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A Bridge to Mathematics
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A Bridge to Mathematics

First Edition
  • Shobha Bagai - Professor, Cluster Innovation Centre, University of Delhi
  • Amber Habib - Professor, Department of Mathematics, Shiv Nadar University
  • Geetha Venkataraman - Professor, School of Liberal Studies, Ambedkar University Delhi.
Additional resources:

January 2019 | 392 pages | SAGE Publications Pvt. Ltd

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

 

 


 
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

Supplements

Key features

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

 

 

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Paperback
ISBN: 9789386446121
$40.00