Embedded Files
Recordings of all past sessions can be found at Math Clinic YouTube channel:
'Sound of Irrational' by Prof. Inder K. Rana (Ex. IIT Bombay)
Event timing: 05:00 PM IST on January 08, 2022 (Saturday)
Abstract: It is well known that the first encounter of fractions (rational numbers) and the task of learning rational number arithmetic poses difficulties. Later encounter with irrational numbers is an equally difficult task.
The shift from rational numbers to real numbers proves to be a major watershed for many students. In school, students meet irrational numbers such as √2, π and e, and begin to realize that the number line has numbers on it that are not rational, though it is not clear precisely what these irrational numbers are! In fact, for the last 2500 years philosophers have been unsuccessful in providing satisfactory answer to the question "What is a Number"?
In this talk we address the following:
1) Origin of the incommensurability / irrationality of numbers and its relation to music,
2) Ways of proving that √2 is irrational (there are about 30 known proofs),
3) Have a look at the irrationality of π and e the Euler's constant,
4) Decimal representations of real numbers.
YouTube Live: https://youtu.be/Tkx0Wrl7fLA
'Some approximate formulae from the ancient times' by Prof. S. G. Dani (UM-DAE Centre for Excellence in Basic Sciences)
Event timing: 05:00 PM IST on January 29, 2022 (Saturday)
Abstract: In this talk I shall discuss various approximate formulae in arithmetic and geometry, from various ancient Indian sources, including the Sulbasutras and Jaina canonical works from the millennium BCE, and the Siddhanta tradition of mathematical astronomy and pedagogical works of Sridhara and Mahavira in the first millennium CE. The historical context of the sources will also be described along with details of the formulae.
YouTube Live: https://youtu.be/wc67eBTdmF4
'Geometrical interpretation of mathematical concepts' by Chanchal Dass (Chairman, Dass Scientific Research Labs Private Limited, Ahmedabad)
Event timing: 05:00 PM IST on February 12, 2022 (Saturday)
Abstract: Difficulty in understanding advanced and abstract mathematical concepts is a global problem. Students face this problem in many math courses. Mathematical Modelling and animation with DassMath can help in making abstract mathematical concepts accessible geometrically. Microsoft Excel worksheet can be used to model and animate concepts. In this lecture cum demo, we will explain how to model and animate in MS Excel and how these ideas can be used in learning mathematical concepts.
YouTube Live: https://youtu.be/1BXQkpoDh58
'Interpolation formulae using Chinese Remainder Theorem' by Prof. S. A. Katre (Lokmanya Tilak Chair, Savitribai Phule Pune University)
Event timing: 05:00 PM IST on February 19, 2022 (Saturday)
Abstract: In this talk we shall first explain Chinese Remainder Theorem for integers and polynomials. Using the polynomial version we shall discuss how to obtain Lagrange Interpolation Formula and Hermite Interpolation Formula. We shall further give an application to partial fractions. We shall also illustrate how to obtain more general Interpolation Formulae using the Chinese Remainder Theorem. These results have applications in Computer Aided Geometric Design (CAGD).
YouTube Live: https://youtu.be/lQJWm8J8KAw
'Mathematical tasks in a holistic learning environment' by Sneha Bhansali (University of Iowa)
Event timing: 05:00 PM IST on February 26, 2022 (Saturday)
Abstract: In this session, we will attempt to develop an intuitive understanding of student-centered mathematics teaching and learning. In particular, we will look at several middle school mathematical tasks and the opportunities they provide for doing mathematics. I will be sharing data from two mathematics classrooms from a holistic school in India where I spent 4 months for the data collection of my dissertation study. In this interactive session, you will get a brief opportunity to engage with the data and contribute to the data analysis process.
YouTube Live: https://youtu.be/pM8beT0bkko
'Design innovative teaching aids and creative activities to help children understand mathematics concepts and excited about learning mathematics' by Teoh Poh Yew (Creative Wizard Pte. Ltd.)
