Fall 2004: Two sections of Math 1a
(First Semester Calculus), meeting 3 hours a week each.
Spring
2005: Two sections of Math 1b (Second Semester Calculus),
meeting 3 hours a week each.
Fall 2005: Two sections of
Math 53 (Multivariate Calculus), meeting 3 hours a week each.
Spring
2006: Two sections of Math 1b, meeting 3 hours a week each.
Summer
2006: Instructor for Math 53 (Multivariate Calculus) meeting 10 hours
per week.
Fall 2006: TA for 202A (Topology)
Sping 2007: TA for 225B (Metamathematics)
Summer 2007: Instructor for 104 (Introduction to Analysis)
For no particular reason, old notices get filed below:
Over the summer, I will be teaching Lecture 1 of Math 104 (Intro. to Analysis), M-Th 10-12. I will be using Numbers and Functions: Steps into Analysis by R.P. Burn as our main text with supplements to be posted here. A week-by-week plan of the course is available. The final will be from 10-12 on Thursday the 16th of August (last day of class). Missing any class is obviously bad, but missing the final will result in an F and you shouldn't take this class if you have a conflict with it.
Office hours (held in 845 Evans Hall) will be W 1-2:30 and F 3-4:30, except during the first week when I can't make Wednesday, so we'll do the same time on Tuesday instead.
Students' grades will be computed from: a final (35%); a midterm (20%); weekly written homework (25%); weekly quizzes focusing on reconstructing an important proof from the week's lectures (8%); participation and oral presentations of problems from the book (all of which have solutions) (8%); (almost) daily short quizzes asking students to recite definitions or statements of theorems from the last lecture (4%). The final can replace one homework and the midterm can replace one of the first three homeworks. After this replacing has happened, the midterm grade can be replaced by the average of the grades for the final and the midterm. The exams (midterm and final) will be designed to test both students' problem solving abilities (often, the problem being to prove something) and their factual knowledge of the material (for instance, the ability to reproduce key proofs).
The course has several aims: (1) To understand what it means to develop mathematics axiomatically and how this method has interacted with other methods throughout history; (2) To appreciate the importance of the completeness axiom in analysis; (3) to be develop the ability to produce proofs of simple but novel statements in analysis; (4) to be able to follow complicated proofs from lectures or textbooks and develop working methods for internalizing them; (5) to gain skills in presenting mathematics both formally and informally and both orally and in writing; (6) to be prepared to take a more advanced course in analysis. Both the teaching and assessment methods are designed with these aims in mind. In particular, the word "developing" is important: students will be encouraged to become more independent learners as the course progresses, not simply through the provision of less support material, but also through explicit guidance on how to cope without it. While I try to teach well (and hope that all your future teachers are good), one of the things I hope to teach you is how to learn well from a bad teacher (or textbook).
Analysis is a fascinating subject which can be badly described as an attempt to understand the theory behind calculus. The following analogy may help: in your calculus classes, your professor blind-folded you, put you in a space ship, and flew you to the Moon. Once on the Moon, you learnt a variety of cool things one could do on the Moon which (if you've used your calculus in other classes) you'll know can be very useful. In analysis, we study the spaceship which took you to do Moon. There are a variety of reasons to do this: firstly, mathematicians are skeptical creatures, and some of us thought that maybe it was all a fake; secondly, if you want to do more advanced calculus, you're going to need to fly to more exotic places than the Moon, so you better understand that journey really well if you're going to try to understand a more complicated one; thirdly, there was a lot of interesting stuff to see on the journey that you missed. Beginning analysis students are often frustrated that they're just proving theorems they already know from calculus, but we will conclude the course by looking at metric spaces which are a "more exotic place" to fly to. I also hope you'll enjoy some of the interesting things we get to look at along the way.
Here are the long promised midterm practice questions, along with more information about the midterm.
Update: 8/15.Here's the practice final questions. There are no questions on all topics. The formatting for the uniform convergence ones is terrible, but I can't seem to be able to fix it and I'm already late for office hours.
Update: 8/3. All homework problem sets are now available. Solutions for the first five problem sets.
Supplemental reading. You may find the following notes helpful as a supplement to Burn in weeks 1-5 and 7. Supplemental reading for weeks 6 and 8 will be posted later. Oxford I covers weeks 1-3 of our course and Oxford II weeks 4, 5 and 7. (You only need download the lecture notes, not the problem sets).
Summer 06.
