Archive for November, 2006

The term is over!!!!…well, almost…

November 30, 2006

As the title says, the term is over!!!!…well, almost…*technically* classes don’t end till Tuesday and *technically* I still have 3 assignments left to do and *technically* I still have to wake up early until then, and *technically* we’re still learning stuff, but term’s pretty much over. So, first, an update:

We’ve finished all the readings in Philosophy. The last one was a tretise on Faith vs. Religion by Late Pope John Paul II. As someone who doesn’t particularly care for religion one way or the other, I found it quite interesting how Pope John Paul managed to link Philosophy, which I’ve always considered a natural discipline (like Science) in the same realm as Religion, which I’ve always considered an abstract discipline (like English Lit). I found it a bit hard to understand the language, but it was interesting nonetheless, especially after reading almost 10 Platonic texts.

Today was the last class Japanese class. I’m a bit sad, because I was having a lot of fun with it, and now I have to wait 5 months (cause it’s not even December yet, so the Summer term doesn’t start for 5 months, and I’m on Co-Op next term) to take 102. We had a great class though. Today was the due date for our final project, in which we had to write a 5-10 minute skit in Japanese and memorize it (as best as possible; we were allowed cue-cards) and present it to the class. My group’s skit was heavily, and I mean HEAVILY based on Anime. We had the whole “pulsing temple”, “water droplet”, and “spontaneous falling on the floor” going on (I was the one who did both the water droplet and the falling on the floor). We had a lot of fun with it. It was kind of sad, though, cause I really liked that class. For anyone even remotely interested in taking that course next year, I would highly recommend it, although be forewarned that Maruoka-sensei speaks A LOT in Japanese, so it may be difficult to understand the lectures for the first month or so. Luckily, Fumie-sensei, who teaches the tutorials (which are mandatory, and even if they weren’t, I would highly suggest going to them), speaks very good English and is very easy to understand.

Music is over :’( The concert was this past Sunday. It went well, especially considering how few practises I went to, although I practised extra hard this weekend to make up for it. We played 6 songs, mostly blues-y stuff, but we had one ballad and one latin song in there too. Michael (a.k.a. Professor Wood, who just told me on Sunday what he would like me to call him) is really cool. I’m not sure if he actually ever lost his temper at me, because he was always really calm, even when something happened that he should have been really upset about. Or maybe I’m just paranoid. I’d post pictures, but last time I tried, WordPress cut them off so I couldn’t use them (pictures of when I was a tour guide for Campus Day). If anyone knows how to post pictures properly, send me an E-mail or a post on this board.

So, now I basically have 3 courses worth of material left: CS, Algebra, and Calculus. Despite next Tuesday being the last day of class, I have an assignment in every one of them. My CS assignment for this week was actually remarkably challenging compared to previous ones. Previous assignments have been long and complicated but really easy. This one was actually, genuinely difficult. I wasn’t even able to finish it completely, although I threw in something that might get me part marks. It was on Binary Tree, which is a bit complicated by itself (and I’m sure I’m going to hear from Professor Ragde about how easy it is in Scheme because both Scheme and Binary Tree are built on recursion, so it should be easier to do in Scheme, so take CS 135 if you want to do Binary Tree really easily, like in 5 lines of code, cause that’s apparentely how long it takes to do it in Scheme, although I’m not sure how large of an implementation that gets you). I was actually, finally, thoroughly satisfied with a CS 134 assignment. It may have taken them until the end of November to do it, but they managed it. Speaking of CS 134, my textbook is still in the original shrink wrap. It’s not really used in the class, although it’s referred to from time to time, and there are “assigned readings” on the course webpage, which don’t really mean all that much since the text isn’t referred to in class.

In other news, apparentely 4 beavers were killed on campus last week-ish. It was in the school newspaper, Imprint. Something about a felled tree, “a danger to students”, and hired trappers. I’m not quite sure of the details, so I’m not going to go into it. It’s apparentely a big event (a story about it was apparentely published in the Toronto Star, according to Imprint), so I figured I should say something about it. I didn’t even know the beavers existed until this story came up, so I suppose it was a waste of time killing them since they were keeping to themselves (then again, I also keep to myself, so perhaps I was just oblivious). That’s my 2 cents.

Until next time, you can reach me at uwmathblogger@gmail.com if you have any questions, comments, or money.

