Embedded Files
Recordings of all past sessions can be found at Math Clinic YouTube channel:
'Calculus: an overview' by Prof. Inder K. Rana (Ex. IIT Bombay) (Undergraduate level)
The talk presents a historical view of Calculus of one variable from antiquity to Riemann.
'From numbers to analysis: a historical journey' by Prof. Inder K. Rana (Ex. IIT Bombay) (Undergraduate level)
The talk presents a historical development of the number system.
'From 2D to 3D: making boxes and cones' by Prof. Inder K. Rana (Ex. IIT Bombay) (Secondary school level)
The session is a workshop on the construction of 3D objects from 2D objects with optimization problems.
'Mathematical thinking' by Prof. Inder K. Rana (Ex. IIT Bombay) (Teachers at middle school level)
The session discusses the mathematical logic and the language needed for teaching and learning Mathematics.
'Calculus of one variable': Session 1 by Prof. Inder K. Rana (Ex. IIT Bombay) (Doubt clearing session)
Event timing: 4:00 PM IST on May 01, 2021 (Saturday)
'Calculus of one variable': Session 2 by Prof. Inder K. Rana (Ex. IIT Bombay) (Doubt clearing session)
Event timing: 4:00 PM IST on May 15, 2021 (Saturday)
'Preparing young minds for math learning' by Dr. Jeny Rapheal (AIHSS, Padoor, Kerala) (Math enrichment session)
Event timing: 4:00 PM IST on May 16, 2021 (Sunday)
Abstract: Readiness to learn is more important than ability to learn. Best learning/ teaching strategies will be futile if student-brain/mind is not ready to learn. There are many psycho-social factors which prepare the mind and brain of the student for learning. Also, these factors do not happen in the learner or in the learning context without some deliberate effort and conscious planning around the act of teaching/learning. Generating the readiness in the student is an integral part of any successful teaching process. Educational psychology has much evidence for what personal characteristics of the learner or the characteristics of learning context (e.g. teacher-student relationship) are crucial for academic success of students. This webinar will familiarize the teaching community about those pertinent findings with special reference to mathematics teaching.
YouTube Live: https://youtu.be/W72GjDszohQ
'Mathematics of resource sharing' by Prof. R. Ramanujam (IMSc, Chennai)
Event timing: 05:00 PM IST on May 19, 2021 (Wednesday)
Abstract: Whenever there is contention for resources, and there is no central authority to ensure division, the parties involved must come to an agreement and share accordingly. We do not want merely equal division, but equitable division. Defining such a notion of fairness, and coming up with (distributed) algorithms to achieve such division is challenging. While the applications intersect many areas like economics, political science and computer science, the mathematics of resource sharing is simple and based on well-known fixed-point theorems. The talk will attempt to introduce basic concepts in this exciting area of current research.
YouTube Live: https://youtu.be/0uj-K-WIIvg
'The notion of distance: an overview' by Dr. Soumya Dey (IMSc, Chennai)
Event timing: 04:30 PM IST on May 22, 2021 (Saturday)
Abstract: We will discuss about the notion of distance in a set, with the help of several different types of examples. Prior knowledge about basics of linear algebra, and metric spaces would be preferable.
YouTube Live: https://youtu.be/Kq8nHO8iPko
'Calculus of one variable': Session 3 by Prof. Inder K. Rana (Ex. IIT Bombay) (Doubt clearing session)
Event timing: 4:00 PM IST on May 29, 2021 (Saturday)
'Number Theory: Some examples from 2000 BCE to 2000 CE' by Prof. Ravi Raghunathan (IIT Bombay)
Event timing: 05:00 PM IST on June 05, 2021 (Saturday)
Abstract: Number theory is perhaps the branch of mathematics with the most ancient pedigree. In this talk I will highlight a small number of important questions in number theory over the last four millenia. The talk should be largely accessible to those who have studied mathematics up to the ninth standard.
YouTube Live: https://youtu.be/ogYBnnNNiuA
'From Handshakes to Bridges, Chess boards and Beyond' by Prof. Ambat Vijayakumar (CUSAT, Cochin)
Event timing: 05:00 PM IST on June 19, 2021 (Saturday)
Abstract: The nature is full of 'relations'. Graph theory deals with the study of relations among objects. Any two objects are related or not. Also, two persons are either friends or strangers. This is the basic principle of networks. In this information era, most of us are networked, the so called extended friendship. This interdisciplinary talk is an invitation to the various puzzles such as diagram tracing, Hamiltonian problem, map coloring etc., that motivated the development of Graph Theory (Network Science). We shall also discuss in a lucid style the Real World Networks including the network theoretical aspects of phylogeny, epidemiology, world wide web etc.
