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
Table of Content
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