Author Archives: arman raina

CRUNCH!

CRUNCH! Zig felt his narrow backseats collapse furiously into his unassuming and extremely ill-prepared back. “Crunch…” Zig mimicked in a dazed voice. He reached out ineffectually before realising that his face and most of his frontal body was severely incapacitated by a rather voluminous airbag. “Crunch” Zig repeated apologetically. As he spoke the airbag popped and this gave him a grainy glance at his now oblong steering wheel. It had ventured precariously into the third dimension. Zig winced.

He clambered out of his mutilated automobile. For some reason, his transporter now had an uncanny resemblance to an overused, double-holed, pencil sharpener. The wheels on the left-hand side had become fused in a hot, rubbery embrace and now showed no desire of disengaging. Zig braved a glance at his car’s bonnet. Or where it should have been: a troll-like truck had invaded the position and was currently in the process of reversing from the depths of Zig’s car. The truck, surprisingly, was untouched; except for an insignificant disturbance above the left indicator lamp, all other evidence suggested that the truck could have been in a showroom the previous week.

Zig waved his arms dejectedly for the driver to halt his slimy retreat and pull-up on the side of the lonely highway. Unexpectedly, the man appeared to acquiesce, whipping his key out of the car and labouring his hefty frame onto the scorching road. The man reminded Zig of a rather grouchy, flattish toad, who has been forced to vacate his favourite lily pad by an energetic fly.

“ HEY YOU!” He started.  “You with the zonked car, wha’ dya mean scratchin’ my truck?” croaked the toad in what seemed to be an accent that varied from an inhabitant of the distant Corfu Islands to a Texas rancher respectively.

“Eh” inquired Zig insipidly.

“Doncha ‘eahh’ me” spouted the agitated amphibian. “You breaka my cah, you h’apoligise h’and pay up, h’okay?

Zig slowly came to his senses. He felt like his brain was a large, entangled bundle of coil that had been hacked, mercilessly, in two.

“Sir…” he said in an attempt to be respectful. “Sir…, you ‘zonked’ my car”, he indicated the smashed sedan.

“Ya stop h’in the middle of the ‘ighway, dats what’s gonna ‘appen!”

“My car stopped because its hind portions were raked by your truck!”

“Eh?” imitated the froggy man. “That ‘cause you braked in the middle of da road.”

Zig started to reply, but then paused. A manic glint had entered his eye and was spreading surreptitiously along his face. He deftly thwacked the pipa-like man, grabbed his keys, hopped into the gleaming truck and sped off. The repetitive ‘thump-thump’ of the truck driver’s preferred club music bizarrely brought memories of thousands of popping airbags. It was all strangely soothing.

Short Story: The Death of a Fish

Fantail goldfish (Carassius auratus) in tipsy fishbowlTerry gazed into the fish’s eyes. Bubbles stared back at Terry. The dull penetration of those eyes was so reminiscent of his uncle, Mr Felinus that Terry had to look away….

“Ooooh…” wailed the fishbowl as it involuntarily embraced the tiled, kitchen floor.
With only a moment’s hesitation, Terry began shuffling the debris into the nearby trash can. However, a familiar, gnarled hand clamped on his shoulder soon inhibited him from making much progress.
“Stop, you blithering idiot! Stop at once!” cried Mrs Felinus “Don’t mix the glass with the garbage. It needs to be recycled.”
Terry immediately changed his course of action. He jerkily dropped the remaining fragments into his pockets at such a rate that his pocked bounced against his leg as if it had a life of its own.
Mr Felinus clambered down the stairs at a rate akin to his droning voice. “Goodness me, was that the fishbowl that fell?” He spluttered pompously.
“Not fell, dropped! By this mongoose of a boy!” Mrs Felinus responded viciously. She was sprawled across the floor, in a manner that would have disgusted a sloth. “And now where could our Bubbles have gone to?” She whispered with an entirely different tone in her voice.
“It’s no good my dear, even if we did find him now, the fish would be dead,” Mr Felinus said grimly before he dropped his unwilling frame to the ground beside his wife.
He then turned savagely to his nephew “Boy, we heard you were an animal-lover. What do you have to say for yourself?” Terry remained silent as he fished out the last grains of glass from the newly formed water feature. Mr Felinus continued with venom “We thought it was the stray cat that we had to worry about, little did we know, that when your mother requested you stay with us, we were to host a murdering menace in our house.”
Terry left the room and scampered towards the main door. He slid into the doorway and waited, perfectly still. He thought he could hear the familiar meowing sound. Sure enough, a stringy cat emerged and pawed his way nervously towards him. He took something from his pocket, brushed of the shards of glass and laid it in front of the cat. “This came from our emergency supplies, you know,” said the boy as he stared into the cat’s hollow eyes. “Don’t worry, I’ll make a plan for tomorrow,” he continued with a bitter smile. He patted the cat and then skipped towards the recycle bin. The cat purred happily and then started eagerly into the fish.

