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Math 105    SURVEY OF MATHEMATICS

Intermediate Algebra

 

Prentice Hall Tutor Center Information

 

Chapter 1   CRITICAL THINKING SKILLS

                 Inductive Reasoning

                 Estimation

                 Problem Solving

                

Chapter 2   Sets

                 Set Concepts

                 Subsets

                 Venn Diagrams and Set Operations

                 Venn Diagrams with Three Sets and Verification of Equality of Sets

                 Application of Sets

                 Infinite Sets

 

Chapter 3   Logic

                 Statements and Logical Connectives

                 Truth Tables for Negation, Conjunction, and Disjunction

                 Truth Tables for the Conditional and Biconditional

                 Equivalent Statements

                 Symbolic Arguments

                 Euler Diagrams and Syllogistic Arguments

 

Chapter 4   Systems of Numeration

                 Additive, Multiplicative, and Ciphered Systems of Numeration

                 Place-Value or Positional-Value Numeration Systems

                 Other Bases

                 Computation in Other Bases

                 Early Computational Methods

 

Chapter 5   Number Theory And The Real Number System

                 Number Theory

                 The Integers

                 The Rational Numbers

                 The Irrational Numbers and the Real Number System

                 Real Numbers and Their Properties

                 Rules of Exponents and Scientific Notation         

                 Arithmetic and Geometric Sequences

                 Fibonacci Sequence

 

Chapter 6   Algebra, Graphs, and Functions

                 Order of Operations

                 Linear Equations in One Variable

                 Formulas

                 Applications of Linear Equations in One Variable

                 Variation

                 Linear Inequalities        

                 Graphing Linear Equations

                 Linear Equalities in Two Variables

                 Solving Quadratic Equations by Using Factoring and Quadratic Formula

                 Functions and Their Graphs

               

Chapter 7   Systems of Linear Equations and Inequalities

                 Systems of Linear Equations

                 Solving Systems of Equations by the Substitution and Addition Methods

                 Matrices

                 Solving Systems of Equation by Using Matrices

                 Systems of Linear Inequalities

                 Linear Programming

 

Chapter 8   The Metric System

                 Basic Terms and Conversions within the Metric System

                 Length, Area, and Volume

                 Mass and Temperature

                 Dimensional Analysis and Conversions to and from the Metric System

 

Chapter 9   Geometry

                 Points, Lines, Planes, and Angles

                 Polygons

                 Perimeter and Area

                 Volume

                 The Mobius Strip, Klein Bottle, and Maps

                 Non-Euclidean Geometry and Fractal Geometry

 

Chapter 10  Mathematical Systems

                      Groups

                  Finite Mathematical Systems

                  Modular Arithmetic

 

Chapter 11 Consumer Mathematics

                 Percent

                 Personal Loans and Simple Interest

                 Compound Interest

                 Installment Buying

                 Buying a House with a Mortgage

 

Chapter 12 Probability

                 The Nature of Probability

                     Theoretical Probability

                 Odds

                 Expected Value (Expectation)

                 Tree Diagrams

                 Or and And Problem     

                 Conditional Probability

                 The Counting Principle and Permutations

                 Combinations

                 Solving Probability Problems by Using Combinations

                 Binomial Probability Formula

               

Chapter 13 Statistics

                 Sampling Techniques

                 The Misuses of Statistics

                 Frequency Distributions

                 Statistical Graphs

                 Measures of Central Tendency

                 Measures of Dispersion

                 The Normal Curve

                 Linear Correlation and Regression

 

Chapter 14 Graph Theory

                 Graph, Paths, and Circuits

                 Euler Paths and Euler Circuits

                 Hamilton Paths and Hamilton Circuits

                 Trees

 

Chapter 15 Voting and Apportionment

                 Voting Systems

                 Flaws of Voting

                 Apportionment Methods

                 Flaws of the Apportionment Methods

 

 

 

 

 

 

 

 

 

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