alex cao

alex cao

Welcome to my website. Here you’ll find my photos, links, and personal blog (scroll down!). I started this website because I wanted a place to document snippets of my life, interests, or simple thoughts. The idea originally came to me after viewing Adam Parkzer’s website, who has been adding posts to his blog since early 2009, when he was only 17. Along with the fact that I also wanted a place to practice my writing, I just thought it’d be a great opportunity.

I use Instagram for talking with friends, if you’d like to reach out to me casually, just DM me on there. I don’t have a secret “spam” account. Please don’t send money to people on Instagram claiming to be me (surprisingly, it’s happened before). For professional inquiries, contact [email protected].

  • finally… a school post

    (this is a long one… at least to me)

    Something that I primarily wanted to do when I first started this blog was to write about my daily life and share any memorable snippets that I might want to remember for the future. The problem was that basically nothing exciting would ever happen during the summer. Everyday became pretty mundane, so much so that I honestly got to a point where I was actually anticipating my first day of Grade 12. Now that school has finally started, it means I’ll finally have something to write about. But more importantly, all that studying I did over the summer will finally come into use.

    Anyone who saw my last blog post would know that my first semester is anything but easy. But you have to understand, I’ve always been interested in math and science, especially so this past summer. And evidently enough, I’m honestly fine with having Physics, Advanced Functions, and Data Management in one semester. All of these classes are simply a different application of mathematics, and I think they can all be interesting in their own right.

    There’s one subject that I left out though, which is English. I’ve never been a fan of English. It might have something to do with the subjective nature and lack of formulas, but I think the biggest reason is that it’s just not interesting to me. Personally, the most important factor that helps me learn something is actually wanting to learn it and being interested in the topic. Of course, your interests can change over time—like how I didn’t love physics nearly as much I did about six months ago—but English is something that never truly clicked for me. It’s not that I hate reading or writing; I’ve actually quite enjoyed both of those things in the past. The ability to analyze an author’s message, and trying to argue for a specific theme is something I’ve pretty much hated doing throughout all of high school. And don’t get me wrong, I’ve always wanted to improve at this. The problem is that it’s just not as easy to study as something like math is. The lengthy process of writing an entire essay, and not even having a subjective answer for it, is what really gets me.

    Anyway, before that rant about English class, I was hoping to write about my classes so far. So here it is.

    Period 1: Physics

    I think this was probably the class that I anticipated the most before school started. The content learned in Grade 12 Physics is immensely more interesting than in Grade 11, at least in my opinion. Mixed with the fact that I just so happened to get a great teacher for Physics, this is probably my favourite class out of the four. I won’t reveal the names of any of the teachers I mention in my blog, ever, but I just feel the need to say that my Physics teacher is someone who seems incredibly enthusiastic about physics in general. Something that I’ve always hated seeing is a teacher who doesn’t seem to enjoy teaching a course, or worse, not enjoying teaching in general. Having a teacher like this is something that takes away something special from the learning process, at least for me. That’s why I was so happy to see someone who genuinely enjoys what they do.

    So far, basically all we’ve done is review, which sucks because I’d rather get to the new stuff earlier rather than later, but it makes sense to go slowly rather than guns blazing. Especially for those who haven’t done physics since first semester of last year.

    Period 2: English

    This class is unsurprisingly the most boring out of the bunch for me. I don’t think the teacher is subpar when it comes to teaching by any means, and I don’t hate his lessons at all. But they’re purposely structured as being very slow and deep into the “theory” when it comes to analyzing texts. I’ve honestly learned a lot from them, but at a heavy price of a ton of boredom. Yesterday we spent the majority of class analyzing this specific exercise from Voice Lessons by Nancy Dean:

    As I watched, the sun broke weakly through, brightened the rich red of the fawns, and kindled their white spots.