Course Review: CPSC 110

Computation, Programs, and Programming 

“Trust the natural recursion!”

Text: (online videos via Coursera on Systematic Program Design)

Prof: Dr Ronald Garcia

Ron is a cool guy. Great sense of humour. He spent a lot of time answering basic questions and doing (generally) simplified examples which annoyed some, since they had already grasped the basics from the videos, and wanted him to explain the more complex aspects of the course. I didn’t mind, since I failed to fully grasp some of the basics from the videos. And sometimes Ron’s simplifications can be applied to a more complex setting. For example, the way he explained built in abstract functions was simple but did not leave out any nuances.


Difficulty

I worked very hard in this course. Some people who had serious prior programming experience, or got really addicted to programming once initiated by this course, found the assignments and tests a breeze. I did not. I got a very good result, but I think that was a result of generous scaling and a lot of hard work on my part. Problem sets are increasingly difficult. Though the first midterm is really easy if you made the faintest attempt to keep up with the material, the second midterm and the final are exponentially harder.


Key Concepts

HTDF recipe

HTDD recipe

Recursion

Abstraction


Hard Concepts

Work-list accumulators: Required me to fundamentally alter the way I saw the structure of  my template, which was a challenge. Lots of moving parts as well.

Back-tracking search over generated trees: Most finals have a question on this, pretty tough, with so many moving parts, but the structure is pretty repetitive.

Abstract fold functions: Making one is easy, but using one to solve a problem is a challenge. Requires practice, insight and being methodical.


Lab

Generally okay lab, since the TA’s are on hand to help. This was in stark contrast to the problem sets which are generally harder, and you have to work on individually. I found the first few labs super-simple, but the one’s after the first midterm increased dramatically in hardness. I generally did not come close to the the 3-hour mark, though many people often remained till the end and many others would finish ahead of me within the first 30 minutes.


 Conclusion

If you are not really  into programming, or have no serious programming experience, be prepared to work very hard to get the most out of this course. I honestly felt that the course was rushed and I didn’t have time to digest what I had learnt.

Course Review: CPSC 121

Models of Computation

 “The laptop that you are using is a lot more powerful than a DFA!”

Text: Discrete Mathematics with Applications 4th Edition by S. Epp (see website for other options)

Prof: Dr George Tsiknis

George Tsiknis is the kindest prof in the world. His amazing accent, and personal warmth really leave an impression. He also has a great sense of humour. Its unfortunate that he had family emergency towards the end. Even though he was really going through a lot, he came to class and made sure we were ready for our final. Great guy. Some of the questions in the slides are worded vaguely, making it difficult to get the I-clickers, but they are only for participation anyway, so its all good.  Really willing to slow down and take questions if you need help, in class. I suppose tutorials and office hours must have been equally beneficial.


Difficulty

I get the sense that the topics on this course are very deep. That said, we skirt at the surface of most of these topics, and as a result, the course is quite straight-forward for the most part.


Key Concepts

Elementary Logic

Proof Strategies

Logic Circuits


Hard Concepts

Algorithm Efficiency: The rigorous definition is quite long-winding. Knowledge of Big-Oh notation from Calculus class could help.

Interpreting Sequential Circuits: I found these really tricky in the lab and on exams. They are kind of puzzle like problems- in that you either get them or you don’t- but you can spend a long time just making sense of what’s going on, even if you understand the fundamentals really well.

Predicate: Conceptually easy, but also easy to make careless mistakes or you can confused in half-way through your own translation.


Lab

Fun lab. I kinda freaked out the first few days since I had no clue how to operate a Magic Box or breadboard, but after a while the labs started making sense and I started to enjoy simulating circuits with Logism (which is freely downloadable, btw) or cracking circuit puzzles. Ultimately you simulate a working computer, but it is still a long way a way from the real deal. Pre-labs are not too intense. Most labs are with a partner, so efficient teamwork can get you done a lot faster.


