LINEAR ALGEBRA

“When in Doubt, think of the curve that has saved hundreds before you.”

- Anyone who has ever taken apsc 174

In Linear Algebra, you'll explore the basics of vectors and matrices. You'll start by learning what vectors are and how to work with them, then move on to matrices and their transformations. The class will cover systems of linear equations, vector spaces, and the concepts of eigenvalues and eigenvectors. These topics are essential for understanding many real-world applications, from computer graphics to engineering (and I promise you… there ARE real world applications). It's a great way to expand your math skills and see how these concepts are used in various fields.

OVERVIEW

The evaluations were done purely through midterms and exams, so there weren’t any assignments or WebWorks you could get extra points on. The mark distribution was 20% for each of the two midterms, and 60% for the final exam.

Midterms

  • Each midterm was approximately 5-6 questions, using a 100 points marking system (so each question was worth approx. 20 points).

  • Grading was very strict for the first midterm, and we estimate the average was below 50% (this is just a guess and not known exactly).

  • “Curving” is case by case. Typically, if a class does get curved, it will not be until the end of the semester, if at all.

Final Exam

  • The final exam was 8 questions, also using a 100 points marking system. Although there were questions from the first half of the semester, there was a heavier emphasis on eigenvalues, diagonalization, and other topics learned near the end of the semester.

  • We never got any information on our final exam grades. This was also the case for Sci 26.

Evaluations

What I would HAVE DONE DIFFERENTLY

  • Don’t just keep up, stay AHEAD. Make sure you’re going into the class already having an idea of what you’re about to learn. Keep in mind that linear algebra is a very abstract topic to teach, and it takes a lot more time for your brain to understand the concepts.

  • Do harder practice problems. Instead of spending endless time on the easier practice problems, try and spend 70% of your practice time on the harder problems, as these are the ones most likely to appear on the exam.

  • If you don’t know an answer on an exam, write something. Try not to leave an answer blank, because if the exam goes badly for everyone (like last year), they’ll be more generous with the points.

  • Ask my TA for more help AND attend the EngLinks help sessions. I find students are sometimes better at explaining complicated topics because their level of understanding is more similar to yours.

PRE-CLASS CONCEPT REVIEW

Make sure to come prepared to class with a general understanding of the concepts that will be discussed. We’ve created this concept review for helping with just that. PLEASE NOTE: this guide is NOT enough to make you pass. If you use this guide as your only resource, you will maybe finish with a 5%. This is only for helping you understand the general concepts that serve as the basis for much more complex practice problems.

ONLINE RESOURCES

ONLINE RESOURCES

If you’re cramming for a midterm or you’re just curious to learn more about the BEAUTIFUL world of linear algebra, I’ve curated a list of some of the best videos online to help you out.

Struggling to understand the visual behind the concepts you’re learning in class? This channel is definitely for you. 3Brown1Blue always nails visuals and simplification of complex topics. Their ENTIRE “Essence of Linear Algebra” playlist is a must-watch if you’re looking to save yourself from hours of struggle. We’ve attached the first video in their playlist:

3BROWN1BLUE

The Organic Chemistry Tutor

The Organic Chemistry Tutor channel has great videos specifically about matrices. They’re perfect for explaining what matrices are, how to utilize proper multiplication techniques, and how they’re applicable to linear transformations. Check out the videos I think will help you out:

THE EXAM

Most Engineering students will tell you second semester exam season was one of the hardest times of first year. With multiple final projects and exams to study for, you’ll struggle to find the time to cover all the content before exam day. Here’s how we recommend you approach exam season. This may seem a bit excessive… but the last month of classes is chaotic, and APSC 174 typically has one of the harder exams:

Complete one practice problem every night before bed (in addition to your linear algebra homework. Even if you can’t figure out the problem, try your best to solve it as close to how you would on an exam. After each problem, take note of what your biggest mistake was. Try and limit these problems to 15 minutes.

4 WEEKS BEFORE THE EXAM

3 WEEKS BEFORE THE EXAM

Review second half of the semester’s content. You’ll likely have midterm 2 around this time, so you can combine your midterm studying with your exam studying. You should also be watching all of the second semester’s worth content on 3Brown1Blue’s YouTube playlist (linked above).

2 WEEKS BEFORE THE EXAM

Complete first practice exam WITHOUT checking the solutions partway through. Use the solutions at the end to give yourself a grade. Identify the 3 main topics you struggled with the most and focus on those. Keep repeating this process. This is also the time to visit professors/TAs with questions about the exam content/format.

1 week BEFORE THE EXAM

Identify your final struggles and work on those the most (approx 65% of your effort should be towards your area of struggle, while the rest should go towards perfecting your other topics).

Although this class may have you crying on the floor some days, I PROMISE you it’s possible. This Linear Algebra Survival Guide, created by Seth Grief-Albert (Apple Math), is such a great resource for concept review and understanding how to write a good proof. In comparison to the pre-class concept review, the survival guide is more problem-oriented and will help you with practice and homework problems.

SURVIVAL GUIDE