Books by Amber Habib
An introduction to the formal approach that underlies university mathematics. Topics covered are:... more An introduction to the formal approach that underlies university mathematics. Topics covered are: Sets and Logic, Relations and Functions, Number Systems, Infinity. The book has arisen out of a first year course taught to Mathematics majors at Shiv Nadar University, with the aim of helping students bridge the different requirements of rigour at school and university.
Sage Publications India, 2017
A bridge to the world of mathematics for readers who want to gain a good foundation in basic math... more 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
The Calculus of Finance
This book is broadly about the mathematical aspects of finance. It introduces the reader to the b... more This book is broadly about the mathematical aspects of finance. It introduces the reader to the basic concepts and products of modern finance and explores various mathematical models dealing with quantification of risk, which form the backbone of modern financial analysis. The emphasis is not so much on the details of the financial world as the basic principles by which one seeks an understanding of it. No prior knowledge of economics or finance is called for—an exposure to basic calculus and probability is all that is required of the reader.
Teaching Documents by Amber Habib
Blackboard - Bulletin of the MTA(I)
These notes are a quick introduction to basic point-set topology. They have their origins in a co... more These notes are a quick introduction to basic point-set topology. They have their origins in a course I conducted at MTTS 2003, and have been refined through subsequent use in MSF's graduate program.
Papers by Amber Habib
Journal of Lie Theory, 2020
Let 0 → a → e → g → 0 be an abelian extension of Lie superalgebras. In this article, correspondin... more Let 0 → a → e → g → 0 be an abelian extension of Lie superalgebras. In this article, corresponding to this extension we construct two exact sequences connecting the various automorphism groups and the 0-th homogeneous part of the second cohomology group, H 2 (g, a) 0. These exact sequences constitute an analogue of the well-known Wells exact sequence for group extensions. From this it follows that the obstruction for a pair of automorphism (φ, ψ) ∈ Aut(a) × Aut(g) to be induced from an automorphism in Aut a (e) lies in H 2 (g, a) 0. Then we consider the family of Heisenberg Lie superalgebras and show that not all pairs are inducible in this family. We also give some necessary and sufficient conditions for inducibility of pairs arising in this family.
The Methods of Mathematics
Routledge India eBooks, May 22, 2022
Indian Women and Mathematics
Fifty Years of Women in Mathematics
This article traces the short history of Indian Women and Mathematics (IWM, https://sites.google.... more This article traces the short history of Indian Women and Mathematics (IWM, https://sites.google.com/site/iwmmath/home) which has been running in a project mode for over 10 years to to encourage more women to pursue higher education in mathematics, and to organise events and networking opportunities that will enable them to take up careers in mathematics.
The Interplay of Mathematics and Finance
Proceedings of the Indian National Science Academy, 2020
Linear and Multilinear Algebra, 2021
Let 0 → a − → e − → g → 0 be an abelian extension of the Lie superalgebra g. In this article we c... more Let 0 → a − → e − → g → 0 be an abelian extension of the Lie superalgebra g. In this article we consider the problems of extending endomorphisms of a and lifting endomorphisms of g to certain endomorphisms of e. We connect these problems to the cohomology of g with coefficients in a through construction of two exact sequences, which is our main result, involving various endomorphism groups and the second cohomology. The first exact sequence is obtained using the Hochschild-Serre spectral sequence corresponding to the above extension while to prove the second we rather take a direct approach. As an application of our results we obtain a description of certain automorphism groups of semidirect product Lie superalgebras.
PLOS ONE, 2019
In this paper, we explore the problem of establishing a network among the stocks of a market at h... more In this paper, we explore the problem of establishing a network among the stocks of a market at high frequency level and give an application to program trading. Our work uses high frequency data from the National Stock Exchange, India, for the year 2014. To begin, we analyse the spectrum of the correlation matrix to establish the presence of linear relations amongst the stock returns. A comparison of correlations with pairwise mutual information shows the further existence of non-linear relations which are not captured by correlation. We also see that the non-linear relations are more pronounced at the high frequency level in comparison to the daily returns used in earlier work. We provide two applications of this approach. First, we construct minimal spanning trees for the stock network based on mutual information and study their topology. The year 2014 saw the conduct of general elections in India and the data allows us to explore their impact on aspects of the network, such as the scale-free property and sectorial clusters. Second, having established the presence of non-linear relations, we would like to be able to exploit them. Previous authors have suggested that peripheral stocks in the network would make good proxies for the Markowitz portfolio but with a much smaller number of stocks. We show that peripheral stocks selected using mutual information perform significantly better than ones selected using correlation.
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Books by Amber Habib
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
Teaching Documents by Amber Habib
Papers by Amber Habib