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Narrative Review of Core Concepts

Exam prep instead of an exam

The famous mathematician George Polya once said "Mathematics is not a spectator sport". By that he meant, you learn math by doing rather than just by reading or listening. One type of doing is solving problems, which is often given the highest priority in math education. However, an equally important companion in doing math is high-quality note-taking.

Even within note-taking, the most common kind is what occurs in the classroom: short notes to copy down what occurs in class, with the aim of substituting for perfect memory. But the better kind is narrative note-taking in which you build an entire narrative, a story, about the material you are studying. By telling yourself the full story, in a kind of dear-diary format, you have the best shot at "bringing it all together" and retaining for the long-term.

So ... what you will do is build a narrative of the key concepts in linear algebra that you will submit electronically. Think of this as review notes that teach yourself now (a review) and later in life (recalling the most important concepts).

What to write:

Write neat notes with your own explanations.
Include original examples that you have constructed.
For any theoretical result, explain what the theorem or proposition is saying, with an example to clarify if appropriate. Do not include the proof.
For any definition, explain the definition with your own original example.
For any "useful fact", explain in your own words and devise your own example.

Which modules and sections to write about:

Module 3: 3.5, 3.6, 3.8
Module 4: 4.2, 4.3, 4.4, 4.8, 4.10, 4.11, 4.12
Module 5: 5.2, 5.5, Prop 5.2, Prop 5.5.
Module 6: definitions of linear independence, span, subspace, basis, dimension, rowspace, colspace. Theorem 6.6, Section 6.6
Module 7: 7.0, 7.2, 7.3, 7.6, 7.7.
Module 8: the meaning of the statements in each of Theorems 8.1, 8.2, 8.3. Not the proofs, just what the theorems state.
Module 9: 9.3, 9.5, 9.6
Module 11: 11.0, 11.1
Module 12: 12.0, 12.2, 12.3
Module 13: 13.0, 13.2, 13.4, 13.7

Think of each term (e.g., basis), each theorem (e.g., Theorem 6.6), and each section (e.g., 12.2) as a unit in your review. At least half the units should have your own examples, thus, approximately 20 examples.

What to submit:

A single PDF called NarrativeReview.pdf. This can be typeset or scanned-in handwritten notes from your notebook. Use 11pt approximately with 1.5-line spacing as a guideline.
Use the module number and section numbers from above as headings and subheadings.
Important: The PDF should not have anything that would identify you. Thus, do not include your name or any other identifying information anywhere, especially the PDF properties. We will of course identify your submission from Blackboard.
For any definition, theorem, proposition, useful fact: write the full text of the statement before explaining.
Use a heading to indicate where your own text and examples start and end.
Draw a horizontal line across the page after each unit (a definition, a theorem, or a section).
Assuming about a half-page per section above, you'd probably need 20-25 pages in all beyond the cover page, the typical size of a substantive term paper.

Scoring:

Each submission will receive five anonymous evaluations, two from the instructional team and three from other students in the class.
You will evaluate the submissions of three others.
How to evaluate someone else's submission:
- Count and report the number of units submitted.
- Count and report the number of units that include original examples.
- Evaluate for each unit whether the topic and numbering is correct. That is, if a unit claims to describe section 7.3 from Module 7, it really should be about that section.
- Pick 8 random units to review, ensuring at least 4 have examples.
- For each unit you've selected, use a 1-5 scale of rating in these categories (1=poor, 5=excellent):
  - Evaluate the unit for clarity and correctness.
  - If the unit has an example, evaluate whether the example is correct and well crafted.
  - Rate the quality of explanation.
  - Perform a websearch to ensure that the writing (and example, if applicable) is original.
  - Overall rating: the sum of the above four ratings.
  - Overall comments by way of feedback and suggestions.
For each of the three submissions you've been assigned, fill in this evaluation form (Word doc), convert to PDF and submit a PDF of the Evaluation form. Thus, you will be submitting three such forms.

Timeline:

By 12 noon on Wednesday May 6: submit your narrative review.
Important: Because others have a deadline to evaluate your review, we cannot allow late submissions.
You will receive other PDFs to review that afternoon.
By 12 noon on Friday May 8: submit your three evaluation forms.