Ethan.

Please start by introducing your professional journey in academia

Doctor M Gunasilan. From Kanjivaram. I did my UG and PG. MPhil, PST. In Saint Joseph College, Trichy. I have 13 years.

Okay, so you did your UG, PG, MPhil, and PhD at Saint Joseph College in Trichy,

Ex. Experience of. Academic. Tell me, Sir. Professor. Hello, Sir. Close up.

You've spent over a decade teaching mathematics. What kind of classroom environment do you find most effective for helping students grasp challenging concepts?

Alright.

I can easily understand. So you can explain step by step.

You mentioned step by step explanations help students understand. Can you give me an example of a mathematical topic you've broken down this way, maybe one that students often struggle with?

Suppose, uh, if you take. Quartetic equation. Axis square. Plus 2X plus one.

Suppose, uh, if you take. Quartetic equation. Axis square. Plus 2X plus one. Equal to 0.

Alright, so you're breaking down something like x squared plus 2x plus 1, which is a quadratic equation. When students get stuck on factoring or solving, what do you do differently to help them past that hurdle?

Alright, so you use step-by-step breakdowns for quadratic equations like x squared plus 2x plus 1 equals zero. When students get stuck—say,

You can apply formula. X equal to minus B.

Okay, so you guide students to apply the quadratic formula, x equals minus b and so on. When you notice a student is still confused even after using the formula, what do you do differently to help them internalize the concept?

Equal to minus. B. So X equal to minus B means X + b equal to 0.

Equal to minus.

You were saying "equal to minus" — go on.

Right, so you're connecting x equals minus b to x plus b equals zero.

So here at. Yes, Sir. So here you can. Apply formula. In excess. Square 0 quiescent of X is square 0. You take a sex square as a 0.

Alright,

Then recruitment of. One then confident term. B Fusoli. Yeah.

You mentioned the recruitment of the constant term, b. Sounds like you're walking students through how to identify and work with different parts of the equation. Over your years teaching, have you noticed students grasp these fundamentals more quickly now, or are there still common sticking points you see year after year?

Different parts of the. How we can identify? You can write a equation. That quartetic equation and comparing. Then you can write. Coercion of X square.

Different parts of the. How we can identify? You can write a equation. That quartetic equation and comparing. Then you can write. Coercion of X square. X then conf.

Okay, so you have students compare equations and identify coefficients step by step. When you introduce a new topic like cubic equations, do you keep the same approach, or do you change your teaching method to fit the complexity?

Okay, so you're teaching students to compare equations and pick out coefficients step by step. When you introduce new material—like moving from quadratics to higher degree equations—do you stick with that same method, or do you try something different to help them adjust?

Yes, Sir. So here a quadratic cubic equation means. We can use uh, synthetic method.

Yes, Sir. So here a quadratic cubic equation means. We can use uh, synthetic method. To factorize. Are reduced in the quadratic equation.

First trial and error you can find.

Dr., your recent book chapter, “New Fixed Point Results in Orthogonal Neutrosophic Triple Controlled Rectangular b-Metric Spaces,” covers a pretty advanced topic. How did you approach teaching those ideas to undergraduate students who might not have a background in metric spaces or neutrosophic logic?

Alright, so you bring in the synthetic method for cubic equations and show how to reduce them, which gives students a pathway from familiar quadratics to more complex problems. Thinking about your research, say from your work on neutrosophic metric spaces, have you ever adapted a concept from your own research to make an advanced topic more accessible to undergraduates? If so, how did you do it?

Mm-hm.

Uh. So. So it is purely depends on the. Ture analysis.

You’re saying it depends on true analysis.

So anyway. So metric is nothing but. Distance between two points. Yes, fixed point means. If you take X axis and Y axis. So if you're drawing any. Points so like 1 comma, 01 comma. And two comma 2. 22.5. 3. And so on. If you're drawing line, it passes through the origin They said all points lying on. Yes.

So anyway. So metric is nothing but. Distance between two points. Yes, fixed point means. If you take X axis and Y axis. So if you're drawing any. Points so like 1 comma, 01 comma. And two comma 2. 22.5. 3. And so on.

Alright, so you explain metric as the distance and fixed points with coordinates. When you're teaching undergraduates, do you find that connecting these abstract concepts to simple visual examples—like points on a graph—actually helps them understand, or does it sometimes oversimplify the mathematics?

Okay, so when students notice all points lie along a certain path, does that spark deeper questions for them, or do you find you need to prompt them to think about the mathematical principles behind it? Have you ever used this moment to bridge into more advanced topics, maybe drawing from your own research?

Yes, Sir, we are used in the research. So TX equal to XNA fixed point X is called a fixed point.

In graphical. 2 comma if you put X equal to 1.

Right,

So plugging in X equals 1 gives you a specific fixed point in your example. When you present this graphically to students, do you find they actually understand the significance of the fixed point, or do they need extra explanation to see why it's important in broader mathematical contexts?