 Conclusion

Fun course. Useful in learning basic logic, mathematical proof and simple models of a computer. But I get the feeling that the computer models we use are so simplified that they are ultimately interesting but have appear to have little real world application. I was waiting to connect what we learnt in class with my PC at home but that happened only superficially for me…The surprising immediate application I got out of this class were proof strategies that helped a lot in Math 121.

The Island

When the People first arrived on the island, the great Captain divided the People into four groups.

Unto the first group he spake

You, the People of the darkness , I give for you the place in the light. Yours is the bright place of the Sun. May you revel in the Sun’s energy.”

A dark man came forward and bowed

Thank you, oh Captain, whose generosity surpasses all. We will take the Sun’s energy, only to give.”

unto the second group he spake

You, the People of the Earth, I give for you a place of the Earth. Yours is the central place of the Earth. May you nourish yourself with the Earth’s soil.”

A brown woman came up and curtsied

Thank you, oh Captain, whose wisdom is timeless. We will be nourished by the soil, only to sow and nurture.”

And unto the third group he spake

You, the People of of the sand, I give for you a place of the water. Yours is the aqueous place of the unmeasurable coastline. May you forever cleanse yourself with the water’s purity.”

An ochre man came forward and bowed

Thank you, oh Captain, whose justice is fairest. We will clean ourselves, only to cleanse our domain.

But to the remaining, fourth group he looked on and was silent.

A fair woman came forward

The island that you have brought us to is wondrous, are we the People of the sky, to have our share of this island?”

The mighty Captain was silent.

A fair man came forward

We have travelled with you for many Suns, is it not only just that we are to have a quarter of this paradise?”

The Captain remained silent.

A silence engulfed the gathering. Though the People were one in this silence, they were divided, now. For the first time, they felt apart from the People. They also felt apart from their groups. For the first time, each person interpreted individually an event that had been experienced collectively. They looked at one another, confused, insecure and suspicious.

A commotion had started amongst the fairer People. However, with a flash of the Captain’s eyes, the silence resumed. People made way as a toddler slowly crawled its way towards the Captain. Without hesitating, the toddler clutched at one of the Captain’s trunk-like legs, and pressed its head against it in a tight embrace.

The Captain’s face broke into a smile.

Oh the People of the Sky! Child is no doubt the father of man. Here you, fair lady, fair man, you would take, giving nothing. Here is your child, he gives his heart, taking nothing. That is how the People have lived best, taking little, giving all. To you the People of the Sky, I give you, yourself. Little though it may seem, now, when you use it to take, you shall take all. It is not for you that you will take, it is for the child at my feet. For it is from your child that you will learn to give, and it is to your child that you will give.”

The great Captain paused.

Henceforth, the People, you are the People of the Island. This Island is yours to take, yours to give. Ultimately, though, it will be the island that takes you. Explore this paradise, People of the Island. People of Darkness, the Sun is easiest found, for the art of discovery itself, is the Sun’s own. People of the Earth, the Earth is not hard to find either, for one must not look neither forward, nor backward, but under, to find it. People of the Sand, on this Island water is all around, however water is inside too. Though this inside water may be uncovered timeously, it is this water that is purest. People of the Sky, when you look upwards, see not the distant shore, hidden peak, the far flung star or galaxy. See nothing but yourself, and you shall find yourself.”

End of Part One

A Marks-ist Dystopia

89.42 had arrived to school early. Only a handful of students wondered aimlessly in the usually crowded hallways. He headed to the library, to kill the remaining 10 minutes before classes started.  On entry, he found a thin brochure of the school and, lowering himself into one of the large blue beanbags, he began to read.

“ Welcome to Brave New-Hill, the Number One Robot Training Academy* in the province! Built on the remains of a human high school, Brave New-Hill has been training the provinces finest robots since 2113. Utilizing the best practice of Marks Identification (MI) for over 50 years, longer than any other academy, has allowed New-Hill to achieve a well synthesized mechanism for academic excellence…”

89.42 skipped a large chunk of the brochure, which seemed to elaborate on the facilities of the school. A paragraph entitled “ What is MI?” caught his eye.

