Monthly Archives: April 2015

Course Review: MATH 121

Honours Integral Calculus 

“Some of the best ideas in mathematics have been very simple ideas”

Text: Robert A. Adams and Christopher Essex: Calculus: Single Variable, 8th Edition, Pearson, Toronto, 2013

Prof: Dr. Young-Heon Kim

Professor Kim is a boss. He challenges us. He aims to make us understand the mathematical thinking behind a proof. He also promised us that if we worked hard and understood the basics, we should get an A, which was probably realized for most people who worked hard at the end of the term. He answers questions generally patiently and tries to sense if the class is understanding what he is doing, instead of just droning on. Highlights of the class:

On the first class. “I looked at the textbook we are using for this course. It was very disappointing. The questions are too easy.”

“Why are you guys looking so dumb today?”

“Let this by a probability distribution of the midterm. As you can see, it isn’t very high.”

Kim: “Should we do this problem this way or that way? It’s a matter of taste.” Student: “So it doesn’t matter?” Kim: “No. TASTE MATTERS A LOT!”

“Hey! doesn’t this parametric curve look like Picasso?”

Near the end of the course. “I just realized that you guys have been working very hard for this course. Please don’t ignore your other subjects. How come nobody complained? Whenever anyone comes to speak to me, it seems like you are saying “please give me more work”.


This course was significantly harder than Math 120. For example. the average on the first homework was 6/15, but it improved dramatically over the course of the term. Midterms were conceptually challenging but only trivial computations. The prof loved to mix multiple concepts into one question. There was generally one proof on every exam. There were often proofs on the weekly homework, and these were significantly more challenging than the ones in the exam. The questions used to nag me for days. The Final exam was 40% of Math 101 stuff and the average was scaled to 75-78. So if you work throughout the course, and make sure you understand the basics well, you should get an A. 16/29 students achieved an A.

Key Concepts

The (Riemann) Integral

Sequences and Series

The Fundamental Theorem of Calculus


Hard Concepts

Riemann Integral: Defining integration in terms of epsilons and partitions. Similar to limit definition, but the hard part is the mathematics, not just the logic.

Probability: Some of the harder questions are difficult to wrap one’s head around, especially on the homework, where we had to find the probability of a series converging. One way is to think of probability as mass.

Functions defined by series: Last question on final was a function defined by a series of functions defined by a sequence. Can get pretty meta. One way is to look at how output function is changing with a small change in x, to understand.

Polar Co-ordinates/Parametric: Drawing, finding derivatives etc can get pretty computationally challenging and technical. But there is a step-by-step process one can follow. Also, to find parametric function it is a good idea to divide motion into motion of the centre of mass and motion relative to the centre of mass.

Centre-of-Mass: Some pretty crazy mass distributions. Make sure to define axis etc clearly, and not to change it during the course of the calculation.

Volumes by slicing: Can get pretty hard to imagine. Might require good 3D geometry imagination skills.


Great course.  I wasted a lot of time studying for the first two midterms by practicing too many questions from the book. It was better for me to just try to understand the concepts. The homework problems were challenging but rewarding. The Webwork was a bore, but that is in Math 101 anyway, so you can’t escape it. Some aspects of the course were a bit rushed, but that is to be expected with an honors course. I would recommend it to anyone who wants to really improve their understanding of mathematics.


Course Review: PHIL 220A

Symbolic Logic I 

“Not-not is not the same as not-not-not-not. But they are equivalent.”

Text: (Logic 2010 Software + Textbook)

Prof: Dr Roberta Ballarin

Roberta Ballarin seemed like she knew her onions. I had very limited interaction with her. One of the two times she spoke to me was to reprimand me, because she thought I started the exam when I was writing my name :P. There were a few interesting points raised in lectures regarding the philosophical implications of logic, but most of the lectures were practice problem sessions.


In comparison to Comp Sci, Physics and Math classes, the weekly problem sets were generally a breeze in terms of length and difficulty. Part of the reason I found this course easy was because I had covered similar material in CPSC 121. That said, if you have not taken anything vaguely computational in while, this course could take more time than you anticipated. Further, even if you do find the concepts easy, one cannot expect to succeed this course without any effort at understanding the material. All the midterms/final were fine if one did the homework and practised a few extra problems by hand. The first midterm was especially easy.

Key Concepts

Propositional Logic

Predicate Logic

Hard Concepts

Symbolizations with predicates: These can get really nasty. One has to symbolize really convoluted English sentences. Make sure you learn the how to deal with specific phrases and connectors.

Derivation with free variables: Tricky. Best to eliminate the free variable using tricks outlined in the software.


Logic 2010 is the name of the software. Some aspects of it are pretty neat, but others are poorly designed. One thing I wish I knew earlier was ‘direct’ symbolization. In any case, later on in the course, the software will start to reject correct symbolizations of sentences, making it pretty useless. The only way to get around this is to try to figure out what the computer wants and only use that. The online book is pretty dry. But there are some useful hints interspersed in the various documentation attached to the software. But it might require some digging.


If I had known the nature of this course, given that I had already taken CPSC 121, I would not have taken it. It does go a little deeper into logic then CPSC 121 though, so that might make it worthwhile for some. I did find the topic interesting. I just felt another course might have used my time more efficiently. Additionally, If you are student used to crunching through problem sets and are looking for an arts elective that is a grade booster, this could easily help you out.

