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Todo.txt
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Todo.txt
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To do list:
HIGH PRIORITY
- More material in Eigenvalues and Eigenvectors sections
- Add the row reduction algorithm for the sifting process in 2.3.5 (or 2.2 wherever it ends up)
- Add algorithm to determine basis in 2.3
- Move sifting one section forward to Linear Independence, so that students get hands-on experience with doing that before they need to grapple with the Steinitz Replacement Theorem.
- Add learning outcomes to the start of each section of exercises
- Break up solutions to multi-part questions into multiple <solution>s so that if a students wants to view one, they don't automatically open all?
- Solutions in Ch2Sec5
- Solution Ch2Sec1 last one.
- Solutions in Ch1Sec3 and Ch1Sec4 have some that ask to check that a set is a vector space. Not really keen on them...
- Add <warning>s for common mistakes:
- when students check whether a list of vectors spans {(x,y,z)| x+y-z=0}, they often just check whether the basis vectors satisfy the equation. Give an example where this argument fails with one vector in a 2-dimensional space.
- when writing down the matrix for a linear map it is easy to fall into the habit of just "writing down coefficients". One possibility is to define a map like T(x,y,z) = (x+y-z, 2x+y-2z, y-x-z), where the x and y in the last entry are deliberately switched. In this case, simply writing down coeffients from left to right doesn't work.
- when computing a basis, you need to make sure that the answer contains elements from the original set.
- Add <reading-question>s that probe understanding of proofs, e.g.:
- For Prop 2.2.8 where we use the set {i|c_i\ne 0}, ask questions like "If (c1,c2,c3)=(0,2,0), what is that set?" and "Give an example of a set where {i|c_i\ne 0} = 1."
- In 3.3 add example(s) and exercises of how to compute inverse of a linear map.
- Think about the ordering of exercises in each section.
- In 3.4, split off a bit on Linear Operators and Change of Basis? and add examples of changing basis.
- Examples of linear maps that connect to Advanced Calculus
- Linear approximation of 2-var function
- Partial derivatives and directional derivatives
- The Total Derivative?
- In the proof of Rank-Nullity Theorem, the phrases (D spans Im(T) and D linearly independent are confusing because they might seem like truths and not "need to be proved")
MEDIUM PRIORITY
- In 2.1, the last theorem is abstract. Add an example or reading-exercise with a small case (m=2, n=3)
- Can the first two lemmas in 1.5 be written using more words? And many others...
- Decide whether to move Steinitz Exchange Lemma to section on bases where it can be explained that its relevance is to show that two bases have the same size.
- Reconsider the use of the homemade symbol \bopen \bclose. I prefer normal parentheses (). Then the convention in Ch2Sec4 line 165 needs reconsidering too.
- longer paragraphs, especially in introductions (sections can also have <conclusion>s and <references> to other reading and/or Youtube Videos).
- overspecified or underspecified problems
- more problems (e.g. <fillin characters="10" /> for fill in questions, like terminology)
- Sometimes go back and show how new "technology" can help you better understand previous problems.
PUBLISHER ISSUES:
- Do we want to use the Stellenbosch University Brand Colors? If so, here they are
- brand-maroon: #60223b, RGB(140, 151, 154)
- brand-gray: #8c979a, RGB(96,34,59)
- brand-gold: #967140, RGB(150,113,64) [#F0AC2F for something lighter]
- off-white: #E9EAEC
- Write Python script to change link to Mathjax to the local one on SunLearn and the links to the pretext css files to local versions. Make sure they are available locally, and build in a test for updates. Make sure to test it! Robert Beezer discourages this in the guides. But maybe this can be done in the latex xsl file!
- Decide whether to un-knowl Examples, but to break them up into <statement> and <solution> so that the page isn't too large upon loading.
LOW PRIORITY OR UNNECESSARY
- First person to first person plural? (I to we)
- Create index? And index of notation?
- Ch2Sec4 (in a few places actually) I commented out video on line 7. One issue with a link to a video on SunLearn is that the link will break from year to year.
- Make sure all <proofs> are inside the <theorem> (etc.) tags and not outside (?)
Ideas for problems and examples:
- Claim: Let T:V to W. Show: If T(v1) and T(v2) are linearly independent, show that v1 and v2 are - already in !
- Application: Show that sin x and cos x are lin. ind. by using the linear map T:Func to R^2 defined by T(f) = (f(0),f(pi/2)).
- Rank-Nullity Theorem to show the rank theorem from 144: #free + #non-0 rows = #columns
Use??
- <objective>?
- <reading-questions>?
- <project> or <activity> or <exploration> or <investigation>
<introduction />
<task />
<conclusion />
- <worksheet>
<objective />
<introduction />
<theorem />
<figure />
<sidebyside>
<exercise width="50%" />
</sidebyside>
List of PreTeXt environments that can go inside a section:
"theorem", "proposition", "lemma", "corollary", "claim", "conjecture", "fact", "question", "proof",
"definition", "assumption", "axiom", "hypothesis", "principle",
"remark", "convention", "insight", "warning", "aside", "biographical", "historical", "observation", "note", "blockquote",
"activity", "exploration", "investigation", "project", "problem",
"assemblage"
"commentary"
"algorithm", "computation", "demonstration", "fragment", "heuristic", "identity", "technology",