Math 250, Fall 2011

Foundations of Mathematics
Emory University

Lecture Room: E406 MSC
Lecture Time: TuTh 1:00-2:15
Final Exam: Th, Dec. 8, 4:30-7:00p
Lecturer:David Zureick-Brown
Office: W430 MSC
Phone: (608) 616-0153
Email: david.zureick.brown@gmail.com

Office Hours: MW 5:30-6:30p, EXCEPT for W 9/7 -- 6:15 - 7:15p (in W430)
Text: "An Introduction to Abstract Mathematics", Bond and Keane
Course Website "http://www.mathcs.emory.edu/~dzb/teaching/250Fall2011/
Please fill out this poll and mark off any times that you are unavailable, so that I can schedule office hours that accomodate everyone.

Moreover, if you didn't receive an email about this, please email me right away to let me know.
Course details

This class will meet 28 times. I will cover roughly one to one and a half sections of our text per class. Near the end of the semester, I will provide extra material from other texts. We will cover 1.1-6.3 except for 4.1, plus some extra material.

There will be lots of short in class activities in addition to lecturing. In fact, there will be an activity every day at the beginning of class, so please show up on time!

Topics
Grading policy

The quiz and midterm dates below are tenative (and may be adjusted if the pace of the course is adjusted), but the date of the final exam is set in stone; make your holiday travel plans accordingly. If you have a conflict with the final exam (e.g., another final) please let me know ASAP.

Quiz I 5% (Th., Sept. 8, Tentative)
Quiz II 5% (Tu., Nov. 1, Tentative)
Midterm Exam I 15% (Tu., Sept. 29, Tentative)
Midterm Exam II 15% (Tu., Nov. 10, Tentative)
Final Exam 25% (Thursday, Dec. 8, 4:30-7pm E406)
Homework 35%

Calculators, notes, and textbooks are not allowed in exams or quizzes.

Homework

There will be homework assigned almost every class. Homework assigned on Tuesday is due on at the beginning of class on Thursday (two days later) and homework assigned on Thursday is due on at the beginning of class on Tuesday (five days later); I will assign fewer problems on Tuesday than on Thursday (roughly 4 on Tu and 6 on Th). I will drop the 2 lowest homework grades.

Later in the course, the homework assignments will include "challenge" problems; these will be for extra credit and thus optional.

Grading

Every problem will be graded for completeness, and a large subset of the problems will be graded very carefully. Many weeks there will be a single problem that you will be required to redo until it is completely correct (upon which you will get full credit).

Late Homeworks

Late homework will not be accepted; as a compromise, the two lowest homework grades will be dropped at the end of the semester.

Plagarism Policy

You are free to consult any sources (animate or inanimate) while doing your homework (working in groups is encouraged!), but if you use anything (or anyone) other than your class notes or the texts listed above, you should say so on your homework -- please state at the end of every problem any sources used.

On the other hand, you are expected to make an honest attempt to do every problem on your own before consulting other sources. Remember that copying another student's work is a violation of the Honor Code and will be treated as such.

A good rule of thumb to avoid plagarism is the following -- when doing the final write up of a problem, do not have any text books, web pages, or classmate's write up in front of you. If you get stuck when writing up an assignment, go back and look again; just make sure that you organize the mathematics in your head before writing a proof rather than copying a solution from some source.

Overloads

Ken Mandelberg handles all overloads for the department. To request an overload you must send an email to Dr. Mandelberg (km@mathcs.emory.edu) with your request. He is the only person who can approve an overload request

Schedule

Lecture Date Section Topic(s) Homework Comments
1 8/25 (Th) §1.1 Mathematical reasoning P. 15; D5, D6, D7, Handout 1 First day of class
2 8/30 (Tu) §1.1-1.2 Statements §1.1, P.12; 5,9. §1.2, P.26; 2, 6, 15(a)
3 9/1 (Th) §1.3-1.4 Implications §1.3, P. 35; 3, 12. §1.4, P. 44; 22, D1. Handout 3
4 9/6 (Tu) §2.1 Proof techniques, Sets Handout 4, §2.1, P. 57; #1a-e, i, #2a-e, g, #4a-e
5 9/8 (Th) §2.1 § 2.1, P. 57; #7,9,12,14,21,D1 First Quiz
6 9/13 (Tu) §2.1, 2.2 Intersections, unions, complements §2.1, #13, #18a, 19a-c, 20e-f, §2.2, #14, #26
7 9/15 (Th) §2.2 De Morgan's Laws §2.2; #15, #16, #17, #18, #22, #23
8 9/20 (Tu) §2.3 Collections of sets, power sets, cartesian products §2.3; #7, #8, #12, #13
9 9/22 (Th) §2.3 More on collections of sets §2.3; #9,#14,#16,#19, create practice exam
10 9/27 (Tu) -- Review bring sample problems to class
11 9/29 (Th) -- First Exam First Exam, Solutions
12 10/4 (Th) §2.3, 3.1 Power Sets, functions Handout 12
13 10/6 (Th) §3.1 Handout 13 (now with extra credit!), §3.1, #3 (only compute im f, not im(X)), #5a, #6, #7, #10a
14 10/13 (Th) §3.1 Images of functions §3.1, #3 (Now compute im(X), and for a,b, and c, prove your claim), 5b, 9, 10b-d, 15
15 10/18 (Tu) §3.1 Images and inverse images Handout 15 §3.1, #18 (only turn in f^-1(W_1)), (e) and (p) from the worksheet.
16 10/20 (Th) §3.2 Injective and Surjective functions Extra problems 16 §3.2, #1, #12, #17, #20, .
17 10/25 (Tu) §3.2 Injective and Surjective functions Extra problems 17, problems h and o.
18 10/27 (Th) §3.3 Inverse functions Extra problem 18, §3.3, #10 (only pick out the ones with inverses, don't compute the inverses), #11, #16, #19, #20.
19 11/1 (Th) §6.1 Countability §3.3, #18, #21, §6.1, #6 (only give the bijection, don't prove that it is a bijection), #7, #9, #11 (except for f). ) (Due next Tue).
20 11/3 (Th) §6.1, 6.2 Uncountable sets Extra problems 20.
21 11/8 (Tu) §4.2 Equivalence Relations §4.2, (ignore the `antisymmetric' part of each problem) #1, #2 #3, #4, #5, #10
22 11/10 (Th) More on countability Here is a worksheet containing everything I'd like you to know about countability for the exam.
23 11/15 Review Session
24 11/17 Here are the solutions to the exam. Exam II
25 11/29 §5.2 Induction §5.2, #2, 4b, 7, 8, 13, 14 16, 41 (Hint: differentiate), 2 problems from the handout from class, to be assigned thursday. No extra problems.