Swimming, Statistics, and the Normal Distribution

As we enter the final stretch of our accelerated summer statistics course, I find it hard to believe that there are only seven class meetings left, including the final exam. Summer courses move quickly, and each class brings us noticeably closer to the finish line.

Last weekend I had the opportunity to relax by the pool, recharge my batteries, enjoy some fresh fruit, and prepare for another busy week of teaching and grading exams. Those moments of rest are important during an intensive summer session, and they help me return to the classroom with renewed energy and enthusiasm.

This week I was pleased to see the progress my students are making. They recently completed their first exam and continue to gain confidence not only in their calculations but also in the language of statistics itself. It is always rewarding to hear students use statistical terminology naturally and to see them support one another as they work through challenging concepts.

Over the past few classes we have transitioned from studying binomial random variables to one of the most important probability distributions in statistics: the normal distribution. Students are now learning how to compute probabilities of the form P(X < x) when X follows a normal distribution, and how areas under the famous bell-shaped curve can be interpreted as probabilities.

The TI-84 calculator has become an important companion in this journey. Students are learning how to use its statistical functions to explore probability distributions and compute probabilities efficiently. Watching them become more comfortable with the calculator has been encouraging, especially as they begin connecting numerical results with graphical interpretations of data.

An interesting conversation this week with a colleague from Lehman College made me reflect on the role of technology in statistics education. She pointed out that in most real-world data science applications, datasets are often too large to enter manually into a calculator. Instead, data are typically imported from files and analyzed using software such as Python, R, or specialized statistical packages. In practice, a data scientist may simply load a dataset into a DataFrame, explore the data, create visualizations, and begin building models.

Yet I believe there is still considerable pedagogical value in tools such as the TI-84 calculator. While modern software is indispensable for working with large datasets, the calculator provides students with an accessible environment in which to explore probability distributions, random variables, and statistical concepts. By computing probabilities, visualizing distributions, and connecting numerical results to graphical interpretations, students develop intuition that will serve them well when they later encounter larger datasets and more advanced computational tools.

In a sense, the calculator acts as a bridge between the mathematical foundations of statistics and the computational tools used by practicing statisticians and data scientists.

Looking ahead, we will continue exploring the normal distribution before moving on to two cornerstone topics in statistics: the Central Limit Theorem and hypothesis testing. These ideas form the foundation of statistical inference and help explain how we can draw conclusions about populations using sample data.

The semester is moving quickly, but I am grateful for the energy, curiosity, and engagement my students bring to class each day. It has been a rewarding summer so far, and I am looking forward to finishing these last few classes together.

For now, it is back to teaching, grading, and preparing for another week of statistics. The bell curve is waiting for us.

Monitoring Arctic Change from Space: A New Student Research Opportunity

Today I had the opportunity to present a proposed undergraduate research project through the CREST undergraduate research program.

The project, Monitoring Arctic Change from Space: Remote Sensing Indicators of Permafrost Thaw Risk, introduces students to an interdisciplinary area that combines environmental science, remote sensing, data visualization, and data science. The project will explore publicly available environmental datasets related to Arctic change, including temperature, snow cover, vegetation indices, and other satellite-derived measurements.

Preparing this presentation was a rewarding learning experience. While my background is in mathematics, machine learning, and data science, developing this project allowed me to learn more about permafrost, Arctic environmental systems, and the growing role of satellite observations in monitoring environmental change.

Monitoring Arctic Change from Space: Remote Sensing Indicators of Permafrost Thaw Risk. Presentation prepared for the CREST Undergraduate Research Program. Image credit: NASA/GSFC/Jeff Schmaltz/MODIS Land Rapid Response Team.

I am excited to mentor a student through this project and to explore together how mathematical thinking, data analysis, visualization, and computational tools can help us better understand complex environmental processes.

One of the aspects I enjoy most about undergraduate research is that every project becomes an opportunity for both mentor and student to learn something new. This summer's journey will take us from mathematics and data science into the fascinating world of Arctic environmental data.

I look forward to seeing where this project leads over the coming months.

Statistics, Swimming, and the Road to the Bell Curve

The summer MAT 1272 Statistics course continues to move at an energetic pace. We are nearly finished with our study of binomial distributions and are about to transition into continuous random variables and one of the most famous probability distributions in all of statistics: the normal distribution.

Earlier in the course, we discussed the Empirical Rule as a way to understand how data are distributed around a mean. At the time, students had not yet learned about probability distributions. Now that students understand random variables and probability distributions, we are revisiting the Empirical Rule from a new perspective. Soon we will connect probabilities with areas under the Gaussian curve and begin using the normal distribution to answer meaningful probability questions.

Yesterday, students completed their first exam. I have also posted a comprehensive review worksheet that covers many of the topics we have studied so far, including basic probability concepts, conditional probability, simple linear regression, correlation, random variables, and binomial distributions. These topics provide a strong foundation for the material that lies ahead.

