A Study of Linear Algebra:
Content Advisor: Dr. Prudhom
Guiding Questions of the Course:
- What is linear algebra?
- Learning strategies for how to struggle on my own with problems, and learn from a “college” textbook?
- What does it look like for two people to struggle and work through problems together as mathematicians?
- What are applications of linear algebra?
Preliminary List of Resources:
Main Course Text: Otto Brescher’s Linear Algebra *previously used in other independent studies with Dr. Prudhom
Helpful resources:
- Linear Algebra, (Khan Academy): https://www.khanacademy.org/math/linear-algebra
- Linear Algebra Full Course for Beginners to Experts, (Geek’s Lessons):
- Linear Algebra-Full College Course, (FreeCodeCamp.org):
Monthly Plan and Assessment: 5 Units
| December | Chapter 1; Linear Equations+ Weekly video posts + posted updates on notes and questions |
| January | Chapter 2: Linear Transformations + Weekly video posts + posted updates on notes and questions |
| February | Chapter 3: Subspaces of R^n and Their Dimensions+ Weekly video posts + posted updates on notes and questions |
| March | Chapter 6: Determinants + Weekly video posts + posted updates on notes and questions |
| April | Chapter 7: Eigenvalues and Eigenvectors + Weekly video posts + posted updates on notes and questions |
| May | Time built in for if some of these assignments or chapters require more time than expected *if time is permitting explore other chapters |
| Final Assessment: | Dr. Prudhom will potentially assign a final problem set as an exam, and he will evaluate the overall learning, engagement, and understanding noted from the rest of the course, as well as the posts that I made and how I used the blog. |
How much time per week:
The amount spent on a normal class period:
- minimum: 5 hours a week like a traditional class: combination: free period (E), outside of school and weekend homework time
- meeting time: Lunches on Day three
Major Commitments:
- Congressional Debate: Once to twice a week practice
- Winter Musical: the number of days a week changes based on the week (not a lead role)
Full Schedule:
- Advanced Latin Lit
- Intermediate Mid French
- AP Seminar
- Western Lit
- Physics M
- Honors Precalculus
- Free period
Description and Reasoning:
This independent study is important to me for several reasons. Firstly, my previous Algebra two math course at my old school covered a lot of Honors Precalculus material at the discretion of the teacher, but not quite enough to allow me to advance to AP calculus. I would really appreciate a way to challenge myself in math this year. My other classes are feeling quite light on homework, and I am ahead in several classes, giving me time to explore this opportunity. Linear algebra appealed to me specifically because I am very analytical, and I want to learn more about some more theoretical, analytical concepts. My homework load is feeling very light this year, and this is a way to challenge myself.
I respond to self guided learning, and often enjoy struggling through extra material on my own, and grappling with concepts. That is one of the reasons why teaching myself out of a college text appeals to me: I can hone my ability for self-guided learning.
I met with Dr. Prudhom several times and we created this month-by-month plan based on his experience teaching the class, and realistic expectations of a good minimum to commit to. We are following a plan based on suggestions that the textbook gave, combined with the topics that Dr. Prudhom and I think would most appeal to what I want to get out of the course. I am, of course, open to any suggestions surrounding the curriculum, as my whole goal is simply to learn and grow in this area.