Over the summer of 2006, I taught Lecture 2 of Math 53, M-F 8-10am in 6 Evans. Math 53 is Multivariate Calculus. This is in the 8 week summer session and hence instruction runs from 06/26 till 08/18/06. Missing any classes will be disadvantageous to you, as the pace over the summer is very intense (we have a whole semester's worth of material to cover in 8 weeks), but you should definitely not take this class if you cannot make the last meeting (8/18) as that is when we'll be having the final exam. My office hours (held in 845 Evans) will be M 5-6, T 10:30-11:30, Th 5-6.
Outline.
The course will be split into four unequal quarters, that in some way model your previous progression through single variable calculus. We'll start off with "warm-up" (which you can think of as being "pre-multiv calc"), some stuff on parametric curves, polar coordinates and 3D geometry. Then we'll do multi-variate differentiation and look at some applications, focusing on multi-variate optimization. The third quarter is on multi-variable integration. This topic has many applications, but two we'll focus on are statics and probability. Lastly, we'll look at some theorems which tie together multi-variable differentiation and integration, in the way that the Fundamental Theorem does in single variable calculus. One way to look at the Fundamental Theorem is this: we all know that distance traveled is speed times time, where speed is constant; the FTC tells us that displacement is velocity integrated with respect to time, where the velocity is allowed to vary. This physical way of understanding the FTC is what we're going to look at generalizing to higher dimensions and we'll see that the natural way to do it is, instead of thinking about a single particle moving, to think about fluids flowing. This last quarter of the class is one students often find difficult and I hope that teaching it in the context of some basic fluid dynamics will make it more intuitive.
Assessment.
The class will be assessed in four ways: homework, quizzes, writing tasks and a final. Instead of having midterms, I will give more weight than usual to the quizzes. This is how your final grade will break down:
Quizzes:
50% [updated 8/14. Solutions to quiz
13 now up.]
Homework:
25% [link fixed 6/19, updated 6/21]
Writing
Tasks: 25% [ updated
8/2]
Those of you who gave me an online code name can access their scores here. [Updated 8/14: predicted grades are valid as of 8/14, not 8/2 like the pdf says.] [Apologies to whoever gave me a 4-digit numerical code beginning with 7 -- I've forgotten who you are, so I deleted you. Let me know who you are and I'll re-add you.] Predicted grades now up on the online grade book.
This is how the final fits in: the grade you get on the final can replace the grade you get on any quiz, homework or writing task, with the following restrictions: there will be 14 homeworks, between 3 and 11 of these may be replaced by the final; there will be 13 quizzes, between 3 and 10 of these may be replaced by the final; there will be 6 writing tasks, between 1 and 5 of these can be replaced by the final. Hence the final may end up making up as little as 21% or as much as 79% of your grade, depending on how you do on it. Is that about as clear as mud? I'll explain it with examples at the first lecture. The good news is that this is the one bit of math that none of us apart from me need to understand... [this paragraph corrected 6/19]
The fact that your final grade can replace any bad HW/ quiz /etc grades means that I won't be dropping the bottom grades for you, they'll (hopefully) just get converted into the final grade. No make-ups, no late anything accepted.
The Writing Tasks you can think of as being like take-home quizzes. They'll often have a slightly open ended nature and you'll be graded on style and clarity as well as mathematical accuracy, completeness and relevance. The general pattern most weeks for the assessments will be this: M HW due; T quiz on yesterday's HW; W writing task due; Th HW due; F quiz on yesterday's HW. The first week (because it's the first week), second week (because of 4th of July holiday) and last week (because of the final) will be slightly different. I aim to finish lecturing on material at least 2 or 3 days before the HW on it is due. [updated 6/20.]
Solutions to writing problems and quizzes will go up here with comments.
I've put two practice finals up here. You will be allowed one side of notes (letter paper), written in your own hand, for the final, which will run from 8 (not 8:10) to 10 on the last day of class. Good luck!
Calendar.
A calendar of what will be happening when during the summer can be found here.
Spring 06.
During Spring 2006, I'll be teaching two section of Prof. Hutchings's 1B class: MWF 8-9 in 4 Evans and 10-11 47 Evans. My office hours will be Tuesday 5-6 and Thursday 1:30-2:30; if you can't make those times feel free to consult my schedule, find a time we're both free, email me to let me know you're coming and come some other time. Quizzes are on Wednesdays arnd homework is due Mondays and Fridays (no quizzes in midterm weeks).
