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How to Discuss Exercises

edited May 2018

Frederik Eisele has done something great: he's started lots of discussions where you can do the exercises in Chapter 1! Not all of them, but lots. Andrew Ardill then created blanks where you can add more.

If you want to see the answer to an exercise, or start a discussion of an exercise, please check the Azimuth Wiki first! Go to this wiki page:

Use this page to avoid creating duplicates. And if you create a brand new one, please note it on that wiki page, so we can find it! Just go down to the bottom of the bottom of the page and click "Edit". You can probably figure out what to do next. But if you have questions, please let me know here!

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1.
edited April 2018

I have added the remaining discussions for chapter 1.

I have started adding discussions for chapter 2. I did not include them in the main wiki page as that page is getting a bit unwieldy to edit.

Also I put in a link to a page the links to the discussions on the puzzles. I did not see a need to add new discussions for the puzzles as the place where the puzzles are created seems like a reasonable discussion already.

You may notice that I have taken slight liberties with the exercise descriptions, including referenced objects so that you should not need to look them up in the book.

Comment Source:I have added the remaining discussions for chapter 1. I have started adding discussions for chapter 2. I did not include them in the main wiki page as that page is getting a bit unwieldy to edit. Also I put in a link to a page the links to the discussions on the puzzles. I did not see a need to add new discussions for the puzzles as the place where the puzzles are created seems like a reasonable discussion already. You may notice that I have taken slight liberties with the exercise descriptions, including referenced objects so that you should not need to look them up in the book. 
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2.

Frederick: thanks! As the main wiki page continues to expand we can start moving stuff out of there and putting it on other wiki pages, with links. For example we may someday have a wiki page "Chapter 1" or "Sketch 1" containing links to all discussions relevant to that. Luckily it's easy to do this in a step-by-step way as the need arises, while keeping some eye to consistency.

I'm saying "Chapter", e.g. in my lecture titles, while you're saying "Sketch". We may someday need to fight a duel to the death over that. Your convention is more cute but I'd need to rename a bunch of things to adhere to it.

Comment Source:Frederick: thanks! As the main wiki page continues to expand we can start moving stuff out of there and putting it on other wiki pages, with links. For example we may someday have a wiki page "Chapter 1" or "Sketch 1" containing links to all discussions relevant to that. Luckily it's easy to do this in a step-by-step way as the need arises, while keeping some eye to consistency. I'm saying "Chapter", e.g. in my lecture titles, while you're saying "Sketch". We may someday need to fight a duel to the death over that. Your convention is more cute but I'd need to rename a bunch of things to adhere to it.
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3.

I started calling them "Sketch" as that was what DSpivak called them. I have been changing them all to "Chapter" as I revisit things.

Comment Source:I started calling them "Sketch" as that was what DSpivak called them. I have been changing them all to "Chapter" as I revisit things.
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4.
edited April 2018

The Exercises mention Definitions and Equations often. Should we have a wiki page for them to be listed? That way the Exercises can provide a link to them much as in the textbook.

Comment Source:The Exercises mention Definitions and Equations often. Should we have a wiki page for them to be listed? That way the Exercises can provide a link to them much as in the textbook.
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5.

Fredrick - that seems like a lot of work, so it's really a question of whether you want to do it... not just today, but for the whole book. (Maybe someone else will help out, but I find it's best if I don't start projects that require someone else to help out.)

Comment Source:Fredrick - that seems like a lot of work, so it's really a question of whether you want to do it... not just today, but for the whole book. (Maybe someone else will help out, but I find it's best if I don't start projects that _require_ someone else to help out.)
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6.

John, I have been putting the Definitions in the first Exercise description where it is mentioned. In subsequent Exercises I have been placing links.

Comment Source:John, I have been putting the Definitions in the first Exercise description where it is mentioned. In subsequent Exercises I have been placing links.
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7.

Nice! Thanks, that's great!

Comment Source:Nice! Thanks, that's great!
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8.

The numbering for exercises has changed in recent drafts, making it a bit harder to figure out which thread goes with which exercise. I'm not sure what would be a good solution other than going back through all of the threads and renaming them -- but if more drafts are forthcoming, that's a lot of work that will have to happen frequently. I'm not sure what a good option is here.

Comment Source:The numbering for exercises has changed in recent drafts, making it a bit harder to figure out which thread goes with which exercise. I'm not sure what would be a good solution other than going back through all of the threads and renaming them -- but if more drafts are forthcoming, that's a lot of work that will have to happen frequently. I'm not sure what a good option is here.
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9.

