MATH 25b
Honors Multivariable Calculus and Linear Algebra
Course Announcements
| Date | Time | Announcement |
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| Wednesday 10th May | 9:00am | The final exam is now on the webpage. See the final exam section below. Hard copies can be found outside my office door. Good luck! |
| Monday 8th May | 12.40pm | More HW solutions now on the webpage (including HW 12). Plus HW 12 has been graded. It will be returned to the Math 25 mailboxes outside SC 325 later today. |
| Monday 1st May | 5.00pm | Optional class to be
held on Monday 8th May from 3-4pm in room 221 SC. We will go over the
proof of Stokes's Theorem and the Poincare lemma. If no one shows up,
I'll be in my office available to answer questions. |
| Thurs 27th April | 11.50am | HW 12 now up. It
is due Friday 5th May. Absolutely no extensions alowed! |
| Friday 21st April | 9.15am | The final
exam will be a take home exam held during reading period. The exam
will go from 9am Wednesday May 10th through 4:45pm Monday May
15th. The questions will vary from calculations to proofs. As it is an
open book exam, some of the questions will be quite challenging. More
details about the exam can be found below. |
| Tuesday 11th April | 3.00pm | Questions about doing a math concentration? Ask the Math Head Tutor, Professor Peter Kronhimer Office 343 SC (in the back of the math library) or email kronheim@math.harvard.edu. His office hours are Wednesdays 3-4pm and Fridays 2-3pm. He will also have extra office hours in early May so that he can sign the study cards for new math concentrators. These will be posted on his webpage. |
| Mon 10th April | 11.35am | Sign up to be a
Math Course Assistant (CA) for the next academic year for Math X,
Math 1a,1b, Math 19, Math 20 and Math 21a,21b. Applications can be
picked up at the SC 435. Note that you will also have to sign up for
an interview. In the interview a preceptor will ask you about your
teaching experiences and ask you a calculus question (to see how you
would explain things to a student). You would all be good at this, so
if you are interested try it out. Questions can be directed to either
Tom Judson (judson@math.harvard.edu) or
Bret Benesh (benesh@math.harvard.edu).
Some of you might be interested in being a CA for Math 23 or Math
25. You'll need to apply to Professor Taubes (chtaubes@math.harvard.edu).
I believe you'll get an email about this later in the week.
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Final Exam information
| The Exam: | CLICK HERE for a pdf version of the final exam. Paper copies can also be found on my office door. Good luck! |
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| What: | Take home final exam done in reading period. |
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| When: | 9:00am Wednesday May 10th until
4.45pm Monday May 15th. |
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| How: | At 9:00am on Wednesday May 10th, I
will have paper copies of the exam available (found on my office
door). I will also put the exam on the class website as a .pdf
file. The exam must be submitted to me by 4:45pm on May 15th. Failure
to do so will result in a grade of zero! Exams may be submitted in
person to my office, or placed in an envelope and put in my (snail)
mailbox outside of SC 325. You can also submit your exam earlier if
you wish. |
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| While the take home is in progress: | (1) You may NOT talk to anybody about the exam (except me). This includes your classmates and any math majors!
(2) The exam is an open book exam. You may use whatever material you
like. However, I would like you to write your solutions the way you
write your HW solutions. That is, if you do use another text or
website please reference it appropriately.
(3) I will be available for consultations during the exam period. I can
help you with the following sorts of problems: (a) you don't
understand the question (b) you are stuck on how to get started (c)
you have done a computation and want to check the result. Note that I
will give the same information out to everybody (especially for hints
to get you started).
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| What will it be like? | The exam in based
on the last part of the course (so material from Spivak). However,
anything in the course is fair game - for example, we are using a lot
of linear algebra at the moment. You can expect some computational
questions and you can expect some questions that will really get you
to think about what is going on. The exam will have 5-10 questions and
it should take you 1-2 days (maybe 3) to do.
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| Practice exam: | There will be no
practice exams from me. Instead try to think about what potential
questions might be asked! |
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| Office hours: | I will be available
Monday May 8th 4-5pm, Tues May 9th 3-4pm, Wed
10th May 3-5pm, Friday 12th May 3-4.30pm, Sunday 14th May
3-5pm. (Note, you will have to ask the security guards to unlock the
elevators for you on the Sunday as the Science Center is locked.) |
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Essential information
Cool Stuff for Math 25'ers To Do
| Thankathon | Lin Cong is helping to organise the following event:
SPRING READING PERIOD THANKATHON, Wednesday, May 10th 5:00 PM
Loker Coffeehouse.
Write just 5 notes to thank alumni for...
24/7 Library Access, Mac Equipment, Financial Aid, Study Abroad, Wireless Internet, House Renovations.,Athletic Gear
and...
Feast on Felipe's! Choose from a variety of Felipe's famous burritos and chips!
Giveaways! Take home a free 32oz Harvard water bottle!
Please contact Kaitlin Murphy at Kaitlin_Murphy@Harvard.edu or X6-9601 with any questions!
|
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| Lowell last minute orchestra |
On May 7, 2006 - Lowell House's annual reading of Tchaikovsky's "1812 Festival Overture" will take place in the large courtyard at Lowell House. A "rehearsal" is at 2 pm and the concert is at 3 pm.
This is the largest annual organized musical free-for-all that takes place
at Harvard University. Featuring:
* The Lowell House 17th century Russian bells, used in a startlingly appropriate
context
* Simulated cannon fire in the form of hydrogen balloons (courtesy
of the Science Center demonstrations department)
* A chorus of kazoos (kazoos will be supplied)
* A chorus of singers (music will be supplied)
* A Last-Minute Orchestra
EVERYONE and anyone can participate in the music-making. We need kazoo
players. We need a Russian choir. We need an orchestra. We need
audience.
