|
Exploration & Proof Fall 2008 |
 |
| Lecture: | MWF 9:10-10:00 BUS 104 |
| Prerequisites: | MATH 226 (Calculus I) with a grade of C or better or consent of the instructor |
| Instructor: | Dr. Matthias Beck |
| Office: | Thornton Hall 933 |
| Office hours: |
M 1:10-2:00 W 11:10-12:00 F 10:10-11:00 & by appointment |
Mathematics is a powerful and flexible language that can be adapted to solve a wide array of problems from many areas. Mathematics connects seeming disparate subjects and provides a unifying philosophy behind logical thinking. Calculus students are acquainted with mathematics as a computational tool but are usually not familiar with mathematics as a language that helps us to explore possibilities, discover conjectures, and prove or refute them. MATH 301 is designed to help students make the transition to more advanced mathematics, where discourse and proof are emphasized. The goals of the course are to improve students' abilities to
- understand the difference between a definition, an axiom, and a theorem;
- read and understand proofs;
- generate and test conjectures when confronted with a new mathematical problem;
- use concepts from logic and set theory in mathematical discussions and proofs;
- present clearly written solutions and proofs.
We will discuss basic mathematical objects (such as the integers, which will form the starting point for the course) that seem familiar to us; however, we will define them axiomatically, pretending that "we don't know anything" aside from the definitions. This will lead us, for example, to proving that n . 0 = 0 for any integer n. The proof of such a seemingly obvious statement requires some care in handling and manipulating the axioms that define the integers. Good proofs require good writing, and writing is difficult. In this course, you will get a lot of practice writing.
Texts: M. Beck & R. Geoghegan, The Art of Proof. We will use a preprint of this book, which is available on the iLearn course webpage.
Here is a copy of the practice midterm.
Grading system & exam dates:
| 40% | Homework |
| 20% | Quizzes |
| 20% | Term paper |
| 20% | Final exam (17 Dec) |
Grades will be assigned according to the following scheme:
| 87-100% | A |
| 75-86% | B |
| 58-74% | C |
| 50-57% | D |
| 0-49% | F |
I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.
Homework: I will assign homework problems as we go through the material. We can discuss the homework problems at any time during class. I will assign certain problems to be handed in; they will be due on the beginning of the Friday classes. For the corrections, I (and my grader) will use the redline method: Almost all of the homework exercises will consist of a proof; we will read your proof until a (real) mistake is found--this might be a sentence that is false or a sentence that has no meaning. We will draw a red line under that sentence and return the proof to you. It is your job to figure out why the red line was put there. Pasting as necessary so as not to have to rewrite the correct part (the part above the red line), you then hand in a new version and the process of redlining is repeated until the proof is right. Once your proof is correct, you get credit for that problem--the same credit whether it is right the first time or the sixth time. Every red line comes with a date stamp; your resubmission of that problem will be due a week from this date (at the beginning of class). If you choose not to resubmit your problem, you will get partial credit. It is your responsibility to file your homework submissions (ideally in a small binder); you should bring your complete works with you to the final exam and I will determine your homework grade then.
Here are two pieces of advice regarding homework: First, if you cannot understand why a red line was drawn, come to my office hours. Second, you may (and should) work together with your class mates. Having said that, the solutions you hand in have to be your own. I expect well composed solutions; you may want to experiment with Math typesetting programs.
Quizzes: I will frequently check your progress through unannounced quizzes given at the beginning of class. A quiz will typically test your concept of a certain definition or concept. There will be no make-up quizzes. At the end of the semester, I will drop the lowest of your quiz grades.
Term paper: This is a project you will be working on throughout the semester. The topic is up to you but needs to be checked with me. Topics could be anything from the history of a mathematical concept to subjects that go beyond the lecture notes. Here is a list of possible topics, but you should feel free to come up with your own ideas. I expect that you will have found a topic by the end of September. A first, possibly incomplete, draft is due on October 20. You will correct each other's drafts; the corrections are due on November 3. The final version of your paper is due on December 8. As with your homework, you may hand in your paper early to be able to get feedback from me.
The way to learn math is through doing math. It is vital and expected that you attend every lecture. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. The iLearn system allows you to send emails to anybody in your class. iLearn also features an online discussion board. Contact each other and work together.
Some more general fine print:
SFSU academic calender
Math typesetting programs
Tutoring
CR/NCR grading
Incomplete grades
Late and retroactive withdrawals
Students with disabilities
Religious holidays
This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.
