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Course Review: MATH 321

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Real Variables II

“And now we have the tools the derive the Fundamental Theorem of Calculus, the formula you’ve been using since you were children.”

Text: Principles of Mathematical Analysis by Walter Rudin (3rd Edition)

Prof:  Dr. Gordon Slade

Dr. Slade was an engaging professor. He was clear while also motivating the content well. Once in a while, he would drop a wry joke, which brought a small amount of necessary levity to the class. One thing that stood out to me is that he would welcome clarifications and inquiries/corrections on the smallest details, especially on Piazza, rather than dismissing them which I think is helpful in such a class. Students’ often lack confidence in their first few serious proof courses and sometimes misunderstandings on seemingly small details can exacerbate that.

Difficulty

I found the course content more manageable than MATH 320, as it felt more well-motivated and we were applying a lot more of the theorems learnt in MATH 320. On the other hand, the homework was slightly harder as the proofs became more lengthy. Sometimes what was an entire proof question in MATH 320 is just a minor trick as part of proving some larger theorem. The midterms and final were all mostly doable, though I believe I made several trivial errors in the final. The final grades appeared to be scaled.

Key Concepts

Riemann-Stieltjes integral

Sequences of functions

Equicontinuity

Stone-Weierstrass Theorem

Arzela-Ascoli Theorem

Power Series

Fourier Series

 Hard Concepts

Metric space of functions: Takes a while getting used to discussing metric spaces where points are functions. Need to understand what neighbourhoods and open and closed sets refer to in this context.  Then you can apply a lot of the theorems already learnt to this metric space.

Inequalities: It may seem ridiculous to mention this, but some of the hardest questions involve finding tight bounds on functions using simple tricks such as triangle inequality, Cauchy, tangent lines, sums of squares in clever ways.

Examples: Coming up with examples (e.g. a point or a sequence) is not only useful in questions that explicitly ask for them, it can also be applied in conjunction with certain theorems taught in the course to show a certain object does not have a certain property. It is also a useful thing to practice before an exam as it helps you remember the conditions for certain theorems.  They can be really tricky to come up with on the spot sometimes.

Conclusion

Rewarding continuation of Real Variables I. Content was well motivated and homework was challenging.

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Course Review: CPSC 311

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Definition of Programming Languages

“I prefer the word ‘thunk’ to expression closures.”

Text: Programming Languages: Application and Interpretation by Shriram Krishnamurthi

Prof: Dr. Steve Wolfman

Wolfman was slightly less flipped in CPSC311, especially as the term progressed. His lectures were pretty entertaining and included a lot of live modification of the interpreter. Instead of sticking to textbook examples of dynamic scope and laziness, we often worked on languages in assignments and midterms where exotic adaptations and variants of these concepts were incorporated into a language in mind-bending ways.

Difficulty

I expected this to be an easy course. It ended up taking a lot of time. A lot of the programming languages concepts were completely new to me and combined with Wolfman’s avant-garde presentation of the material, I spent a great deal of time preparing for midterms and understanding the readings. The project we selected was in Elixir, and it was also very time-consuming as we had to learn distributed systems concepts in a new language with little guidance. That said, I feel the project was kind of a ‘choose-your-on-adventure’. You could do very well in the project with far less work if you chose wisely initially. Overall, the average was quite hight (around 77%) even though the midterm averages were quite low.

Key Concepts

Scoping

Deferred evaluation

Recursion

Continuations

Functional programming

SKI combinator

Interpreters

 Hard Concepts

Dynamic scope: Really messes with your brain, helps to write out the context.

Continuations: Odd concept. Helps to think of what function the continuation is bound to and apply it.

SKI combinator: Takes practice to get used to ‘algebraic’ manipulations of functions.

Conclusion

Learnt a lot. Enjoyed the project. Challenging course.

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Course Review: MATH 320

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Real Variables I

“You don’t really need a metric. All you need is the open sets.”

Text: Principles of Mathematical Analysis by Walter Rudin (3rd Edition)

Prof:  Dr Joshua Zahl

Dr Zahl was a structured, clear professor. He also provided useful insights into the ideas behind various proofs. I don’t think he has taught this course many times before, so he is probably still in the process of fine-tuning his delivery. Also, his surname literally means ‘number’ in German!

