Yes you can.

Please start by introducing your professional journey in academia

OK, so. My name is Doctor Manoj Kumar and I have completed my. It's cooling from my hometown.

Alright,

And that is from Carson in Uttar Pradesh. After that I. After that I. So after completing my schooling, I have pursued my graduation from. Shivaji College, University of Delhi in BSc Maths honors after that. I have pursued my masters from Aligarh Muslim university in the. Department of Mathematics. And I have completed my PhD PhD degree. From the same places. The title of my thesis is the Unraveling the role of certain special function in advancing approximation theory. So basically the. Core theme of my research is approximation theory and special problems.

You mentioned approximation theory as your core research area. When you're teaching undergraduates, what foundational concept in mathematics do you find most rewarding to explain—and why?

OK, so. Related to approximation theory, if we are uh. Uh, teaching a students of B.Tech particularly or. Any graduation?

Alright,

Like BS, Anything else so. Suddenly.

You were starting to explain how you’d introduce error estimation to students—can you give me a concrete example of how you’d present that in your classroom?

OK, so. As we have, we have already knew in. As we are already uh. Familiar with the? Specific #5. So. There the approximate value of π is 22 upon 7, but the. Real value of. Π is 3.14.

OK, so. As we have, we have already knew in. As we are already uh. Familiar with the? Specific #5. So. There the approximate value of π is 22 upon 7, but the. Real value of. Π is 3.14. For the. The largest bit. After the decimal. So, umm.

OK, so. As we have, we have already knew in. As we are already uh. Familiar with the? Specific #5. So. There the approximate value of π is 22 upon 7, but the. Real value of. Π is 3.14. For the. The largest bit. After the decimal. So, umm. Here the the. Difference between the. 22 upon 7 and 3rd. 3.14.

That's an interesting point. Could you elaborate a bit more on that?

India at 22 upon 7 is the approximate value of the π.

Okay, so you're showing students how 22 over 7 is an approximation for pi and comparing it to the actual value, which highlights the idea of error in approximation. How do you help students quantify or visualize the "gap" between the approximation and the real value—what's your go-to method for making that error concrete?

Okay, so you use the classic example of approximating pi with 22 over 7 to highlight the error between an approximation and the actual value. When students struggle with the abstract idea of approximation, how do you connect it to something tangible in their daily lives so it clicks for them?

Mm-hmm.

OK, so. OK, so. Hayaway ban 1m.

OK, so. OK, so. Hayaway ban 1m. Slide the. More precisely, 1M tiles.

Alright, you were about to give an example relating to one meter. Can you finish your thought—how do you use that example to make error estimation real for students?

Tight. OK. So. I have 20.

Mm-hmm.

Mm-hmm.

No, no, no. I.

Alright, you mentioned having twenty—were you going to give an example involving tiles and measurement? If so, can you finish that example for me?

No, no, I am telling the. How to? How I am uh. So I have 1M tiles.

Tiled. Uh uh. And I have 22. This is uh, similar pieces, so I.

Right, so you use the one meter tile as a tangible example.

Okay, so you have 22 similar pieces—were you using that as an analogy for approximation? Can you explain how you connect those pieces to the concept of error when teaching students?

We pick. Of the tile. As a circumference of the circle.

Alright, so you use the circumference of the circle with tiles as a way to make the concept of approximation and error more tangible.

And uh, we I have another seven pieces of the. Similar. Sorry I could not understand your.

You were about to explain how having seven more similar pieces fits into your teaching example. Go on.

20 the seven other. Since I will fix the diameter.

So you’re fixing the diameter and using those 22 and 7 pieces to represent the relationship between circumference and diameter—kind of embodying pi for students. When you do this in class, do you have students actually lay out the tiles themselves, or is it more of a demonstration from you?

20 the seven other. Since I will fix the diameter. So, uh. Diameter.

So you’re fixing the diameter and relating the 22 and 7 pieces to that—basically showing the ratio with actual objects. When you’ve used this method, have you noticed students grasping the limitations of approximations better compared to starting from a strictly symbolic explanation? Or do they still struggle with the leap from concrete tiles to abstract numbers?

OK, so. Another temptation for the. OK, so. What tough example of? We are. The route trip.

Okay, you brought up the idea of a tough example involving a route trip. Were you thinking of using real-world journeys or distances to push students' understanding of estimation and error? How do you structure that kind of example so it both challenges and supports them?

Any particular occasion? So if we are considering any.

Alright, you’re talking about considering any particular occasion—so when you bring up route trips or real-world journeys in class, do you tie those directly to estimation exercises or error analysis? How do you help students connect the math to the everyday experience in those moments?

Every outcomes in the science is the. Is a out? It's all doing something. Because it's not the fixed.