Comments on Midterms. I've edited and collated a bunch on comments that graders made on the midterms. You'd do well to look at these as part of your your preparation for the final. They can be found here.
Final Review Session: Will be Wed 5/17 3:30-5, 4 Evans. During the finals week, instead of my usual office hours, I'll have office hours on Thu 5/18 11-12:30, 3:30-5. Office hours will be as usual in the week with the dead days in. You can also go to Patrick's review session, which will be Tuesday 5/16, 3-5 PM in 60 Evans.
5/11: My office hour on this day (the Thursday during the dead days) will be 1-2 instead of 1:30-2:30.
Comment on physics on the final: My reading of the situation is this: you don't have to memorize any physics formulae (eg. Newton's Law of cooling, definitions of over-/under-/critically- damped). However, you should be able to do all the math, given the equations, or set up equations from a simple word problem which doesn't require any knowledge of physics.
Solutions to all quizzes are up now (but, see correction), as our section scores correct as of 5/3. The section "totals" are now calculated as follows: first, if it helps, the worst quiz from before the 1st Midterm is replaces by the best quiz from after; then the bottom two quizzes and six homeworks are dropped and then everything is added up.
Comments on the twelth quiz: The differential equation was pretty well solved, especially given that some of the integration was tricky. For both Qq.s 1 and 2, (a) was good, (b) was bad. so I'll go over those on Friday. One disturbing thing was that the horrible fallacy that (sum a_n)^2 = sum (a_n^2) cropped up on a number of people's solution: this is false and you should stop believing it... it's not even true for finite sums: (a+b)^2 is not equal to a^2 + b^2.
Comments on the eleventh quiz: Not much to say, really, it was pretty good. I'll make a couple of small clarifications on Friday, but, apart from that: well done!
Comments on the tenth quiz: A decent number of you had forgotten when / how to do inverse trig substitutions: you need to review section 7.3 in the book. Question 2 was better than last week, so it's clear some of you really put some work into this topic. I'll go over it for those of you still confused on Friday. The question on complex numbers was pretty well done.
Comments on the ninth quiz: What can I say? Qqs 1 and 3 involved some difficult integration, but were expertly done [Note: we did an integral very similar to 1 in group work on Wednesday... proof of its usefulness for any skeptics reading this?]. Question 2 was... um... less good: I'll go over it Friday.
Comments on the eightth quiz: Overall, a pretty good quiz. A few common errors though to clear up. Firstly, not really an error, but partial fractions is a much easier way to do Q1 than trig functions, as wirntessed by the large number of people mucking up trig subsitutions (large relative to the number of people who tried to use trig here, most people did this correctly, but used partial fractions). Secondly, I'll go over 2(c) on Monday, a lot of people got this wrong. Thirdly, many people forgot the constant solution of the ODE in Q3. Looking at the scores, you can see a lot of 9's -- that's due to a lot of people getting almost everything right apart from making one of the last two errors I mentioned. But, overall, as I said, a nice start to our work on ODEs.
Review sessions for the second midterm: 3/18
2-3:30pm. Room 3 Evans. (Me)
3/19 3-5 Room 60 Evans (PlV...
another GSI).
Comments on the seventh quiz: I have to admit: this quiz was disappointing. 3(a) was hard, but the rest of it really wasn't -- if you got 5 or less you really need to put a lot of work in to do OK on the coming midterm. That said, I think those of you who got 7 or more have demonstrated a really good foundation for the midterm (but no resting on laurels!). Question 1 revealed two misunderstandings: firstly, people seemed to think that bounded convergent sequences had to be montonic, this is false, stop thinking it; secondly, people didn't seem to remember the definitions of increasing and decreasing -- in Stewart, decreasing means a_{n+1}=< a_n for all n and increasing means a_{n+1} >= a_n for all n. Correction: Stewart actually defines decreasing and increasing using < and >, not =< and >=, so in fact there are no increasing and decreasing functions. It's very important to learn the definitions and statements of theorems as well as to have a "feel" for them. I've just seen the practice midterms, and some of the questions are very theoretical, so you have to be ready for this. Question 2 was better. Question 3 wasn't particularly well done, but was quite hard (though definately something people hoping for A's and strong B's should have been able to do). In particular, almost all of you need to review how to get derivatives from a power series.
