Tan S.T. Finite Mathematics for the Managerial, Life, and Social Sciences
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Upon entering the University of Kansas as an undergraduate, Chris Shannon knew she enjoyed
mathematics, but she was also interested in a variety of social and political issues. One of her
mathematics professors recognized this and suggested that she might be interested in taking
some economics courses while she was studying mathematics. She learned that economics
enabled her to combine the rigor and abstraction of mathematics with the exploration of complex
and important social issues involving human behavior. She decided to add a major in economics
to her math major. After graduating with B.S. degrees in economics and in mathematics, Shannon
went on to graduate school at Stanford University, where she received an M.S. in mathematics
and a Ph.D. in economics.
Her current position as professor in both the mathematics and economics departments at the
University of California, Berkeley, represents an ideal blend of the two fields, and allows her to
pursue work ranging from developing new tools for analyzing optimization problems to designing
new models for understanding complex financial markets. The photos on the front cover of this
text represent one of her current projects, which explores new models of decision-making under
uncertainty and the effects of uncertainty on different markets.*
Look for other featured applied researchers in forthcoming titles in the Tan applied mathematics series:
About the Cover
PETER BLAIR HENRY
International Economist
Stanford University
MARK VAN DER LAAN
Biostatistician
University of California,
Berkeley
JONATHAN D. FARLEY
Applied Mathematician
California Institute
of Technology
NAVIN KHANEJA
Applied Scientist
Harvard University
CHRIS SHANNON
Economics and Finance
University of California, Berkeley
*Shannon, Chris, and Rigotti, Luca, “Uncertainty and Risk in Financial Markets,” Econometrica, January 2005, 73(1), pp. 203–243.
87533_13_FES2 1/30/08 10:36 AM Page 2
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Formulas
a. point-slope form: y y
1
m(x x
1
)
b. slope-intercept form: y mx b
c. general form: Ax By C 0
y mx b
where m and b satisfy the normal equations
nb (x
1
x
2
. . .
x
n
)m y
1
y
2
. . .
y
n
(x
1
x
2
. . .
x
n
)b (x
2
1
x
2
2
. . .
x
2
n
)m x
1
y
1
x
2
y
2
. . .
x
n
y
n
A P(1 i)
n
(i r/m, n mt)
where A is the accumulated amount at the end of n conversion periods, P is the principal,
r is the interest rate per year, m is the number of conversion periods per year, and t is the
number of years.
r
eff
1
where r
eff
is the effective rate of interest, r is the nominal interest rate per year, and m is
the number of conversion periods per year.
S R
P R
R
Pi
1 11 i 2
n
c
1 11 i 2
n
i
d
c
11 i2
n
1
i
d
a1
r
m
b
m
Equation of a
Straight Line
Equation of the
Least-Squares Line
Compound Interest
Effective Rate
of Interest
Future Value of
an Annuity
Present Value of
an Annuity
Amortization
Formula
87533_13_FC1 2/18/08 10:27 AM Page 1
R
P(n, r)
, where n
1
n
2
. . .
n
m
n
C(n, r)
P(A 傽 B) P(A)
P(B 兩 A)
P(A
i
兩 E)
E(X) x
1
p
1
x
2
p
2
. . .
x
n
p
n
P(X x) C(n, x)p
x
q
nx
(x 0, 1, 2, . . . , n)
E(X) np
Var(X) npq
X
1npq
P1A
i
2
#
P1E 冨 A
i
2
P1A
1
2
#
P1E 冨 A
1
2 P1A
2
2
#
P1E 冨 A
2
2
. . .
P1A
n
2
#
P1E 冨 A
n
2
n!
r!1n r2!
n!
n
1
!n
2
!
. . .
n
m
!
n!
1n r2!
iS
11 i2
n
1
Sinking Fund
Payment
The Number of
Permutations of n Distinct
Objects Taken r at a Time
The Number of
Permutations of n Objects,
Not All Distinct
The Number of
Combinations of n
Distinct Objects
Taken r at a Time
The Product Rule
for Probability
Bayes’ Formula
Expected Value of
a Random Variable
Bernoulli Trials
87533_13_FC1 1/30/08 10:35 AM Page 2
FINITE MATHEMATICS
FOR THE MANAGERIAL, LIFE,
AND SOCIAL SCIENCES
EDITION
9
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FINITE MATHEMATICS
FOR THE MANAGERIAL, LIFE,
AND SOCIAL SCIENCES
S. T. TAN
STONEHILL COLLEGE
Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States
EDITION
9
87533_00_FM_pi-xxiv 1/30/08 3:07 PM Page iii
Finite Mathematics for the Managerial,
Life, and Social Sciences, Ninth Edition
S. T. Tan
Senior Acquisitions Editor: Carolyn Crockett
Development Editor: Danielle Derbenti
Assistant Editor: Catie Ronquillo
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Photo Researcher: Terri Wright
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Cover Designer: Irene Morris
Cover Images: Chris Shannon © Cengage
Learning; Numbers, George
Doyle/Stockbyte/Getty Images; Produce,
Dimitri Vervitsiotis/Digital Vision/Getty
Images; Chess Strategy © David
Arky/Corbis; Stock Traders, Scott
Olson/Getty Images News/Getty Images
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TO PAT, BILL, AND MICHAEL
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