    Over half of that class was spent deciphering what the author could’ve possibly meant by the word “kindled.” Our teacher eventually showed us how the process of kindling mimics the slow structure of the sentence by being an inherently slow procedure of creating fire from what seems like nothing (along with a lot of other things, but I won’t bore you). He went on to explain how it’s actually absurdly difficult to come up with a synonym to replace “kindled” and have the same connotation. I’m going to be honest, although I heavily dislike English, this lesson actually was a little interesting to me, as I’ve never thought so deeply about what the meaning of a specific word in a sentence could imply without being directly written. This, unfortunately, does not mean at all that I’m good at it. But it does mean that I get more opportunities to practice since the original practice book was riddled with sentences just like this one.

    Period 3: Advanced Functions

    If you’re wondering why I decided to post this blog post 2 days after the first day of school, this class is exactly why. Our MHF4U teacher decided to give us a “fun Friday,” (what she called it, verbatim) by giving us a quiz on factoring on the third day of school. Originally I didn’t mind at all, since it makes sense to have a quiz on basic skills you learned in Grade 10. But I was really, really wrong. These weren’t Grade 10 level questions at all. These questions required genuine algebraic skill and pattern recognition way beyond normal trinomials. Take this question for example:

    x4+4y4x^4+4y^4

    A question of this difficulty was luckily not on our quiz, but a similar question was on a practice sheet of another class. From a Grade 10 perspective, this question looks just about impossible, since it really doesn’t make sense for a sum of two even powers to be able to be factored. Factoring problems you deal with in Grade 10 usually are quite straightforward, with the next step usually being quite obvious when you do a couple problems. In harder factoring problems though, the next step to take is very often not obvious whatsoever. For this case specifically, you must complete the square to create a perfect square trinomial, and then use the difference of squares property.

    Although this and other factoring problems seemed incredibly difficult at first sight, it really does make sense for it to be a first quiz in the course: It tests both your factoring skills and your algebra. Because at the end of the day, MHF4U is just a precalculus class that tries its best to ready your algebra skills for calculus. And these problems were always as rewarding as they were algebraically challenging.

    Period 4: Data Management

    Yeah, there really isn’t a whole lot to say about this course, mostly because all we’ve been doing is review content. Not difficult review either, it’s mostly just basic algebra skills and stuff you’d normally learn in Grade 9 or 10. Out of all the STEM courses that I have for Grade 12, Data Management is by far the one that I know the least about. I originally took it because I needed something to take in order to swap out of Biology, and it made the most sense to me to take a math course.

    I honestly have no idea if I will enjoy this course or not. Statistics is a type of applied math that I’ve never tried dabbling in before, and I’m not familiar with probability whatsoever. When it comes to applied mathematics, I’ve only really ever looked into the math that govern real world phenomena, rather than trends or numerical data. But I have found certain parts of math in statistics quite interesting, notably the normal distribution and factorials. A while back I watched an incredibly interesting video on why π is in the normal distribution, and I would recommend it to any math people out there.

    Yeah… a bit of a long post this time. That’s ok.

  • grade 12 timetable

    This is probably the only time I’ve ever been mad at the guidance department at my school—and it just had to be during the most important year of high school.

    I’m not even mad about the teachers; I don’t hold a grudge against any of those names beneath the censor bars. If anything, I should be happy about miraculously getting physics and English first semester, which is exactly what I wanted since those are the main courses that I wanted to improve on going into Grade 12.

    What makes me so angry is the fact that they somehow put me into the only advanced functions class in second semester, which shouldn’t even exist because they’re meant to be prerequisites. I mean, they’re technically co-requisites as stated by the school board, but it really doesn’t make any sense to take a precalculus class at the same time as a calculus class. The entire point of advanced functions is to ready your algebra skills for what’s to come when you finally leave the realm of algebra.

    I also requested to swap out biology for data management, since every sliver of interest that I had for the medical field had faded away in the last six months. This of course, did not happen. This was especially irritating to see, since there perfectly happened to be slot for MDM4U at the exact same time as my biology class. It might be a smaller inconvenience than having advanced functions second semester, but the lengthy process of asking for another course change in a guidance appointment is really something I don’t want to experience again for my own sanity.

    Edit, Sept 8, 2026 9:20 AM:

    I didn’t think this would happen, but guidance actually fixed my schedule pretty fast, and miraculously placed the new courses exactly where I wanted. Maybe I don’t hate them as much as I thought I did.