YouTube Live: https://youtu.be/gwxPEk9DEbs
'Preparing Students for Mathematics Competitions' by Prof. V. M. Sholapurkar (S. P. College, Pune)
Event timing: 05:00 PM IST on June 30, 2021 (Wednesday)
Abstract: In this talk, we propose to outline the importance of various mathematical competitions conducted at school and undergraduate levels in India. We shall also take a survey of some prestigious competitions held abroad. Competitions have a distinctive role in the education system. They provide a chance to the learner to test the knowledge and skills acquired during the training in a competitive but sporting surrounding. The emphasis of any mathematics competition is on solving problems of higher difficulty levels. The purpose of a competition is to expose students to intriguing problems and engage them in the process of making subtle logical arguments. In the process, it is desired that the contestant develops a keen interest in the subject and starts experiencing the beauty of tackling mathematical problems. The process of preparation for a competition is extremely crucial and ultimately turns out to be more important than the competition itself ! In the present talk, we shall deal with this process, especially in the context of some popular mathematics contests like Mathematical Olympiad Competitions and other such prominent events at school levels. We shall also briefly share the information about different math competitions at undergraduate level in the country and abroad.
YouTube Live: https://youtu.be/Tk64HloOET4
'An introduction to non-Euclidean geometry' by Prof. Krishnendu Gongopadhyay (IISER Mohali)
Event timing: 05:00 PM IST on July 10, 2021 (Saturday)
Abstract: In this lecture, I shall give a brief introduction to geometric ideas where sum of the angles of a triangle is not equal to pi!
YouTube Live: https://youtu.be/XRaj11JwKYM
'From Quadratic Equations to Groups: A history' by Prof. Geetha Venkataraman (Ambedkar University Delhi)
Event timing: 05:00 PM IST on July 17, 2021 (Saturday)
Abstract: In this talk we will trace one of the trajectories that lead to the development of modern group theory. Students learn to solve quadratic equations in school whereas solutions of cubic and quartic equations have formulae that are difficult to express. Sixteenth century Italy was the setting for the drama and intrigue that surrounded the discovery of solutions to cubic and quartics. The question then shifted to whether a general formula existed which could express the roots of a quintic equation. It was not until the early nineteenth that Abel was able to show that no such formula existed for the quintic. Galois, a young French Mathematician, showed soon after that this was the case for any general equation of degree five or higher. To prove this he invented groups and was able to settle the question of solutions of equations in its most general form.
YouTube Live: https://youtu.be/5nr90zu_kVU
'Transition from High-School Algebra to College Algebra' by Prof. Amartya Kumar Dutta (ISI Kolkata)
Event timing: 05:00 PM IST on July 24, 2021 (Saturday)
Abstract: The algebra taught up to the higher secondary stage is a part of "Classical Algebra" which is primarily a study of polynomials: solutions of polynomial equations, relations between the roots and coefficients of polynomials. At the college level, students get introduced to "Modern Algebra" or "Abstract Algebra" which is primarily a study of abstract structures like groups, fields, rings and ideals. The late Prof. S. S. Abhyankar gave the names "High-School Algebra" and "College Algebra" to "Classical Algebra" and "Abstract Algebra" respectively.
Though we use the common name "Algebra", the High-School Algebra and College Algebra may appear to the students to be completely different branches of study, mysteriously linked by a common name. In this talk we shall try to indicate a link between the two: how the study of groups and fields emerged from the study of the cubic and higher degree polynomials.
YouTube Live: https://youtu.be/DvKTLzSEiHg
'Art of asking questions - math explorations' by Mr. Rajiv Jha (Dhirubhai Ambani International School, Mumbai) and Prof. Inder K. Rana (Ex. IIT Bombay)
Event timing: 05:00 PM IST on July 31, 2021 (Saturday)
Abstract: One powerful way to get students engaged in mathematics WITHOUT letting their math anxiety prevent them from getting started is by Open-ended math explorations. Open-ended math explorations feature a simple scenario with no explicit problem to solve. Students ask questions and try to find answers. In the International Baccalaureate (IB) diploma programme with Mathematics, explorations form an integral part. In the talk we will illustrate explorations both from the mathematics point of view and what is expected as an IB course.
YouTube Live: https://youtu.be/DbdcHCUrgAc
'Functional Analysis: A glimpse into some of its facets' by Prof. M. Thamban Nair (IIT Madras)
Event timing: 05:00 PM IST on August 14, 2021 (Saturday)
Abstract: Functional Analysis is an indescribably large body of subjects encompassing most of the branches of analysis and its applications. In this talk, I shall try to have a glimpse into some of its aspects originating with basic real analysis and linear algebra, and also will try to show how results from basic functional analysis enters into some of its offspring, namely, operator theory, Banach algebras, operator algebras, Fourier analysis, and PDEs.