One of the most rewarding aspects of teaching this course has been watching students become increasingly comfortable with the language of statistics. They are beginning to use statistical terminology with confidence, ask thoughtful questions, and support one another during class discussions and group activities. It is encouraging to see students engage with ideas that initially seemed unfamiliar and gradually make them their own.

The class remains active and interactive. Students regularly stop the lesson to ask questions, seek clarification, or make connections between concepts. Those moments of curiosity and engagement are often the most enjoyable part of teaching.

Overall, this has been a wonderful start to the summer session. I feel grateful for such an enthusiastic group of students and for the opportunity to spend these weeks exploring statistics together. This weekend I plan to recharge with a good swim, catch up on a few projects, and enjoy plenty of fresh fruit before returning on Monday ready for another week of teaching.

It is hard to believe that only eight class meetings remain. There is still much to learn, but I am excited to see how much growth these students will continue to demonstrate in the weeks ahead.

From Counting to the Binomial Distribution

Today was another energetic day in my summer statistics course. We completed our introduction to the basic concepts of probability and began discussing probability distributions. Before reaching this point, we spent time distinguishing between discrete and continuous random variables, an important foundation for understanding how probability models are used in practice.

One of the highlights of the class was introducing the binomial distribution. After completing our discussion of counting techniques, including factorials, permutations, and combinations, I reminded two students of a simple experiment: tossing a coin repeatedly and counting the number of heads. It turned out to be the perfect example for motivating the binomial distribution. What had started as a counting problem naturally evolved into a probability model.

Throughout our discussions, I was encouraged by the students' comments and questions. From their participation, it became clear that many were beginning to understand the computation of a conditional probability and how is linked to determiening if two events are independent or dependent. These are subtle concepts that often require time and practice to develop, so it was rewarding to see students applying the ideas correctly in examples and classroom discussions.

The students also took a quiz on box-and-whisker plots. This assessment included identifying outliers using inner fences. I am not yet sure how many students successfully identified all the outliers, but the results will help me determine what concepts may need additional review.

There is rarely a dull moment in this class. Today we worked together with the TI-84 Plus calculator, computing factorials, permutations, and combinations. We then began calculating expected values and standard deviations for the binomial distribution. It was satisfying to see students connect the formulas with actual computations and interpret what the results mean in context.

As class was ending, I asked a couple of students whether they felt they were learning something from the course. They responded that they were learning a lot. It seemed like a genuine comment, and I certainly hope it was. More importantly, I can see evidence of their growth through their participation, engagement, and the thoughtful questions they ask during class. Students who were initially hesitant are becoming more comfortable contributing to discussions and working through problems in front of their peers.

Teaching an intensive summer course is always challenging because of the pace, but it is rewarding to watch students make connections across topics. In just a short period of time, we have moved from descriptive statistics and boxplots to probability, counting techniques, random variables, and probability distributions. I look forward to continuing this journey as we build toward more advanced statistical models and applications.

Teaching Statistics in an Accelerated Summer Course

Over the past two weeks in my MAT 1272 Statistics course, we have covered a wide range of foundational statistical ideas while balancing computation, interpretation, and technology. Because this is an accelerated summer course, I have been focusing on helping students build intuition through examples, visualizations, board work, and hands-on calculator practice.

We began with the fundamentals of statistics, including populations and samples, qualitative and quantitative variables, and the distinction between descriptive and inferential statistics. Students then learned how to organize and visualize data using frequency tables, bar graphs, histograms, stem-and-leaf displays, and box-and-whisker plots. Along the way, we discussed measures of center and spread, including the mean, median, mode, range, variance, standard deviation, quartiles, percentiles, and outliers.

More recently, we shifted our attention to relationships between two quantitative variables. Students learned how to construct and interpret scatterplots, determine whether a linear trend is present, and identify whether the trend is increasing or decreasing. We discussed how a regression line can be used to model data and make predictions, as well as how the slope and y-intercept describe the behavior of the model. Using the TI-84 Plus calculator, students learned how to compute the regression equation and the correlation coefficient r, which measures the strength of a linear relationship between variables.

Our next unit focused on probability. We studied basic probability concepts, conditional probability, independent and dependent events, the multiplication and addition rules, and counting techniques such as permutations and combinations. Throughout the unit, students used their TI-84 Plus calculators to perform calculations while developing a deeper understanding of how probability can be used to model uncertainty and real-world decision making.

The next chapter introduces one of the most important ideas in statistics: probability distributions. Students will learn about discrete random variables, probability distributions, expected value, and standard deviation for random variables. We will then study binomial and hypergeometric probability distributions and use technology to compute probabilities in realistic scenarios.

One aspect of this chapter that I am especially excited about is helping students visualize probability distributions. By constructing histograms of binomial distributions, students can begin to see how these distributions become increasingly bell-shaped as the number of trials grows. This observation provides a natural bridge to one of the central topics in statistics: the normal distribution.

Throughout the course, my goal has been to connect formulas, graphical representations, technology, and real-world applications so that students can see statistics as more than a collection of calculations. Whether analyzing data, modeling uncertainty, or making predictions, statistics provides a powerful framework for understanding the world around us.