Comments on the sixth quiz: Good quiz: for most of you this was your best quiz in this third of the course. Questions one and two were very well done in general., just a few minor slips (a few people forgetting to check end-points). Question three was OK and revealed that a lot of you know your tests inside out, but there were a couple of concerns. Firstly, quite a few people seemed to think that (sin^2(n)/n-> 0 as n->oo) is false, but it's true. Also, I realized that the proof I gave in part (c) that a_n->0 didn't work. Lots of you noticed this too, and if you just pointed out that the proof was wrong you got the point. However, quite a few people either said that a_n doesn't tend to 0 (it does, even though my proof didn't show that) or seemed to be critisizing a much simpler proof than the one I wrote. So, I'll actually give you a proper proof of this on Friday.
Comments on the fifth quiz: The first two questions were pretty well done. There was some confusion in statements of the Integral Test about when to talk about f and when to talk about a_n: note that it doesn't make sense to talk about a sequence being continuous, or the integral of a sequence. Question three didn't fare quite as well, though it was nice that some of you found a different way to do it from the one I'd had in mind. There were some particularly notable bogus "facts" (which were, in fact, falsehoods) that I'll share with you here (note: these are false! Stop believing them!): (Sum a_n b_n) = (Sum a_n)(Sum b_n); sin (1/n) < sin (n); sin (1/n) > sin (n); (Sum sin (a_n)) = sin ( Sum (a_n)); (Sum a_n) = Int a_n (dn?).
Comments on the fourth quiz: The first question could be done pretty quickly by comparison or quite cumbursomely by direct integration. Either way worked, but comparison was definately better (if you did it right! Remember which way round the implications / inequalities go!). The second question was the worst done, very few of you knew the definition of what it means to say a series converges. All you had to say was "the limit of the sequence of partial sums is 17." I'll say something about definitions vs. consequences in section on Monday. Some of you don't seem to understand what the word "hence" means: if part (b) of a question begins "hence", it means you have to use part (a) -- this was relevant in Q3. I also had to read some horrible things which made it look like you could evaluate a series by evaluating an integral -- go back and read what I said the integral test didn't say!
Comments on third quiz: There was only really one problem which I saw on a large number of people's work and that was the statement of the Comparison Theorem. Two common mistakes were to forgot to point out that the two functions both have to be positive and to talk about the functions converging and diverging (whatever that means) rather than the integrals.
Review Session for first Midterm: Saturday 2/11, 2-3:30pm, 3 Evans. (note room). Hopefully there will be some practice midterms on the professor's website by then and we can work on those together.
Office Hours in Midterm weeks: In the weeks of the midterms, instead of having an office hour Tuesday 5-6 (after the Midterm), I'll have it Monday 5-6 (before it).
Some comments on the second quiz: the first question revealed that about half of you have a good understanding of limits and half of you don't. You'll find improper integrals (and sequences and series -- our topic after MTI) very hard without a good understanding of this topic. Not many of you seemed to understand what I wanted for the second question. Each of these questions could be tackled by a method outlined in sections 7.2 or 7.3 (though there were other ways of doing some of them). I just wanted you to tell me the substitution you would have made and the identity you would expect to use. While most of you did this, you also wrote a whole lot of other things as well, which wouldn't have been that big a problem if a lot of you hadn't have run out of time on Q3. As for question three, the algebra was mostly pretty good (well done), with only a few common mistakes I'll go over on Friday. However, a lot of the integration was pretty poor.
A small point on the first quiz: on the last
question it was nice to see a few of you use u2=x
to find the differentials instead of u=x?.
I didn't think of this when writing the solutions and both ways are
fine, but that way's better. Quiz performance was pretty good
on the whole, though presentation could use some work in general.
During Fall 2005, I'll be teaching two sections of Prof. Weinstein's Math 53 class: MWF 1-2 in 105 Latimer and 2-3 in 425 Latimer. My office hours for this course will be Tuesdays 3-4 and Thursdays 1:30-2:30. Note: I've now moved offices to 845 Evans.
Homework will be due every Monday in section (except the second week of classes when Monday is a holiday, so it will be due on the Wednesday) and will be graded for effort. Your best 10 homeworks will be counted for 10% of your grade. Each week we will alternate between either having a quiz on Monday, or having one of your homework questions graded for accuracy and presentation (you will be warned which one). All but your worst 2 quizzes will count for 10% of your grade, as will all but your worst two of these special homework problems. There will be no quiz set or homework due in the first week of classes. In the second week, we will have a quiz on Wednesday (on the material covered by the first homework).