  • thanks, prof leonard

    (short lil post this time)

    I’ve finally finished Professor Leonard’s Calculus 1 course on YouTube, and I need to admit that this guy is nothing short of a perfect teacher. Never have I seen a teacher with such a clear, informative, and meticulous style of teaching.

    All of this might sound like a complete exaggeration, but mind you, Calculus 1 is miles more rigorous and covers topics in much greater detail compared to a high school course like MCV4U. For someone to teach all of that, and most importantly get you to understand it on a conceptual level, is absolutely incredible. I originally never thought I’d ever want to go through Calculus 2, but now that I’ve actually finished everything that Calculus 1 has to offer, it really just seems like the sensible decision to do. Especially when such a great teacher is teaching it.

    School’s starting up in a little over a week, and I hope Professor Leonard’s statistics course will be a huge help when it comes to Data Management as well.

    Edit, Aug 29, 2026 11:10 PM:

    This somehow happened by sheer coincidence, but Professor Leonard’s first upload in over three years came out a little over an hour after I originally wrote this blog post. It’s almost surreal to see him post something after all this time, and I’m glad to finally see him return to teaching. He’s a big reason why I started to love math this past summer, and I’d recommend him to anyone with even a slight interest in learning math.

  • strangers on a bench

    A few days ago I realized how dry my music has been getting recently. All the artists that I’ve been listening to have gotten pretty boring with how much I’ve used Spotify over this past summer, and I really felt like I needed something new.

    This is when I remembered that I also haven’t listened to a single podcast episode in like, half a month? I used to love listening to podcasts (Casefile in particular!) so I honestly have no idea what happened. But I didn’t just want to return to the same old stuff I was already listening to, so I went looking for some new material for once. A few podcasts caught my attention, notably Ologies and Lore, but one really intrigued me when I first read about it.

    This podcast was Strangers on a Bench by Tom Rosenthal. The premise is pretty obvious upon reading the title. Tom goes up and sits beside people on benches across the UK, and asks them if he can record their conversation. But of course, the episodes go a lot deeper than just that. We may learn about the struggles other people have been going through, or what things in life may occupy them at that moment. Everyone has a story to tell, and this podcast perfectly encapsulates that. Every participant remains completely anonymous, and we walk off never knowing who these people are, making the conversation a lot more human.

    I listened to the first episode of this podcast only a few hours ago, and it really was something special. Tom talked to a stranger who had a past in prison, and tries to spend his life trying to better himself and discover new interests. The entire thing was extremely heartwarming, seeing the life story of a stranger and their experience in prison, and how they’ve managed to recover from all of it. I highly recommend this podcast to anyone who happens to read this, as it really is a one of a kind experience.

    This podcast is actually very reminiscent to another one that I’ve mentioned in a previous post, Heavyweight. Both try to portray the struggles and regrets of average people in their life, except the stories in Strangers on a Bench feel a lot more open, since they are completely anonymous and unscripted. I do plan on going back and listening to more episodes of Heavyweight soon, but it’s always nice to have a similar podcast as a go-to.

  • kinematics epiphany!?!

    There hasn’t been a lot to blog about recently, so this is another calculus post. Sorry to the math dislikers…

    I’ve reached the second last chapter of my Calculus 1 self studying journey, which inevitably includes a fundamental part of calculus, the indefinite integral. I’m not particularly deep into the topic, but it’s surprising how much of this you can relate to basic physics, even with a simple understanding. The lesson from Professor Leonard that I watched today includes an example where you must solve for the max height and time of flight for a projectile, using only initial speed and vertical displacement:

    A catapult accidentally shoots straight up with an initial velocity of 128 ft/s, from a height of 16 ft. Find:

    • The position function for the height, s(t)
    • The maximum height of the projectile
    • The time it takes the projectile to hit the ground

    For a physics class, this would be an absurdly easy question, but the aim in this context was to keep taking the antiderivative of acceleration (-g) until you’d end up with a function that gives you position (s):

    I originally considered this problem as being pretty different than anything in a physics class, especially since you don’t really deal with any functions in physics, every variable you’ll deal with will be compacted into a simple formula. This was until I realized something: To solve this problem, you are literally doing the exact same thing you’d do in a physics problem. You are simply deriving the formula first, rather than just finding it off of your formula sheet.