“MI or Marks Identification was a landmark innovation in robot training. The idea of associating a student with a percentage was not new, human high schools had been doing it for centuries, however MI goes beyond this. MI is more than just a mark or even a name. MI is an identity. Furthermore, since all robots achieve percentages of between 99 and 100, the percentage used is in fact the first four decimals that follow. (In highly irregular cases of duplicate identity, a fifth decimal place is used). In addition, since marks fluctuate throughout the year, the average overall mark at the end of the previous academic year is a student’s MI. Countless studies have shown that robots with MI are far better trained than those without…“

89.42 stood up and replaced the brochure in the newsstand. He had hoped that the brochure would tell him something about the academy that he didn’t know. Checking his watch, 89.42 mooched his way to ‘English in Communication’ class.

When he arrived, the room was already full. As per usual, the class self-sorted itself into groups of students with similar marks. And 89.42, being the lowest, sat alone at the back of the class, behind a group of rather talkative 92’s.

On the latest poetry analysis he had received a .25 mark deduction for using the word “abstract parallelism” instead of metaphor.

“Abstract parallelism” had been a hobbyhorse of his for sometime.  According to him, it was a concept that not only united English concepts like “allegory”, “simile”, “analogy” and “metaphor,” but also it was also evident in the abstractions made by all arts and science. He had arrived at this concept after finding the categorization of “similes” and a “metaphors” as arbitrary. What was the reason behind this specific theoretical classification over another? His “abstract parallelism” was logical though. He could prove it.

In the last thirty minutes of the class, a piece of creative writing was demanded, based on a rather hackneyed prompt. Unlike his peers, 89.42 enjoyed creative writing. He liked telling stories. However, whenever he knew the piece was to be marked, it would give him the bizarre and unnerving impression of being a trick dolphin that was being coaxed to jump through hoops. This was because of the unsaid requirement to lace one’s writing with metaphors, motifs, symbols and similes. Why was writing that included these devices always superior to those that did not? Was it not possible to jump to the side of the hoop, or daresay, over the hoop? All this was stirring in his mind as his hand darted across the page, relating the affair of one Pedro Sears.

Thirty-five minutes and three pages later, he was in the ‘Science in Reasoning’ class writing a pop quiz. His teacher for this class was a big proponent of pop quizzes. The slightest misbehavior or disrespect would result in a quiz for the entire class. It was possible to discipline students to the finest details with marks, in a way physical punishment never could. As 89.42 often reflected, marks were scars that never went away. They followed one to university and supposedly determined what sort of career one would have after university.

As the teacher was collecting 89.42’s quiz, he heard her whisper “-.25, for trying to cheat”. 89.42 was initially surprised, but then realized his fault. He had written the so-called ‘free response’ section in pencil. The adolescent automaton shook his head, before sinking it into his hands that were resting on the table.

He had always held that there was nothing ‘free’ about the response. One’s answer not only had to be obtained by following the rather mechanistic process outlined in the previous class but must ignore the countless assumptions that the question itself was making. While 89.42 was interested in scientific innovation, he was not interested in the mechanistic applications of an innovation. And now that very same, hypocritical free-response had cost him dearly.

After an excruciating hour of Science, 89.42 hurried to his locker deposit a doodle he had made in class. His locker was crammed with an odd collection of abstract paintings, sketches and doodles. Most of these artworks were his attempts to portray “abstract parallelism”. Lately he had found plane surfaces insufficient. It was for this reason that after depositing his latest scrawl, he proceeded to Art Room that housed his sculpture. As he jostled passed he peers, he noticed, as he did everyday, that they spent there lunchtime doing schoolwork. Furthermore, they again seemed clustered into groups with similar MI. A particularly noxious group of high achieving students, whose leader was a hundred, sneered at him as he walked past. “Cheating in Science? Well I’m not surprised. Remember the time he was absent and actually asked me if he could borrow my notes, for that day?” Said the hundred, watching 89.42.

“Its not that we see him as a threat,” Agreed the 99.76. “ But he’d barely comprehend the first page.”  89.42 ignored them. He was used to it by now.

Anyway, 89.42 had his sculpture for company. The moment he entered the room and touched the model, a jolt of energy seemed to whirl through his frame. His intense concentration often gave way to genuine excitement as he rolled the clay in his fingers, smoothing the edges. After half an hour of sculpting and increasingly jumpy behavior, the teen robot took a step back and admired his handiwork. A magnified DNA strand in the shape of infinity stood at the centre of the table. He was done. This was it! It suddenly occurred to him that the principal would be impressed with this particular piece of art. As if following orders, he carefully picked up his unbaked sculpture and proceeded to the principal’s office, which happened to be down the passage.

To 89.42’s surprise the principal invited him in immediately.  “ I’ve been expecting you, please put your artwork down and take a seat,” he said.