Alright.

Yes.

So you bring the fixed point definition right into the classroom, connecting TX equals X to research. When you do that, do you typically walk students through a full proof, or do you focus more on hands-on examples so they can see how the concept actually works?

Uh, yes. So if you take a. One comma, one point. If you put X equal to 1 TX equal to 1 so which means that. T from X to X.

Uh, yes. So if you take a. One comma, one point.

You’re illustrating the fixed point with one comma one. When you use those kinds of concrete examples, do you ever see students start to generalize on their own,

So you’re linking T from X to X, which is the formal mapping for fixed points. When you introduce this mapping to students, do you find they grasp the abstraction easily, or do you need to relate it back to concrete cases like the ones you mentioned earlier?

I.

Okay, so your PhD was in Fixed Point Theory and you've published extensively—over a hundred papers, including on topics like fractional calculus and fuzzy metric spaces. Thinking about your recent paper, say “New Fixed Point Results in Orthogonal Neutrosophic Triple Controlled Rectangular b-Metric Spaces” from CRC Press, how do you adapt those kinds of advanced results for undergraduate teaching? Do you ever bring elements of that research into the classroom, and if so, how do you simplify without losing rigor?

Yes, Sir, we can Boo. Since nowadays they are using neural network.

You mentioned neural networks as a way to connect your research to current trends. When you introduce neural networks in relation to fixed point theory or metric spaces, how do you make sure undergraduates understand the mathematical foundation before jumping into applications?

For fixed point theory. So we are. Yes.

You’ve tied fixed point theory to neural networks, showing you’re thinking about modern applications. Let’s shift a bit—given your research in fixed point theory and its extensions, where do you see the most fundable directions over the next few years? Are there specific grants or agencies you’d target to support this work?

UK.

Shifting gears a bit, Dr.—you’ve taught both advanced and foundational math courses. Suppose you’re running a session with two hundred students and you can’t use slides or a traditional lecture. How would you keep everyone engaged and make sure they’re actually grappling with the material, not just passively listening?

So. A simple way to explain fixed point theory.

So. A simple way to explain fixed point theory. So different session. That ordinary differentiation or differentiation.

So. A simple way to explain fixed point theory. So different session. That ordinary differentiation or differentiation. So existent and uniqueness up.

Alright, you’re focusing on simple ways to explain fixed point theory. Let’s say you notice some students aren’t engaging or are struggling to connect with the material during this interactive session. What’s your approach to bring those students back in, or to assess whether your engagement strategy is actually working?

Okay, switching gears—accreditation cycles can be demanding. If you joined our department and found that outcome assessment data was inconsistent across courses, how would you approach fixing that?

You’re connecting fixed point theory to existence and uniqueness, which is core in differential equations. When you teach that, do you build the bridge for students between these theoretical concepts and how accreditation standards expect you to evaluate their understanding? For example, how would you ensure your assessments are both rigorous and transparent, especially in large courses?

Yes Sir, we are without fixed point theory. We cannot find a solution of the differential equation.

You’re right, fixed point theory is fundamental for existence and uniqueness results in differential equations. But if you’re facing inconsistent outcome assessment data across courses—how would you actually go about standardizing those assessments to meet accreditation requirements? What practical steps would you take?

So whether uniqueness or existence. So it is more. Uh. Yes. Yes, Sir, if you find a. Of D square. +1. Of Y equal to 0. If you solve now you're getting solutions That solutions.

So whether uniqueness or existence. So it is more. Uh. Yes. Yes, Sir, if you find a. Of D square. +1. Of Y equal to 0.

Alright, you’re referencing existence and uniqueness for differential equations, but I still need to hear how you’d handle inconsistent outcome data across courses. Can you give me one concrete step you’d take to standardize assessments for accreditation—maybe a process or tool you’d use?

Let’s get into something a bit more real-world. Imagine you’re teaching Mathematics at VIT, and a student files a formal complaint saying your grading is biased. At the same time, your department head is pressuring you to improve pass rates. How would you handle that situation to ensure fairness and integrity?

Yes, Sir, we, we can focus on the important questions.

Mind giving practice? I'm giving more. Homework.

You said you’d focus on important questions, but that’s pretty broad.

You mentioned giving more homework and practice. If the department head disagrees with that and insists you make grading easier instead, what would you actually do?

Open Ledger Bikes in 1/6.

And the, uh, factories inside the classroom Yes, yes, Sir. So. Many applications there. So intensity wastage. There is a depositing in the land.

Open Ledger Bikes in 1/6. You can give tutorials.

You’re saying you’d give more homework, but if the department head keeps pushing for easier grading and disagrees with your approach, what’s your next move? Would you stand firm or compromise—walk me through how you’d actually decide.

Let’s shift focus a bit, Professor. Given your expertise in fixed point theory and differential equations, do you have connections to industry or professional bodies that could help students access internships or placements—maybe through consulting, collaborations, or joint projects?

