1
Math Review

• Dont worry about your difficulties in
  Mathematics,
• I can assure you that mine are still greater
• Albert Einstein

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NASANational Space Grant Network

• The greatest sin committed by formal education
  is the continued and relentless extermination of
  the natural pleasure of learning and the
  greatest sin committed by "progressive" education
  is the delusion that such pleasure need not be
  accompanied by a certain measure of pain.
• Sydney Harris, Thoughts at Large

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Math ReviewThursday-Monday, June 3-7 2003

• Introduction
• Symbols
• Operations
• Central Tendencies
• Linear Algebra
• Correlation/Regression Analysis
• System of Equations Linear/Quadratic
• Applied Calculus

4
Math Review 1Thursday, June 3 2003
http//www.columbia.edu/itc/sipa/envp/louchouarn/c
ourses/mpa.htm

• Introduction
• Symbols
• Operations
• Central Tendencies
• Linear Algebra

5
Basic Math Review

1. Symbols

We need symbols to simplify expressions and
develop abstract arguments
N ike
? particularly for quantitative analysis.
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A Better Math Curriculum Dr. Tom Davis (B.Sc.
Math at Caltech, Ph.D. in Math at Stanford,
post-doc in electrical engineering at Stanford)
The problem today math is generally taught by
and aimed at mathematicians (In many
universities, engineering Depts teach their own
math courses since students are unable to solve
engineering (applied) problems with the tools
they learn from the math Dept!)

• Basic Math
• Finances (household)
• Problem-solving skills!!!
• Basic numeracy
• Estimation (including probability statistics)
• Visualization, and
• Bullshit detector!!!

7
Whats in a number
Sex Drives
Or the Gender Wars
8
Whats in a number
Really, shouldnt we be serious?
9
Whats in a number
Sex Drives
vs.
10
Whats in a number
Sex Drives
vs.
11
Whats in a number
Bullshit detector
12
Whats in a number
Bullshit detector
13
Basic Math Review

1. Operations

Summation S (sigma) Sxi x1 x2 x3
xn Where n, represents the sample size x
represents the variable, and xi represents the
value of the ith observation
S(xiyi)2 (x1y1)2 (x2y2)2 (x3y3)2
(xnyn)2
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Basic Math Review

1. Operations

Powers (Exponents) xa ? xb x(a b)
xaya (xy)a
(xa)b x(ab)
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Basic Math Review

1. Operations

Logarithms (base 10) logb(x) y if and only if
by x
Warning logb(x)?logb(y) ? logb(x?y)
logb(b) 1
logb(1) 0
logb(x?y) logb(x) logb(y)
logb(x/y) logb(x) - logb(y)
logb(xn) nlogb(x)
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Basic Math Review

1. Operations

Logarithms (natural log) ln (x) y if and only
if ey x
ln(e) 1
ln(1) 0
ln(x?y) ln(x) ln(y)
ln(x/y) ln(x) - ln(y)
ln(xy) yln(x)
ln(ex) xln(e) x ? 1 x
eln(x) x
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Basic Math Review

1. Operations

• Solve for x ln(ea) bx
• Solve for y using common logarithms (base 10)
• y 175
• Solve for y using common logarithms (base 10)
• y 175 - 127

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Basic Math Review

1. Central Tendencies

The most commonly used descriptive statistics are
measures of central tendency The sample mean (
pronounced x bar) is
Where Sxi represents the sum of all values in the
sample and n represents the sample size
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Basic Math Review

1. Central Tendencies

Lets assume we have a student population (n 47)
But what happens if we have an outlier (skewed
distribution )?
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Basic Math Review

1. Central Tendencies

Lets assume we have a real student population (n
47)
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Basic Math Review

1. Central Tendencies

• Mean arithmetic average
• Median middle value of a set of values
• Mode the data value that occurs most often

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Friday

• Populations Lecture 1
• Math Review 2 Linear Algebra -
  Correlation/Regression Analysis
• Dont forget the website AND the math sheets!

Monday

• Lamont orientation (LDEO Exec. Director and DEES
  Chair)
• Math Review 3 System of Equations
  Linear/Quadratic - Applied Calculus

http//www.columbia.edu/itc/sipa/envp/louchouarn/c
ourses/mpa.htm