    This was a rather unexpected epiphany for me. For a long time I’ve just memorized the kinematics equations without even knowing how simple it was to see where they came from. I know that there’s a more straightforward, algebraic way to prove this using the area under a graph, but I really do think the calculus is what ties everything together. In the past I’ve viewed physics and mathematics being two separate entities for whatever reason, and this is what really bridged the gap for me.

  • calculus

    This summer has undeniably been about the busiest summer of my life. School’s starting up in 3 weeks, and so far I’ve gone through both Physics and Advanced Functions. After finishing that, I made the grand decision to work through calculus with the time I have left. Because why not? it just seemed like the sensible thing to do after finishing the “precalculus” of the Canadian curriculum.

    Now, any normal person would’ve just went on JensenMath for free math lessons, but I didn’t really want to do any of that. I’ve used JensenMath in the past for Grade 11 Functions, and it’s incredibly helpful, but I just wanted lessons that were a bit more in-depth. This is when I decided to learn calculus off of Professor Leonard on YouTube instead, who posts his US college math lectures. His lectures are often over an hour long, but are extremely insightful when it comes to the actual mathematical concepts, which is why I’d recommend him so much.

    So I started his Calculus 1 series. Originally, I was fully aware that Calculus 1 was much harder than the Canadian MCV4U, and I was willing to accept the challenge, since this was all done under my own discretion. I’ve looked into the concepts of calculus before, and they’ve all seemed pretty interesting, which is why I wanted more in-depth lessons in the first place.

    Currently, I’ve made it to Lecture 3.4, which covers the second derivative test of functions, equivalent to the curve sketching unit in MCV4U. Most of the material I’ve learned so far hasn’t been horribly difficult, with two notable exceptions: trigonometric limits and related rates. Thankfully, neither of those topics are taught in the Calculus and Vectors course, but it’s notable they’ll likely serve as a roadblock if I ever take a math course in university. Related rate problems are especially difficult, not because the calculus is difficult, but because it’s often very difficult to interpret what a word problem wants you to do. I’ve always had trouble with word problems when it comes to math, and this is no exception. Take this example from the textbook I’m using:

    Now I might look pretty stupid to anyone reading this who happens to know a lot about calculus, but I had just about zero clue how to even start this problem when I first laid my eyes on it. The actual calculus isn’t difficult at all; just get an equation that ties in all variables involved, and take the implicit derivative with respect to time. But the method to get to that setup is something I could never work out. You have to figure out on your own to use similar triangles between the man and the streetlight in order to solve it, something that isn’t immediately obvious after inspecting the problem.

    Calculus has a lot of other concepts not taught in MCV4U as well, one of them namely being integration. I’m hoping I won’t find that section awfully difficult, since Calculus 1 introduces a mere introduction to integration methods, rather than going in guns blazing. Also, Calculus 1 doesn’t actually have anything relating to vectors, so I’ll just have to wing that when I actually get to it in school. But for everything else, I’ll be pretty much ready for. That’s why self-studying will hopefully be all worth it in the end.

  • of mice and men

    I recently finished Of Mice and Men by John Steinbeck and felt just about obligated to blog about it. I won’t go in depth on any major spoilers in this post, but if you do plan on reading this book in the future, I’d stop reading right about now.

    For a book that’s only about 100 or so pages, you get a surprising lot out of it. It’s about the unlikely duo of George Milton and Lennie Small. George is portrayed as being small and intelligent, while Lennie is large and strong, but intellectually disabled. The story follows the journey of these two through the times of the Great Depression, and follows many themes of companionship, loneliness, and false hope.

    Throughout the book, it becomes more and more evident how unlikely the duo of George and Lennie truly are, as many ranch men during that era survived alone, making loneliness extremely common. Lennie and George become practically inseparable, as Lennie is pretty much unable to survive without George due to his unspecified intellectual disability. Despite being incredibly strong, Lennie often doesn’t realize his strength due to his disability, resulting in many minor and major mishaps throughout the novella.