Jonathan, I prepared a list of needed changes, then saw your "recent drafts" comment - has there been a draft since the April 20 version which changed the "poset" terminology? (Apologies for being clueless, went away for awhile:-)

Comment Source:Jonathan, I prepared a list of needed changes, then saw your "recent draft**s**" comment - has there been a draft **since** the April 20 version which changed the "poset" terminology? (Apologies for being clueless, went away for awhile:-)
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10.

Hah, sorry -- I was hedging my bets there, since I wasn't sure if the changes had occurred only as of the draft I was working from. The latest draft I am aware of is at http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf, which is still the April 20th version.

Comment Source:Hah, sorry -- I was hedging my bets there, since I wasn't sure if the changes had occurred only as of the draft I was working from. The latest draft I am aware of is at [http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf), which is still the April 20th version.
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11.
edited May 2018

Thanks Jonathan. OK here's a prioritized list (hopefully not all to be done by John:-).

1) Update above hotlink labels (the text, not the URLs) as follows

a) 30-59: add 2 (so e.g. "Exercise 30 - ...) becomes "Exercise 32 - ...)

b) 65 & 72-97: add 5

c) 67: change to 66


2) Add hotlinks pointing to Ex. 65 (discussion exists, correctly titled), 9 (no existing discussion), & 76 (ditto)

3) Update existing discussion titles to match labels updated in step 1)

a) except 32-37, 41-50, 54-56, 61, 70 which are correct now


4) Content of the following exercises seems off from that in revised text: 4, 28, 41, 50, 66, 77, 87, 92

a) most deltas are just xref numbering & poset terminology

b) a couple may require judgement (as the Comments may become confusing)

Comment Source:Thanks Jonathan. OK here's a prioritized list (hopefully not all to be done by John:-). 1) Update above hotlink labels (the text, not the URLs) as follows a) 30-59: add 2 (so e.g. "Exercise 30 - ...) becomes "Exercise 32 - ...) b) 65 & 72-97: add 5 c) 67: change to 66 2) Add hotlinks pointing to Ex. 65 (discussion exists, correctly titled), 9 (no existing discussion), & 76 (ditto) 3) Update existing discussion titles to match labels updated in step 1) a) except 32-37, 41-50, 54-56, 61, 70 which are correct now 4) *Content* of the following exercises seems off from that in revised text: 4, 28, 41, 50, 66, 77, 87, 92 a) most deltas are just xref numbering & poset terminology b) a couple may require judgement (as the Comments may become confusing)
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12.

Jerry, I'm willing to do some of this, but I'm a bit confused: I don't actually see how to edit the page. I see John's comment at the top ("Just go down to the bottom of the bottom of the page and click "Edit". You can probably figure out what to do next. But if you have questions, please let me know here."), but I don't see any Edit buton.

Comment Source:Jerry, I'm willing to do some of this, but I'm a bit confused: I don't actually see how to edit the page. I see John's comment at the top ("Just go down to the bottom of the bottom of the page and click "Edit". You can probably figure out what to do next. But if you have questions, please let me know here."), but I don't see any Edit buton.
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13.

Rif - you can can edit the page Applied Category Theory, or any Azimuth Wiki page, by going to the very bottom and clicking on Edit.

Comment Source:Rif - you can can edit the page [Applied Category Theory](http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory), or any Azimuth Wiki page, by going to the very bottom and clicking on **Edit**.
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14.

Thanks for the to-do list, Jerry! I've been posting links to all the exercises and puzzles for Chapter 1 here, and as I've been doing it I've been updating the exercise numbers. As you can see on our Applied Category Theory wiki page. I think I've fixed everything up to but not including Exercise 67 in the old numbering scheme. But there's more to do!

At present everyone can edit the wiki page but only I can edit the names of articles on this forum... except for the people who first posted them. I would be happy to grant powers to responsible people who want to do work.

Comment Source:Thanks for the to-do list, Jerry! I've been posting links to all the exercises and puzzles for Chapter 1 [here](https://forum.azimuthproject.org/categories/applied-category-theory-exercises), and as I've been doing it I've been updating the exercise numbers. As you can see on our [Applied Category Theory wiki page](http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory). I think I've fixed everything up to but not including Exercise 67 in the old numbering scheme. But there's more to do! At present everyone can edit the wiki page but only I can edit the names of articles on this forum... except for the people who first posted them. I would be happy to grant powers to responsible people who want to do work.
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15.