Lyle Waldman

Two Weeks: An Overview

November 25, 2006

Wow, it’s been about 2 weeks since I last wrote anything meaningful. So let’s begin:

Math 137 is significantly easier than Math 147. I have officially switched into that class and, while Professor Marshman isn’t as energetic or interesting as Professor Zorzitto (and, quite honestly, I don’t think there is a professor at this University who outclasses Professor Zorzitto in that respect), the course material is much more manageable. Gone are the days when I had to memorize the proof of the Intermediate Value Theorem, Mean Value Theorem, Continuity Theorem (all of them; there are several), and more others that I don’t care to name. In Math 137, we learn the theorem and apply it, without having to memorize any pesky proofs (so far, anyway). I was tempted to write a post after my first Math 137 class, basically just talking about how refreshing it was to go through an entire hour of Calculus without the use of the word “proof”.

The downside of Math 137 is that you need to pay a lot more to take it. In Math 147, Professor Zorzitto often refers to a book called Calculus, 3rd Edition, by Michael Spivak. Word is that it’s a spectacular book if you’re really interested in learning Calculus. However, you don’t actually *need* the book to take the course, because Professor Zorzitto teaches it all anyway. The text for Math 137 you need because the assignments come out of there. Also, Professor Zorzitto recommends getting a copy of Maple (a Math program which is much more useful than it is costly), while there are assignments in Math 137 that you can’t do without Maple (called Maple Labs for a reason). The class size in Math 137 is also much larger than Math 147; there are easily 150 students in my Math 137 class. That doesn’t bother me much though because Professor Marhsman still teaches the class well despite the size.

I’ve only done one assignment for Math 137 so far (a Maple Lab) and there are no more to come, so I can’t give a good representation of the homework load. From what I’ve seen, though, Professor Zorzitto gives less questions, but each of his questions take much longer than the questions in Math 137, which are primarily knowledge, while the questions in Math 147 are primarily theory. For those wondering, I do not know if/how much my mark has been curved, although I was told that it would be curved to prevent getting a penalty for taking the advanced course.

In Math 145 right now, we’re proving stuff about polynomials. We finished about 2 days worth of lectures on Complex numbers, which covered pretty much everything from High School about them, but not much more. The stuff we’re doing with Polynomials right now is pretty easy.

My Japanese oral exam was two weeks ago. We were given 3 passages in the textbook. We had to choose one and memorize it, then say it the following week. It wasn’t very difficult to memorize, but saying it was a completely different story. I knew exactly what it was, but I couldn’t speak properly, so I didn’t get as good a mark as I would have liked *sigh*. We had the second of two major tests this past week, and I think I did well, so I’m hoping that’ll raise my mark. We also have a project to do where we have to write a 5-10 minute skit to present to the class on any topic we like, in groups of 2 to 5. Coming up with a script was the easy part. It took us a good 4 hous to translate the script we came up with in half an hour into Japanese. Now we have to learn it for Wednesday…I wish they gave us more time.

In other Japanese-related news, we learned about using adjectives in the past tense yesterday. It’s kinda complicated, because there are two rules, and they totally contradict each other. One is used for one set of adjectives, the other for another set. It’s a bit confusing (especially for an Anglophone who doesn’t even think about conjugating their adjectives :P ).

In CS, we’re finally past Binary Tree. We spent a good 2 weeks on it. We didn’t spend as much time on recursion (an important aspect of Binary Tree) as I would have liked, though, especially because recursion is one of my weak points. Last class we started sorting algorithms. We took a full hour to do the two easiest sorting algorithms, Selection Sort and Linear Insertion Sort. Selection Sort is where you search the list for the smallest element and put it first, then search for the next smallest and put it second, etc. Linear Insertion Sort is where you take the first element and put it “in order”. Then you take the next element and put it in order with respect to the first. Then you take the third and put it in order with respect to the other two, etc. Easy stuff, but Profesor Case managed to make it into an hour lecture.

Why an hour? Course Evaluations have begun. Near the end of term, every student has the opportunity to give input on how they liked their course and how to improve it for next term. So far I’ve done course evaluations for 3 of my courses. Course evaluations are anonymous, so you can be as truthful as you like, plus they take half an hour out of whatever class they’re in. I have had nothing bad to say about any of my professors, but I liked the fact that I was able to tell the professor if I thought their class was good or what they could do to improve.