YouTube Live: https://youtu.be/hsIcv1JlO7g
'Linear Algebra: an introduction and applications' by Prof. R. K. Sharma (IIT Delhi)
Event timing: 05:00 PM IST on August 21, 2021 (Saturday)
Abstract: In this introductory lecture we talk about linear algebra in its most elementary sense and talk about some applications. We also will connect with vector space, matrices and some other concepts.
YouTube Live: https://youtu.be/ch9FZHW0icI
'Creative Teaching Learning of Mathematics' by Ms. Rashmi Kathuria (Mathematics and ICT teacher, Kulachi Hansraj Model School, Delhi)
Event timing: 05:00 PM IST on August 28, 2021 (Saturday)
Abstract: Creativity is an essential part of the teaching learning process. For catering to the needs of different types of learners we need to use a variety of strategies and techniques. Mathematics is a beautiful subject, full of incredible creativity. Until we enjoy exploring Mathematics as a teacher we cannot reach all learners. In this session we will explore the power of teaching creatively to achieve learning outcomes. We will explore joyful ways of visualising Mathematics and engaging children in a self learning mode.
YouTube Live: https://youtu.be/nlnia0Es5Dk
'Digital Tools for Mathematics Classroom' by Ms. Sangeeta Gulati (Sanskriti School, New Delhi)
Event timing: 05:00 PM IST on September 04, 2021 (Saturday)
Abstract: The importance of representing abstract math concepts in a visual manner in order to support deeper understanding and make connections between concepts is a well known and appreciated fact. Technology plays a key role in making it possible for all levels and all topics of Mathematics. Pandemic has forced us to adapt to an online environment and thus the need to replace the physical manipulatives with online digital tools has become a necessity. In this workshop, participants will explore a variety of free virtual tools that have engaged students in a meaningful manner while learning in a virtual environment. Educators will walk away with a toolkit of effective and easily accessible free solutions which they can implement in their classrooms. GeoGebra, Desmos, Mathigon Polypad and Google apps are some of the well used and tested tools that will be shared.
YouTube Live: https://youtu.be/YmL8PU6HvNs
'What makes a good definition and why does it matter?' by Prof. T. E. Venkata Balaji (IIT Madras)
Event timing: 05:00 PM IST on September 11, 2021 (Saturday)
Abstract: Can you define a polynomial ring in several variables using neither the notion of variable nor of polynomial? Can you define a basis of a vector space using neither the notion of linear combinations nor of linear dependence (or independence) nor of spanning sets? What makes a good definition anyway? Is there a philosophy that always allows you to make it? And what is the worth of such a definition? In this talk we shall try to explore the nexus between good definitions, universal properties, the importance of studying categories and functors, indicating examples from familiar situations in Algebra, Topology, Analysis etc.
YouTube Live: https://youtu.be/TVLjMcy5Mh0
'Machine Learning – A basic overview' by Prof. Niteesh Sahni (Shiv Nadar University)
Event timing: 05:00 PM IST on September 18, 2021 (Saturday)
Abstract: This talk is meant to encourage students and teachers of Mathematics into the fascinating world of Artificial Intelligence and Machine Learning. This lecture will make it clear that Mathematicians not only belong to this domain but can do it better than Computer scientists. The talk would be accessible to all undergraduate students having a background in Calculus, Linear Algebra, and Probability & Statistics. The lecture shall cover two fundamental categories of problems in Machine learning namely Regression and Classification. We will demonstrate the key ideas of Machine Learning by applying Linear regression and Logistic regression to real world data in this introductory lecture.
YouTube Live: https://youtu.be/6IPYBbnnMPA
'Humane Mathematics' by Ms. Monica Kochar
Event timing: 05:00 PM IST on October 02, 2021 (Saturday)
Abstract: We do not learn just by using our minds only. We learn using our emotions, body and most importantly we learn when there is a connection between the student and teacher. How do we teach math using these 4 aspects? How can we convert every lesson day after day to a 4 dimensional lesson? Monica has explored this question all her life and is still exploring. Here she shares some examples from math which she used when she was teaching.
YouTube Live: https://youtu.be/M5shoJVL6rA
'Complex Analysis - an overview' by Prof. Anant R. Shastri (Ex. IIT Bombay)
Event timing: 05:00 PM IST on October 09, 2021 (Saturday)
Abstract: We begin with a brief historical / heuristic comment on the question 'why complex numbers?' and go on to discuss the complex derivative of a complex valued function f of a complex 1-variable vis-à-vis the Fréchet derivative of the associated pair of real valued functions of two real variables. We try to make the lecture accessible to anybody who has done (and not forgotten) a calculus course.
