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A Bridge to Mathematics

A Bridge to Mathematics

  • 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.

© 2017 | 392 pages | SAGE Texts

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

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
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
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


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Shobha Bagai

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.... More About Author

Amber Habib

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... More About Author

Geetha Venkataraman

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... More About Author

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ISBN: 9789386446121