Over the past couple of weeks, there have been a few days where UW turned into Silent Hill. For those who don’t understand the reference, Silent Hill is a horror video game series/movie in which a town gets…well, I’m not going to give it away. The only part that matters is that on the border of Silent Hill is an impenetrable fog that no one can see through, so it feels like you’re encapsulated in a bubble. It’s kind of weird. I’ve posted some pictures.

Spooky Fog 1 Spooky Fog 2

The other weird happening I noticed at UW was about a week ago when I was passing by COM (a building you’ll probably never have to go to unless you take over this position next year). Somebody drew the “V” symbol from V for Vendetta on the roof of COM. I have no idea who or why (or how they did it that big and that accurately), but I suspect the Engineers were tangentially involved.

V for Vendetta

In future news, tomorrow is the Big Band Jazz concert performed by two bands, one of which is the Music 116 Ensemble, of which I am a part. I should probably practise at some point :P

If anyone knows how to post pictures or just wants to give me some general feedback, feel free to drop me a line at uwmathblogger@gmail.com. Until next time,

Lyle Waldman

The Golden Rules of Programming (especially in Java)

November 17, 2006

In the Math Faculty here at UW, all students must take a 1st-year CS course. CS 125 and 133 are designed for people who don’t know a lot about programming, but still I see people in my building in those classes struggling desperately to figure out what’s going on. Thus, I’ve decided to put this together for the benefit of anyone who reads it and plans on (or is) taking CS 125 or 133. I call it “The Golden Rules of Programming (especially in Java)”:

1) The computer is a moron. Sure, it can do much higher levels of mathematics much faster than you or I could even comprehend, but the computer is still a moron. Just because YOU know what you want the computer to do doesn’t mean the COMPUTER knows what you want the computer to do. Don’t program implicitly.

2) Computers don’t skip lines. When you write code, the computer reads it the same way you write it: left to right, top to bottom. That means the computer will read in an order on a line above before an order on a line below. That means if you increment a variable and then use it in an equation, you’ll get a different answer than if you use the variable in an equation, then increment it.

3) Method calls (when you learn them) can be used as variables for return values. Over time, you can save a lot of code this way.

4) Objects in Java use something called “pointers”. Without going into too much detail (I could go on for 3 or 4 good pages about pointers if asked), if you add something to a pointer, you’re changing the adress in memory that the pointer refers to. Essentially, it will point to a different thing, so you’ll have lost your original object. There are exceptions, but this is a good rule to follow in general. Pointers may not be learned to a full extent in CS 125 or 133 and are learned for about half a class in CS 134 (and given the speed at which they taught LinkedList, Stack, and Queue, this is equivalent to about 30 seconds in your ICS4M class), but they probably are covered at least tangentially (as well they should be; you shouldn’t be writing Java without a good knowledge of pointers).

5) When a method ends, any changes to class-level variables will also end at the end of the method, and any method-level variables will cease to exist. This means you have to return the value to use it outside the method. Unless you call by reference, but that’s a whole other story that’s not really covered in any 1st year CS course (it’s a very, very minor point in CS 134 that’s not actually related to much of anything…except pointers).

6) Equals vs. “double equals”. In Java, the = operator is used to set one value to another. The == operator is used to check if two values are equivalent. Don’t mix them up. Note that with pointers, the == operator will check the values of the adresses, not the values of the objects. Yeah. Learn pointers. It makes me cry when I try to explain something to someone in terms of pointers and they tell me halfway into October that they don’t know what a pointer is.

7) Important Algorithm #1: The Swapping Algorithm: This algorithm is used when you need to swap 2 numbers (or other type of variable, for that matter). By Rule #2, if you say x = y, y = x, then when you’re done, x and y will be the same value, even if they started out differently. In order to swap 2 values, you need a temp value. Then you set temp to x, x to y, and y to temp. That way, x will be what y used to be and y will be what x used to be.

8 ) Important Algorithm #2: Array Traversal: Most programming languages (word is Scheme does not have this, which is one of the reasons I’m not in CS 135) have something called a “for” loop. CS 125 and 133 students should learn all about for loops by the end of September, maybe beginning of October. In a “for” loop, you set a counter, and the for loop runs until the counter reaches a certain value. You can reference the counter inside the loop like another variable. You can use this if you need to go through an array (also something you should learn in September in CS 125 and 133) and do the same thing to every element.