Ah, I see. I was trying to edit this forum page, but of course I can't. I can edit http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory. John, maybe better to edit your first post in this thread to make clear the right place to find links is on the wiki page, maybe even remove the (likely outdated) links from the first post here?

I'm happy to do a bit of editing today. Is it correct that up through and including the "new 70" on the wiki page, everything (including links and titles on the linked pages) is correct? I see that for the "new 70" (and each exercise) links to a forum thread, but can we change the titles in those threads?

Comment Source:Ah, I see. I was trying to edit this forum page, but of course I can't. I can edit http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory. John, maybe better to edit your first post in this thread to make clear the right place to find links is on the wiki page, maybe even remove the (likely outdated) links from the first post here? I'm happy to do a bit of editing today. Is it correct that up through and including the "new 70" on the wiki page, everything (including links and titles on the linked pages) is correct? I see that for the "new 70" (and each exercise) links to a forum thread, but can we change the titles in those threads?
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edited May 2018

Rif - I'll delete the outdated links on the first post in this thread, and make it clearer that the definitive place to look for exercises is the wiki page.

Is it correct that up through and including the "new 70" on the wiki page, everything (including links and titles on the linked pages) is correct?

I have attempted to correct everything up to this point. So, the main work involves the exercises after that point. If you could fix those, that would be great. Please compare Jerry Wedekind's comments to the latest version of the book and what we're claiming on the wiki page. I haven't checked that Jerry's comments match the reality of the book.

I see that for the "new 70" (and each exercise) links to a forum thread, but can we change the titles in those threads?

Alas, no. As I mentioned:

At present everyone can edit the wiki page but only I can edit the names of articles on this forum... except for the people who first posted them. I would be happy to grant powers to responsible people who want to do work.

For now I'll be happy to fix the titles of all exercises after "new 70", since I need to go through all of these and polish them up anyway. I'm developing a mental list of people whom I'd trust to mess with the Forum.

Comment Source:Rif - I'll delete the outdated links on the first post in this thread, and make it clearer that the _definitive_ place to look for exercises is [the wiki page](http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory#chapter_1). > Is it correct that up through and including the "new 70" on the wiki page, everything (including links and titles on the linked pages) is correct? I have attempted to correct everything up to this point. So, the main work involves the exercises after that point. If you could fix those, that would be great. Please compare [Jerry Wedekind's comments](https://forum.azimuthproject.org/discussion/comment/17738/#Comment_17738) to [the latest version of the book](http://math.mit.edu/~dspivak/teaching/sp18/7Sketches.pdf) and [what we're claiming on the wiki page](http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory#chapter_1). I haven't checked that Jerry's comments match the reality of the book. > I see that for the "new 70" (and each exercise) links to a forum thread, but can we change the titles in those threads? Alas, no. As I mentioned: > At present everyone can edit the wiki page but only I can edit the names of articles on this forum... except for the people who first posted them. I would be happy to grant powers to responsible people who want to do work. For now I'll be happy to fix the titles of all exercises after "new 70", since I need to go through all of these and polish them up anyway. I'm developing a mental list of people whom I'd trust to mess with the Forum.
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17.

OK, later today, I'll try to go through exercises 67-97 on the APC page, edit the wiki page as appropriate, and leave comments on the wiki page if I'm not sure. I'll ping this thread again when I'm done.

Comment Source:OK, later today, I'll try to go through exercises 67-97 on the APC page, edit the wiki page as appropriate, and leave comments on the wiki page if I'm not sure. I'll ping this thread again when I'm done.
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18.

Thanks.

Comment Source:Thanks.
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19.

OK, I took a look. Jerry was pretty on. 67 is now 66, and all of exercises 72, 75, 77, 79, 80, 82, 83, 85, 87, 90, 91, 96, 97 in the "old ordering" needed 5 added to their numbers, so I edited the numbers in the wiki. All the forum links need their titles updated. I also give per problem issues below.

