Announcements
Final Course Grades
The exams were pretty good and final course grades have been submitted to the registrar. Here's my program for the Monte Carlo integration problem:
Have a great Summer and best wishes for all your future work!
Final Exam
Here is the final exam. It's due at 8:00 am on Thursday, May 21.
The last day of class is tomorrow. Let's meet in the Computer Lab in Kiely 061.
Updated: Corrected the typo in problem 3. Thanks Marlon!
End of semester party
The math department end of semester party is today at 12:30 on the first floor of Kissena hall. Lunch will be served. You are all welcome!
Two notebooks from class today
Here are the two notebooks from class today:
Thursday, we'll meet in Kiely 061 again.
Mathematica basics
To get started using Mathematica, I recommend the following screencasts (both about 12 minutes) from Wolfram's learning center:
You might also want to check out a few of the screencasts in Hands-on Start to Mathematica.
As first programming exercises
- Write a program that selects two integers (from an interval) at random and checks if they are relatively prime. What percentage of them are? How does this percentage depend on the interval?
- Approximate pi using a Monte Carlo approach. Select numbers x, y randomly in the interval [-1,1] and determine the percentage of them that lie withing the unit circle.
Colloquium Today
There's a colloquium today:
- Title: Combinatorial Approaches in Homotopy Theory
- Speaker: Dr. Phillip Hackney
- Time and Place: 12:15 in Kiely 258.
Homework
Here is some homework on probability.
- Read sections 13.1, 13.2, 13.3 in Apostol and do exercises 1, 2, 3, 4, 5, 6, 7, 9, 10 in section 13.4
- Read sections 13.5, 13.6. Do exercises 1-12 (these are short) and exercises 13, 14, 16 in section 13.7
- Read section 13.8 and do exercises 2, 3, 4, 5, 8 in section 13.9
- Read section 13.10 and do exercsies 2, 3, 7, 13 in section 13.11.
- Read section 13.12 and 13.13 and do exercises 1, 2, 9, 11, 14
That's too many exercises to write solutions for, so here's an exercerpt. I'll invite each of you to put your solutions to the following on the board on Tuesday, April 28:
- 13.7 #14
- 13.4 #6
- 13.14 #2
- 13.11 #7
- 13.9 #5
Midterm Exam Solutions
Here are my solutions to the midterm exam and a Mathematica notebook with supporting calculations and checks:
- In pdf: midterm_answers.pdf. For LaTeX source: midterm/.
- Notebook: Midterm.nb.
For Thursday, study Chapter 12 in the book on surface integrals.
Midterm Exam
Here is the midterm exam. It's due in class on Tuesday, April 14.
- In pdf: midterm.pdf. For LaTeX source: midterm/.
Correction: As I typed solutions to the midterm, I found a couple of typos. So, I made two corrections to the midterm exam: first, I changed the integration problem 2(a) slightly and second, I changed the notation in problem 4 by emphasizing the transpose.
Homework for the weekend
To finish your study of integration, read sections 11.12, 11.13, 11.14 and 11.17 and do exercises 1, 7, 11, 23 in section 11.15.
Read sections 11.19, 11.20, 11.21 on Green's theorem and do exercises 1, 2, 4 in section 11.22. Then read the rest of chapter 11. That's sections 11.23 through 11.33.
Begin studying the classification of critical points. Read sections 9.9-9.12 and do exercises 1, 2, 3, 4 in section 9.13.
Prepare for your review session on Tuesday. Choose the right topics and prepare to present them.
Homework for Thursday
Read sections 11.1-11.8 and do exercises 1, 7, 10, 11 in Section 11.9 (pages 362, 363).
Look up the "Small span theorem" in section 9.17, and read sections 11.10, 11.11, and 11.12.
Homework: Chapter 10
Here's a little outline to guid your self-study of chapter 10 in Apostol. While you work through this material, translate between the language of vector fields and differential forms. The Wikipedia page on curl might help.
- Read the basic definitions and properties in sections 10.1-10.4 and do exercises 1, 2, 9, 10 in 10.5.
- For an application, do exercise 2 in section 10.9. Skim through enough of the previous sections to solve this problem.
- Read sections 10.10 and 10.11 and do exercises 1, 2, 3, 4, 5, 6 in 10.13
- Read section 10.14-10.17 and do exercises 1, 3, 17, 18 in 10.18.
Also, catch up over the next week. Be sure you've worked through the notes on curves and completed the problems.
Notes on vector calculus
Here are some notes on vector calculus. Read through the first section or so and do exercises 1 and 2.
- In pdf: vectors.pdf. For LaTeX source: vectors/.
Also, catch up over the next week. Be sure you've worked through the notes on curves and completed the problems.
No class Thursday Feb 12 and Tuesday Feb 17
There will be no class on Thursday, February 12 and no class on Tuesday February 17.
Notes on curves
Here are my notes on curves. Do the exercises at the end for homework.
- In pdf: curves.pdf. For LaTeX source: curves/.
Math club
The first meeting of the Math Club will take place at 12:15 on Wednesday, February 18, 2015 in Kiely 258. There will be free pizza and drinks.
CUNY math challenge
You should know about the CUNY math challenge: http://math.cisdd.org. Starts 9:00 A.M. on Monday, February 9, 2015.
Homework
Read sections 9.1, 9.2, 9.4 in the book and do exercises
- Exercises 3, 8, 9 in Section 9.3
- Exercises 1, 2 in Section 9.5
Information about Piazza
The math 208 discussion forum is hosted on Piazza. I encourage you to post questions and answers about the course on the Q & A page of the forum. The link to the forum is piazza.com/qc.cuny.edu/spring2015/math208/home.
Welcome to Math 208
This page will contain announcements. For now, take a look at the syllabus, which has practical information such as references, office hours, and a calendar.