Difficulty

While the readings are pretty dense, the homework was quite doable by honours mathematics standards. I found the first midterm surprisingly easy. The second midterm was significantly harder, and I had not fully understood the concept of compact sets, so I did not do well at all. The class also got wrecked so there was a lot of scaling. The final was very reasonable.

Key Concepts

Properties of Real Numbers

Metric Spaces

Open Sets

Sequences

Continuous Functions

The Derivative

 Hard Concepts

Compact Sets: This concept has a deceptively Byzantine definition but is actually really fundamental to the course. Reading the history of the concept from Wikipedia and understanding many examples/counter-examples of sets that are or are not compact gave me a better intuition.

Sequences: Not a hard concept to understand, however an invaluable tool in certain seemingly intractable problems. Many times, it’s helpful to construct a sequence of points or even intervals and then use properties of such sequences in that space to prove the theorem.

Conclusion

Tough though doable class, if you have any background in mathematical proofs. One of the key learnings I took out this class, was the importance of spending time understanding complex definitions.

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Course Review: CHIN 101

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Basic Chinese I: Part 1 (Non-Heritage)

“bā lā kè  ào bā mǎ (Barack Obama)!”

Text: Integrated Chinese: Simplified Characters Textbook & Workbook, Level 1, Part 1 by  Yuehua Liu

Prof:  Lee (An-Yi) Laoshi

Lee Laoshi is super funny and passionate. The class was the most enjoyable class I took that term because of interactive nature of the lessons. It was the only class that I didn’t occasionally look at the clock to see when it was ending. She was also very helpful and understanding. Unfortunately, she was only hired as a Visiting Lecturer and will be leaving UBC soon.

Difficulty

The workload was a lot. Weekly quizzes, character sheets, and the occasional workbook chapter created an onslaught of homework, even when there wasn’t a midterm. Most of it was memorization, so it was just a matter of spending the time. Most of the stuff was on the computer. Unfortunately, my computer packed up on the final, so I didn’t do as well as I did during the rest of the course and I lost a letter grade.

Key Concepts

Pinyin (pronunciation) with tones

Character reading

Character writing

Understanding oral Chinese

 Hard Concepts

 

Recognising pinyin orally: Really hard, be sure to get a lot of practice before the final. I advise recruiting a first language speaker friend to help out.

Writing characters: Quite painstaking, especially if you are not the best artist. Lots of practice.

Conclusion

Fun classes, exhausting homework and worthwhile introduction to one of the world’s most widely spoken languages.

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Course Review: MATH 215

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Elementary Differential Equations I

“UBC is a very progressive place…Because you get to learn Linear Algebra before Differential Equations!”

Text: Notes on Diffy Qs: Differential Equations for Engineers, by Jiri Lebl

Prof: Dr Dan Coombs

Dr Dan Coombs has great British accent, and a wry sense of humour which helps to keep interest in the class. He tries to balance between tolerating conceptual questions and making progress in the more recipe-oriented curriculum. He spent a lot of effort restructuring the curriculum to be based on Linear Algebra, so as to make the class more conceptual and slightly less “formula-up-my-sleeve” math, though it still is.

Difficulty

The homework is really exhausting. The hand calculations have awful numbers in them, making them really tedious. The Matlab is … Matlab. As a CS student I thought Matlab would be a breeze, but that was not the case, as the language has a lot of quirks. The number of questions in a homework set is a lot considering the time each one takes. With the exception of the first homework, where we were given real world problems and had to come with models for them, I didn’t feel I got a lot out of the homework, except learning a few random facts about Matlab after trial and error.

Key Concepts

Modelling nature as a differential equation

First order linear equations

Linear systems of differential equations

Laplace transform

Non-linear systems

 Hard Concepts

Partial fractions: Thought they were pretty easy, but had a really gross one on the final

Non-linear classification of fixed points: Can get a bit confused between different fixed points

Classification of 2nd order linear systems: If you don’t want to re-derive them, need to be able to recall them quickly.

Conclusion

Homework was a schlep. Interesting topic, but recipe-driven curriculum almost kills it. IMHO, focus should be modelling natural phenomenon. The problem with the recipe driven approach, even for non-math students, is that (1) Engineers will probably just use Wolfram/computer system to solve it anyway. (2) While it might be helpful for them to classify what can/cannot be solved etc, odds are if it is non-linear you will try your luck, or use a linear approximation anyway.

