This is the web site for Math 170 (section 910) in summer session I.
Here is the syllabusInstructor: Michael Lugo, mlugo at math dot upenn dot edu, DRL 4N27.
Time and place: This class meets on Monday, Tuesday, Wednesday, and Thursday from 4:20 PM to 5:55 PM in DRL 3C4.
Office hours: Monday from 3 PM to 4 PM (that is, before class); Wednesday from 6 PM to 7 PM (that is, after class), DRL 4N27, or by appointment.
The announcements are in reverse chronological order.
Junly 1: I've posted solutions to Homework 8. (If you're handing in the homework late, please be honest and don't look at these!)
June 29 (9:30 pm): I've posted the updated version of the solutions to Homework 7.
June 29: It turns out that I omitted solutions to problems 1b, 1c, and 6 from the posted solutions to Homework 7. This was unintentional; I'll put up a revised version tonight.
June 27: I've posted a study guide for the final exam.
June 27: I've posted solutions to Homework 7.
June 25: The eighth (and last!) homework has been posted; it is due on Wednesday, July 1 in class.
June 23: I've posted solutions to Homework 6.
June 22: The seventh homework has been posted; it is due on Thursday, June 25 in class.
June 19: I've posted solutions to Homework 5.
June 18: I was a bit overly ambitious in constructing homework 6. We did not get to the material which problem 7 is about in class today. Therefore, you do not need to do problem 6 for Monday. I expect to put it on the next homework, though.
June 17: The sixth homework has been posted; it is due on Monday, June 22 in class.
June 15: I've posted solutions to the midterm.
June 12: The midterm has been graded. The score distribution was as follows. Letter grades are indicated in parentheses; you should know, however, that I will use your numerical grades and not these letters in computing your final grade. The letter grades are just to give you an idea how you're doing.
83 or above (A): 3 students
75-82 (A-): 4 students
67-74 (B+): 3 students
59-66 (B): 2 students
51-58 (B-): 1 student
43-50 (C+): 0 students
35-42 (C): 3 students
below 35 (C-minus or below): 1 student
As you can see, there was a wide distribution of scores; the last four questions on the exam were quite difficult, which ahd the effect of spreading out the scores. This distribution of grades is approximately the distribution of grades I will give at the end of the semester, assuming things don't change too much. In general I'm happy with how you as a class did on the exam.
I also assigned a tentative letter grade for each student (taking into account homework and attendance/participation); for about half of you this is the same as your midterm grade, and for most of the other half (whose homework and participation were notably better or worse than your midterm) it's either one-third of a grade above or below your midterm grade.
If you'd like to find out your midterm score or your tentative letter grade feel free to e-mail me. I don't expect to spend much time in Monday's class discussing the midterm. I will post solutions, but I have not yet prepared them.
June 11: The fifth homework has been posted; it is due on Wednesday, June 17 in class.
June 10: I've posted solutions to homework 4.
June 8: Here is a guide to the midterm exam.
June 4: The fourth homework has been posted; it is due on Wednesday, June 10 in class. Please carefully read the instructions at the top of the page.
June 2: The third homework has been posted; it is due on Thursday, June 4 in class.
June 2: The course calendar in the syllabus is not correct. The actual correspondence between sections of the text and days of class, up to the end of the second week, is as follows:
Tuesday, May 26: Section 2.1 (pigeonhole principle, counting)
Wednesday, May 27: Section 2.2 (Fibonacci numbers)
Thursday, May 28: Section 2.3 (prime numbers)
Monday, June 1: Section 2.4 (modular arithmetic)
Tuesday, June 2: Section 2.5 (cryptography)
Wednesday, June 3: Section 2.6 (rational and irrational numbers)
Thursday, June 4: Section 2.7 (real numbers)
I'll post an updated course calendar sometime in the next few days.
May 28: The second homework has been posted; it is due on Tuesday, June 2 in class.
May 27: In light of what we got to in class today, don't do Problem 6 on the homework; we didn't cover it.
May 27: I've also posted some advice on the first homework..
May 26: The first homework has been posted; it is due on Thursday, May 28 in class.
May 21: Welcome to Math 170. Read the syllabus. It will give you the basic information about the course: time and location, textbook, subjects to be covered, and so on. I intend to post announcements about the course here on a regular basis once we get started on May 26.
Here are the solutions to the midterm (the solutions include statements of the problems, so this document is self-contained) and the midterm study guide.
Here is the final exam study guide.
May 26 (I didn't get to all of these.)
Definitions from the first book of the Elements.
The Pythagorean theorem.
One plus one equals two.
Some symbols of modern experimental mathematics:
The bifurcation diagram of the logistic map.
The Mandelbrot set.
Jim Propp's tiling applets and pictures from Cris Moore: Aztec diamond, stop sign.
Cris Moore's pictures of quantum random walks are at the bottom of this page.
A four-colored map of the United States.
Here are some pieces of supplementary reading that may interest you:
The Wikipedia article on the Millennium Prize Problems; here are also links to articles on the seven problems. The ones which are the most understandable are the Poincare conjecture, Riemann hypothesis, and P = NP. (Whole books have been written about Poincare and Riemann, and there's a book which purports to explain all seven Millennium problems; I don't know of a book about P = NP.) Here is an article from the New Yorker about the controversy surrounding Perelman's proof.
The Tower of Hanoi
The full text of A Mathematician's Apology, if you have some time to kill. (See page 14 for the quote on ugly mathematics.)
May 27
Kirkwood gaps histogram -- not about the Golden Ratio, but this does illustrate the importance of certain rational numbers in physics.
Some plots illustrating why being far from a rational number impairs synchronization.
The Golden Ratio used to sell pants.
The Golden Ratio in the Mona Lisa and the Last Supper.
Lots of other architecture and art with golden rectangles drawn on them.
June 15 (map projections):
Mercator projection (circles are all "really" the same size)
From halfway down at this page: stereographic projections of the western and eastern hemispheres, and of two other hemispheres. Note the distortion near the edges. Stereographic projections over more than a hemisphere do a much worse job, which is why I couldn't find one.
The Gall-Peters equal area projection
The Dymaxion map: with nearly connected landmasses and with connected oceans.
