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The Nature of Mathematics – 13th Edition

Section 5.6: Groups, Fields, and Real Numbers

  • Essential Ideas
  • Homework Hints
  • Individual Research Projects
  • Links
    • Video Links
    • History Links
    • Reference Topic Links
  • Chapter 1
    • Section 1.1: Problem Solving
    • Section 1.2: Inductive and Deductive Reasoning
    • Section 1.3: Scientific Notation and Estimation
    • Section 1.4: Review for Chapter 1
  • Chapter 2
    • Section 2.1: Sets, Subsets, and Venn Diagrams
    • Section 2.2: Operations with Sets
    • Section 2.3: Applications of Sets
    • Section 2.4: Finite and Infinite Sets
    • Section 2.5: Review for Chapter 2
  • Chapter 3
    • Section 3.1: Deductive Reasoning
    • Section 3.2: Truth Tables and the Conditional
    • Section 3.3: Operations and Laws of Logic
    • Section 3.4: The Nature of Proof
    • Section 3.5: Problem Solving Using Logic
    • Section 3.6: Logic Circuits
    • Section 3.7: Review for Chapter 3
  • Chapter 4
    • Section 4.1: Early Numeration Systems
    • Section 4.2: Hindu-Arabic Numeration Systems
    • Section 4.3: Different Numeration Systems
    • Section 4.4: Binary Numeration System
    • Section 4.5: History of Calculating Devices
    • Section 4.6: Review for Chapter 4
  • Chapter 5
    • Section 5.1: Natural Numbers
    • Section 5.2: Prime Numbers
    • Section 5.3: Integers
    • Section 5.4: Rational Numbers
    • Section 5.5: Irrational Numbers
    • Section 5.6: Groups, Fields, and Real Numbers
    • Section 5.7: Discrete Mathematics
    • Section 5.8: Cryptography
    • Section 5.9: Review for Chapter 5
  • Chapter 6
    • Section 6.1: Polynomials
    • Section 6.2: Factoring
    • Section 6.3: Evaluation, Applications, and Spreadsheets
    • Section 6.4: Equations
    • Section 6.5: Inequalities
    • Section 6.6: Algebra in Problem Solving
    • Section 6.7: Ratios, Proportions, and Problem Solving
    • Section 6.8: Percents
    • Section 6.9: Modeling Uncategorized Problems
    • Section 6.10: Review for Chapter 6
  • Chapter 7
    • Section 7.1: Geometry
    • Section 7.2: Polygons and Angles
    • Section 7.3: Triangles
    • Section 7.4: Similar Triangles
    • Section 7.5: Right-Triangle Trigonometry
    • Section 7.6: Mathematics, Art, and Non-Euclidean Geometries
    • Section 7.7: Review for Chapter 7
  • Chapter 8
    • Section 8.1: Perimeter
    • Section 8.2: Area
    • Section 8.3: Surface Area, Volume, and Capacity
    • Section 8.4: Miscellaneous Measurements
    • Section 8.5: U.S. – Metric Conversions
    • Section 8.6: Review for Chapter 8
  • Chapter 9
    • Section 9.1: Euler Circuits and Hamiltonian Cycles
    • Section 9.2: Trees and Minimum Spanning Trees
    • Section 9.3: Topology and Fractals
    • Section 9.4: Review for Chapter 9
  • Chapter 10
    • Section 10.1: Exponential Equations
    • Section 10.2: Logarithmic Equations
    • Section 10.3: Applications of Growth and Decay
    • Section 10.4: Review for Chapter 10
  • Chapter 11
    • Section 11.1: Interest
    • Section 11.2: Installment Buying
    • Section 11.3: Sequences
    • Section 11.4: Series
    • Section 11.5: Annuities
    • Section 11.6: Amortization
    • Section 11.7: Summary of Financial Formulas
    • Section 11.8: Review for Chapter 11
  • Chapter 12
    • Section 12.1: Permutations
    • Section 12.2: Combinations
    • Section 12.3: Counting Without Counting
    • Section 12.4: Rubik’s Cube and Instant Insanity
    • Section 12.5: Review for Chapter 12
  • Chapter 13
    • Section 13.1: Introduction to Probability
    • Section 13.2: Mathematical Expectation
    • Section 13.3: Probability Models
    • Section 13.4: Calculated probabilities
    • Section 13.5: Bayes’ Theorem
    • Section 13.6: Binomial Distribution
    • Section 13.7: Review for Chapter 13
  • Chapter 14
    • Section 14.1: Frequency Distributions and Graphs
    • Section 14.2: Descriptive Statistics
    • Section 14.3: The Normal Curve
    • Section 14.4: Correlation and Regression
    • Section 14.5: Sampling
    • Section 14.6: Review for Chapter 14
  • Chapter 15
    • Section 15.1: Cartesian Coordinates and Graphing Lines
    • Section 15.2: Graphing Half-Planes
    • Section 15.3: Graphing Curves
    • Section 15.4: Conic Sections
    • Section 15.5: Functions
    • Section 15.6: Review for Chapter 15
  • Chapter 16
    • Section 16.1: Systems of Linear Equations
    • Section 16.2: Problem Solving with Systems
    • Section 16.3: Matrix Solution of a System of Equations
    • Section 16.4: Inverse Matrices
    • Section 16.5: Modeling with Linear Programming
    • Section 16.6: Review for Chapter 16
  • Chapter 17
    • Section 17.1: Voting
    • Section 17.2: Voting Dilemmas
    • Section 17.3: Apportionment
    • Section 17.4: Apportionment Paradoxes
    • Section 17.5: Review for Chapter 17
  • Chapter 18
    • Section 18.1: What is Calculus?
    • Section 18.2: Limits
    • Section 18.3: Derivatives
    • Section 18.4: Integrals
    • Section 18.5: Review for Chapter 18
  • Epilogue Video Links
  • Math Nature – 12th Edition
  • Transparencies
  • Group Research Projects
  • Individual Projects
  • Keyword List
  • About Karl Smith
  • Karl Smith’s Textbooks
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    • Trigonometry/Precalculus
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