Modern Mathematics - 1st Edition - ISBN: 9780434985456, 9781483280035

Modern Mathematics

1st Edition

Made Simple

Authors: Patrick Murphy
eBook ISBN: 9781483280035
Imprint: Made Simple
Published Date: 1st January 1982
Page Count: 286
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Description

Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed.

Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional statements; and biconditional sentences. Subsequent chapters focus on switching circuits; multibase arithmetic; finite systems; relations, vectors, and matrices; tessellations; and linear programming. The book concludes with an analysis of motion geometry and rubber sheet geometry, paying particular attention to radial enlargement and composite reflections as well as topological equivalence, networks for maps, and incidence matrices.

This monograph is intended for students, parents, and teachers who are interested in modern mathematics.

Table of Contents


Foreword

1 Sets

Notation

Numbers

The Empty Set

Finite and Infinite Sets

Subsets

Universal Sets

Complement

Intersection

Union

Basic Operations on Sets

The Distributive Law

Equations

Solving Problems with Venn Diagrams

2 Elementary Mathematical Logic

Inductive Reasoning

Deductive Reasoning

Mathematical Sentences

Replacement and Solution Sets

Compound Statements

Conjunctions

Disjunctions

Negation

Conditional Statements

Biconditional Sentences

3 Switching Circuits

Connectiops in Series

Connection in Parallel

The Distributive Law

Obtaining Functions Direct From Truth Tables

Negation

Gates

4 Multibase Arithmetic

Notation

Conversion From Base 10

Approximation

Addition

Subtraction

Multiplication

Division

Fractions

Puzzles

5 Finite Systems

Clock Arithmetic

Subtraction

Additive Inverses

Multiplicative Inverses

Modular Arithmetic

Fractions

A More Formal Discussion

Other Finite Systems

Groups

Isomorphisms

Subgroups

6 Relations

Relation Diagrams

Types of Relations

Cartesian Product

Inverse Relations

Graphs

Correspondences

Functions

Inverse Functions

Composition of Functions

7 Linear Programming

Equations for Straight Lines

Optimisation

Extreme Points

A Further Constraint

Non-Linear Programming

8 Vectors

The Triangle Law

Vector Subtraction

Multiplication of a Vector by a Scalar

The Associative Law

Vector Geometry

Unit Vectors

Perpendicular Unit Vectors

The Dot Product

The Distributive Law

More Dot Products

9 Matrices

Reflections in the Axes

Reflection in y = ±x

Matrices for Reflections

Dot Products

Rotations

Radial Expansion

Matrix Multiplication

The (2 ÷ 2) Inverse Matrix

Simultaneous Equations

A Group of Matrices

Addition

10 Tessellatons

Quadrilaterals

Quadrisides

Pentagons

Hexagons

Off Cuts

11 Motion Geometry

Radial Enlargement

Reflection

Axes of Symmetry

Composite Reflections

Rotations

12 Rubber Sheet Geometry

Topological Equivalence

Networks

Euler's Results

Networks for Maps

Incidence Matrices

V + F - E = 2

Surfaces

Experiments in Topology: The Moebius Strip

The Punctured Torus

The Four-Colour Problem

Solutions

Appendix: Some Abbreviations and Definitions

Index

Details

No. of pages:
286
Language:
English
Copyright:
© Made Simple 1982
Published:
Imprint:
Made Simple
eBook ISBN:
9781483280035

About the Author

Patrick Murphy