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
Author's Description
Shobha Bagai is currently a Professor at the Cluster Innovation Centre, University of Delhi. Professor Bagai completed her masters in 1989 and PhD in Mathematics in 1993 from Indian Institute of Technology (IIT) Delhi. She was a gold medallist from Panjab University in 1987 scoring 100% marks in Mathematics.
Having taught a myriad of courses—calculus, algebra, analysis, differential equations, mechanics, probability, statistics, discrete mathematics, linear programming—to undergraduate and postgraduate students for the past 22 years, she has been invited by a number of institutions to talk on various topics and applications of mathematics. She had also been a Visiting Assistant Professor at IIT Bombay (2002-2004) and a fellow in mathematics at the Institute of Lifelong Learning, University of Delhi (2008-2009). Professor Bagai has published a number of research papers in reputed journals and has edited and co-authored a book on building mathematical ability. Along with her teaching and administrative assignments, she is actively involved in various projects with her students, many of which have resulted in undergraduate research papers.
During her free time, she enjoys doing puzzles that keeps her mentally active, dancing that keeps her physically fit, and nature photography that lets her enjoy the beauty of the nature
Amber Habib is currently a Professor, Department of Mathematics, School of Natural Sciences, at Shiv Nadar University (SNU), Uttar Pradesh. Professor Habib did his MS (Integrated) in Mathematics at IIT Kanpur and PhD at University of California, Berkeley. These were followed by postdoctoral positions at the Harish-Chandra Research Institute, Allahabad, and the Indian Statistical Institute, Bangalore Centre. His research interests include representation theory and mathematical finance.
For over 15 years, he has been involved in efforts to make mathematics education at the school and college levels more interesting and fulfilling through special topics, projects and an appreciation of the myriad links of mathematics with other disciplines. This began during his time as a teacher at St. Stephen’s College, University of Delhi, and was his main focus during the years he spent with the Mathematical Sciences Foundation. He has also served several times as a resident faculty for the Mathematical Training and Talent Search Programme sponsored by the National Board for Higher Mathematics.
He has received the SNU Faculty Excellence Award for Excellence in Teaching during 2011-2014. Apart from his academic interests and responsibilities, he finds fascination and recreation in nature photography. One can find a rich repository of the same in https://www.flickr. com/photos/amberhabib/.
Geetha Venkataraman is a Professor of Mathematics at Ambedkar University Delhi (AUD). She did an MA and DPhil (doctorate) in Mathematics at the University of Oxford. Her area of research is finite group theory. She is a co-author of a research monograph titled Enumeration of Finite Groups, published in 2007.
Prior to joining AUD as a Professor in 2010, Professor Venkataraman taught at St. Stephen’s College, University of Delhi. She has published several research papers related to group theory and articles related to education, with an emphasis on undergraduate education. Apart from her interest in group theory and related areas, she is deeply interested in popularising mathematics, mathematics education and issues related to women in mathematics. She has given several research talks and popular talks on mathematics in India and other countries to a varied audience ranging over middleand high school children, schoolteachers and mathematicians.
Professor Venkataraman did a BSc (Honours) in Mathematics at St. Stephen’s College, University of Delhi. She stood first in Delhi University in BSc (H) Mathematics. The Inlaks Scholarship and the Burton Senior Scholarship from Oriel College, University of Oxford, enabled her to complete a masters and a DPhil respectively from the University of Oxford.
She is a keen birdwatcher and photographer of birds. Recently, four of her bird photographs have been published in a bird book for children, written in Manipuri, titled On the Lap of Nature: Let’s See Let’s Find, by Dr Kh. Shamugnou. Some of her photographs have been chosen for the database
Table of Contents
List of Tables
List of Figures
Preface
Acknowledgments
About the Authors
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
