Book:Patrick J. Murphy/The New Mathematics Made Simple/Second Edition

Contents

 * Foreword


 * $1$
 * The empty set
 * Set equality
 * Subsets
 * Numbers
 * Union of sets
 * Intersection of sets
 * Disjoint sets
 * Universal sets
 * Complement
 * Operations. Commutative and associative laws


 * $2$
 * Operations with whole numbers
 * Addition
 * Addition is commutative
 * Identity number for addition
 * Addition is associative
 * A number line
 * Addition on a number line
 * Order of whole numbers
 * Inverse operations
 * Subtraction
 * Subtraction on a number line
 * Properties of subtraction
 * Multiplication as repeated addition
 * Identity number of multiplication
 * Multiplication is associative
 * The distributive property
 * Estimating a product
 * Division
 * Properties of division
 * Remainders in division


 * $3$
 * Closure under addition
 * The integers
 * The number line
 * Order of the integers
 * Additive inverses
 * Addition of integers
 * The meaning of the $`-'$ operation
 * Multiplication on a number line
 * Multiplication of integers
 * Property of negative one
 * Division of integers


 * $4$
 * Relation symbols
 * Grouping symbols
 * Number sentences
 * Open sentences
 * Replacement set
 * Solution set
 * Equations
 * Addition property of equations
 * Multiplication property of equations
 * Division property of equations
 * Solving equations
 * Translating English phrases
 * Solving problems


 * $5$
 * A need for new numbers
 * Other names for rational numbers
 * Multiplication of rational numbers
 * Renaming rational numbers
 * Mixed numerals in multiplication
 * Reciprocals or multiplicative inverses
 * Mixed numerals in addition
 * Subtraction of rational numbers
 * Decimals
 * Decimal numeration
 * Repeating decimals
 * Density of rational numbers


 * $6$
 * Clock arithmetic
 * Additive inverses and subtraction
 * Multiplicative inverses and division
 * Modular arithmetic
 * 'Fractions' in finite arithmetic
 * Other finite systems
 * Groups
 * Isomorphism
 * Sub groups


 * $7$
 * Conversion to base ten
 * Conversion from base ten
 * Rounding off
 * Addition,
 * Subtraction
 * Multiplication
 * Division
 * Nim
 * Recurring bicimals


 * $8$
 * The lines
 * Line segments and rays
 * Assumptions about points and lines
 * Planes
 * Parallel lines and planes
 * Separation properties
 * Simple closed figures
 * Circles
 * Angles
 * Measuring angles
 * Types of angles
 * Perpendicular lines and planes
 * What measurement is
 * Approximate nature of measurement
 * Precision
 * Congruence and similarity
 * Bisecting line segments and angles
 * Constructing congruent angles
 * Perpendicular lines
 * Congruent triangles
 * Conditions for congruent triangles
 * Identity congruence
 * Vertical angles
 * Parallel lines and transversals
 * Proving two triangles congruent
 * Similar triangles
 * Angles of a triangle
 * More about similar triangles


 * $9$
 * Classification of relations
 * The inverse relation
 * The graph
 * Co-ordinate axes
 * Functions
 * Inverse relations and functions
 * Function notation
 * Composition of functions


 * $10$
 * General equations to the straight line
 * Inequalities
 * Maximizing and minimizing
 * Non-linear programming


 * $11$
 * Transformations
 * Reflections
 * Rotations
 * Radial expansion
 * The general transformation
 * Matrix multiplication
 * Scalar product
 * Matrix algebra
 * Multiplication by a number
 * Addition
 * Subtraction
 * Matrix equations
 * A group of matrices with respect to multiplication
 * The inverse $2 \times 2$ matrix
 * Simultaneous equations


 * $12$
 * Reflections
 * Axis of symmetry
 * Translations
 * Vectors
 * Vector addition
 * Subtraction
 * Associativity
 * Components
 * Rotations
 * Rotation of a line
 * Radial expansion or enlargement


 * $13$
 * Topological transformations
 * Networks
 * Unicursal networks
 * Networks for maps
 * Trees
 * Betti numbers
 * Surfaces
 * Classifications of surfaces
 * The Moebius strip
 * The punctured torus
 * The four-colour problem







Source work progress
* : Chapter $1$: Sets: Subsets