Quiz solutions (solutions for seventh quiz now up) and scores for quizzes and homework (Scores for the 7th **'ed HW problem now up...) can be found here (11/3: I checked these yesterday and found a bug in the program that puts them on-line (it only affects people who have the same fore-name as some-one else in their section, and not all of those) I think I've fixed everything now). I've also put up your final section scores, calculated as described above. I haven't yet had the conversation with Prof. Weinstein about where grade cut-offs should go on those, but for your guidance the median grade on the two midterms has been a low B and the median section score is 27.1, so you might expect those to go together. Home work solutions can be found on Prof. Weinstein's website.
Final Review Session: Monday 12/12,
2-4 (pm), 6 Evans.
Finals week office hours: Thursday 12/15
11-12:30; 3:30-5 (845 Evans).
For 11/23 only: If it's more convenient for you travel plans to go to my 1-2 section (which is in 105 Latimer), you're welcome to do that, even if you're enrolled in the 2-3 section. Happy Thanksgiving!
Review Session for second Midterm: I'll be holding a review session for the second midterm on Monday, 5:30-7 in 81 Evans. Details of other review sessions can be found on the professor's website.
A note on the 5th Quiz: As you can see from the averages, this was our worst quiz yet, in fact the only one that's caused me concern. This can't be blamed on question 3, which was pretty well done (especially the explanation of why tripling works: well done). The main cause of error was not reading the question properly. For instance, 1(a) asked you to use rectangular co-ordinates and 1(b) asked you to use cylindrical. The correlation between which co-ordinate system people used and which one I asked them to use was pretty much null. Also, in question 2, only a few of you bothered to calculate z_m (that exact calculation was asked for on your homework and none of you asked me about it, so I'm assuming you can all do it). I'll try and get solutions up soon.
A plug: (Especially for
those of you contemplating math majors / minors, or just generally
intersted). The Bowen lectures are coming up and this year will
be given by John Conway, who's well-known for his excellence in
presenting mathematics clearly. His three lectures are on
symmetry (in shapes, surfaces, and space, respectively) which sort of
ties in to our themes in class. When mathematicians talk about
symmetry they often us the language of groups, so if you plan on
going and don't know what a group is, you might want to check out an
introduction, like the first two sections of this
one. The time and place will
be:
11/1, 5pm,
Dwinelle 145 (followed by a reception in 1015 Evans);
11/2,
5pm, Dwinelle 145;
11/3, 5pm, VLSB
2050.
A note on the 4th ** HW: I think the question was worded confusingly and most of you mis-interpreted it. In your favour, the solution manual also (in my opinion) mis-interpreted it. Given that the question was confusingly worded, we've decided to be lenient in grading: so long as your solution is correct for infinitely many values of R, you get full credit. (There were two, wrong, solutions that people gave. One is right for infinitely many R and wrong for infinitely many R. The other is right for only one value of R).
Some notes on the 4th quiz: Question (3) was meant to be challenging and you shouldn't feel bad if you missed that one; we'll go over it on Wednesday. However, the other two questions should have been straightforward. Question 1(a) asked for a picture labelled with dimensions, and over half over you didn't label it. A good few people got a negative answer for 2(a) and, apparently, were unconcerned that this was impossible. Also, there seem to be some people confused about how to integrate 0.
A note on the third ** HW: All but a couple of you blithely cancelled (s-z) (etc) factors, without considering the case when these are 0. Also, the standard of presentation was a lot lower than it has been on previous homeworks (which were proofs, but only of the generalized calculation kind; whereas this week's was a `proper' proof). So, instead of doing multi-v integration on Wednesday, we'll spend some time looking at how to improve performance on the ** HWs (sloppy presentation is more tolerable on quizzes, where you have pressure of time).
My review session for the first midterm will be 9/24 1:30-3 in 9 Evans.
This semester (Spring 2005) I'm teaching two sections (section numbers 203 and 213) of Math 1B , the second semester calculus course at Berkeley. Homework is due in section on Thursdays, when there will be a short quiz. My office hours for this course will be Monday 9:30-10:30 and Wednesday 11-12. If you want to discuss something and can't make those, take a look at my schedule, pick a time we're both free and email me to let me know you're coming then (do this with enough notice that I can let you know if I won't be in, unless you don't mind that).
Scores for quizzes 1-12 are available here (for those students that didn't opt out). These now have final section points on them. I've calculated these by dropping your bottom three scores. I think I managed to get scores for quizzes you took with other GSIs for all of you, but if any-one has a 0 for a quiz that they actually took while enrolled in another GSI's section, let me know.
