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CITATION

Thomas, Christopher. Schaum's Outline of Mathematics for Liberal Arts Majors. US: McGraw-Hill, 2008.

Schaum's Outline of Mathematics for Liberal Arts Majors

Authors: Christopher Thomas

Published:  August 2008

eISBN: 9780071544306 0071544305 | ISBN: 9780071544290
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  • Contents
  • Chapter 1 Number Systems
  • 1.1 The Base-Ten Decimal System
  • 1.2 Tally Marks
  • 1.3 Egyptian Numbers
  • 1.4 Roman Numerals
  • 1.5 The Babylonian Number System
  • 1.6 Binary Numbers
  • 1.7 Hexadecimal Numbers
  • 1.8 A Fast Algorithm for Changing Bases
  • Chapter 2 Sets
  • 2.1 Sets
  • 2.2 Subsets
  • 2.3 Unions and Intersections
  • 2.4 Venn Diagrams
  • 2.5 Russell's Paradox
  • 2.6 Cantor's Diagonal Proof
  • Chapter 3 Logic
  • 3.1 Definitions
  • 3.2 Statements
  • 3.3 Conjunctions
  • 3.4 Truth Tables
  • 3.5 The Nature of Mathematical Proof
  • 3.6 Conditional Statements
  • 3.7 Contrapositives and Converses
  • 3.8 Comparing the World of Mathematics to Cartoons
  • Chapter 4 Fair Division
  • 4.1 Sharing among Two People
  • 4.2 Sharing among Three People
  • 4.3 The Last-Diminisher Method
  • 4.4 Sharing the Indivisible by Making Bids
  • Chapter 5 Functions
  • 5.1 Computing with Functions
  • 5.2 Graphing Functions
  • 5.3 Inverses to Functions
  • 5.4 Exponential Functions
  • 5.5 Logarithms
  • 5.6 Logarithmic Scales
  • Chapter 6 Geometry
  • 6.1 Lengths
  • 6.2 Areas
  • 6.3 Volumes
  • 6.4 Angles
  • 6.5 How Eratosthenes Measured the Earth around 250 B.C.
  • 6.6 Non-Euclidean Geometry
  • 6.7 Higher Dimensions
  • Chapter 7 Graph Theory
  • 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
  • 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
  • Chapter 9 Probability
  • 9.1 Expectations
  • 9.2 Equally Likely Events
  • 9.3 Independent Events
  • 9.4 Complementary Events
  • 9.5 Combinations and Permutations
  • 9.6 Probabilities with Combinations
  • Chapter 10 Statistics
  • 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 Empirical Rule
  • 10.5 Z Scores
  • 10.6 Collecting Statistics
  • Chapter 11 Weighted Voting
  • 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
  • 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
  • 13.1 Translations
  • 13.2 Translation Symmetry
  • 13.3 Reflections
  • 13.4 Reflection Symmetry
  • 13.5 Rotations
  • 13.6 Rotation Symmetry
  • 13.7 Combinations of Transformations
  • 13.8 Groups of Symmetries
  • Chapter 14 Iterative Processes
  • 14.1 Fractals
  • 14.2 The Golden Ratio
  • 14.3 Sequences
  • 14.4 Series
  • Chapter 15 Trigonometry
  • 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