Two Days into a Four-Week Statistics Course

June in New York City, on the way into an intensive summer teaching rhythm.

This summer I am teaching MAT 1272, an introductory statistics course compressed into just four weeks. Sixteen class meetings. One entire semester packed into sixteen mornings.

At the same time, I am trying to keep research projects moving forward before July conference deadlines arrive. Balancing teaching and research is always part of academic life, but summer courses have a unique intensity. There is very little time to waste, and every class meeting matters.

What is remarkable is that we are only two days into the course.

Just two class meetings.

Yet it already feels as though we have covered a tremendous amount of ground. In those first two days, we have discussed descriptive statistics, statistical inference, variables, populations and samples, parameters and statistics, qualitative and quantitative variables, and discrete versus continuous variables. We have also started organizing and visualizing data through bar charts and histograms. These may seem like simple topics, but they form the foundation for everything that follows in statistics.

Before students can analyze data, they must learn how to describe it, organize it, visualize it, and communicate what it means.

A quiet moment between teaching, research, and the pace of summer in the city.

One of the highlights of the course has been the group work. Students come from a wide variety of backgrounds and experiences, and it has been exciting to watch them engage with one another's ideas. Discussions often take unexpected and interesting turns. This week, for example, students have already begun grappling with the distinction between a sample statistic and a population parameter. They are starting to understand that while we may know the average of a sample, the true population mean often remains unknown.

Those are important moments because they signal the beginning of statistical thinking.

The first day of class also brought an encouraging surprise. A student who had previously taken the course approached me at the end of class to introduce herself and tell me that she appreciated my teaching methodology. As instructors, we never really know what students will remember from previous experiences, so moments like that are especially meaningful.

This summer I have relied heavily on the blackboard. There is something timeless about developing ideas step by step in real time, allowing students to see the reasoning process unfold. Eventually I will project visualizations and technology-based demonstrations, but for now the old-school approach seems to be working well. Chalk, dust, and all. The students seem to appreciate it, and the classroom conversations have been lively and engaging.

Chalk, dust, and statistics: the old-school classroom is still alive and well.

At some point, the TI-84 Plus calculators will make their appearance in the classroom. For now, however, the focus is on concepts, language, and interpretation. I want students to understand what a histogram represents before asking a calculator to create one, and to understand the difference between a sample statistic and a population parameter before pressing a button to compute a numerical value. Technology is an important tool, but it is most effective when it supports understanding rather than replacing it.

I've also been fighting a cold and have spent much of the week feeling under the weather. Teaching an intensive four-week course leaves little room for slowing down, however, and the positive energy in the classroom has made it easier to push through.

Perhaps my favorite part so far has been getting to know the students. I am still learning names, and they have been amused by some of the memory tricks and mnemonics I use to remember them. There is a good atmosphere in the classroom. Students seem appreciative, engaged, and willing to participate.

What makes me happiest is hearing them begin to use statistical terminology naturally. Words such as population, sample, parameter, statistic, qualitative variable, quantitative variable, histogram, and distribution are already finding their way into classroom conversations. These may seem like small victories, but they represent the beginning of statistical literacy. Students are asking thoughtful questions, debating ideas during group activities, and becoming more confident in their reasoning.

Tomorrow is already our first quiz.

That fact alone captures the pace of a four-week summer course. We have only met twice, yet students have already learned a substantial amount of new material and are preparing to demonstrate their understanding.

Time moves quickly for all of us. One student will be graduating next week, while another will be starting a master's program at the Graduate Center this fall. Other students are balancing work, family responsibilities, and their own academic goals. It is a reminder that every classroom brings together people at different stages of their journeys, each moving toward something new.

Before long, these sixteen class meetings will be behind us as well.

For now, I am grateful for a classroom full of curious students, thoughtful discussions, and the opportunity to spend June exploring statistics together. Only two days have passed, yet the classroom already feels alive with questions, new ideas, and aspirations for the future. It has been an exciting start to the summer.

A Classroom Built on Growth - MAT 1190 (Spring 2026)

As the semester comes to an end and tomorrow’s final exam approaches, I have been reflecting on Math 1190 CO. Independently of the grades my students will receive, this semester has been another reminder that I am not only a mathematician who teaches at the college level, but also a mathematician who continues learning through teaching each semester.

This class became a space where I witnessed growth in many forms. I saw a group of students who showed up regularly, participated actively, and genuinely engaged with the class activities. I watched communities form inside the classroom. I saw students helping one another, discussing ideas together, and becoming increasingly comfortable sharing their thinking openly.

Throughout the semester, we explored many topics: voting theory, probability, statistics, correlation, the normal distribution, z-scores, counting techniques, growth models, compound interest, and linear models. Beyond computations, we focused on interpretation, discussion, and applying mathematics to real situations. Some of the conversations that emerged from these topics were thoughtful, honest, and surprisingly rich.