My 2pm (213) section should note the following room change: from Thursday 2/10 on, this section will be taught in Evans 71, rather Dwinelle. This will get us more board space and mean I will be able to get to section earlier.
I've had to take down the solutions to the quizzes that were up here: Prof. Ratner wrote the questions, so she owns the rights to them and doesn't want them online. Sorry about that, nothing I can do - I'll have to distribute hard copies in class from now on.
I'm offering the following review sessions for the first Midterm.
Monday 3/7 (Lecture style) 85 Evans 6:30-8
Tuesday 3/9 (Individual / Group work) 2334 Bancroft Way (opposite
RSF) 6-7:30.
The first midterm will be during the lecture hour (12-1) on Friday 3/11. It will be in 100 Lewis (note: not the usual lecture room). Good luck!
The next midterm will be during your lecture hour (12-1) on 4/15 in 100 Lewis. Review sessions will be as follows:
Wednesday (4/13) 6-8 in 215 Dwinelle, group
work / individual help (feel free to come and go) and
Thursday
(4/14) 5:15-6:45 in 221 Wheeler, lecture style.
Here's some important information about the final:
Reviews: Th 5/12 5-6:30 70 Evans
F 5/13 8-9:30 (pm) The room booking people *still* haven't got
back to me about a room for this one yet (any-one would think it was
finals week or something..!), so meet at my office 854 Evans.
If there are few enough of us, we'll work there, otherwise we'll go
somewhere else. Where-ever we go, I'll put a sign on my door
letting you know. IMPORTANT NOTE: JUST REMEMBERED, THEY SOMETIMES
LOCK ALL BUT THE GROUND FLOOR OF EVANS AFTER 7:30, SO YOU MIGHT NOT
BE ABLE TO GET TO MY OFFICE. I'LL BE THERE, AND HAPPY TO TALK TO
PEOPLE, BUT YOU MIGHT BE BETTER OFF COMING ON MONDAY.
Office
Hours: M 5/16 11-12:30, 3:30-5, 854 Evans.
Final:
T 5/17 12:30-3:30, 100 Lewis. Bring your IDs. Good luck!
Also, I spotted more errors on both sets of quiz solutions I handed out on Tuesday. Sorry about, I don't think I'd have got a very good grade on those... I'm happy to talk the quiz over with any-one who wants to. The substance of the solutions is fine, but there are too many small slips to make them worth reading if you don't already know what's going on. If you do know what's going on, then there'd probably be little point reading them anyway.
Students may find it helpful to look a Prof. Reshetikhin's webpage for his 1B lectures. They should, however, be warned that there is no guarantee that Prof. Ratner's exams will be in any way like Prof. Reshetikhin's. Administrative details will certainly vary between the two courses.
This semester (Fall '04) I'm teaching
two sections of Math
1A , the first semester calculus
course at Berkeley. My office hours for this course are Mondays
10-11 and Fridays 12:30-1:30. I have prepared some rather
minimal revision
notes for the second mid-term.
I'll also use this space to remind you of a course announcement: I
give back homework and quizzes the lesson after they were due in.
If you are not there at the next lesson please note that I do not
carry them around after that, I carry them back to my office and they
sit there until you come to my office and pick them up, either in
office hours or at some other time. If you plan on popping
round on the off-chance, please check my time
table first, as this will tell
you when I definately won't be in.
I'm offering the following review sessions for the second midterm: 11/1 (Mon) 6-7 in 81 Evans (lecture style); 11/3 (Wed) 7:30-8:30 2334 Bancroft Way (peer support style). I am also moving my Friday the 5th office hour to 9:30-10:30 (ie. before the mid term, rather than after it).
And for the final: As requested, I'm offering a practice exam (to be peer graded) on 12/10 (Fri) 6:30-8:30 in Wheeler 0213. This is for both of my sections and for Li-Chung's sections. Here's the exam paper we used for that and here's the solutions (with grading scheme) (note: I have some hard copies of this in my office, so if you fancy saving a tree, pop by). If you did it, it's a good idea to read through the grading scheme and see how many points each of your responses deserve. This will give you a good idea of what we're looking for. I will also be available in my office 12/13 (Mon) 10-12 and 2-4 to answer question, or work with groups that want to come in. (I will have some questions for you to work on if you don't have any of your own).