YouTube Live: https://youtu.be/lFzBmmoFqIY
'Graspable Math integrated with GeoGebra and vice-versa' by Mr. Satvinder Singh (Ed-Tech Consultant Lead and Associate Curriculum Director)
Event timing: 05:00 PM IST on October 16, 2021 (Saturday)
Abstract: Graspable Math and Activities: A wonderful online platform (to teach, write, solve, visualize and assess) based on Arithmetic, Algebra and Calculus branches of mathematics. I have been using this platform for 2 years and found it very useful to both teachers and students. It has a Canvas (to explore algebra with or without GeoGebra) and ways to assign activities. GMA Canvas: digital scratch paper that students can draw on, add text to, and work on algebra expressions. Graspable Math and Activities: Assign algebra tasks to your students and see live feedback of their step-by-step work. Discover, create, and share engaging math activities for 4th to 12th graders. GeoGebra can be integrated easily (2D and 3D both) on this platform to visualize solutions to math problems dynamically and step by step.
YouTube Live: https://youtu.be/tmtEjyx9mPk
'Integration from antiquity to Riemann, and beyond' by Prof. Inder K. Rana (Ex. IIT Bombay)
Event timing: 05:00 PM IST on October 23, 2021 (Saturday)
Abstract: The aim of this presentation is to trace the development of the concept of Integration from the Greek period (about 400 B.C.) to the modern times. We will also explore the other developments that motivated the concept of integration and those that necessitated to refine the concept of integration.
YouTube Live: https://youtu.be/NZjzEDzrJ3U
'Technology enabled explorations: a rich context for integrating computational thinking and mathematical thinking' by Prof. Jonaki B. Ghosh (Lady Shri Ram College for Women, New Delhi)
Event timing: 05:00 PM IST on October 30, 2021 (Saturday)
Abstract: In recent times computational thinking (CT) has been identified as an important skill to be developed in children right from the school years. While CT encompasses a broad skill set applicable across contexts and domains, it is also intimately connected with mathematical thinking (MT). Thus mathematics as a school subject becomes the natural choice for integrating CT based activities. However, developing appropriate tasks, which foster both CT and MT in students, is a key pedagogical challenge.
This talk will illustrate the synergistic interplay between computational thinking and mathematical thinking through examples of CT – MT integrated tasks enabled by technology. Such tasks enable students to engage in the processes of visualisation, recursion, generalisation, decision-making and analysing algorithms - all of which are critical from computational as well as mathematical perspectives. Evidence of progression in students’ thinking, as they engaged with such tasks and their positive feedback leads to a convincing argument for integrating such tasks in the mathematics curriculum.
YouTube Live: https://youtu.be/aC9U2a9PefM
'Statistical Estimation and Testing - a basic overview' by Prof. Siuli Mukhopadhyay (IIT Bombay)
Event timing: 05:00 PM IST on November 06, 2021 (Saturday)
Abstract: In this lecture I will be talking about basic concepts in statistical estimation and hypothesis testing. The key ideas will be introduced using practical examples based on real world data. Two types of estimators will be studied. The first of these will estimate the quantity of interest with a single number whereas the second will provide an interval of values. In testing, I will explain ways to use data to test the plausibility of a specified hypothesis. The concept of the p-value will be introduced. The talk would be accessible to all undergraduate students having a background in Calculus, Linear Algebra, and Probability.
YouTube Live: https://youtu.be/UaP9PEn17OI
'Math behind Google search engine' by Prof. B. Surendranath Reddy (Swami Ramanand Teerth Marathwada University, Nanded)
Event timing: 05:00 PM IST on November 20, 2021 (Saturday)
Abstract: In the current technological world, search engines provide information within a fraction of seconds. Some know search engines are Google, Yahoo, Bing among which Google Search is most popular and gives more accurate search results. Google Page Rank algorithm gives rank to each page and shows the results as per hierarchy. The concepts of Mathematics behind the Google page rank algorithm are dominant eigenvalue, Markov chain, power method, Perron-Frobenius Theorem, etc. In this talk, we discuss these mathematical concepts in detail for the Google page rank algorithm.
YouTube Live: https://youtu.be/4VjgorI2XcY
'Mathematics in disguise' by Vinay Nair (Raising a Mathematician Foundation)
Event timing: 05:00 PM IST on December 04, 2021 (Saturday)
Abstract: There is a general notion amongst people at large that learning math is necessary for using it in daily life. The common examples that adults give students of using math in daily life is the math that is involved around money exchange, calculating speed/distance, ratio & proportion, or even examples like construction of houses. While all these are good examples that a student can relate to and even may (probably) use to find motivation to learn and do math, there are a lot of other skill sets that math allows us to build. These are actually skills that are hard to be replaced by computers or AI as compared to other skills like computation.
In this talk, we will be focusing on mathematical thinking that comes in a 'disguised' form, how it really helps everyone in daily life, how can a student/teacher build these skill sets, are they hard or easy to build them, and so on.
YouTube Live: https://youtu.be/HjIB7kHcFfg
Seminars on Geometry and Topology : a series of research seminars on various topics in Geometry and Topology.
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