## Math 250 -- Fall 2013

#### Foundations of Mathematics Sections 000 and 004 Emory University

 Lecture Room: W306 MSC (000) W304 MSC (004) Lecture Time: TuTh 10:00-11:15 1:00-2:15 Final Exam: Dec 18, 6:30-9pm (Group final) W301 Lecturer: David Zureick-Brown Office: W430 MSC Phone: (608) 616-0153 Email: dzb@mathcs.emory.edu Text: "An Introduction to Abstract Mathematics", Bond and Keane Office Hours: Mon 4:30-6:30p (in E406) NO OH Mon Sept 9, Oct 21, Nov 11, Nov 18

"There are two situations when it's good to know what's under the hood of a car: one is when it breaks, the other is when you need to make a new car. Neither of them should prevent you from getting behind the wheel and learning to drive. And if you know what a car does and when it breaks, you'll be surprised by how much more sense the fancy technology under the hood will make.

That said, a lot of great math has been done by digging around under the hood." -- Dmitry Vaintrob
Syllabus

We will cover the following topics.
• Logic -- statements, negation, converse, etc.
• Sets, relations, functions -- the building blocks of mathematics
• Techniques of proof -- proof by contradiction, induction; non-constructive proofs, "consider a minimal X" proofs, pigeonhole principle
• Cardinality -- different sizes of infinity
• Numbers -- what they are, transcendental numbers vs. algebraic numbers (i.e., the difference between pi and 2^(1/2))
• Mathematical prose and rigor-- how to write mathematics correctly and in complete sentences.
Here is an official pdf of the syllabus for this course. (There is no information on this pdf that is not on the webpage.)
Course details

This class will meet 28 times. I will cover roughly one section of our text each class. Some sections will be skipped and many will be covered out of order.

There will be many short in class activities in addition to lecturing.

The midterm is worth 25 percent and the quiz is worth 10 The final exam will be comprehensive and will count for 30 percent. Homework is worth 35 percent. Seriously! If you do not stay on top of the homework, you will have a bad time in this class.

Note well that this class has a group final that differs from the time and date on OPUS 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 summer travel plans accordingly. If you have a conflict with the final exam (e.g., another final) please let me know ASAP.

 Homework 35% (Weekly) Midterm 25% (Oct 10) Quizzes 10% (Nov 19) Final Exam 30% (Dec 18, Room TBD)

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

### Homework

There will be homework assigned every week, usually on Thursday. There will be many simple problems, checking your understanding of the definitions, that will be collected and graded for completness but not correctness. Most weeks there will be a number of proofs assigned. You are expected to write them up very carefully. I will very carefully grade 1-2 of these per week; re-writes will be allowed and in fact expected, and students will be able to recover up to half of the missed points. Homework assignments will typically be worth 20-40 points, depending on the length of the assignment. The homework assignments are available at this link, and will be updated after each lecture.

### Quizzes

There will be 0-2 quizzes throughout the semester, dates and content to be announced. The schedule and content of the quizzes will be available at this link.

Make up quizzes

There will be no make up quizzes. If you miss a quiz for a documented, legitimate reason, I will simply not count the quiz in your final grade.

### Exams

Since I am teaching 2 lectures of this course, there will be a common final. The exam problems will be similar to the homework and worksheet problems (some will be identical, and some will be similar but not identical).
Plagarism Policy

Remember that copying another student's work is a violation of the Honor Code and will be treated as such. If you must leave class during an exam for any reason, please leave all of your belongings (including your handheld supercomputer phone!).

For homework: 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. This is a generous homework policy. Please do not abuse it.

Extra Help:

There is a helpful, 10 minute video of every subtopic we will cover on Khan Academy. When you are confused about a concept, please watch the corresponding video! Remember, you can pause and rewind a video, but you can't pause and rewind lecture!