Yesterday, during our final review session, there were still several review problems left to discuss. Instead of simply presenting solutions myself, I asked students to come to the board and present problems to the class so they could take a more active role in preparing for the final exam. What followed was one of those moments teachers remember.

One student went to the board for the first time all semester. I could see the satisfaction and confidence that came with simply trying. Two students worked together at the board as a team, discussing the exercises openly with the class while I stepped aside and observed. There was collaboration, openness, laughter, and genuine engagement. I saw students explaining ideas to one another instead of waiting passively for answers.

What stayed with me most this semester was not perfection, but growth. I saw integrity and accountability when students admitted they had not studied enough or had made mistakes. That level of honesty reflects maturity and a sincere desire to learn and improve.

One student told me she was actually enjoying studying mathematics. I told her that was a win for both of us.

I will miss this group.

To my students from this semester: thank you for showing up, for trying, for participating, and for contributing to the atmosphere we built together in the classroom. If you ever want to stop by my office just to say hello, please do. I would truly love to be present one day at your graduation. It was a privilege to teach you.

Now I will be shifting gears for the summer — returning more intensely to research, conferences, and catching up with that side of my profession, while also teaching an intensive summer course.

For the students who kept showing up even when things felt difficult: that matters. There is real power in continuing to show up, especially when something does not come easily.

Starting the Spring Semester (S26) with Conversation

Starting the Spring Semester with Conversation

The spring semester for MAT 1190 CO at New York City College of Technology (City Tech) began in an unusual way. Our first day of classes was held on Zoom due to a snowstorm. Rather than letting the format create distance, I made a conscious effort to turn that first meeting into an interactive space—one where students could talk, reflect, and begin to see each other as part of a learning community.

That first day already revealed how different this group is from last semester’s. As students introduced themselves, I learned that some love basketball, others work with children with special needs, some are majoring in hospitality or human services, and others are pursuing nursing. It is a uniquely diverse group, shaped by very different paths and motivations, all coming together in the same course.

A colleague later mentioned that this course can be challenging because many students do not arrive with the math background I am accustomed to seeing. That comment made me pause—not in disagreement, but in reflection. The course uses Math in Society, and one of the first topics we explore is voting theory. Almost immediately, I could tell the students were engaged. They were not just learning procedures; they were thinking about fairness, decision-making, and how systems affect people’s lives. There is a lot of group work, discussion, and interaction, and I make it clear from the beginning that they need to get to know one another and work as a team. I often tell them: never turn your back on your teammate.

On our second day of classes, our first meeting in person, something unexpected happened. As soon as class ended, six students followed me to my office. They wanted to keep working. We stood at the board, solved problems together, and worked through the new material until it started to make sense. There was no requirement for them to be there—just curiosity and a desire to understand. I started calling them the class “ambassadors.” Not because they are the strongest mathematically, but because of their attitude. Their engagement and openness toward learning has already begun to influence their peers and shape the culture of the classroom.

Later that same day, another moment quietly stayed with me. A student stopped by my office before class—not to work through problems, but to look for a new friend she had met in the course, and also to see me. As she was leaving, she told me she was genuinely looking forward to coming to campus—to seeing her friend and coming to class, and to seeing me as well. She shared this simply, almost in passing.

That comment touched me deeply. Sometimes we create spaces where connection happens without even realizing it. A classroom becomes more than a place to learn material—it becomes a reason for someone to show up, to feel connected, to feel seen. And when that happens, it reinforces what I believe deeply: teaching, especially in a course like this, is not just about math. It is about conversation, community, and the small moments that can quietly light someone’s path.

A proud MAT 1630 moment: when a former student became the “guest panelist” we didn’t plan

This week, something happened in MAT 1630 that reminded me exactly why my colleagues and I do this work.

During class, while my students were working on an activity, I stepped out briefly—and I ran into a familiar face in the hallway: a former student from our department.

She graduated with honors this past summer. She was a mathematics student, worked with me on a machine learning research project, and now she’s starting a master’s program in mathematics at NYU Courant, one of the most respected places in the world to study math.

I made a quick, spontaneous decision.

I asked her if she could stop by the classroom for a few minutes and talk to my current students. She said yes.

What happened next turned into something I didn’t plan, but honestly couldn’t have designed any better.

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The Best Panels Are Sometimes Improvised

The last part of class became a mini “panel experience.”

My students jumped in with real questions, the kind students actually want answers to:

• How did you get from City Tech to a top graduate program?
• What is the workload really like?
• How many hours do you study each week?
• How do you stay focused and consistent?
• What do you do when things get difficult?

She answered with honesty and confidence.

She didn’t make it sound easy. She talked about discipline, learning how to manage time, and staying committed even when motivation isn’t there.

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A Moment I Won’t Forget

One of the things that moved me the most was when she said something very personal:

She told me she once wanted to follow my path—“to be like me”—and that in a way, she’s now doing exactly what she said she would do back when I first interviewed her for a seminar and workshop I co-organized with colleagues from Utah.

That hit me.

