Thursday 1 September 2011

MATH 223 - Course Review


MATH 223 Linear Algebra

Matrices, eigenvectors, diagonalization, orthogonality, linear systems, applications. Intended for Honours students.
Credits: 3.  Pre-reqs: Either (a) MATH 121 or (b) a score of 68% or higher in one of MATH 101MATH 103MATH 105SCIE 001


My first task on the Wednesday which marked the start of my classes was to locate the small and aged mathematics building on campus under a blanket of rainy weather.  This is nothing new to a seasoned UBC student, but I was heading to my very first class.

This is my personal addition to the reams that have been said regarding the intimidation of approaching University classes for the first time.  I had a sneaking suspicion that MATH 223 was not going to be easy, and I was not sure I had even close to enough background to handle it.

I'll get some details out of the way.  I attended University Hill Secondary School from 2004 to 2009, a school known by many as one of the consistently highest academically rated public schools in the lower mainland.  My study focus was primarily in the sciences.

I took an accelerated science course in 8th grade, which covered 9th grade material as well, and took Science 10 in my 9th grade.  I then took our school's AP version of Chemistry, Physics, and Biology courses, as well as Math 12 in the following years, and AP Calculus BC at Kerrisdale academy.  I received 4's and 5's on AP exams in Chemistry, Physics B and C (mechanics), Biology, and Calculus BC.  In my 12th grade, I shifted my focus slightly and took many humanities courses.

Long story short, I entered UBC with transfer credit for MATH 100, 101; CHEM 121; PHYS 100, 107, 3 additional credits; BIOL 121, 140, 7 additional credits.  

I had no idea how MATH 223 would pan out, considering I had not taken any University courses in mathematics.  The day before the first class, I read through some basic matrix algebra concepts including matrix addition, subtraction, multiplication, and determinants.  As a result, the first class was relatively comfortable, touching on these concepts and using them to determine the properties of inverse matrices.

Professor Anstee was extremely welcoming and friendly, displaying expertise, wit, and warmness.  I was surprised that he gave us his home phone number rather than his office number.  My impression was that he was quite dedicated to his role as a teacher and cared about his students' learning.

He said something on the first class which both unnerved and excited me.  He looked through the class list, checking on the specialities of the students.  There were students from mathematics, physics, and computer science, all expected.  He appeared slightly confused, however, at the number of students from other fields, and advised that most of us were likely in the wrong course. I smiled, driven by the same academically masochistic drive that led me to take AP courses in high school.

But MATH 223 was like no course I had thus far experienced.  The proofs started at the second class.  I realized quickly that this would be a course in which I desperately copy down chalk markings during lectures in hopes that I might have time later on to actually understand them.

Weekly assignments were difficult.  I cannot put it any way but frankly.  The majority of questions were proofs, which took anywhere between 10 minutes and one hour each.  Assignments were made up of anywhere between 8 and 12 questions, some with multiple parts.  I would often get stuck on questions for long stretches of time.  I would take breaks, ask friends for their thoughts, and come back to the questions after some time, burning up pages and pages of blank paper scribbling every approach I could come up with.

Exams were similarly difficult, but definitely fair.  Professor Anstee was careful to give us exams which were hard to ace, but easy to pass.  60% of every exam would be based on basic algorithmic concepts, and usually required little cleverness (gaussian elimination, the determinant, inverse matrices, Gram-Schmidt process etc.).  The remaining 40% would usually be made up of four 10% questions of increasing difficulty.  These would usually be based on smaller concepts derived in proofs in class, and some were proofs themselves.  Often only 1 or 2 students in the class would get any points at all on the final question of the exam.

My conclusion, the hardest part of this course was the homework.  I spent from 5-10 hours on homework weekly for this course alone (why this course is worth only 3 credits, I have no clue).  Exams were not easy, but doable, and if I had studied more, I imagine I could actually have done well.  Unless you're very confident in your abilities, don't expect to get over 90% in this class, but I think with solid effort devoted to studying for exams, the 80's are attainable.