[edit] Sez Professor Ragde, CS135 Prof: A “for” loop is a particular iterative construct. Scheme does have iterative constructs; for example, “map”, which does the same thing to every element of a list. Scheme doesn’t provide something which exactly matches “for” in Java because it properly supports recursion, which is much more general, and because Scheme is self-extending, meaning you could write a few lines that implement for-loops and then use them. People tend not to, because it’s too limiting. (Scheme also has arrays, but they’re used sparingly, because lists are more flexible.)[/edit]

9) Important Algorithm #3: The Mod Operator: This isn’t really an algorithm, it’s just easily the most useful thing in Java (aside from pointers, and perhaps the “for” loop). Java has something called a “mod operator”. It’s the % (percent) sign on your keyboard. Saying x % y will return the remainder when you divide x by y. More about Modulus is covered in Math 135/145. This operator is probably the most useful operator in Java. If you need to check if a number is even or odd, take the %2 of it. If you have an n-case algorithm, you can use the %n to decide which case you’re using. In floating-point arithmetic, you can take the %1 to store the decimal expansion of the number you’re looking at. Just remember: Only Chuck Norris can divide by 0.

10) A short list of the most useful Java-based methods/constants you’ll need to know:

Integer.parseInt(String): Takes the integer representiation of a string of numbers (will fault if the string contains characters).
Integer.MAX_VALUE: The largest number an int variable can hold. Useful for trivializing comparisons (sometimes you need to do it).
Integer.MIN_VALUE: The smallest number an int variable can hold.
Math.pow(int x, int y): Returns the y’th power of x.
Math.min(int x, int y): Returns the smaller of x and y.
Math.max(int x, int y): Returns the larger of x and y.
String.trim(): Removes any leading or ending white space from the string you call it on. Note that white space is considered “non-numerical characters” for the purpose of Integer.parseInt(). That’s why this method makes the Most Useful list.

11) The most important distinction of all: Java has classes (*sigh* I need a good page or 2 to discuss pointers and classes and stuff, but I don’t want to stomp on the feet of the CS 125 and 133 profs) called “Integer”, “Double”, “Character”, etc. These are NOT, I repeat, NOT the same as the primitive data types “int”, “double”, “char”, etc. The former are objects, the latter are not. Remember objects are pointers, and carry all the requisite restrictions (which you won’t learn until September/October at least if you take CS 125 or 133…*sigh*).

I apologize if any of this goes over anyone’s head, but it will likely make more sense when you begin your CS course. If you have any questions, ask your local CS teacher. If you have any other questions or comments, feel free to E-mail me at uwmathblogger (at) gmail (dot) com.

Lyle Waldman

The Midterms are Over!!! Part 2

November 10, 2006

Well, the Midterms are now, officially, REALLY over, as I now have all of them back (including the 2nd of 3 Philosophy tests, the 3rd of which is the final). After I wrote my post yesterday, my day continued to get worse. First, I got my Japanese midterm back. I didn’t hit my goal. I (ironically enough) forgot how to say “I don’t know”, and wrote nothing, losing me 2 marks, even though, had I guessed, I would have gotten it right (I had a guess in mind that I didn’t write down, even though it was correct). Then I wrote one word wrong in Hiragana; a really stupid mistake considering I know my Hiragana by rote and I knew the word, which cost me another mark and a half. And then I lost a lot of marks on verbs, considering I didn’t study them at all (as I said; I studied completely the wrong stuff). So I missed my goal on that midterm; not by much, and it’s stuff I’ll be sure to know for the final. On a brighter note, the questions I answered by Boolean Equality Logic I all got correct (for those not versed in Computer-eeze, “Boolean Equality Logic” means, for a language course, if one word is the same as the other word, the answer is “yes”, otherwise “no”. It only works for yes or no questions, though).

That didn’t bother me nearly as much as what happened when I got my Math 147 midterm back. I’ve been having problems in this course all year (as you’ve probably figured out by now), but I never thought I would do this badly on the midterm. It was quite a shock to see that my new “official worst mark ever” is in, of all things, a math course, especially considering I was one of the 3 or 4 top students in my math classes back in High School. Yeah, I even managed to surpass (depending on how you define “surpass”) marks I’ve gotten in Visual Arts, French, and Phys Ed (3 courses I was never particularly good at. I can’t draw. It’s a weakness). So I felt like crap for the rest of the day, even while I was eating pizza in the caf for dinner (Wednesdays are Pizza Night at Village 1; it’s awesome).

