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Full Description
A bridge to the world of mathematics for readers who want to gain a good foundation in basic mathematical skills for research and other activities.
This book aims to help students of social sciences, liberal arts, and humanities to develop the ability to analyze and reason mathematically, to model situations and problems, and to be able to infer, present, and communicate their analysis effectively. Mathematical concepts are presented in both historical and everyday contexts to ease their utilization in the real world.
Readers are introduced to the skills of expressing mathematical ideas using the language of sets, logically analyzing arguments and their validity, processing and interpreting data, and using probability to handle the inherent randomness of our world. Chapters dedicated to symmetry, perspective, and art will enable readers to reason, model, and evaluate everyday situations. The book will also increase awareness of how mathematical patterns pervade the world around us.
Key Features
• Gentle and non-calculus-based treatment of the topics
• Real-life examples and data along with numerous visual aids
• Plethora of solved examples and exercises to develop hands-on experience
• Material on computational tools for data handling, analyses, and presentation
Contents
Preface
Acknowledgments
Chapter 1 Why to Solve It
Marking Time
Measuring Value
Making the Best Selection
Finding the Path
Learning from Nature
Chapter 2 Sets
Describing a Set
A Variety of Sets
Set Operations
Euler Diagrams
Venn Diagrams
Counting with Venn Diagrams
Chapter 3 Logic and Reasoning
Statements
Analysing Statements
Negating Simple Statements
Compound Statements: An introduction
Conjunction and Disjunction
Truth Tables
De Morgan's Laws
Conditional or Implicative Statements
Analysis of Arguments
Chapter 4 Data Analysis and Modelling
Interacting with Data
Introduction to Spreadsheet Programs
Bar Charts, Histograms, and Pie Charts
Tracking Trends: Line Plots
Finding Relationships: Scatter Plots
Locating the Centre: Mode, Median, and Mean
Measuring Diversity: Range and Deviation
How to Lie with Statistics
Advanced Examples
Chapter 5 Probability
Measuring Chance
Probability and Sets
Conditional Probability
Random Variables, Expectation, and Variance
Jointly Distributed Random Variables
Bernoulli and Binomial Random Variables
Sampling
Chapter 6 Symmetry
Working Definition of Symmetry
Symmetry of Finite Planar Figures
Symmetry of Strip Patterns
Symmetry of Wallpaper Patterns
Case Study: Humayun's Tomb
Case Study: Abstract Art
Symmetry Around Us
Chapter 7 Perspective: Art and Mathematics
Introduction to Perspective
Mathematical Principles: Coordinates and Projections
Linear Perspective
Doing It Yourself
Solutions to Selected Exercises
Index