    Something that the book often deals with is the concept that some people just cannot be destined to live their dream life, simply due to the circumstances they were born with. Many characters in the story have their own “American Dream,” one that they’ll never be able to achieve, despite all the struggle and work they might put in. The inherent limitations that are implanted into one’s existence can prevent them from living the utopia that they wish to live. I was incredibly intrigued when I first read about this interpretation of the novel, as human nature can often be a very interesting topic, especially when it ties into such an tragic story like this one.

    Without revealing anything, I want to say that this book contains an incredibly emotional, and deeply upsetting ending. It’s not something I’m not used to, but it was certainly unexpected. Midway through the book I was asking myself “where could this possibly be going?” But now after reading, I realize that these segments were very purposeful in creating the themes that the book portrays, as we learn a lot about the backstories of certain characters, and how their life was impacted by the depression happening at that time.

    For a book to get into reading, I don’t regret choosing Of Mice and Men at all. It had the perfect blend of storytelling and themes for me, and I hope I enjoy my next book just as much as this one. I’m hoping to get my hands on Never Let Me Go by Kazuo Ishiguro soon…

  • ipad for notes

    Last summer when I went to see my family in China, my uncle insisted that he would get me a gift. He originally wanted to get me a drone, but I’m not really interested in those things, nor is it super legal to fly those in Ontario. So he got me an iPad Air instead. Originally I didn’t really know what I’d use it for, but it’d obviously be pretty rude to decline a gift.

    So that iPad went pretty much unused for 6 months. During that period I really had no idea how useful an iPad could be for school, since I didn’t exactly have a pencil for it yet. Once I finally got a “like-new” Apple pencil from Amazon, I finally discovered how much better an iPad was compared to carrying actual lined paper in your binder. You get all the upsides of handwriting—better memory retention and being able to write different notation—with the upsides of having a digital device, like clean erasing and copy paste, along with a lot more. When you can immediately condense hundreds of note papers into one singular device, it seems almost bizarre I didn’t invest in iPad note-taking earlier.

    Take my organic chemistry notes from earlier this summer for example:

    Something about digital notes just has that feel that paper doesn’t. You can highlight in whatever colour you want, without needing 50 highlighters. You can choose to have lined or grid paper, without taking a trip to Staples. Now obviously not everyone can afford to have an iPad or tablet, but I just wanted to show how much of an upgrade it can be, and why I recommend getting one if you’re ever on the fence about it.

    I’ve pretty been much using my iPad nonstop for my self-studying this summer, and it’s really been amazing. One of the things that keep me studying is just the feeling of writing on an iPad, it’s much smoother than any sensation you could get on paper, and a hell of a lot more satisfying.

    That being said, I still have a lot of calculus to get through, so best of luck to me I guess.

  • top of my school

    I wanted to blog about this gem of a video I found today.

    I’ve probably watched a handful of short films and musicals in my life, and I’ve never had any strong opinions about any of them, but I think this one might be up there with one of the best videos I’ve found on the internet. Before reading this post, I highly recommend you to watch the film first. I don’t think you’ll come by a video like this very often, and this post will definitely contain spoilers.

    I want you to understand that I grew up in a pretty stereotypical Asian household. My parents have always been rather strict about grades when I was growing up, especially my mom. I remember her signing me up for Kumon back in elementary school, which is pretty much the signature nightmare for any Asian kid. I did tutoring at a couple other places throughout middle school, and I was almost always yelled at for any mark lower than an 80%. That’s just how it was in the house, and I’m obviously not the only person this has happened to. Inevitably, my mom has gotten a lot less strict ever since I started caring more about my grades in high school, but it sure was a traumatizing childhood at times.

    I mention this because Top of My School is about a girl, Bree, who strives for perfection in school due to the pressure from her parents, and does whatever it takes to be on top. It might not be a new concept, but the way it’s presented is genuinely incredible, and I’m not even getting into the themes and the plot twist. The film is filled with incredible songwriting and cinematography, specifically the first section, which I want to talk about.