89.42 obeyed, glancing fearfully at the principal as he took his seat. The tall man was not only famed for his severity, but was rumored to have had a strange history.

“From your locker,” continued the aged machine, indicating a neatly stacked pile of 89.42’s “abstract parallelisms”.

89.42 gazed from his sculpture to his artwork, to the principal, dumbstruck.

The man laughed, “Are you wondering how I know about your artwork, or should I say, “abstract parallelisms”? Or is it how I knew you were coming to see me? “

The teen robot nodded, speechless.

“You had a chip planted in you when you first came here. It allows us to track your thoughts, but, more importantly, if you think of something, lets say “unique” you are programmed to come to me.”

89.42 found words. “My world is now…different…warped…Why are you telling me this now?”

The man was silent for a moment. Then he responded slowly, with almost mischievous glint in his eye. “ At Brave New Hill, that is the … let us say “reward” for being unique. Congratulations. You are not the first to malfunction, by the way” As he said the last words, he opened the door behind his chair with a flourish.

89.42 peered inside. In it he saw at least a dozen, dilapidated stacks of the same form, in clay, over and over again. It was a DNA strand merged with infinity. The principal picked up 89.42’s one and placed it with the others.

89.42 reeled. The principal was now watching him.

The broken boy started muttering to himself. “ All exactly the same. Unique? Huh! All exactly the s-”

The principal interjected “Not exactly the same, minor differences in scale. A handful of your doodles are almost genuinely unique.”

“What is “genuinely unique” mean anymore?”

“Interesting question, we robots have been wondering about that ever since we rid this planet of humans. In fact, I once claimed that creativity became extinct with the Homo sapiens sapiens. That was why I was made to leave my university position and come here-”

But 89.42 was not interested “MI kills creativity” he almost yelled.

“Robots have no creativity to kill. At least MI makes us productive.”

“Teachers misuse it. They take MI lightly, as if it doesn’t affect our future. At the same time, they use it to keep discipline.”

“They are just preparing you for your future. Nobody cares about your MI except you. They actually want you to succeed”

“MI will determine my future!”

“While you may care about your future, nobody else will. Especially at university.”

“Is it even possible to be successful in this system without an adequate MI?”

“Of course, in fact, its quite likely. While MI significantly increases your chances of success, its main benefit is in security.”

“The focus of classes is on parrot knowledge. We are not supposed to ask ‘why’, in order to achieve a high MI. Its preventing real learning”

The principal sighed.

“Do you think you are some sort of Bernard Marx? Or the Savage? Or should that be Bernard Marks?” The man chuckled slowly as he said this. He seemed to have made a decision. He continued.

“Well, let’s find out, shall we? I’ll play Mond. You have a choice. Either you leave this place, become a “unique”, crazy, malfunctioning, wild, homeless robot. And get your so-callled creativity. He paused and smiled ironically at the pile of doodles that had remained at the table.

“Or?” Inquired 89.42, breathless.

“Or, we reprogram your brain, remove the bugs. And you automatically start behaving normally.”

It was a no-brainer, really, for 89.42. Especially after what he had just learnt. But something was still perturbing him.

“My MI is so low. No matter what I do after you reprogram me. There is no way I can improve my MI to the high nineties required by universities in one term.”

The elderly automaton laughed again.

“Worried about you MI, are we? Well, its not difficult for us to accidentally reformat your MI, while reprogramming you…”

89.42 smiled. For the first time in years he felt the urge to become 100. He could get there. He just knew it.

Course Review: PHYS 107

Enriched Physics I 

“In the same way that Calculus was invented for Mechanics, most of Mathematics was invented by physicists”

Text: Matter and Interactions Vol 1, Modern Mechanics 3rd Edition by Chabay and Sherwood

Prof: Dr. Ian Affleck

Google Ian Affleck. He’s got stuff named after him. Physics stuff. He’s a bad-ass.

Dr. Affleck was actually a lot humbler in person then you would expect. He doesn’t talk to his students as if he is an all-knowing-master. The in-class discussions are pretty useful, as are the tutorial discussions. The I-clickers come pretty fast though, so watch out! I lost many participation marks, overly engrossed in a discussion. Quite often during the lectures, there were large chunks of time when I had no clue what the prof was talking about, and neither did my neighbours. Dr. Affleck would sense that he had lost half the class at some point and would ask, optimistically, “Any questions?”. When no-one raised their hand because they could not sensibly articulate their wide-ranging confusion about what was going on, Dr. Affleck would continue, with renewed confidence. At the same time though, when I did my readings thoroughly and did the homework, I noticed that Dr. Affleck boiled down the concepts mentioned in the textbook to a simplicity and tangibility that was really rewarding when I got it, that is.