Professor Zorzitto isn’t going to have office hours until next week, but as of Monday, I’m dropping to Math 137. I made a promise to myself that I would stay in Math 147 until the midterm, and if I did poorly, I would drop down, and I’m keeping that promise. I like the people in my class though, so I feel really bad about it, but I’m not going to commit academic suicide over a group of friends I can see outside of class. Plus most of them are still in 145 with me anyway.

On a lighter note, the second Philosophy test was returned today. Just like the previous one, Professor Tremblay opened by saying “the marks were very good” and promptly detailed everything I thought I didn’t say, making me think I did absolutely horribly, but I was pleasantly surprised with my mark. To think, of all the courses, my subjective Arts course is going to offset my Math course (I’ve always done significantly more poorly in Arts courses than Math courses; English singlehandedly dropped my admission average about 3%, while Data Management raised it at least 1 or 2). It’s a new one, at any rate.

Just a minor update on Japanese: I said in my last post that “sometime in the next 2 weeks we’ll be starting past tense”. We did that yesterday in class.

Anyway, it’s after midnight and I don’t want to be asleep in my only class of the day (and last one of the week, as Calculus is cancelled), so I should be off to bed. G’nite all! Until next time,

Lyle Waldman

The Midterms are Over!!!

November 8, 2006

Well, as the title says, the Midterms are over. But I’ll get to that later. As always, the topic of the post comes last (it’s a running theme I’m working on for those who haven’t noticed). First I’ll talk about everything else. Let’s go in reverse-chronological order this time, starting from about 4 hours from now.

In about 4 hours from now, I’ll be getting my Math 147 midterm back. The one midterm I never, ever want to see again. Man, I think I did so bad on that one. I just hope it comes back better than I expect. I’ll write another post likely tomorrow about that.

Speaking of Math 147, we did something in class today that was awesome. Professor Zorzitto only tangentially mentioned the term “Taylor Series”, but that’s basically what we did. For those who don’t know, a Taylor Series is a specific type of series of numbers. I’m not exactly sure what the definition is, only that there are two specific Taylor Serieses that correspond to the exact values of sine and cosine of a particular value, so you can solve sine and cosine without a calculator. It was really awesome how he got there though, but it’ll go over the heads of most of the people reading this, so I’m not going to go into it. It was really cool though.

In about 2 hours from now, I’ll be getting my Japanese midterm back. I think I did fairly well, although, to me, “fairly well” is subject-dependant. For example, for CS 134, a 90% is not “fairly well”, while, in Math 147, an 80% is “fairly well”. In Japanese, my goal is to round off the term with an 85%, so anything that gets me closer to that is OK with me. Then again, considering I studied completely the wrong material and basically got by on the exam with what I knew of grammar, I suppose I should lower my standards a bit. Nah.

Speaking of Japanese, just to keep you out there who may be interested in JAPAN 101R informed, last week we covered time-telling and movement towards a place. I haven’t looked at what we’re doing this week yet, but I think we’re going to be doing past-tense within the next couple of weeks.

In Math 145 today, Professor Willard FINALLY returned our midterms. I didn’t do as well as I thought I did, and I didn’t even come close to beating the class average (then again, the class average was 90%), but I’m satisfied. At least I’m not doing terribly in that course.

Right now we’re learning about Complex Numbers in Math 145. It’s really nothing you shouldn’t have learned in Grade 11 or 12 Math (whichever year it’s covered in your particular school discrict)…yet. I’m sure Professor Willard is going to make it interesting soon.

This past weekend I managed to make a working plan for getting all my homework done so I wouldn’t be swamped with it during the week, and then promptly managed to get absolutely nothing done the whole weekend. Friday afternoon, I was sitting in the Comfy Lounge when Gayle Goodfellow (some of you may have gotten or will get E-mails from ggoodfel@uwaterloo.ca; that’s her) came in recruiting people to be student volunteers to do tours of the MC on Campus Day this past Saturday. As I was going to be out already writing another one of UW’s math contests (the Special K; no affiliation with the cereal), I decided to do it. Thus, from 9:00 am to 4:45 pm, I was engaged in various activities at the MC, returning to my room about 5:00 pm, and getting absolutely nothing done for the rest of the night. On Sunday, I woke up planning to get my CS assignment done. About 5 minutes after getting dressed, a res-mate of mine asks for CS help. He said “it will only take a second”. 2 hours later, I return to my room and begin working on my CS assignment. Luckily it didn’t take me long, and I got most of it working within an hour or two. Then I go to the lounge for a movie night, where we watched Monty Python and the Holy Grail.