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Course Review: MATH 227

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Advanced Calculus II

“Consider an infinitesimal paddle wheel…”

Text: (none)

Prof: Dr. Joel Feldman

Dr. Joel Feldman strikes a great balance between being really organized, while still pretty relaxed. He is very helpful, in that he is always available between classes for questions. He is also really knowledgeable about the field (as he is a mathematical physicist) which is great, though he did give us a particularly tragic expression when we said we didn’t know what curl was, halfway through the course and he had to explain it.

Difficulty

The weekly assignments are generally all straightforward. The questions vary from computational to small proofs. I missed the first midterm, but a lot of people got wrecked, and it looked tough so watch out. Each question in the second midterm was manageable, though it required thinking. The challenge is that there are only four questions, so the cost of getting one question completely wrong is quite high. The final was similar except it had more questions. The challenge then was that often it was not clear which of the various techniques we had learned in the course was the correct approach to a question.

Key Concepts

Analysing/ parameterizing curves in 2,3-space

Analysing/ parameterizing surfaces in 3-space

Analysing/ parameterizing vector fields in 3-space

Integrating over curves, vector fields, and surfaces

Integral Theorems

 Hard Concepts

 

Applications of integral theorems: Hard to pick the right strategy that is going to work.

Biot-Savart Law: Really abstract, not sure if I understood it.

Conclusion

Feels like a fun physics course. Wish we had more time to discuss differential forms, but other than that pretty interesting class.

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Course Review: CPSC 221

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Basic Algorithms and Data Structures

“After 221 all of you should use “divide-and-conquer” when handing out exams, its a lot more efficient!”

Text: Objects, Abstraction, Data Structures, and Design Using C++ by Koffman, Elliot B., and Wolfgang, Paul

Prof: Dr. Alan Hu

Dr. Alan Hu is great at making everyday metaphors (often involving Justin Bieber) out of abstract computer concepts. He is also very patient in class, answering questions in detail. His classes have a slightly “free-wheeling” style because of this, so the lack of structure could distract some. Dr. Hu is a super approachable guy, (except during exams!), and he seems genuinely passionate about teaching computer science.

Difficulty

The assignments and labs are all do-able, though the penalties for small compilation errors on assignments are harsh. The midterm was pretty long and it had a mistake on it and I (and many others) got wrecked. The final was significantly easier and the scaling was huge. There is a lot of material in the course though, and the questions on exams definitely require some thinking. However, if you are okay with mathematical proofs and work consistently you should be okay after scaling.

Key Concepts

Big-O, Theta, Omega (Time and Space Complexity)

Sorting Algorithms

Basic Data Structures

Iteration and Recursion

Basic Graph Theory

Parallelism

 Hard Concepts

Proof of program correctness: Slightly different than mathematical proof, make sure to fully understand the conditions for a program to be correct. I only realized towards the end of the course, that this requires you to really read and understand the code fully.

Implementation in C++: Algorithms can look a lot less elegant in C++, so one needs to be familiar with common coding style in that language to interpret algorithms well.

Evaluating time complexity of given algorithm: Generally easy, but curve-balls can be thrown. Try breaking it down or stepping through the code.

Conclusion

Really important course for interviews, (along with 213). Felt like I improved a lot of reading code, and Dr. Hu was pretty entertaining.

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Course Review: CPSC 310

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Introduction to Software Engineering

“The only things that matter are lives and money.”

Text: (none)

Prof: Dr Elisa Baniassad, Dr Gail Murphy, Dr Marc Palyart

Elisa shares a lot of her experience, and how things work in the “real world”, which is helpful for an engineering class. She is also pretty approachable and sympathetic to any concerns that you might have. Dr Murphy created a lot of useful examples, and live-coded in class which was also a great way to learn. Dr Palyart followed a similar approach to Dr Murphy.

Difficulty

The on going “agile development” project during labs is the only thing that really matters. It is where most of your learning takes place, and you don’t get a lot of help for that, so its pretty tough. The classes look at various buzzwords, design patterns and software development processes and these are assessed in the exams. The in class material is not very hard to understand at all.

Key Concepts

Design of Web Applications

Implementation with TypeScript, JavaScript, Mongo etc

Software development processes

Testing

 Hard Concepts

 

Networking: If, you, like me, have never taken a networking course, a lot of how the internet etc is working will seem like magic.

Nodejs: Return of asynchronous programming. Common source of bugs.

Git: Took me a while to get comfortable uploading etc with git.

Self-learning: Sometimes, you just have to use google and your own ingenuity to come up with a band-aid solution to get stuff working when you understand less than you would like and don’t have time to learn more.