Event timing: 05:00 PM IST on March 05, 2022 (Saturday)
Abstract: Helping children understand Mathematics concepts and getting them excited about learning mathematics is the teachers’ constant challenge. The answer lies in incorporating creative techniques into our classroom practice. Spicing up our mathematics lessons with some magic tricks, puzzles and innovative teaching aids could easily help increase attention, understanding and retention significantly. Appropriate recreational activities/problems stimulate intellectual curiosity, develop problem-solving skills, promote discovery and thinking skills, as well as unleash creativity. In solving these problems, students actively participate in discovering or deciphering the hidden principles underlying each problem and in the process construct their own knowledge of mathematics. This presentation also stress on the need for excitement to encourage mathematical thinking. Mathematical magic can serve as an effective means of motivation at almost all levels of instruction. The major purpose of its use in the classroom is to enable students to discover that mathematics is easy and interesting, and thus stimulate interest in their further study of mathematics.
Presentation outline:
1) The importance of excitement need (Kano Model)
2) How to be a more creative teacher
3) Using Magic and Puzzle as Set Induction
4) How to develop new teaching aids
5) Doing revision the magical way
YouTube Live: https://youtu.be/_RmloS-T_gA
'The century of a mathematician' by Prof. Shripad M. Garge (IIT Bombay)
Event timing: 05:00 PM IST on March 26, 2022 (Saturday)
Abstract: Sharadchandra Shankar Shrikhande (19 October 1917 – 21 April 2020) was an Indian mathematician with notable achievements in combinatorial mathematics. He was notable for his breakthrough work along with R. C. Bose and E. T. Parker in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that there do not exist two mutually orthogonal latin squares of order 4n + 2 for any n. In this lecture, we will try to understand this famous result.
YouTube Live: https://youtu.be/lgTHKaKi9WE
'The game, MATHAMBOLA! You have the knowledge, but are you lucky also?' by Prof. Inder K. Rana (Ex. IIT Bombay)
Event timing: 05:00 PM IST on April 02, 2022 (Saturday)
Abstract: Each participant will have a ticket (as in bingo). The players are presented math questions (of level grade 4-8), one at a time. You are supposed to solve it in specified time and cross the right answer in your ticket, if it is there. Once you get five cuts in a row, you qualify for a prize! So, there are three row-prizes, one for each row. There is a prize if the four cornered numbers are cut: Finally, there is a prize when all the numbers on the ticket are cut. To claim a prize, you should announce it as soon as you qualify. You will be asked to share a copy of your ticket for verification. If your claim is found wrong, you will be disqualified. Typical question: Calculate: 2(6÷2)-1= 5. So you have to cut / cross the number 5 on your bingo card, if it appears.
'Concept of Mathematics Laboratory' by Prof. P K Chaurasia (NCERT)
Event timing: 05:00 PM IST on April 16, 2022 (Saturday)
Abstract: The classroom practices in many schools of the country are dominated by textbooks as well as teacher centered pedagogy. The main objective of mathematics teachers, in the present day scenario is the timely completion of the course. Most of the textbooks provide a single solution to all the problems. This presentation of material has a profound impact on the assessment processes, thereby affecting the mathematics learning of students. Even the orientation programmes conducted by the States are not focused on issues like ‘how to use books, the way to transact the content, how to link problems to students’ daily life, what types of learning resources are used during teaching, how to assess students’ performance, after assessing what type of remedial measures are to be given etc. NCF 2005 also mentions about the use of multiple teaching learning materials, including books for a dynamic learning classroom. Read more...
YouTube Live: https://youtu.be/4V-_HMa41uQ
'Consider a Cylindrical Boy! -- Assumptions and Approximations' by Prof. Ananthnarayan Hariharan (IIT Bombay)
Event timing: 05:00 PM IST on April 30, 2022 (Saturday)
Abstract: We will discuss the idea of converting a real-world problem into a mathematical one, using some examples. Points of emphasis will be to observe that (i) certain assumptions have to be made for the conversion, (ii) there may not be one "good" universal method, and (iii) one can expect only approximate answers. I hope to begin and end the talk with a story related to the title.