Difficulty

Not knowing what’s going on happened a lot to me in this class.  The readings are quite challenging and the lectures can be pretty out there. However, thanks to generous scaling, innovative grading and a final exam that focussed a lot more on high-school Physics, one can do quite well in this course. Some of the key concepts in this course are from high-school Physics, just generalized.


Key Concepts

Momentum Principle

Energy Principle

Angular Momentum Principle


Hard Concepts

Entropy: Though I didn’t include it in the key concepts, this is a fundamental concept within Physics and can it take a while to get your head around it

Angular momentum esp. gyroscopes: Angular momentum meets vector calculus for some crazy, yet rewarding Physics

Energy Quantization: Quantum physics can get pretty funky when there are multiple types of energies being quantized. Esp. with a ball-and-spring model of matter.

Collisions: Can involve some tricky geometry and hairy systems of equations

Relativity: Particles may suddenly start travelling at relativistic speeds rendering multiple carefully derived formulae useless. Intuition also fails you.  One has to use first principles.

 


Lab with Doug Bond and Joss Ives

Not so much Physics as a Statistics course. Not too much pre-lab but some experiments can be pretty repetitive. They attempted to prevent us from collaborating with our lab partners on lab notebooks and spreadsheets but it didn’t really prevent copying.

I suppose I will eventually be grateful for what I learned during those 3-hour chunks, but at this stage my memories are of frustration with Excel and a mercilessly fast learning and implementing speed. The statistical tools you learn are not rigorously proved, in stark contrast to the more theoretical physics class, which could peeve some, but I infer the lab is intentionally meant to be more “hands on”.


 Conclusion

Really rewarding course. Could change the way you see the mechanical processes in nature.

Course Review: MATH 120

Honours Differential Calculus

“For any topic in mathematics, you just need to do a few ‘cute’ problems. Otherwise, your mind starts ‘turning'”

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

Prof: Dr. Yue-Xian Li

The thing that I’ll remember the most from Dr. Li’s class were his bizarre one-line quips including:

“You should have asked me that question weeks ago! You are going to fail the midterm tomorrow!”

“How can you confuse a “gamma” with an “r”? The “gamma” looks like the thing you use to hang people!”

“I have some  videos I could show you… people driving on a bridge while it is collapsing… some really great videos”

“There is some theory behind this, but I don’t really understand the theory… let me show you how to get the solution though”

“My third-year students keeping making this mistake, but you guys are honours, so you shouldn’t have a problem”

Dr. Li is actually a mathematical biologist. He was alots of fun and very passionate. He was also really nice during office hours. The best part of his classes were when he deviated from the textbook a bit. That said, he took most of his examples  directly from the assigned readings in the textbook.


Difficulty

I am sure most people who takes this class are a bit apprehensive about the word honours. Is that apprehension justified? I am not so sure. I think that the key to this course is identifying the handful of additional/challenging concepts early on, and being prepared to put some extra effort into them. Both the midterms and the final were really fair, since the prof gave us very similar practice exams. I found the last few questions on the weekly homework pretty hard, though. I often had to think over the questions for a few days to understand them. I also tripped on an optimization question in the final, but I think that was just me…


Key Concepts

Limits

Derivatives

Mean-Value Theorem

Continuity


 Hard Concepts

Epsilon-delta Definition of Limit: Arguably  the hardest concept to understand quickly in the course. Make sure you understand the “logic” of it before diving into the math.

Proofs: Proofs often involving mean value theorem on tests, but anything course-related for homework.

Differential  Equations: Lots of Physics often involved, could be hard if that’s not your strongest subject.

Derivatives of inverses: Some of these questions can be computationally difficult and you can get really confused if you don’t notice that a function evaluated at its inverse is x.

Continuous and Differentiable Functions: Often involving piecewise functions with parameters. Its best to go back to definitions when dealing with either or both of these properties.

Chain rule: If you don’t like computation, some chain rule questions could bring you down. Its just a matter of practice and accuracy though. Not really smarts.

Optimization and Related Rates; If geometry’s not your strongest point, these could be a challenge. Once again, practice is key. ( I didn’t practice optimization enough for my final)


Conclusion

Great course, but be prepared to put in extra effort.