And now I arrive at the last bullet point in my post; my Japanese midterm. Well, I studied and studied for it (in total, about 4 hours worth of studying), and, upon turning the paper over, realize I studied completely the wrong things. So I got by by knowing grammar and using the “boolean equality approach” (if this word is not equal to that word, the answer to the question is “no”). In about an hour, I’m going to find out if it worked.

So now I must run (literally) to Japanese class. One more thing, though: I’ve noticed I’m not getting a lot of replies and feedback on this forum. Perhaps it’s because I have, up till now, neglected to give my E-mail adress for non-subscribers to reach me by. If you have any questions, comments, or money, you can reach me at uwmathblogger@gmail.com. No insults, though, please.

Until next time,

Lyle Waldman

Three Down, One to go!

November 1, 2006

All Right! The Math 147 Midterm is done! I can breathe again!

Well, first of all, I still haven’t got my Math 145 Midterm back (Professor Willard promises next Monday). I did, however, get my CS 134 midterm back. Despite being 10 minutes late for the exam and leaving 10 minutes early, I wound up with 49/53 on it (or 92.5%). I made a stupid mistake in one of the short answer questions and got 3 wrong on the multiple choice, but I’m quite satisfied with it. Right now I’m probably riding about a 93%-ish in the course (even though I got over that on 2 assignments, the midterm is worth so much that the assignments are practically meaningless markwise, and the final is worth even more).

So, yeah, my Math 147 exam was on Monday. I don’t think I’ve ever studied that much for any test ever, and definately not for any math test. I spent pretty much all of Sunday at my desk. I meant to spend most off Monday with my book in front of me, but somehow didn’t manage it. Oh well…

I still managed to screw up the exam though. Of the 6 questions (5 of which were split up into 2 or more parts), I completely botched one and messed up a couple others. I’m expecting about a 70% on this one. I probably could have done much better in Math 137, though. Oh well. I’m probably not going to take Math 148 next term, so as long as I can keep this mark well above 70%, I’m happy. Unfortunately, there were no interesting adventures surrounding the Math 147 exam to share, so that’s about all there is to tell.

After the Math exam, a bunch of us went to a restaurant off-campus to hang out. It turned out to be a long string of those “You know you’re a math nerd when” moments, because, while a couple of us tried to steer the conversation as far from Math as possible, the majority kept talking about various exam questions and other math facts. Nevertheless, my first unsupervised University hangout session was pretty cool. I’d like to do it again.

In other news, Halloween was last night. All over campus, I saw people in weird costumes. I didn’t get any pictures (and, honestly, I should have, because some of the costumes were awesome), but I saw a Captain Jack Sparrow, complete with drunken swagger and whatever accent Johnny Depp puts on in the movie (ostensibly British), a group of hippies, a pair of what looked like Power Rangers, a ninja, and that’s just to name a few. I saw Annie, our own resident AHS blogger, dressed up as a nerd, complete with coke-bottle glasses. She didn’t notice me sitting in the caf studying Japanese though.

Speaking of Japanese, instead of going to either of the on-campus parties last night (one wet, one dry, although I’m not 19 yet), I spent my evening studying Japanese and doing laundry. Rule for not living at home: Clean socks and underwear > Anything else (well, except sleep, although apparentely homework > sleep and laundry > homework, so it’s like rock-paper-scissors, I suppose, except for the fact that, logically, paper doesn’t beat rock…I suppose dynamite would beat rock, but scissors wouldn’t beat dynamite, plus “Rock-Dynamite-Scissors” doesn’t have quite the same ring to it…I guess that’s why they used paper). Anyway, where was I? Oh yeah, Japanese. Well, I suppose that’s a good place to end this entry as well, since my midterm is today and I’m in the process of studying for it while writing this post as well.

Until next time,

Lyle Waldman