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Preview
Preview
Another example of a real-world phenomenon with a hidden vector space structure is color. We’ll discuss the details in this lesson, with a special focus on how we can break down colors into primary colors and what the analogue of that process is for a general vector space. This will lead us to the concepts of basis and dimension of a vector space, two of the fundamental notions that will underpin the rest of the work we will do in the course.
In Module I we’ll discuss the general definitions of basis, dimension, and related concepts and also work through examples of these concepts.
In Module II we’ll explore the notions of basis and dimension in the context of ODEs, where we’ll discover that we’ve been working with these concepts since Lesson 1 without knowing it!
Review
Review
Learn
Learn
Work through the lesson notes below, consulting the videos below it when you get to the "See Class Notes" boxes. For your records, the annotated lesson notes are below the videos. Some tips for you as you work through these resources:
I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.
Lesson Notes
Lesson Notes
Lesson 11.pdfClass Notes A
Class Notes A
Class Notes B
Class Notes B
Class Notes C
Class Notes C
Class Notes D
Class Notes D
Class Notes E
Class Notes E
Reflect
Reflect
If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:
Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.
Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.
If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:
Please summarize the main mathematical takeaways from the lesson notes.
What was the most interesting part of what you learned, and why?
What, if anything, do you still find confusing?
Practice
Practice
Work through the practice problems suggested below to see how much of this lesson you've understood.
Lesson 11 - Practice Problems.pdfPage updated
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