Short Story: The Ideal Gift


Mr Pedro Sears was not happy. His manservant had just informed him that his chauffeur would be unable to take him to his friend Robert’s birthday party. Unfortunately, the car was still at the garage for repairs. This meant he would have to take what was euphemistically known as public transport. Pedro’s frail frame shivered involuntarily at the prospect.

As he proceeded down the wide-ish staircase to his front door, Pedro glowered at a rather dull painting of a bowl of supposedly “fresh” produce. In that instant, that painting had come to represent all his annoyances with his present predicament. The painting, quite out of character, glowered back at him with a ferocity that forced Pedro to look away. Pedro reached the front door. His manservant enveloped him in a thick black trench coat as he burst out into the almost equally thick, piercing rain.

Despite the downpour, Pedro was not the sole pedestrian that day en-route to the bus stop. A burly man in an attire that would have been more appropriate in the Bahamas, seem to be of the same purpose. Though he was a few blocks behind Pedro to start, he soon caught up with him and started walking in step. Pedro eyed the water dripping off the man’s khakhi trunk shorts suspiciously, before crossing over to the other side of the road.

Since he was on the wrong side of the road, Pedro only just caught the bus. After a mad sprint across the middle of the road he arrived just in time for the bus. He also arrived just in time for a muddy green tsunami that coincided with the bus’s traversal through the large puddle near the bus stop. “Eh…eh…eh!” Spluttered Pedro, as he felt the liquid seep through his formerly impenetrable coat and trickle down his spine. He staggered onto the bus, paid for his ticket, and headed for the sole vacant seat, that was covered by a greenish shawl. Pedro gave a large sigh of relief as he lowered his rear into it. The bus started move. At last he could relax.

And that was when he sat on the baby.

The amorphous green blob that Pedro had mistaken for a shawl proved to be particularly spongy. Yelping as if he had been stung, Pedro leapt to his feet. After regaining his senses and unfixing his clasp from his lower back, he looked around. He could not identify a likely mother, in what appeared to be bus load of rowdy university students. Feeling a sense of guilt at having concussed the unfortunate toddler, he decided to pick up the baby and take him to the bus driver, who could contact the relevant authorities.

Just then, the bus driver slammed on the brakes and Pedro lurched into the group students, who were now exiting the bus en masse. Still clutching the child, Pedro waved his unoccupied arm frantically, but it was no good. He was swept through the door and landed face first in the unforgivingly hard pavement. Pedro, or rather, his face, remained attached to the moist concrete for several minutes, as his body performed emergency repairs and the shawl carrying the baby started to roll down the nearby slope.

With excruciating pain, Pedro managed to unglue his face from the pavement orient it more favourably.  After affirming both his own and his unconscious companion’s continued existence in this realm, Pedro looked around in a daze, trying to simultaneously ascertain his location and recall the series of events that could have brought him here. Out of the corner of his eye, he spotted a neon sign in the familiar murky shade of green that seemed to be following him that day. Half in a trance, he proceeded towards the discount grocery store beneath the sign, half-dragging his new, blobby-green friend.

Pedro, at this point, wasn’t very sure why he was entering the store, but he vaguely recalled that he had intended to purchase a gift for some party he was attending. Upon entering, a giant snake of harried looking shoppers blocked his way. They all wore a hollow, scaly expression that Pedro was almost led to believe that they were in fact enacting a mime of a play featuring an anaconda. After slithering through the queue, he began to realize that this might not be the place for his purchase. However, upon noticing a huge display declaring “Our Gift to You!”, he decided to proceed further into the store.

Under the display, there was a barrel full of the greenest cabbages Pedro had ever seen.

Pedro cracked up. He lowered his free hand into the barrel and began to stroke the smooth flesh of the nearest cabbage. The cabbage seemed to absorb all Pedro’s woes in its succulent leaves. Pedro made a decision. He grabbed the cabbage and, still fondling it, joined the human snake, grinning from ear-to-ear.

After exiting the store, Pedro sped of down the street at top speed. He had asked the cashier for his location and was surprised to find that he was within two blocks of Robert’s residence. He didn’t even notice the mother who, after seeing Pedro in his swamped attire, had crossed to the opposite side of the road.

At long last, Pedro reached his destination. He heard the familiar voices of his friends as clambered up the cobbled stairway to the front-door. He rang the bell and after a few moments, Robert’s manservant opened the door.

“Hi…” Pedro said, his eyes shining.

The manservant eyes darted quickly from cabbage that Pedro was stroking nervously, to the baby swinging from his other hand. He took in the several layers of filth that coated Pedro’s skin and his soaking clothing. Finally, he stared right back into Pedro’s manic gleaming eyes and closed the door with a flourish.

Pedro stood at the door slightly dazed. He overheard the manservant explaining to Robert. “Just a tramp, sir. Trying his luck I suppose…”

He sat down on the stairway, placing the baby and the cabbage beside him. The baby had woken up and had started to gurgle. Pedro’s face broke into a relaxed smile. Resting either hands on the cabbage and the baby he slumped his back on a nearby banister. He had got the ideal gifts.