Monthly Archives: December 2015

Course Review: BIOL 111

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.


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





 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


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.

Course Review: MATH 226

Advanced Calculus I

“The point of calculus is to understand how and when we can approximate non-linear transformations with linear ones.”

Text: Calculus: Several Variables by Robert Adams

Prof: Dr Julia Gordon

Dr Gordon is a really kind and gentle prof. Her classes focused on explaining the intuitive motivations for various theorems or algorithms. The classes did seem to get bogged down with administrative concerns. Since this was the first time she taught the course, she made a lot small errors, but not more than your average prof. However, she did get rather thrown-off by her errors and this, along with administrative concerns, probably slowed the class to the extent that we had to rush a bit towards the end of term. While her midterms were similar in difficulty to practice midterms, her homework was a great deal easier then what we have come to expect in honours. She generally explained the intuition behind theorems, but omitted proofs because she felt that the definitions we were using were not efficient/well-suited for proving those theorems. She is very helpful during office hours, but I don’t think she approves of too much hand-holding in an honours class, even though she will help you a lot if you ask for it. I also get the sense that her life is very busy!

Some quips:

“Please don’t cheat. In Russia, they never took it very seriously, but for some reason they take it very seriously here.”

“I sense some unrest in the class…”

“I haven’t taught you improper integrals, but you can extrapolate from you understanding of proper integrals.”

“Does everyone believe that this is an honest approximation to the function? Good”

“WAIT!! WAIT!! Before you pack up, let me deliver the punchline!”

“At some point in your mathematical career, you will have to solve a 100 difficult integrals. Here they are.”

“The Fundamental Theorem of Calculus is : ‘Never differentiate in public’. I am now going to ignore that rule.”


I have found this course the easiest honours Math course I have taken at UBC. However, people who are new to honours Math were slightly overwhelmed by a combination of n-dimensional space, epsilon-delta and the scarcity of example-based learning, all of which were prevalent in first year honours calculus. The workload was very manageable, with Webwork and a short written assignment due in two weeks. Scaling was generous, because people did poorly on the midterms. This was partly because of the people that were new to honours Math but also because the homework did not challenge us to demonstrate deep understanding of all the necessary concepts, which comes in handy on honours Math midterms, where conceptual understanding often trumps computation.

Key Concepts

N-dimensional intervals/balls (topology), limits (epsilon-delta), differentiability and continuity

Partial derivative of N-dimensional curve

N-dimensional derivative (Gradient and Jacobian Matrix)

Integration over N-dimensional space

N-dimensional optimization (Lagrange)

 Hard Concepts


Implicit Function Theorem: Found explanation in book confusing. Found it easier to think in terms of Jacobian Matrix.

Lagrange: Computationally difficult, have to solve non-linear system of equations.

Topology: Found it difficult to do proofs under time pressure.

Change of variables using Jacobian: Make sure not to get confused between image and source.

Geometry: Have fun visualizing N-dimensional intersections of various curves 🙂


Good class. It was nice to understand calculus from a linear transformation perspective. Felt that my understanding of key theorems of the class is still sketchy though, and that the end of the class was rushed.

Course Review: MATH 223

Linear Algebra

“This is really useful. You might get a call one day from Downtown, asking you how to take the inverse of a two-by-two matrix.”

Text: Linear Algebra and its Applications by David C. Lay (optional)

Prof: Dr Richard Anstee

Professor Anstee looks kinda like a classic Prof. Fuzzy white hair, check. Kindly yet contemplative expression, check. He is also a natural teacher, having a cavalier attitude yet still able to get the material across. He says the most whimsical things in the middle of lecture, making his classes really entertaining. He spent the first week teaching many of the major concepts intuitively for two-by-two matrices. The following weeks till the second midterm were both applying and more rigorously fleshing out the ideas discussed in the first week, so don’t get psyched by the first week if the material is really new for you. Anstee tends to switch perspectives a lot during lectures, without explicitly informing you. I have a feeling he does this on purpose, to keep us on our toes, because viewing things from multiple perspectives is a core  feature of Linear Algebra. He is also a really kind Prof, holding many-many office hours and always willing to chat to his students. He also brought home-made cookies on the last class :D.

Some quips:

“You never know who you will meet on the bus!”


Since I had learnt this material before, I am not a fair judge. However, for people who have either never taken an honours math class or have no familiarity with matrices this course is probably both challenging and do-able. More then any other course I have taken so far, conceptual understanding is key. In calculus you can memorize a ton of algorithms and you can go pretty far. In linear, the questions are deceptively simple if you can make the connection to theory. On exams, some ten mark questions were literally two or so lines. He also gives you practice exams where the first few questions (these are often the ones that test computation) are exactly the same as the one on the real exam, except with different numbers, so there is really no excuse for losing many marks on the first 40%. Some of the homework questions are significantly more challenging then exam questions, but they are do-able, and he gives you lots of help if you ask him. Conceptually, since linear algebra is about multiple perspectives, to do very well in this course, I would suggest consulting a variety of sources. In terms of marks, after generous scaling, I think that one can get a decent grade in this course, though those who are new to honours math might have to work extra hard.

Key Concepts

Representing linear transformations as matrices

N-dimensional Vector Spaces (generalization of R^n)

Properties of matrices/transformations (characteristic, determinant, trace, rank, eigenvalues)

Types of matrices/transformations (diagonal, diagonalizable, invertible, orthogonal, hermitian)

 Hard Concepts

Change of basis: Got really confused by this. What I realized was, depending on the context, one can interpret a matrix as a change-of-basis, or as a linear transformation on a given basis. Another thing to keep in mind is that a change-of-basis matrix has column vectors that form a basis of the domain in the co-ordinates of the image.

Complex conjugate: Didn’t go to deep into complex numbers, but got confused about which theorems apply in the complex/real case respectively.

Entry-wise manipulation of arbitrary matrices: Had difficulty visualizing the a_ij element in a matrix.


Fun, intelligent class. Favourite class this term.