You mentioned there are many applications and referred to intensity wastage and depositing in the land—sounds like you're thinking about mathematical modeling in industry contexts. Can you name any specific companies or professional bodies you've worked with, or describe a concrete project where you helped connect students to real-world industry problems?

So we may. This situation has a differential equation. That differential equation you can solve yours. Yes. Yes, and nowadays they are using Plitalis. In the land. So cultivating agriculture purpose. Show it will affect that soil.

Alright,

And it create more disease. To the plant. Yes. Survey will try to find a. Industry. Suitable for this.

Finding and collaborating.

Alright,

You mentioned finding and collaborating with industry. Can you give me one example of how you’d initiate a partnership—like would you reach out to companies, organize joint research, or something else?

Finding and collaborating. So already we. A survey are taking one problem. In companies. Some. The uh. Some wastage. That TVA stage. So we may convert this as a mathematical problem.

So you’re saying you’d convert that company wastage problem into a mathematical model.

And finding a solution. And also applying that optimize techniques. Yes. Yeah, that, that one is a. A basic uh. So normally nowadays we are a. Conducting that. Data in analysis. And after that? We are making that analytical solution. Solving the differential equations.

You talked about collecting data, analyzing it, and then applying optimization techniques—sounds like you use a mix of statistical analysis and mathematical modeling. Can you walk me through how you'd explain this process to a student who's struggling to connect the math theory to real-world supply chain problems?

So and also I'm learning. The deep learning and numerical solutions. Ah, yes Sir, I will do. Because if you're taking that equations. So. That the. One problem. That a suspectable and infected. And recovery. Show many parameters there. That parameters we are called it as. So P then the compartments variables that are state variables. We are constructing neural networks. A deep learning to analyse.

You’re bringing up neural networks and deep learning to analyze compartmental models—susceptible, infected, recovered—so you’re connecting math theory to real-world disease modeling. If a student struggled to understand how the neural network actually maps those variables, what’s a simple way you’d explain the connection between the math equations and the deep learning model?

To fit a parameter estimation. From that value we are going to make.

So you’d use parameter estimation to fit the values from your data. If you’re teaching this in a lab course, how do you make sure students actually understand how to implement parameter fitting—not just in theory, but coding it themselves?

Yes, yes, Sir. We are using Python. To make visualize. How it? It can be.

And how it will affect that parameter values?

Okay,

You’re asking about how parameter values are affected when you visualize them in Python. When students see the results shift as they tweak those values,

We are visualizing. Uh. I yes sorry, we may visualize inside the classroom also.

Right, so you’re visualizing parameter changes right in the classroom.

So we will explain step by step in the mathematical solution. Yes Sir, we can explain in the inside the classroom. Uh, we are actually they are using matrix. So neural networks and. Deep Learning. They are given equation converted as a matrix. So after that they are finding a solution. Then we'll use Python to make a. Uh, cow fitting. Cow fitting to evaluate perimeter values.

Okay, so they’re working through the equations, converting them to matrices, and then using Python for curve fitting to estimate parameters. When you’re guiding student research or projects—especially at the graduate level—how do you help students choose a meaningful research question that’s both mathematically rigorous and practically relevant?

Yes, Sir, we will explain.

You mentioned explaining step by step and working through matrices and neural networks, then using Python for curve fitting. When you’re guiding students on their projects, what’s your strategy for making sure they get enough feedback and guidance from you so their work stays on track, but you’re not doing the research for them?

Uh, uh, how that he situation that is. To set up differential equation. So. Yes, Sir, we can. So like dy by DX equal to a pop X comma.

You’re setting up differential equations—like dy by dx equals a function of x—and using that as a foundation for analysis. When you’re teaching students how to guide their own research, what’s one way you help them connect these mathematical tools to real industry problems, not just academic exercises?

Uh T so that equations. Converted into. Yes, yes. Yes. Yes, Sir. So how? Who will convert into mathematics? So far still can make it. A Karan Suji sent Into a different equation. Number of susceptible. And Into a different equation. Number of susceptible. And. Yes, also we can ask the basic questions. To build a complex problem.

Uh T so that equations. Converted into. Yes, yes. Yes. Yes, Sir.

Uh T so that equations. Converted into. Yes, yes. Yes. Yes, Sir. So how? Who will convert into mathematics?

I hear you—sounds like you’re comfortable converting equations and working with matrices, and you’re guiding students through that process. Let’s shift a bit: when you’re teaching, how do you make sure your explanations are clear and structured, especially when introducing complex topics like deep learning or advanced statistics to students who might not have much background?

Alright,

After we can easily understand from. Move to ANU.

You mentioned building complex problems by starting with basic questions—so you’re scaffolding student understanding,

You mentioned moving to ANU after understanding problems—sounds like you’re thinking about next steps or transitions. Is there anything else you'd like to know about the role or the department before we wrap up?