• 67->66. There is already a page for 66 in the updated version, so we now have two pages on this exercise. 67 in the old version is the same-ish question with s/poset/preorder/ and some rewording. I think it's best to remove the current pointer to 67 and put a link in the old discussion or just remove it. (It's not that substantial, but I don't want to be rude to anyone.) I didn't touch the wiki link on this one so as not to sow confusion.
• 72->77. (Jerry suggested the "content may be off" for this one. I didn't see any differences except that Frederick numbered the two exercises 1. and 1. instead of 1. and 2.)
• 75->80. The forum page has a diagram that's not in the current version of the text, and I'm not expert it enough to verify it yet; I'm assuming it's correct.
• 77->82.
• 79->84. s/1.76/1.81/ in the text of the problem.
• 80->85. The diagram's not from the text and I haven't verified it.
• 82->87. The wording is fairly different from in the text (it's clearly the same-ish question), and I'm not 100% sure the meaning is identical.
• 83->88.
• 85->90. s/1.84/1.89/ in the text. (It would also be better if it clarified it was only restating part of Proposition 1.89.)
• 87->92. s/1.86/1.91/ in the text.
• 90->95. Example 1.94 (formerly 1.89) is included and I'm not sure why; if it does belong there it should be updated with s/1.89/1.94/.
• 91->96. The text refers to Proposition 1.81 (now 1.86) and Definition 1.70 (now 1.74), although I these could likely be deleted from the problem.
• 96->101.
• 97->102. Question seems to have been reworded substantially. It's the same-ish but I'm not sure it's the same.
Comment Source:OK, I took a look. [Jerry ](https://forum.azimuthproject.org/profile/1773/Jerry%20Wedekind) was pretty on. 67 is now 66, and all of exercises 72, 75, 77, 79, 80, 82, 83, 85, 87, 90, 91, 96, 97 in the "old ordering" needed 5 added to their numbers, so I edited the numbers in the wiki. All the forum links need their titles updated. I also give per problem issues below. - 67->66. There is already a page for 66 in the updated version, so we now have two pages on this exercise. 67 in the old version *is* the same-ish question with s/poset/preorder/ and some rewording. I think it's best to remove the current pointer to 67 and put a link in the old discussion or just remove it. (It's not that substantial, but I don't want to be rude to anyone.) I didn't touch the wiki link on this one so as not to sow confusion. - 72->77. (Jerry suggested the "content may be off" for this one. I didn't see any differences except that Frederick numbered the two exercises 1. and 1. instead of 1. and 2.) - 75->80. The forum page has a diagram that's not in the current version of the text, and I'm not expert it enough to verify it yet; I'm assuming it's correct. - 77->82. - 79->84. s/1.76/1.81/ in the text of the problem. - 80->85. The diagram's not from the text and I haven't verified it. - 82->87. The wording is fairly different from in the text (it's clearly the same-ish question), and I'm not 100% sure the meaning is identical. - 83->88. - 85->90. s/1.84/1.89/ in the text. (It would also be better if it clarified it was only restating part of Proposition 1.89.) - 87->92. s/1.86/1.91/ in the text. - 90->95. Example 1.94 (formerly 1.89) is included and I'm not sure why; if it does belong there it should be updated with s/1.89/1.94/. - 91->96. The text refers to Proposition 1.81 (now 1.86) and Definition 1.70 (now 1.74), although I these could likely be deleted from the problem. - 96->101. - 97->102. Question seems to have been reworded substantially. It's the same-ish but I'm not sure it's the same. 
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20.
edited May 2018

Thanks hugely, Rif! I'll go through these soon and fix everything. Your notes will make it much, much easier. =D>

Comment Source:Thanks hugely, Rif! I'll go through these soon and fix everything. Your notes will make it much, _much_ easier. =D>
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21.
edited May 2018

Rif #19: Thanks, that's great! Responses to 4 of the issuesin your list ("x->y" means the exercise w/ old number x and new number y):

• 72->77: Either I was hallucinating or whatever it was got fixed:-)

• 82->87: Looks like "one stop shopping" has been enabled by including relevant context. (It would help to more clearly label Eqn 1.6, and to clearly distinguish context, exercise, & solution)

• 90->95: The (partial) example was I think included in order to define $$f_! (A)$$ and $$f_* (A)$$. It would help to label it as context, and to indicate that it's partial.

• 97->102: Looks like the Exercise has been updated in light of the Comments, though I didn't check details. Also some nuances in the original Exercise wording are gone.