Okay, you’re highlighting that outcomes in science aren’t fixed, and that it’s all about doing something and observing change. When you’re teaching undergraduates, how do you help them internalize that uncertainty and variability are part of mathematical modeling—and not just mistakes to be avoided?

Testing app if. We are. Fix the value of. Any.

You’re talking about fixing the value during testing, maybe as part of an experiment. When you’re guiding students through that process, how do you help them distinguish between controlled variables and variables that can change—especially in mathematical investigations where both types often appear?

No, I'm not. Like that? Variable I'm just. Example of the approach. That you have asked all that?

Alright, so you’re clarifying that you were just giving an example of your approach, not specifically talking about variables. If you’re explaining complex mathematical concepts—say, something from your thesis or a published paper—how do you adapt those ideas for students who might not have the same background? Can you give me a concrete instance where you had to do that?

Uh, communicated one paper which is in under review and in that. I have. Ex Data interpret.

By. Proximation operator that we have introduced through the. Metallica operator.

So you mentioned communicating a paper that's under review, and that you had to interpret experimental data in it. When presenting that interpretation to students,

Alright, so you introduced a proximation operator through the Metallica operator in your paper. When you teach this to students, what’s your strategy for making the idea of a proximation operator accessible to those who haven’t encountered advanced abstract algebra before?

Talk to interbat. Do you have done? We have taken.

Talk to interbat. Do you have done? We have taken. Play me some friends.

Okay, sounds like you were starting to talk about interacting with the interpretation part. If you’ve taken an advanced approach—like the proximation operator you mentioned—how do you scaffold students’ understanding so they can follow the logic step by step, even if they haven’t seen that kind of operator before?

Alright.

In India. During the. Uh, no. In in the class is uh. How many the? Uh, concept of. My paper that we have done so I'm just starting from the basic.

Okay, so you start from the basics when introducing concepts from your paper in class. When you take that approach, do you notice students are able to connect those foundational ideas to the advanced material later on, or do you have to revisit the basics more than once as the complexity increases?

So we have a. Large number of data. So in India. We have considered 5. No type of complexity you are talking about. Are you there?

Right, so you’ve got a large dataset and mentioned considering five types of complexity in India. Can you give me an example of how you used that data to help students understand different levels of mathematical complexity in a classroom setting?

Sectors and each day. So we have. For each day.

Sectors and each day. So we have. For each day. Is in. We have. 365 into 5.

Alright, let's shift gears a bit. Given your work with sector-wise data analysis, where do you see the most fundable research directions over the next three years? What kinds of grants would you target to sustain that research?

Air. Last number data.

Alright,

You mentioned handling a large amount of data—can you walk me through how you decide which part of that dataset to focus on when designing a research project for grant proposals?

We can. We can.

You’re saying “we can, we can,” but I’m not sure I got the rest of your thought. Go ahead and finish what you were going to say.

I'm not. No.

Given your experience working with large datasets and advanced mathematical modeling, suppose you couldn't use traditional lectures or slides. How would you engage a class of 200 students to get them actively working with real data—so they're not just listening, but actually experimenting and discovering mathematical insights themselves?

Of just like 10 issue.

You mentioned "just like 10 issue," but I didn't catch the rest. Are you talking about breaking the class into smaller groups to tackle different problems with the data, or something else?

We can divide them into. Instruments is. Yes.

Okay, let’s switch 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?

Alright.

Saying.

Seems like you might’ve been about to explain your approach, but you didn’t get to finish. When you notice inconsistency in assessment data across courses, what’s your first step to ensure the department meets accreditation standards?

The data just like. If you are, If I have. All all the papers that has been published in the previous year, five years.

Okay, so if you have all the papers published in the last five years,

So will. And Esci. Just like that. And in. So they only publish paper in Sci. Classes like. QQ 3.

End of top 10. Dentals, uh, of the. NVIDIA data.

Let’s tackle a real-world scenario. Imagine a student files a formal complaint alleging your grading is biased, but at the same time your department head pressures you to improve pass rates.

You mentioned "end of top 10, dentals, NVIDIA data." Sounds like you're referencing specific datasets or issues. Can you clarify how you'd handle a situation where your research data is being questioned for integrity, especially if a co-author is involved?

In that, in that particular research. I will very. All the data that. This data. Yeah, we I.

Alright, so you’d verify all the data in that research if concerns came up. But say your co-author insists the dataset is fine and pushes to publish quickly—what would you do if you’re still not confident about its integrity?

Is to be published.

So if the paper is set to be published but you still have doubts about the data's integrity, what exactly would you do—would you escalate it, delay your approval, or something else?

So. Change the data.

Alright, let’s look at the industry connection side. Given your research focus on advanced statistical methods, have you built relationships with companies or industry partners that could help your students land internships or work on real-world projects?

