Schaum's outlines : mathematics for liberal arts majors

237 Pages·2009·1.489 MB·English

by  Christopher Thomas

SCHAUM’S
outlines
Mathematics for
Liberal Arts Majors
This page intentionally left blank
SCHAUM’S
outlines
Mathematics for
Liberal Arts Majors
Christopher Thomas
Schaum’s Outline Series
New York Chicago San Francisco Lisbon London Madrid Mexico City
Milan New Delhi San Juan Seoul Singapore Sydney Toronto
Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except as permitted under the United
States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval sys-
tem, without the prior written permission of the publisher.
0-07-154430-5
The material in this eBook also appears in the print version of this title: 0-07-154429-1.
All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in
an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this
book, they have been printed with initial caps.
McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate training programs. For more
information, please contact George Hoare, Special Sales, at [email protected] or [phone].
TERMS OF USE
This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the work. Use of this work is
subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile,
disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or
any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly
prohibited. Your right to use the work may be terminated if you fail to comply with these terms.
THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY,
ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANY INFORMATION THAT CAN
BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
McGraw-Hill and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be unin-
terrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in
the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no cir-
cumstances shall McGraw-Hill and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result from the
use of or inability to use the work, even if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim
or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.
DOI: 10.1036/0071544291
Professional
Want to learn more?
We hope you enjoy this
McGraw-Hill eBook! If
you’d like more information about this book,
its author, or related books and websites,
please click here.
For more information about this title, click here
Contents
CHAPTER 1 Number Systems 1
1.1The Base-Ten Decimal System 1.2Tally Marks 1.3Egyptian Num-
bers 1.4Roman Numerals 1.5The Babylonian Number System 1.6Bi-
nary Numbers 1.7Hexadecimal Numbers 1.8A Fast Algorithm for
Changing Bases
CHAPTER 2 Sets 16
2.1Sets 2.2Subsets 2.3Unions and Intersections 2.4Venn Diagrams
2.5Russell’s Paradox 2.6 Cantor’s Diagonal Proof
CHAPTER 3 Logic 29
3.1Definitions 3.2Statements 3.3Conjunctions 3.4Truth Tables
3.5The Nature of Mathematical Proof 3.6Conditional Statements
3.7 Contrapositives and Converses 3.8 Comparing the World of Mathemat-
ics to Cartoons
CHAPTER 4 Fair Division 42
4.1Sharing among Two People 4.2 Sharing among Three People 4.3The
Last-Diminisher Method 4.4 Sharing the Indivisible by Making Bids
CHAPTER 5 Functions 53
5.1Computing with Functions 5.2Graphing Functions 5.3Inverses to
Functions 5.4Exponential Functions 5.5Logarithms 5.6Logarithmic
Scales
CHAPTER 6 Geometry 71
6.1 Lengths 6.2 Areas 6.3 Volumes 6.4 Angles 6.5 How Eratos-
thenes Measured the Earth around 250 b.c. 6.6 Non-Euclidean Geometry
6.7 Higher Dimensions
CHAPTER 7 Graph Theory 97
7.1 The Bridges of Königsberg 7.2 Graphs 7.3 Euler Paths and Circuits
7.4 Hamiltonian Paths and Circuits 7.5 The Traveling Salesman Problem
CHAPTER 8 Financial Mathematics 113
8.1 Simple Interest 8.2 Compound Interest 8.3 Annual Percentage Yield
8.4 Compound Interest with Payments 8.5 Saving for a Goal 8.6 Paying
Off a Loan 8.7 The Time Required to Pay Off a Debt
v
vi Contents
CHAPTER 9 Probability 121
9.1 Expectations 9.2 Equally Likely Events 9.3 Independent Events
9.4 Complementary Events 9.5 Combinations and Permutations 9.6 Proba-
bilities with Combinations
CHAPTER 10 Statistics 132
10.1 The Depiction of Data 10.2 Averages: Mean, Median, Midrange, and
Mode 10.3 Standard Deviation 10.4 The Normal Curve and the Empiri-
cal Rule 10.5 ZScores 10.6 Collecting Statistics
CHAPTER 11 Weighted Voting 147
11.1 Describing Weighted Voting Systems 11.2 Dictators, Dummies, and
Veto Power 11.3 Setting Up a Weighted Voting System 11.4 The
Banzhaf Power Index
CHAPTER 12 Voting Methods 154
12.1 Majorities and Pluralities 12.2 Preference Schedules and Instant
Runoff Voting 12.3 Pairwise Comparisons and the Condorcet Criterion
12.4 The Borda Count Voting Method 12.5 Two More Fairness Criteria
12.6 Arrow’s Impossibility Theorem
CHAPTER 13 Transformations and Symmetry 172
13.1 Translations 13.2 Translation Symmetry 13.3 Reflections 13.4 Re-
flection Symmetry 13.5 Rotations 13.6 Rotation Symmetry 13.7 Com-
binations of Transformations 13.8 Groups of Symmetries
CHAPTER 14 Iterative Processes 197
14.1 Fractals 14.2 The Golden Ratio 14.3 Sequences 14.4 Series
CHAPTER 15 Trigonometry 204
15.1 Similar Triangles 15.2 The Pythagorean Theorem 15.3 Pythagorean
Triples 15.4 Trigonometric Functions 15.5 Trigonometry on a Calculator
15.6 Using Trigonometric Functions 15.7 Inverse Trigonometric Functions
15.8 Using Inverse Trigonometric Functions 15.9 The Law of Sines
15.10 The Law of Cosines
Index 223
SCHAUM’S
outlines
Mathematics for
Liberal Arts Majors
This page intentionally left blank