Conclusion

Project is great experience, working as a group and learning new skills. Really hard though! Classes are okay, not much you couldn’t read from a book.

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Course Review: CPSC 213

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Introduction to Computer Systems

“You’ll probably never code in assembly again. But the ability to understand complex computer systems made up of about 20 simply understood lines of code is something you should keep.”

Text: Computer Systems: A Programmer’s Perspective by Randal Bryant

Prof: Dr. Mike Feeley

Feeley is a really hard-working, knowledgeable, helpful and supportive prof. He built a complex simulator to help us understand how assembly works, and his web-page for displaying marks is awesome. It has detailed bar-graphs on how we are performing on key learning outcomes throughout the course. He is really patient during office hours and is really friendly after class. His classes attempt to give us the “big-picture” perspective, so we often have to figure out the details in the lab on our own. He also makes the lab problems quite challenging, to push us further. He does “redemptive grading”, so if you perform better on a learning goal later on in the course, your mark for that learning goal can go up to 80%.

Difficulty

The part of this course that took me the most time was the labs. Some of them were really hard, and we took ages trying to just understand the question because a lot of the concepts were just being introduced and were still new to us. The exam/quiz questions might require a little bit of thinking, because they often have little tricks to them, but are quite doable. Especially since it is clear what concept is being tested in each question, and because the practice material is similar to the real exams. On the midterm, the really challenging question was reading assembly and converting it to C. You only have about 10 minutes to interpret 20 lines of assembly, so I suggest getting a lot of practice for that before the midterm. Following the midterm, the class is less in depth and we blitz through a lot of big topics in computer systems at top speed. Since a lot of this stuff was new to me, it took me awhile to grasp the concepts. However, the way the concepts were assessed on the final was such that if you understood the example on the slides well, you could do quite well. The labs at the end of the course are intense though, so watch out!

Key Concepts

The basic hardware and software architecture of a computer running a single program

Compiling C-code into assembly (and Vice Versa)

Computer bugs at an assembly/hardware level

Event-based programming

 Hard Concepts

Reading assembly: Sounds easy, takes time. It might be worthwhile to draw pictures/keep track of variables while reading assembly.

Solving problems of asynchronous programming: Tested in the labs. Quite hard but really rewarding. Suggest testing ideas with TA before rushing to implement them.

Reference counting: A bit painstaking, it is important to understand when exactly something is losing and gaining a reference in a specific program.

Bitwise operations: Come in handy at random places in the course, so try to remember them

 

Conclusion

Hardest Comp Sci course so far. Probably matured the most as a student of computer science as a result of this class. Realized the limitations of abstractions.

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Course Review: BIOL 111

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Introduction to Modern Biology

“If there is one thing you get of this course, it should be bio-magnification. It’ll make you think twice before eating sushi!”

Text: Essential Biology with Physiology by Eric Simon and Jean Dickey

Prof: Dr Jennifer Klenz

Dr Klenz does her best to make a class full of students who do not particularly like biology, hate it slightly less. She posts a lot of interesting links on the course website, especially about climate change. However, a combination of misleading i-clickers, ill-designed group projects, badly printed exams and arbitrary marking schemes left a bad taste in my mouth on my completing this course. The lectures also lack depth, since this is an introductory class. However, since the scope of this class is so wide, you might find a few of the topics interest you, and Klenz is an engaged lecturer, though she does misunderstand students questions and get sidetracked sometimes.

Difficulty

Conceptually, this course is straightforward enough. If one doesn’t flop of the group projects, there is no reason not to do well. The exams are full of common sense questions, usually based of the slides. Practice exams are pretty similar to the actual exam. The biggest place to lose marks is if you misinterpret the question, don’t have enough detail in your explanation or fall victim to the arbitrary marking scheme. I would recommend having as much control over the quality of the work on the group project has possible, and checking with TA’s to see if one is understanding the criteria correctly, because the assignment specifications are vague, though they are marked strictly.

Key Concepts

Ecology

Genetics

Immunology

Cancer

 Hard Concepts

 

Mitosis and Meiosis: While not very complex, this was one of the few things one had to remember

Structure of genetic material: Another thing that need to be remembered

Conclusion

Enjoyed some links about global warming. Felt that my knowledge of any other biological topics lacked the depth to be of any use and group projects were awful. Frustrating class on the whole.

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