Maths Club Iiserb

Signing off,
Maths Club Core 2022-2023.

"The beauty of mathematics lies in its universality. It is a language that transcends borders, cultures, and backgrounds. A math education that embraces this universality is essential to its progress and understanding." 
- Maryam Mirzakhani, Mathematician and Fields Medalist

Mathematical Writing workshop, held in four sessions, by a Post-Doc Dr Swapnil Tripathi and a senior PhD Mr Prerak Deep on 30th March and 4th April, 2023.

Recap: Talk-12 on K-means clustering

After seeing Physics in Mathematics in our previous talk, we returned to the general notion of using maths in other fields. In this 12th talk of the year, we brought you the application of mathematics in computer science. The speaker, Harsha Vardhan, an EECS Major minoring in the Mathematics, talked about K-Means clustering.

K-Means clustering is a widely known unsupervised machine learning algorithm with applications beyond machine learning. There are also many variations to the algorithm based on different settings. We discussed an online version of the algorithm in a constrained environment. The problem is to find the clustering in an online scenario when the movement of the centres is restricted. How is the clustering affected by this constraint? Can this problem be solved? Can it be solved optimally? We tried to answer these questions from both mathematical and computational perspectives.

The talked piqued the interest of people of various batches and majors, and gave us an understanding of what works behind technology we use regularly. The audience interacted with the speaker to discuss various clusterings possible.

What algorithms do you know that fascinate you? Which would you like to understand from a mathematical perspective? Share with us in comments below! ✨

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"Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality."

— Richard Courant, German-American mathematician

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Talk-11 Recap

In this talk, the speaker Ankit talked about using Physics in Mathematics (as opposed to using math in physics). We started in the steps of a drunkard, sat with gamblers for a while and finally met the scientists. Sounds random, right? 

A Random Walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. What happens to an object taking a random walk in a finite and infinite d-dimensional space?
A theory of Probability which is a branch of Mathematics was be studied using the classical theory of electrical circuits like Ohm’s law and Kirchhoff's law to answer this question. The answer is formally known as Pólya's recurrence theorem.

The application of the above theory can be seen in various sciences. One of the applications that got a lot of attention in this talk was the Brownian motion.

Despite Bhopal's rains (or maybe because of it?), this talk succeeded in engaging the audience and sparking up a lot of interactive learning and discussions.

“If there is a problem you can't solve, then there is an easier problem you can solve: find it.” 

- George Pólya, Hungarian Mathematician

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P.S. Slide to Snap #5 to tell us if you agree!

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16 March '23, Talk-10

In the second (independent) talk titled "Mathematical Visualisation of Objects" in the series "Understanding Objects", we started with playing different versions of the game of Snake (and Ball) we remember from our childhoods. Now, grown-up, we are quite familiar with snakes, but the speaker asks, "How familiar are you with the spaces the snake lives in?"

Hence we started our mission to understand different spaces based on how the snake moves on the square arena we see. We saw some familiar and some unfamiliar spaces, locally both 2-D and in 3-D looking (i.e. when the arena looks like a square and when it looks like a cube).

A lot of questions were posed, and conjectures discussed, with an intrigued audience as one can swipe to see in the photos. One such was 'What if the square-looking arena is a sphere? What will the movement of the snake look like?"

What weird spaces would you like to play this game in? Strategically, what would be your favourite (non-trivial) space? Tell us in comments below! ✨

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"Thought is only a flash between two long nights, but this flash is everything." - Henri Poincaré, French Mathematician

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Hello all,
With the beginning of the new tenure, we are delighted to invite you to apply for the post of Core Committee Member. This is a fantastic opportunity for all passionate maths enthusiasts to contribute to the growth and success of the club and foster a vibrant mathematical community.
We are looking for enthusiastic, reliable, dedicated individuals committed to shaping the future of the maths club.

To apply for a core-committee position, scan the QR above or click on the link below.
https://forms.gle/RJ1QyXDRjdKbHQYF6
The deadline for the application is 10/06/2023, Saturday,11.59 PM.

We eagerly anticipate receiving your application and exploring the possibility of working together to make our mathematical journey truly remarkable!

On 02 March '23, we had the first talk in the series "Understanding Objects". This talk was delivered by our club coordinator Saumya Jain, and involved exploring topological and geometric properties of objects, introducing ideas from algebraic topology. Based on pictorial thinking, about 90% of the talk was accessible to everyone with no knowledge of +2 mathematics.

In this talk, the speaker talked about understanding (topological) objects through experimentation and intuition instead of rigid theory. We attempted to understand objects (like spheres, the Mobius Strip, etc) and their properties through drawing pictures and craftwork. We circled back to understand why pictures often carry the rigidity of mathematical arguments.

It was indeed an interactive talk with a happy audience! (Swipe for pictures.)

