that
Samge Qaiz iii
E. and 2. imagine that there are 27 deégaéeg {voters} {e a psiisai pays maveniion a? which four
peeple Ann, Bab, Claire, and Dave have bean nominaied as the payig Qaniiééates far gawmer.
ASSlmle the {ieiegies pmferems scheduies are as fgow
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Geometry and scaling
Computing areas and volumes
Rectangle
Area of a rectangle: If a rectangle is l units long
and w units wide, then the rectangle has area
l w
square units.
Circle
If a circle has radius
square units.
r
units, then it has area
r
2
3.14
Unit 7A
Fundamentals of
Probability
Probability: Historical Background
Much of the early work in probability concerned games
and gambling. One of the first to apply probability to
matters other than gambling was the father of
probability theory: Pierre Si
Unit 4A
Taking Control of your
Finances
What is a budget?
A budget is a
written record of
the money that
flows in and out of
your household or
pocket every
month.
Why budget?
Budgeting is the first step on the road to
financial success.
Controlling your d
Exponential
Astonishment
Chapter 8
Unit 8A
Growth: Linear versus
Exponential
Growth: Linear vs Exponential
Imagine two communities, Straightown and Powertown,
each with an initial population of 10,000 people.
Straightown grows at a constant rate of 500 pe
Mathematical Patterns
Instructor:
Pepe Gimenez
gimenez@temple.edu
Wachman Hall, Room 1044
Office Hours: MW 1:00-2:00.
Lectures:
MWF 10:40 - 11:50.
Gladfelter Hall L013.
Contact:
We will communicate through a Facebook Group. If a student has an urgent ques
Purpose
Linear growth
Formula
y=mx +b
Explanation
This is used when the growth/decay is the
same quantity with each increment.
y= final quantity
m= slope, growth/decay rate, rise
over run
b= initial amount
This is used when the quantity is
increasing/d
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Social Choice and Voting
Elections - social choice
55 voters in six different sized groups. Each group
of voters shares the same preferences about
candidates, for example, 18 of the voters think A is
the best, D is second best, E is 3rd best, C is 4th
bes
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Review Homework
Name:
31 Jan 2014
Question:
1
2
3
4
5
6
7
Total
Points:
12
4
12
12
6
14
12
72
Score:
Order of operations
1. Do anything inside grouping symbols rst, then exponents. Do multiplication and division (leftto-right) next, and then nally additio
MATH 824
Topics: Number; Probability; Elections,
Social Choice; Geometry, Scaling; Logic,
Puzzles, and illustrations from everyday
life, topical issues in the news.
3 quizzes,
weekly sectional quizzes and homew
Probability of either A or B happening when there's some overlap:
P(A) + P(B) P(A and B)
39% of Ph residents subscribe to Inquirer
13% to NY Times (made up figures)
7% to both
so the number of people who subscribe to at least one is:
39+13-7=45%
Percent t
To count combinations excluding various permutations of the same combination, multiply as if
you're doing permutations, then put that number over a factorial of the number of figures
multiplied above.
Ex:
31*30*29
3! (3*2*1) = number of Baskin Robbin's fl
Our first quiz is Valentine's day, 14 Feb.
Today: review of parity, pigeonhole, multiplication principle
Pigeonhole principle: if one has more pigeons than holes, pigeons must double up in at least one
hole.
10 blue socks
10 red
10 white
To be certain you
Order of Operations
1. Parenthesis/items in fractions
2. exponents
3. multiply/divide (order doesn't matter)
4. addition/subtraction (same)
The subjects discussed include pigeonhole problems and the multiplication principle (look this
up)
15 boys pick 100
Anchoring Effect The tendency of people to select and understand numbers by context,
regardless of relevancy of other information
Q. What's the population of Turkey, but first, is it more or less than _?
If the number offered was 7 million, people would g
Multiplication and division of large numbers
Breaking a number into its primes and then building back up is a useful way to determine
different combinations of multiples it has.
20,000 leagues under the sea is an impossible number:
A league equals about t
Notions of Central Tendency
The average or mean of a set is all the numbers added, then divided by the number of numbers.
The median is just the middle figure of a set.
The mode of a set is the most frequently occurring number in a set (less often used in