Not because it was about me, but because it showed how powerful it is when students can see a future and then work their way toward it step by step.

She’s not just dreaming about the next level. She’s doing the work to reach it.

And she’s already talking about her next goal: a Ph.D. in Mathematics!

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“Don’t Listen to People Who Underestimate You”

She also shared advice that my students needed to hear:

Don’t listen to people who underestimate you.

Some people will assume you can’t do it. Some people will try to limit you based on what they think is realistic.

But you are the one who decides what is possible.

Then you prove it through your actions.

She also spoke about being an immigrant and an ESL student and how she never stopped believing in herself.

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Why This Matters at City Tech

My colleagues and I do what we do because we want to see students graduate, succeed, and go further than they thought they could.

This was one of my proud moments of the year, because my current students got to meet someone who walked the path they’re on right now and is already opening the next door.

Sometimes students need more than encouragement. They need examples. They need proof that it can happen.

This was proof.

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To My Students Reading This

Dream big.

But don’t stop there.

Work for it.

Stay consistent.

Ask questions.

Seek mentors.

And when someone tells you it’s not possible—remember: you are the one who decides what’s possible.

Teaching with Google Colab + Private GitHub Repos

This semester in MAT 1630 I tried a small change that made a big difference: I created a private GitHub repository for each student and added them as the sole collaborator, then had them work in Google Colab and submit via a pull request. Everything happens in the browser, every step is a click, and yet students are quietly learning real professional habits—commits, branches, pull requests, merges—without touching a command line.

The day-to-day is simple. Students open my Colab notebook, work through the exercises, and when they’re ready, choose File → Save a copy to GitHub. On GitHub they press the big green button to open a pull request, and then merge. On my side, each pull request becomes a clean, time-stamped submission with a place to leave feedback. Because I own the repositories, nothing gets lost, I can always see the work, and the record is there if we need to revisit grading or progress later on.

Why Google Colab clicks with students

• No setup, no stress: opens in a browser—no installs, no configuration, works on Chromebooks and shared lab machines.
• Autosave peace of mind: work is saved to Google Drive, so nothing vanishes with a laptop hiccup.
• Clear, beautiful results: run cells, see output immediately, add explanations in Markdown or LaTeX.
• Easy help: sharing a notebook link makes quick coaching in class painless.

Why private repos owned by the instructor help everyone

• Reliable access: I keep ownership, so submissions don’t disappear if a student changes settings or accounts.
• One tidy place: consistent naming and structure make reviewing and grading faster.
• Natural feedback loop: pull requests are built-in checkpoints for comments and review.
• Privacy by default: student work stays private, and GitHub masks personal emails with a no-reply address.

The submission flow students actually follow

1. Open the assignment in Google Colab.
2. Work through the notebook and verify outputs.
3. Choose File → Save a copy to GitHub and select their private repo.
4. On GitHub, click Compare & pull request, then Create pull request, then Merge.

What I appreciate most is how this nudges students to see programming as collaboration. They start to understand version control as a normal part of the process: small commits, clear messages, respectful reviews. It also happens to be free—private GitHub repos and Colab are both zero-cost—and it keeps everyone’s personal email private. For instructors, the setup is sustainable because once the repositories are created, everything else runs smoothly: students submit with a few clicks, feedback happens directly on GitHub, and there’s no need to chase files or manage endless attachments. The workflow stays organized, low-maintenance, and easy to reuse each semester, which lets us focus our energy on teaching, not on handling logistics in classes with a coding component.

Welcome Back, Fall 2025

What I’m Teaching (and why I’m excited)

Intro to Computer Science (Python)

I started teaching Intro to CS this semester and I’m keeping the momentum going. We’ll learn to solve problems by thinking first and coding second. Expect small, meaningful projects that build real skills, live coding in class with my inevitable typos and quick fixes, and lots of practice turning a messy idea into a clean plan before we touch the keyboard. If we do it right, you’ll feel your problem-solving muscles getting stronger each week.

Discrete Structures

In Discrete, we’re in the middle of propositional logic: truth tables, connectives, and the whole toolkit for precise thinking. Students already completed their first group activity, and it was great watching people learn each other’s names while debating whether one statement is truly equivalent to another. I’m sticking with the Socratic method, asking more questions, keeping explanations short, and giving space to wrestle with ideas out loud.

Why This Work Feels Big

I’ve been thinking about our mission at City Tech. We’re here to support and uplift a new generation of students so they can flourish in school, at work, and in life. I’m lucky to be around colleagues who are strong researchers and who also believe in giving back and paying it forward. That kind of community keeps me grounded and pushes me to show up better for my students.

What You’ll See on This Blog

Expect class updates and project highlights, little teaching wins along with the flops we learn from, Python tips and discrete math nuggets, and thoughts about learning, belonging, and building confidence.

If you’re in my classes, welcome. Bring your questions and your curiosity. If you’re reading from afar, I’m glad you’re here too. Here’s to a semester of clear thinking, kind collaboration, and code that finally runs after that one missing parenthesis.