What other objects to you want to understand? Tell us in comments below!
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“You don't see what you're seeing until you see it but when you do see it, it lets you see many other things.” - William Thurston, American Mathematician and Fields Medalist (1982)

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On 16th February 2023, we had talk-08 titled "Isometries" by Raj Soni, who at the time was a 2nd year BSMS student and a core committee member of the club.

Isometries are some of the very basic transformations in Euclidean geometry. Raj talked about 2-dimensional isometries. He explained four types of isometries -- translations, reflections, rotations and glide reflections, with their matix forms and further analysis. He concluded talk by introducing frieze patterns (a two-dimensional design that repeats in one direction) and connected it to group theory. The set of symmetries of a frieze pattern is called a frieze group.

Do you see any frieze patterns around you? Or are you an artist who plays with these patterns? Tell us in comments below! ✨

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“The moving power of mathematical invention is not reasoning but imagination.” - Augustus De Morgan, British mathematician and logician

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A glimpse of an Open Hour

The idea of an Open Hour is simple-- people come together and do maths, without any restrictions of field, level of expertise, etc. The aim is to cultivate a culture of discussion of mathematics across batches and interests, in a post-covid world.

Study. Discuss. Learn.

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"The beauty of mathematics lies in its universality. It is a language that transcends borders, cultures, and backgrounds. A math education that embraces this universality is essential to its progress and understanding." - Maryam Mirzakhani, Mathematician and Fields Medalist

08 Jan '23 : Alumnus Interaction Session with Mr Ranveer Kumar Singh

Mr Ranveer Kumar Singh, an alumnus of the Department of Mathematics, IISER Bhopal visited us in the beginning of this year.

He graduated with a BS-MS degree with a major in Mathematics and a minor in Physics in 2020 and proceeded to pursue a PhD at Rutgers University, USA. There, he is a graduate student in the New High Energy Theory Center (NHETC), Department of Physics and Astronomy. His master’s thesis in mathematics was under the supervision of Dr. Ajit Bhand. It was aimed at investigating the connections of modular forms, class groups and mock modular forms, with black hole microstates counting problems in string theory. His research interests include mathematical physics (Applications of number theory in string theory), mathematics (Automorphic forms, number theory) and physics (Quantum field theory, string theory). A quick google search can tell you more about his achievements.

He talked to us about navigating college years, studying maths and physics individually as well as together, and answered numerous questions about these. It was extremely beneficial for people wanting to pursue physics after developing a strong mathematical background. It was indeed an enlightening talk with HUGE participation from all batches, and was perhaps our most diverse offline talk this year.

“Three things cannot be long hidden: the sun, the moon, and the truth." - The Buddha

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What did you take away from this interaction? Are there other alumni you would like to interact with? Tell us in comments below! ✨

14th December, 2022 : Career Talk - 01 with Alumnus Dr Mahesh Sunkula

On this day, we conducted an interview with Dr. Mahesh Sunkula, with interviewers being Samyak and Suhanee. Dr Sunkula was a student of the first batch of IISER Bhopal and is currently an Assistant Professor in the Department of Mathematics at Purdue University, USA.

Before moving to Purdue, he was a Visiting Assistant Professor in the Department of Mathematics at the University of California, Riverside. In 2019, he received his Ph.D. in mathematics from the University of Oklahoma, Norman, under the supervision of Dr. Nikola Petrov. In 2013, he graduated from the Indian Institute of Science Education and Research Bhopal with a BS-MS dual degree in Mathematics, where he carried out his MS thesis under the supervision of Dr Nikita Agarwal on “Stability analysis of Switched Coupled Dynamical Systems”. 

His research is in applied mathematics, on the intersection of Mathematical Physics, Hamiltonian Dynamics and Symplectic Geometry. He has worked on research projects related to inverse problems, wave scattering, optimal control, and quantization. His other interests include Mathematical Biology, Stochastic Processes, and Data Assimilation.

We talked about careers in mathematics, interdisciplinary research and his experience in academia.

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“Regarding the fundamental investigations of mathematics, there is no final ending... no first beginning.” - Felix Klein

On 11th December 2023, we witnessed one of our most popular talks, with the 80+ attendees. I would say we hit a century but we forgot to count! So here we are 😉. (However, I did learn how to approximate after the last club talk 😎.)

The talk-07 titled "The Inclusion Exclusion Principle" was delivered by one of the coordinators of the club, Dhawal Patil, who loves approaching mathematics in a way most of us are afraid to -- with honesty.

In this talk, we discussed a problem that got us all here. It is not the Big Bang, not Abiogenesis, not the primal need of humans to pass on their genetic legacy. We all got here -- in this meet -- to discuss the problem of counting!

We gave in to our desire to count and generalized a technique we already know, to get to the Inclusion-Exclusion Principle.

To know more, find the slides on our website > past talks.

What are your favorite counting techniques? Tell us in comments below! ✨

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"The moving power of mathematical invention is not reasoning, but imagination." - Augustus De Morgan, British mathematician and logician.

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