YouTube Live: https://youtu.be/0rLCezTGzqU
'Explorations in knot theory for middle school' by Prof. Shantha Bhushan (Azim Premji University)
Event timing: 05:00 PM IST on May 07, 2022 (Saturday)
Abstract: In this talk we start with a few explorations using strings and this will provide the motivation for the beautiful branch of mathematics called Knot theory. We will then give a short overview of this branch of mathematics. Then we will discuss the role of mathematics in math curriculum at the school level using the math curriculum of Japan as a case study.
YouTube Live: https://youtu.be/tq4spzER7uE
'Mathematics of Digital Transmission: Algebraic Coding Theory' by Prof. Sudhir Ghorpade (IIT Bombay)
Event timing: 05:00 PM IST on August 13, 2022 (Saturday)
Abstract: Algebraic Coding Theory has its origins in the problem of information transmission and the seminal work of Claude Shannon in his 1948 paper A Mathematical Theory of Communication. Here one is concerned with the transmission of a message, typically in the form as a large string of digits from a finite alphabet set such as {0,1}, that are sent across a 'noisy channel', which can corrupt the message. The problem is to determine the original message from the received message that is likely to have some errors. A solution is found by encoding the message in the form of a codeword, in such a way that errors can be detected and, often, corrected. The collection of codewords that arise from a given encoding scheme constitutes an 'error correcting code' or simply a 'code'. Error correcting codes that are most widely studied and used are the linear codes.
In this talk we shall give a gentle introduction to algebraic coding theory, with an emphasis on linear codes. We will briefly describe the initial motivations for the subject, outline relevant background from algebra, and then discuss some basic notions and results as well as a few important examples of linear codes such as Reed-Solomon codes and Reed-Muller codes.
YouTube Live: https://youtu.be/aRfpdv4mjoE
'Using Mathematics while Investing' by Prof. Amber Habib (Shiv Nadar University)
Event timing: 05:00 PM IST on August 20, 2022 (Saturday)
Abstract: The world of finance is heavily dependent on mathematics, and its needs have also motivated new concepts and developments in mathematics itself. In this talk, we will take a broad look at this relationship and especially at the use of basic calculus and probability in optimising bond investments and protecting them from fluctuations in interest rates.
YouTube Live: https://youtu.be/0wfRRhJG9RQ
'Math Talk for K-8' by Ms Monica Kochar
Event timing: 05:00 PM IST on September 17, 2022 (Saturday)
Abstract: Whether math class is happening online or in person, when kids are encouraged to talk about their math thinking, it can help teachers assess progress, improve students’ math proficiency, and be a powerful equity strategy that allows kids to see themselves as valued math thinkers. A well-designed math conversation can make it easier for all students - even those who rarely talk in class - to participate. Hence the benefits are for academic as well as personality traits.
YouTube Live: https://youtu.be/ixPdxqGRUHc
'Number theory and secure communication' by Prof. Srinivas Kotyada (IMSc, Chennai)
Event timing: 05:00 PM IST on September 24, 2022 (Saturday)
Abstract: The public key cryptography aims to address the issues of communicating securely through insecure channels. The security of many of these cryptographic protocols are based on the hardness of solving some number theoretic problems. In this talk we shall discuss some popular schemes like RSA, Diffie-Hellman key exchange protocol, ElGamal cryptosystem and the underlying mathematical problems.
YouTube Live: https://youtu.be/Cdpgst2yWAc
'Pigeon hole principle' by K. Maheshwari (Sir Mutha School)
Event timing: 05:00 PM IST on October 08, 2022 (Saturday)
Abstract: The pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item. For example: A bag contains beads of two colours: black and white. What is the smallest number of beads which must be drawn from the bag without looking so that among these beads two are of the same colour?
YouTube Live: https://youtu.be/Iw0L8b-tXGE
'Nonorthogonal expansions in finite dimensional inner product spaces' by Prof. P Devaraj (IISER Thiruvananthapuram)
Event timing: 05:00 PM IST on November 05, 2022 (Saturday)
Abstract: Nonorthogonal decomposition using frames provides a versatile methodology for applications such as signal reconstruction, erasure reduction, resilience against perturbations, quantization robustness, compressed sensing, filter banks etc. We discuss signal decomposition using finite frames in finite dimensional inner product spaces.
YouTube Live: https://youtu.be/ElhGui1NAKI
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