4-week summer intense precalculus course...an enthusiastic, refreshing and fun crowd!

I decided to teach a four-week summer class this year. Sometimes I had doubts because I usually use the summer months to do research in a more relaxed way. However, I wanted to try an intensive four-week course, teaching from 8:30 am to 11:08 am with office hours afterward. I must say, it was incredibly fun. The students were enthusiastic about learning. Some were very expressive about their concerns regarding the exams, and one student even placed his hand on his heart in relief when I mentioned that I wouldn't ask them to sketch complicated graphs. More than a quarter of the class were outstanding individuals with a very positive attitude toward learning. Some of them took my feedback very seriously, improving the way they wrote their solutions and articulated their ideas in general. They were engaged, and some of them want to continue working with me on a project. I observed significant growth by the end of the course and was moved by a letter they sent to the chair of my department, requesting me as a calculus instructor in the fall semester. They mentioned being impressed by my teaching methodology, depth of knowledge, and ability to make complex mathematical concepts comprehensible. One of my students even mentioned that my passion for teaching and genuine care for their progress was truly inspiring. We had so much fun, laughs, and interesting discussions. It created a beautiful summer memory that ended with an endearing letter. It makes me realize why I chose to take the academic path. Perhaps I am influencing other lives in a positive way. I am sharing an image of the letter, concealing identities to respect their privacy. I am truly grateful for having the privilege to teach these outstanding individuals. Every class, I started with a lecture but quickly moved to group activities. It was a pleasure to see students helping each other understand concepts, share ideas, and improve their problem-solving skills. This collaborative environment fostered a sense of community and mutual support among the students, which was incredibly rewarding to witness.

It has been a while: from Yoda to trigs

Our SIAM student chapter recently hosted an insightful talk by a mathematician from Brigham Young University. They delved into the mathematical principles behind animating Yoda from Star Wars, which piqued the interest of our students. Additionally, they discussed the mathematical techniques used to create more realistic snow in Frozen, which fascinated the audience. The speaker also distributed math-themed T-shirts, adding a nice touch to the event. And of course, we enjoyed some pizza together afterward. These experiences are helping to build a sense of community among our students. The recent exam on exponential and trigonometric equations highlighted the importance of practice for success. During our discussions on Yoda's animations and the creation of realistic snow in Frozen, students were engaged in understanding the technical aspects behind these iconic cinematic elements. With spring break now here, I look forward to grading and pursuing research opportunities before returning to class.

Students lost track of time on Tuesday! Ants are not controversial...

This last class, we focused on solving exponential and logarithmic equations and discussing the properties of log functions to facilitate solving such equations. We concluded by delving into exponential growth models and illustrating population growth/decay through examples. During a group conversation, one student mentioned reading about the maximum population Earth can sustain. Another student countered, stating there wasn't enough supply. This sparked a thought in me; I vocalized that numerous areas worldwide remain unpopulated while cities suffer from overpopulation, leading me to question the prevailing alarm regarding population growth. Further discussion ensued when another student argued that there isn't enough food to support the population, prompting another to interject that there's actually a considerable amount of food wastage and potential to produce more with current technology. This led to a discussion on GMOs. What began as a precalculus class morphed into a thought-provoking conversation, which I found quite amusing. I then prompted them to consider an ant population problem to steer clear of controversy. This elicited laughter from the students. Working in groups, they successfully formulated equations to determine the time required for the initial ant population to triple. I typically assign students numbers and reorganize the class accordingly into groups. Observing their engrossment in discussing ideas was remarkable, especially considering that students often anticipate leaving promptly. They even stayed an extra 11 minutes! Their enthusiasm truly made my day!

https://www.washingtonpost.com/climate-environment/2022/09/19/ants-population-20-quadrillion/

BYU- City tech undergraduate data science collaboration workshop, the visit, the reflections