If you can sing, can play any instrument (or a kazoo), you can show up at
2 pm in the courtyard for a crash rehearsal. The performance itself will
be at 3 pm. Bring a wire stand if you have one.
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| Amazing cello's | Hear Heather play the
cello on Saturday May 6th at 3:00pm at Paine Hall - no tickets
required. Heather and 7 others will play Bachianas Brasileiras no 1 for
Eight Celli by Heitor Villa-Lobos. |
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| Handel's Messian | See Sam and Heather
sing in Handel's Messiah. Friday May 5th at the Sanders Theater
starting at 8:00pm. (Students $14.) Featuring Harvard Glee Club, Harvard-Radcliffe
Collegium, Radcliffe Choral Society and Orchestra of Emmanuel Music
Collegium event. |
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| Math Table: | Each Tuesday undergraduates interested in mathematics eat dinner together in Mather house and hear a 30min math talk. Talk to Alison or Ivan about this or see http://www.math.harvard.edu/mathtable/index.html. |
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| Numb3rs: | TV show on CBS each Friday 10pm about a math professor from ''CalPsi'' help his brother in the FBI fight crimes using mathematics. (See also http://www.cbs.com/primetime/numb3rs/.) I'm personally very happy to see a mathematician on TV who is a) young b) not insane c) not wearing glasses and d) very cool. |
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Textbooks
Principles of Mathematical Analysis by Walter Rudin, third edition,
published by McGraw-Hill.
Calculus on Manifolds by Michael Spivak.
Both of these are available from Harvard COOP, or from on-line bookstores.
The following texts are on reserve in Cabot library:
Principles of Mathematical Analysis by Walter Rudin, third edition,
published by McGraw-Hill.
Calculus on Manifolds by Michael Spivak.
Course Assistants
| Who: | Alison Miller | Ivan Corwin |
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| Email: | miller5@fas.harvard.edu | corwin@fas.harvard.edu |
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| Office hours: | Loker 8-10pm Tuesdays | Loker 8-10pm Tuesdays |
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| Problem Sessions: | SC 101B 5-6pm Tuesdays | SC 310 7-8pm Tuesdays |
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Course Summary and Course Outline
Summary: This course is a continuation of Math 25b. It contains a rigorous treatment of real analysis, multivariable calculus, differential forms and (time permtting) an introduction to manifolds. Emphasis is placed on careful reasoning, and on learning to
understand and construct proofs. You should take this class if you are
very interested in mathematics and want a thorough proof-based review of the
topics before moving on to other mathematics. You will be required to
work hard (at least 10 hours each week) during this course!
Outline: CLICK HERE for a day to day calendar of material covered in
class. This page also contains the readings and references for each class.
Confused about which course to take?
CLICK
HERE for an excellent description of the differences between Math
21, 23, 25 and 55.
In the end, you should take the course which challenges, but not
overwhelms you. You should aim to find the classroom environment where you will
produce your best work.
Grades, Attendance and other matters
| Exams: | 1 midterm and 1 take home final exam. The midterm is currently scheduled for Wednesday March 22nd at 7.30pm in room 109 SC. |
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| Grading Policy: | Homework 2/5; midterm
1/5; final exam 2/5.
The class will not be graded "on a curve": if
everyone deserves an A, everyone will get an A. |
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| Attendance: | Attendance will not be taken at each
class. However, it is much harder to learn the material on your
own, so you are strongly encouraged to attend each class.
You must attend the midterm and final exams. Make-up exams will only be given in special circumstances. |
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| Problem Sessions: | You should attend,
each week, at least one of the problem sessions held by the course assistants. |
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| Final exam: | Take home exam done during reading week. Time, dates etc TBA. |
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Handouts
| Date: |
What it's about: |
Where to fnd it: |
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| 28th April |
Worksheet on integration and Stokes's theorem. |
Worksheet
(pdf) (Note is missing a picture of the surface in question, see me
for details.) |
| 15th Feb |
Correction to Ascoli-Arzela Theorem. |
Given out in class - see me for spare copies. |
| 13th Feb |
Another proof of Stone-Weirstrass Theorem. |
Given out in class - see me for spare copies. |
| 8th Feb |
Practice questions for the Midterm exam. |
Practice questions (pdf) |
| 3rd Feb |
Example of a continuous function that is nowhere differentiable. |
Given out in class - see me for spare copies |
| 15th Feb |
Proof writing tips |
Proofs (pdf) |
Homework Assignments
Homework policy
| Homework: | Assignments are handed out each
week. They will form an essential part of the course. The assignments
and the dates they are due will be posted on the course website. |
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| Submitting HW: | Homework should be turned
in to the course mailbox (outside 325 Science Center) by noon on the
day that the assignment is due. |
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| Late HW: | Late homework will be accepted only in
exceptional circumstances and only with prior approval. |
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| HW grade: | Your lowest homework
score will be dropped at the end of the semester. |
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| Working together: | You are strongly
encouraged to discuss the homework problems both with your fellow
students and with the course assistants. However, you must write up your
solutions by yourself. (Copying someone else's homework is unacceptable.) Collaborating on exams is not permitted. |
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| Keeping the graders happy: | To make the job of grading easier, could you please follow the following
guidelines:
Write your name on your HW.
Neat, legible handwriting. We will not grade anything we cannot read!
Write on one side of the paper only.
The problems should be in the order assigned.
Staple (or paper-clip) all pages together. |
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