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 101, MATH 103, MATH 105, SCIE 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.