Comment Source:Rif #19: Thanks, that's great! Responses to 4 of the issuesin your list ("x->y" means the exercise w/ old number x and new number y): - 72->77: Either I was hallucinating or whatever it was got fixed:-) - 82->87: Looks like "one stop shopping" has been enabled by including relevant context. (It would help to more clearly label Eqn 1.6, and to clearly distinguish context, exercise, & solution) - 90->95: The (partial) example was I think included in order to define \$$f_! (A) \$$ and \$$f_* (A) \$$. It would help to label it as context, and to indicate that it's partial. - 97->102: Looks like the Exercise has been updated in light of the Comments, though I didn't check details. Also some nuances in the original Exercise wording are gone. 
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22.
edited May 2018

Loose ends:

• Either we had a regression or I missed it, but Ch1 Exercise numbers 9-26 need to be incremented by 2 (in link text and in Discussion titles)

• Exercises 9 and 67 still need Discussions to be created

• The Ch 1 exercises still contain a number of cross-refs (to Examples, other Exercises, etc.) which need updating. I guess most of these are in Exercises <= 28. If Discussion owners could check for these that would be nice:-)

Comment Source:Loose ends: - Either we had a regression or I missed it, but Ch1 Exercise numbers 9-26 need to be incremented by 2 (in link text and in Discussion titles) - Exercises 9 and 67 still need Discussions to be created - The Ch 1 exercises still contain a number of cross-refs (to Examples, other Exercises, etc.) which need updating. I guess most of these are in Exercises <= 28. If Discussion owners could check for these that would be nice:-)
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23.

John #14: I forgot to thank you too! (Not to mention all else you do; I've about decided we're in a multiverse and you've managed to leverage it as a productivity multiplier).

Comment Source:John #14: I forgot to thank you too! (Not to mention all else you do; I've about decided we're in a multiverse and you've managed to leverage it as a productivity multiplier).
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24.
edited May 2018

I have been making updates to the chapter 1 exercises for which I have edit rights. I was not sure what you wanted to do with the pair of E66C1. Should the "preorder" "poset" note be added to the title?

Yes, in an effort to make the exercises self contained I changed the wording on some of them a bit.

Comment Source:I have been making updates to the chapter 1 exercises for which I have edit rights. I was not sure what you wanted to do with the pair of E66C1. Should the "preorder" "poset" note be added to the title? Yes, in an effort to make the exercises self contained I changed the wording on some of them a bit.
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25.
edited May 2018

Thanks, Fredrick. I had slacked off in my plan to renumber exercises when I got busy editing Brandon's thesis - I gave him about 230 numbered corrections! #:-S So, I'm very happy that you stepped in.

I'll check out exercise 66. This must be related to how Brendan and David changed their terminology regarding posets and preorders, bringing it in line with the rest of the universe.

Comment Source:Thanks, Fredrick. I had slacked off in my plan to renumber exercises when I got busy editing Brandon's thesis - I gave him about 230 numbered corrections! #:-S So, I'm very happy that you stepped in. I'll check out exercise 66. This must be related to how Brendan and David changed their terminology regarding posets and preorders, bringing it in line with the rest of the universe.
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26.

I've deleted the preorder version of Exercise 66 after copying all the material in that discussion to the other version. Thanks, guys!

Comment Source:I've deleted the preorder version of Exercise 66 after copying all the material in that discussion to the other version. Thanks, guys!
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27.

@JohnBaez I am interested in @BrandonCoya thesis. Where does it fit in the progression of "7Sketches"?

Comment Source:@JohnBaez I am interested in @BrandonCoya thesis. Where does it fit in the progression of "7Sketches"?
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28.

If anyone knows exercises that still need to be renumbered, let me know; I have the power.

Comment Source:If anyone knows exercises that still need to be renumbered, let me know; I have the power.
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29.
edited May 2018

I think the discussion is limited by the idiosyncrasies of formatting posts. The availability of good examples for formatting comments and discussion headings. Putting them in the Wiki does not really work because the rendering rules differ slightly. If you make a 'category' for writing forum examples people will populate it. I will certainly include samples of the patterns I have used.

https://forum.azimuthproject.org/discussion/comment/18531/#Comment_18531

Comment Source:I think the discussion is limited by the idiosyncrasies of formatting posts. The availability of good examples for formatting comments and discussion headings. Putting them in the Wiki does not really work because the rendering rules differ slightly. If you make a 'category' for writing forum examples people will populate it. I will certainly include samples of the patterns I have used. https://forum.azimuthproject.org/discussion/comment/18531/#Comment_18531
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30.
edited June 2018

The latest version of the text had a major relabeling of all labeled items. I believe this was due to the inclusion of Equations in the labeling scheme. So, it is a good thing but it will require renumbering everything.

I updated the labels for Exercises # - Chapter 3 on the discussions themselves and the TOC.

Comment Source:The latest version of the text had a major relabeling of all labeled items. I believe this was due to the inclusion of Equations in the labeling scheme. So, it is a good thing but it will require renumbering everything. I updated the labels for Exercises # - Chapter 3 on the discussions themselves and the TOC.