The immediate step. Are you peculiarly in writing what exactly?

Right, you asked if I’m being particular about writing, but I was actually hoping for a concrete example—like, have you personally connected students to specific companies, or are there any industry collaborations you’ve helped facilitate for advanced statistics or supply chain projects?

A gap in the proof.

You mentioned a gap in the proof, but I was actually asking about industry collaborations—have you ever worked directly with a company, or helped students solve a real business problem as part of an advanced statistics or supply chain project? Even a small example would help.

Industry tie UPS. But I can.

Industry tie UPS. But I can. Advanced, replied mathematics.

Alright, Dr., now I’d like to touch on a few core skills we look for in this role. Starting with your expertise in supply chain management, advanced statistical methods, and AI or machine learning—can you describe a real project where you applied advanced mathematics to solve a practical problem, and walk me through your approach?

Alright.

Very close, close to of my. In front of the industry.

Alright, you said you're very close to industry but didn't give specifics. Can you walk me through a real project where you helped students apply advanced mathematics in an industry setting—what was the problem, and how did you structure their involvement?

Hello, can you?

You said "Hello, can you?" but didn't finish your thought. If you're asking whether I can help, I need you to work through these questions yourself—so, about guiding student projects and research, can you share how you structure student involvement in a research project from start to finish?

I can. A message from. Give uh problem.

I can. A message from. Give uh problem. A problem.

You started to say you can give a problem—can you actually walk me through how you’d assign a research topic to a student, help them refine the scope, and guide them as they tackle the project?

Mm-hmm.

Run Bunuchi. Decide the. Problem state.

Okay, so you mentioned deciding the problem statement—can you give me an example of a real student project where you helped shape the research question, and explain how you guided them from that initial idea through to their final results?

The time demand.

Alright, you mentioned time demand—when guiding student projects with a heavy workload, how do you help them manage their time and keep the research moving forward without letting deadlines slip?

Hotels for in. What big red line?

Hotels for in. What big red line? Hard in my big.

Okay, you asked about a big red line in the context of hotels—can you clarify what you mean by “big red line” here? Are you referring to a specific constraint or boundary in an industry project, or something else?

Alright.

A. Early under Paris. Every decision.

You mentioned “early under Paris” and decisions, but I’m not sure I follow—can you clarify what you mean, or maybe give a concrete example from your experience where you had to make an important decision early in a student project or industry collaboration?

OK, so. See. End up.

You were starting to say “OK, so. See. End up…” but didn’t finish the thought—can you clarify what you meant, or give me a concrete example from your work with student research projects where an early decision changed the result at the end?

OK, so. One demanding.

So you mentioned “one demanding”—can you describe a situation where you had a student struggling with a particularly tough research project, and what specific steps you took to support them through it?

Hey. Time timeline.

Alright, you keep referencing time and timelines—can you tell me about a specific tool or method you use to help students plan out their research milestones and track progress, especially when the workload is high?

Involve. Sorry, improve.

You said “involve, sorry, improve”—sounds like you’re thinking about helping students improve their work. Can you give a real example of how you gave feedback or structured guidance that helped a student make a significant improvement on a project or assignment?

Uh, support.

You mentioned support—can you give me a concrete example of how you’ve structured your communication or approach to really help a student overcome a tough spot, maybe with feedback, meetings, or some specific strategy?

It's a. But. Like.

It's a. But. Like. Uh, implemented.

You’re hesitating a bit—sounds like you’re thinking through how support works in practice. I’ll shift gears for a moment. When it comes to communicating complex mathematical ideas to students, what’s your go-to teaching strategy to make sure everyone understands, even those who struggle with abstract concepts?

Mm-hmm.

OK, so. Technical, mathematical, mathematical. And not. Representation. Like. Term in real terms. Increase and OK, so. But they. Realism of how I would. Take a concept distribution. Show experience usually find abstract and make it. New York, 1st 26.

OK, so. Technical, mathematical, mathematical. And not. Representation. Like. Term in real terms.

You’re talking about technical mathematical representation and translating terms into real-world meaning. Can you walk me through a recent lecture where you took a complex mathematical concept and made it relatable for students, maybe using a real-life scenario or analogy?

Time domain but FW. Up to domain, so imaging.

Alright, we're wrapping up. Is there anything you'd like to ask about the role or the team?

Mm-hmm.

You are listening.

You are listening. On your phone.

Right, you said "You are listening"—I am, and thanks for sharing your thoughts throughout. We’re at the end—anything you want to ask about the Assistant Professor role or the team before we wrap up?

Alright.

Signal but. So I want to ask anything.

You mentioned signal and wanting to ask something—go ahead, what’s your question?