Last week, on Thursday, March 14th, and Friday, March 15th, we had the pleasure of receiving Professor Mark Hughes from Brigham Young University (BYU) and the six students who are participating in the undergraduate data science seminar that we are running together. This was the first time that the students from BYU and our three City Tech students would meet up in person. On Thursday, Professor Hughes gave an excellent talk on how AI has been used to aid in proving mathematical propositions. We had more than 40 people attending his talk, sponsored by the Math Club on Pi Day! Most of the audience were students, and they asked very intriguing questions about neural networks and other machine learning topics. Following that, we continued with our workshop where students engaged in a neural net tutorial conducted by Professor Hughes. Students were very engaged in trying different things on the Python notebook and interacting with their peers. The next day, I gave an intro to autoencoders and showed them the general parts of a notebook I acquired for LiDAR data exploration and how to apply PCA and autoencoders to LiDAR. My student, Charlotte, presented a great summary of her NLP team project from last year, which opened very exciting discussions on Topic analysis and depression in college students. We had lunch and then brainstormed about data and topics in order to define three different teams and the passions and interests of each. I was in charge of the NLP group where many possible topics were discussed, from US elections to depression in university professors, and lastly took the direction of working on social media comments to analyze how social media affects young women's self-esteem. I was excited to see the passion of the team members since they seemed to be really concerned about the mental health issues online interactions are producing in women. The overall experience was very satisfying. I had the opportunity to hear how one of the students expressed great concern about how online communication is affecting relationships and the emotional distress of these interactions. I had an insightful conversation with one of the students while walking back from our outing in DUMBO. He mentioned that he would like to have more in-person experiences like this, where he can learn very concrete things while discussing ideas with his peers and having breaks to enjoy the social interactions. He says most of his week is about going to college and from college to work back and forth. I was happy to see that we were able to create such a positive learning experience. On my side, coming from another generation, I personally observe a dehumanization in online interactions, including emails, text messages, and apps of all kinds. This is a personal opinion, but I wonder if many people are substituting building relationships based on personal interactions with online interactions. It seems that the pandemic played an important role in this, but I wonder if the foundations of meaningful relationships can be built on these very shaky grounds. The final part of the workshop will take place in May when City Tech students and I will be visiting BYU. I am so looking forward to seeing their final presentations and enjoying Utah!

Starting Spring 2024 semester. The little man is back!

I just noticed this draft has been siting here for days: It's been a few weeks since we returned to campus, and I'm still in the process of learning my students' names. However, the joy of being back, interacting with both students and colleagues, has brought a sense of home that energizes me, making me temporarily forget life's challenges. As an introvert-extrovert, diving into teaching allows me to explore my more outgoing side. This semester, I find myself solely focused on teaching precalculus, thanks to a teaching release that provides me with additional time. With this newfound time, I'm aiming to finalize some pending manuscripts. In these initial weeks, I've managed to learn several students' names and have already encouraged them to break the ice with each other. We've formed little teams to discuss precalculus problems collaboratively. Our topics have ranged from real numbers, understanding functions, and exploring graphs, to delving into domains, ranges, and transformations of basic functions. Our most recent discussion involved the composition of functions. During our exploration of functions, I revisited the analogy of the little man walking on the x and y-axes. The students chuckled, and I acknowledged that many find this visualization helpful when grasping domain and range from a graph. So, the little man has made a comeback to aid in understanding the intricacies of functions. I introduced the online graphing calculator, Desmos, and we dived into various graphs, exploring the tool's capabilities. Students were able to locate coordinates for x and y-intercepts, extract tables with values, and identify local extrema. As we progressed, we began experimenting with applying horizontal and vertical transformations to graphs from what I playfully referred to as the "alphabet of graphs." In contemplating future lessons, I'm considering the creation of a fun animation featuring the little man to visually explain the determination of the domain and range of graphs. Should I?

Overdue reflection on Fall Semester 2023. Never give up!

This post is long overdue, and today I want to share a different side of myself with my students. More than just the mathematician who delves into axioms, proofs, calculus, and other intriguing mathematical concepts, I recently visited Brigham Young University to give a talk. This presentation, unlike my usual technical talks, was part of Math Circles within Dr. Michael Dorff's course. In the academic world, mathematicians are often perceived as intellectual beings effortlessly navigating life's challenges. However, mathematics is a human endeavor, and I decided to reveal a vulnerable side of myself, discussing the personal struggles in life, family dynamics, and the hurdles of job hunting, particularly after completing PhD and postdocs. This career, like many STEM paths, goes beyond mere intelligence; it requires patience, persistence, hard work, grit, and an unwavering commitment. I shared a poignant moment from my time as a visiting postdoc at ICERM (Brown), when I was still searching for a job to support my family. Many students approached me afterwards, expressing gratitude for sharing this personal story. The journey includes facing rejection, especially during on-campus interviews, and I emphasized the importance of growing from rejection, using it as fuel for personal growth. Dealing with rejection is a crucial aspect of this journey. I encouraged my students and colleagues to remember their worth, to never give up, and to understand that all professors and colleagues have encountered challenging times. This resonated with my students, fostering a disciplined approach throughout the semester. I aimed to influence them positively, emphasizing the importance of directing their efforts towards things they can control, rather than succumbing to distractions like excessive social media or constant cellphone use, which I referred to as mere noise. I urged them to cultivate independent thinking and form their own opinions, even if they differ from the majority. In essence, my message is clear: never give up and practice compassion. While possessing strong skills is advantageous, being a compassionate and supportive team player sets one apart. In the face of challenges, remember – you are amazing, and you will emerge stronger. Never forget that both success and resilience are part of every academic journey.