    The song that plays first in the film is “Top of My School,” which was released way back in 2021, five years before the release of this film. It’s definitely my favourite song of the bunch, and also the most popular song written by Katherine Lynn-Rose, the producer of the film. The first couple lyrics really do resonate with me, and they are that follows:

    Some people live the life that was given
    Some people just get by
    Some people never learned how to be driven
    Some people don’t even try

    But some people know what their heart desires
    Some people lead with a passionate fire
    And some people know that they’re destined
    To fly

    As you can probably see, these lyrics describe someone who is heavily driven by success and their accomplishments, someone who considers themselves “destined” to achieve something truly great, even at the price of burnout and overworking themselves. In the context of Bree, this is all done to please her parents, who continuously pressure her to focus on her studies. In the film, Bree’s father tells her the Chinese myth of the Dragon Gate, which is a legend that states while many carp swim upstream against the river’s current, very little are brave enough or capable of making it through the final leap of the waterfall. Those who do, are transformed into dragons. This was used as an analogy for Bree’s effort to do well in school, and I believe the lyric “to fly” was a subtle nod to this.

    The pressure that Bree’s parents put on her is what made her try to do anything to succeed in school, which is what made her be so determined to win the position of council president. But when another girl, Avery, joins the race, Bree knew that she had to do something about it. She began to get to know Avery through an English project, and eventually found out that Avery had harboured an affection for her.

    This is when Bree thought of the idea to manipulate Avery, and kill her by taking advantage of her peanut allergy. Sure, it’s an incredibly dark ending, but it shows the true lengths Bree would take just to please her parents and show them that she wouldn’t remain just an ordinary carp. The film has many parallels with another one of my favourite films, Whiplash, which shows the absolute destruction that perfectionism can have on an individual. After all, when you live your entire life up to someone else’s expectations, is it really your life?

    In some ways, I admire the character traits of Bree. When it comes to academics, I’ve always tried my hardest to become this hardworking individual, someone who truly dedicates their time to achieving something that they believe, is great. But when this dedication consumes your entire everyday life and overworks you, when does it become a problem? At what point does this obsession with success truly take over you? I’m obviously not at that level of insanity, but it is an interesting thing to think about.

    I’ve yet to watch other productions made by Katherine Lynn-Rose, and I do intend on watching her other musical short film, Class Crush, sometime soon. I never thought I would discover someone so ridiculously talented on a random Sunday afternoon, but here we are. It’s always a nice thing when you relate to others who grew up in an immigrant household, as you tend to discover that your experiences have been felt by many others before.

  • emotional stories

    It’s 9:43 PM, just finished my tutoring homework for the day and I remembered that I still have a website. Might as well post something.

    When I was first searching for a book to read, I was considering things that I enjoy in other media. To be frank, I’m not much of a movie or TV show person, but I’m always a big fan of any video game with an incredible story. Something I feel that always makes a story better is a deep, emotional ending. I wanna talk about that.

    I remember when I finished the story of NieR:Automata for the first time. The game itself deals with themes of existentialism, and contains one of the best written tales in gaming in my opinion. Without spoiling anything, it’s an incredibly sad and tragic game with a rather cathartic ending. It takes you on an emotional roller coaster, and ends by making you feel an immense emotional void—exactly what the game is about.

    It’s been over 2 years since I last played NieR:Automata, yet I still remember how I felt after finishing it. This, to me, is a story done right. It’s why I enjoy sad storytelling so much; the plot takes you on a journey that’s hard to forget.

    Over the years I’ve played many tragic or depressing video games, and something they all have in common is the emotional “high” that they deliver at the end of them. This is similar to why people enjoy horror—sometimes it’s just fun to have a physical high if it doesn’t impose any real danger. I feel the same way about heavily emotional stories. Sometimes it can just be enjoyable to elicit a strong or painful reaction when you know you’re in a safe environment.

    One time, when I recommended a particularly tragic video game to my friend, they asked me, “Why would I want to feel sad?” I realize now that this simple question is a lot more complicated than I thought. Many people play video games or watch TV to enjoy themselves, not feel an emotional bullet. This made me grasp the fact that I don’t consume media in order to feel good; I consume media to feel, and I think I’ll leave it at that.

    Had no idea what to write after that so I’ll just end it here. Here’s a great song from NieR that I wanted to share.