One last point up for debate is whether this course is better as a base in linear algebra than 221.  After the fact, I barely remembered any but the most key concepts in this course.  I feel that material raced by so rapidly that I had no time to grasp much of the conceptual framework with confidence.  However, where this course was useful was that it challenged me to think at a level of mathematical abstraction that I had never even knew I could.  The homework beat into me a new-found confidence for approaching problems of a mathematical nature, and this, I feel, has helped me immensely in subsequent courses.

5 comments:

  1. Hey Eric,
    Nice blog you have!
    If you're wondering who I am, I'm Carolyn from the physics review session. Remember circular glasses? I found your blog when I googled "ubc physics minor." I'm honoured to be the first comment haha.
    I will be going into CS so I will be needing 223 as well. It sounds extremely challenging, satisfying, and I'll be honest, quite intimidating. Are there TAs to bug for help?
    I'm quite amazed that you are both in Honours Physiology and you're minoring in Physics. You mentioned in your earlier blog posts something about study habits. I'm really (like really really) interested in hearing about that. We all have the same amount of time, but you seem to be especially good at efficiently capturing information, kind of like how you helped us review based on the objectives, synthesizing the concepts instead of going at it one question type but one question type.

    I know you are probably busy with finals right now, but once you've wrapped up, it'd be awesome to hear back from you.

    Btw, do you know Junghoo? He hangs out at Trans a lot. He said he was from Uhill too... should have been in your year?

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    1. Hey Carolyn. Thanks for your kind words. I was a little surprised someone found my blog (and through Google no less). I believe I'm procrastinating at the moment, so I'll answer now :).

      Math 223: Yes, very challenging and satisfying. Like I think I mentioned, the result is I actually have trouble remembering much from it, but it helped my problem solving skills in general. The instructor doesn't take much time to cover things conceptually, and you kind of need to figure that out for yourself from the proofs. There are no TAs (only one for marking), but depending on your instructor, you may be able to take good advantage of office hours. Dr. Anstee was particularly good about that, and he gave helpful hints on HW.

      Study habits: This comes largely from work with Science Peer Academic Coaches (SPAC), which I'm a part of. Their website is http://my.science.ubc.ca/spac. It's a peers helping peers resource for developing study skills. For short-term reading, I'd recommend the tips and tricks page which is a blog that all the members of SPAC contribute to. Feel free to email me if you want to hear more about this :).

      Junghoo: Yes, we went to U-Hill together. He was very keen and skipped a grade, so he graduated with me. I suppose, in that sense, he embodies the Transition spirit. I know his social circle became close knit with that of the Trans grads in first year, and I suppose that's carried on.

      Good to hear from you, and I'm glad you found the physics review session well organized and helpful. I hope your exam went well today!

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    2. Yay, exams are done! Ok got it, I'll remember that.
      I just read your article on studying for math/physics, and I'll try to apply what you said. I find office hours are only good for some profs though. Other profs aren't very helpful. (you might wanna check the end, I think part of the article got cut off). I also checked out your "preparing for exams" article. Neat stuff.
      One thing that screwed me over these past two semesters is that we would finish learning the material the last week of class, and I would be about one week behind, and the final would be like the next week, leaving me a week or a week and a half to study for two weeks of material PLUS an entire course overview, times five.
      You said be done content overview by the time class finished. So when exactly would be the right time to start? How many hours a day, what kinds of things do you do when reviewing, (math esp), and most importantly, how do you deal with the "new stuff" as it hasn't been taught before...
      I definitely hate finals stress...

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    3. Congrats on finishing exams and surviving first year :D.
      Yes, that kind of scheduling really derails studying. Personally, I couldn't get started on reviewing until the end of classes because I had 4 papers due in the last two weeks. It can be very difficult to know when best to start studying, balancing finals studying with ongoing coursework.

      If you're interested, I'm open to discussing all this in more detail by email over the summer (ezhao15@gmail.com). I hope your grades turn out well :).

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    4. Sure, I'll add you on gchat! Watch out for a supreme overlord heh... Not a spam account.

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