DataCamp classroom for my classroom :)

I want to give a shoutout to the DataCamp classroom team for their fantastic support in making my classes more engaging, all the way back to when I was teaching a Programming Languages course at Yeshiva University in 2020. I also suggested the use o DataCamp classroom for the ANMIGAs workshop this last summer at IPAM-UCLA. The participants worked on their programming background before the workshop started and it helped them jumpstart with the tutorials. I've shared this cool idea with my colleagues at City Tech, and it's working wonders. I suggested making a simple 4-hour certificate course a mandatory homework for our students to help them kickstart their Python programming skills. It's awesome to see that many of them are now using DataCamp in their classes. Students really enjoy it, and it's a great confidence booster. I often advise my students to share their DataCamp "Intro to Python" certificates on LinkedIn if they have an account. It's a fantastic way to get them ready for the job market! I also encourage them to complete the free 6-month DataCamp Data Science track certification. It's available for my classes for six months, which is a big help. I want to extend my heartfelt thanks to the DataCamp team for their assistance in resolving any issues we faced when setting up our online classroom. I'm planning to explore even more of their resources in my classroom regularly. Just to be clear, this isn't a sponsored post. I'm genuinely appreciative of how DataCamp has made teaching and learning more interactive and beneficial for my students.

Building little communities in the classroom

It's been a while since my last post, and we're well into the middle of the semester with more exciting math to explore in our classes. I wanted to kick things off by sharing a wonderful classroom moment from this week's group activity. It's fascinating how we can pick up valuable teaching tips from professional development workshops and see them make a big difference in our students' behavior and confidence. Let's dive into a typical Monday at 10 am in my precalculus class. We were diving into the world of polynomials, learning how to find their zeros, discover linear factors, and tackle polynomial factoring one step at a time. But here's where things got interesting: I decided to ask the students to count out loud and remember their numbers. Starting with "1," one student, the next one with "2," and so on until "7." We'd then restart the counting. The students with the same number became a group. This simple activity worked wonders in breaking the ice between students who hadn't interacted much throughout the semester. Let me take you to Group #7, which had three members: David, Angel, and Michelle. Right from the start, they were in deep discussion, checking calculations, and taking notes. When I approached them to ask about their progress, David gave a general answer but pointed out that Michelle had all the detailed calculations in her notebook. As time was running out, I asked if one of them wanted to tackle questions 1 and 2 on the whiteboard. With enthusiasm, they chose Michelle to take the stage. She confidently explained the procedure, I offered a few corrections, and the whole group was fully engaged. Members from other groups took turns at the whiteboard. I revisited Group #7 and asked if one of them wanted to tackle the final question on the board. Angel stepped up, and his teammates eagerly checked everything he wrote. Suddenly, Michelle rushed to the board to lend a hand and quietly corrected a mistake with her marker. At that moment, I exclaimed, "This is what teamwork is all about!" I expressed my desire to see more of this collaborative spirit in our class—students having each other's backs, helping one another learn and succeed. I encouraged the rest of the class to observe and learn from this heartwarming anecdote. This experience demonstrated how we can uplift each other as individuals. I shared this story with one of my mathematician friends, who felt that the term "empowering" is often overused and misused. However, she believed this anecdote was a perfect example of true empowerment. It was, without a doubt, the highlight of the week!

Fall 2023: The first post of the semester

It's been a while since my last update, and I've had a busy summer filled with various enriching activities. I had the privilege of participating in an undergraduate workshop in Utah, where I shared my insights. Additionally, I was invited as a speaker at a Data Science workshop hosted by IPAM at UCLA, where I had the opportunity to deliver an engaging one-day tutorial. My summer also included a visit to my former PhD advisors in Oregon, during which we engaged in discussions about some truly exciting research. At present, I'm deeply engrossed in teaching precalculus and statistics with probability this semester. I must say, I'm genuinely thrilled about the progress my students are making and the lively interactions taking place within the classroom. It's become increasingly evident to me how crucial it is to establish open and honest communication with students to truly gauge their comprehension. In my precalculus class, we've delved into topics like absolute value inequalities, functions, and the transformations that can be applied to function graphs. Just recently, on Wednesday, 9/20, I assigned a class activity comprising six questions, expecting it to take no more than 30 minutes. Initially, my plan was to introduce my students to the various features of the TI-84 calculator. However, due to technical constraints (I didn't have the visual calculator installed), I decided to spend some time assessing their grasp of vertical and horizontal shifts. Specifically, we explored how to formulate functions after applying horizontal or vertical shifts, as well as stretching away from or compressing towards the y-axis. To my pleasant surprise, I witnessed several "aha" moments among my students, and I firmly believe that these breakthroughs are some of the most gratifying occurrences during class time. In the statistics with probability course, we've covered fundamental statistical concepts such as sample mean, median, variance, and more, along with the intricacies of box plots. I've also introduced a DataCamp classroom for this course, and I'm pleased to report that the students have successfully completed the introduction to Python course. Furthermore, they've become adept at creating Google Colab notebooks and tweaking Python code. They can do now a basic loop. They've worked extensively with the statistics library and pandas, they had fun importing CSV files into data frames and conducting basic data exploration. In the near future, we'll be delving into linear regression using the classic advertising data from the "Intro Statistical Learning" book by James et al. I've encouraged my students to proudly display their Intro Python certificates on their LinkedIn profiles, should they have one. All in all, I'm ecstatic about the commencement of the fall season!