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].
If you’ve read more than one of my posts, you’ve probably realized that I don’t tend to post things on time. This one is no exception.
I went to Algonquin Park on (Canadian) Thanksgiving last week. But it turns out that last week was gonna be the most stressful one so far in grade 12, so I didn’t have any time to post something here. Oh well.
Here are some pictures.
I actually went to another lookout after this one, but my phone had died about 20 minutes before I could make it there. It was a lot more colourful, that’s for sure.
This is me writing about a school week on a Sunday lmao.
So… a lot of things happened this week. And not a lot of them are preferable, but that’s okay. It’s always good to learn how to survive through things thrown at you.
Imagine a scenario like this—you’re sitting in your English class on a pretty ordinary Monday. You flip to page 274 in the textbook and get forced to analyze some essay about mosquitoes. Implicit, explicit thesis, whatever. But about thirty minutes into the period, the vice principal barges into the portable and starts talking about some timetable changes and re-org.
This is what my Monday looked like. It wasn’t anything abnormal until the vice principal unexpectedly told everyone that the entire class was getting cancelled. I remember my heart sank pretty heavily when I first heard that word. It was pretty awful timing, especially since I happened to have a math unit test on that same day, which meant I had something else to worry about. But also, the guidance department just so happened to engineer an almost perfect schedule for me this year, with some great teachers. Was I really gonna have to watch all of that get taken away from me?
Luckily my schedule wasn’t altered too much. I originally had Physics first period, and English second. These two switched, giving me an entirely different physics teacher (the same one I had in grade 11 in fact!). I wasn’t particularly mad about that, but it really does suck when you get used to a classroom and a teacher just to be moved out. Also, since I didn’t even know what my situation would be until the day after, the added anxiety of not knowing what would happen to my schedule was definitely enough to make me make some silly mistakes on a math test. But other than that, I don’t think this change was worth more than a day of anxiety. I guess I got pretty lucky.
I actually have a little more to talk about. Next week is gonna be an especially stressful week. I have a permutations test, kinematics test, and a polynomials quiz. I guess the silver lining is the fact that all of these are happening early in the week, so I can just get everything over with. But since I already did a kinematics test in my old physics class, I’m essentially just doing this one as a grade booster. My teacher is just gonna take the higher mark out of the two kinematics tests that I’ll do. I’m obviously not complaining about that, but at the same time, I don’t even know how I did on that previous test. I guess that kinda gives me an actual drive to do well on this one, but doing two different kinematics tests was not gonna be super ideal in the first place.
Goodnight to any of my readers out there, if you exist.
It’s been pretty eventful this past two weeks, which is why I didn’t really have much time to write something up., but here we are. This post isn’t really gonna have a main topic, but I’ll just write about what’s been happening since my last post.
First of all—things got pretty busy as soon as the first weekend of the school year flew by. Not anything I didn’t expect for Grade 12, but it was pretty surreal having to study for multiple classes every night, multiple days in a row. You don’t really have that happening often in Grade 11, unless you were genuinely aiming for high 90s, which wasn’t super necessary back then. This made me pretty envious for anyone lucky enough to have a spare first semester, especially when you’re urgently trying to juggle studying for three tests in the same week. But it is what it is.
I think something that really surprised me going into this semester was how difficult Data Management turned out to be. I never thought I’d ever struggle with counting ever since graduating the first grade, but it’s almost funny how wrong I was. For anyone wondering, no, you don’t do that type of counting. The first unit we’re starting in MDM4U is called Organized Counting, which is unlike any other math I’ve done in my life. Instead of learning about functions or theorems like any other math class, you take a deep dive into the number of ways a number of events could happen, like rolling a die or flipping a coin. This in itself obviously doesn’t sound hard at all, but it really does get challenging once you get to problems that seem to be closer to competition math than anything else. If anyone wants to see what I’m talking about, just take this problem for example.
How many even six-digit numbers have all their digits different?
I’m not gonna lie, I struggled pretty hard when I first tried solving this one. It’s not as hard to me now, but I would’ve had no idea how to even start this problem if you gave it to me a week ago.
Now, onto something a little more recent. Yesterday I wrote a physics test on kinematics. If I’m being realistic, I was pretty prepared for it, but I was incredibly anxious for every single moment prior to writing it. I normally get test anxiety, but it’s reasonably multiple magnitudes worse when you know that the grades are directly tied to you getting into university. I remember that O Canada was being played right before the test, which meant I had a solid minute and a half to listen to nothing but my rapid heartbeat and heavy breathing. It wasn’t my proudest moment, but I guess test anxiety is what everyone suffers from at one point.
If you’re wondering how that actual test went, it really depends on your standards. For someone aiming for a competitive engineering program like me, you really can’t be sure if a test went well unless you feel 100% confident after taking it. And I sure don’t. Don’t get me wrong, I really can’t say that the test went bad, but the reason why I’m not completely optimistic about it is because the last projectile motion question was particularly difficult, which drained all the time I had to check any of my answers. The worst part is that I’m not even completely sure if I got that last question correct. I’ve always believed that the most important part of a test other than actually solving the problems is checking your answers, because it gives you a final chance to fix any mistakes you might’ve made while you weren’t thinking clearly.
But of course, there’s nothing I can do about that test right now other than just reminisce about it. I’m sure there’s a universe out there where I got 100%, and it sure as hell might be this one. But I seriously doubt it.
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:
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 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 intriguing video on why π is in the normal distribution, and I’d recommend it to any math people out there.
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.
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.
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.
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.
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.
