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!

Some perspective for students on these times and how to reflect about life in the classroom

Sometimes when we think about teaching, we imagine this very serious professor on a podium or a blackboard dictating a very technical lesson. The professor is the only one speaking. If this is a math professor, he or she will only talk about math. Now in this era of multiple distrations and instant gratification, we need to go the extra mile and make students reflect about where are they going in life and if their habits are helping towards achieving their dreams. I mentioned to them that I read books in the subwway or the bus and do some grading or prepare the lesson of the day. The I asked them if they could count how many people in the wagon are looking at their cellphone: texting, playing a game, looking at some social media platform (the picture of someone eating pasta), etc. They smiled at me because they knew this is common. I did not want to sound like a broken record or that mom who is giving unsolicited advise. However, I suggested for them to take advantage of those moments of solitude to read a book, journal or reflect about an idea. We do not need to be making videos to gain approval from other people. Do it if you like but be careful with what is motivation behind it. I remembered sending and assignement where they had to take a picture of a proof of a proposition in the subway or other place outside campus or a classroom...a place where it is not common to see people writing proofs. I got pictures of people working on stairways in the city, a laundroamat, at the subway station while waiting for a train, the beach and during a subway ride. I hope this connected them with their own thoughts. At least they did not look at their cellphone screen for a few minutes :) We need independent thinkers, not that person who is competing in social media to post better pictures or catchy phrases than his/her friends. Dare to be different, it does not matter how you look, what is your financial situation, your life circumstances. Many things in life are ephemeral but your essence as a human being and as an intellectual is unique and can persist through time.

Algorithms, big-O and number theory

It has been a while since last time I published in this blog. Today I posted final grades and started to reflect about what we learn during the semester. We talked about big-O. We did an example where we found that a fucntion was O(x^2) by finding an upper bound for the orginal function when c is greater of equal for some real number k. We showed some plots to illistrate this point. We then moved to talked about module m atithmetic, reminders, Euclidean algoritm, etc. I was surpised to see that students really liked this part of the course. I wish I would have spent more time on it. We gave simple examples of how to ecrypt messages. Also, we showed propositions related to the greated common divisor between two numbers and how to find it using the Euclidean algorithm. Perhaps students will never forget about this french mathematician, Bezout (I'll add the tilda later.) With Bezout's identity, they can find the Bezout's coefficients of them is the inverse of one of the numbers involved in the greatest common divisor. Finding the inverse help us solve equations involvinf arithmetic module m. So every time we needed to find an inverse modul m, I would ask: "Do you remember the french name we need?" It makes me so happy to say "Bezout, Bezout!!!" at loud.