Full Syllabus (PDF)
Midterm Exam: Friday, 21 July (Solutions | TeX)
Take-home Final, due 18 August (TeX)
Take-home Exam Guidelines
In-class Final Exam: Friday, 18 August (Solutions | TeX)
Sample Exams: by John Palmieri, by Alexandra Nichifor
Review problems posted to homework page...

Instructor: Luke Gutzwiller
E-mail: gutzwill@math.washington.edu
Office: Padelford C-8M
Office Hours: Fridays 12-2, or by appointment
Textbook (Required): Mathematical Thinking, by D'Angelo and West
Further Reading (Optional!):

An Introduction to Mathematical Reasoning, by Peter Eccles
Naive Set Theory, by Paul Halmos
(Both should be on reserve at Odegaard.)

Homework and Readings
Schedule
Worksheets and Handouts
Discussion Board

Course Description
Most, if not all, math classes you have taken in the past have focussed on practical problem-solving, with calculus, linear algebra, probability, or what-have-you. This class is completely different. We are going to learn not how to use math, but how to actually do math. We are going to learn how to prove rigorously that mathematical statements are true or false, and how to communicate this to other people convincingly. In essence, we're going to learn how you go about creating new mathematics. This will be the cornerstone of any and all higher-level mathematics you go on to study. We will start off on logic and set theory, cornerstones of modern mathematics. We will go on to study induction, cardinality, number theory, and possibly topics from combinatorics, modular arithmetic, and other fields as time allows.

The Texts
The only required book for this class is Mathematical Thinking by D'Angelo and West. All our reading assignments will be taken from that. However, if you find this book less than fully satisfying, you may also wish to look at An Introduction to Mathematical Reasoning, by Peter Eccles, which offers a somewhat different take on the same basic material. A copy of this is on reserve at Odegaard. If you would like, for your own benefit, to read a more detailed yet not too formal treatment of set theory, I recommend Naive Set Theory by Paul Halmos. If you would like a very lengthy and comprehensive introduction to many of the ideas in modern algebra, topology, geometry, and mathematical physics, without requiring much background beyond the sort of mathematical literacy we will develop in this class, I might also recommend The Road to Reality by Roger Penrose. Just for fun.

Homework
Homework will be due (almost) every week on Monday. Assignments will be posted on the web. Late homeworks will not be accepted after 3.30 on the due date. The homework problems will go beyond simple calculation: you will be required to write up detailed and logical step-by-step arguments, in the form of proofs. Most of you will likely not be very familiar with such things yet, but this is no cause for alarm. We will start off slowly and gently. You will be graded not only on your reasoning, but also on your writing, to a degree. A vitally important part of learning to write proofs is learning how to put mathematical reasoning into clear, comprehensible ordinary human language other math fans can read and grasp. This is not an English class, so I will not nail you on minor points of grammar or style, but I do expect you to put your proofs into simple, unambiguous, readable sentences. We will see examples of good (and bad) mathematical writing as the course progresses.

We will spend Fridays working on the homework in small groups. You are all responsible for writing up and turning in the homework individually, though; please list on your paper which classmates you worked with.

Homework will be worth 35% of your final grade.

Reading Reports
You will not be able to succeed in the class unless you spend a significant amount of time independently reading the text and making sense of the material. To this end, every week you are required to submit a reading report on that week's assigned sections from the book. This should be a short paragraph summarizing the main ideas of the reading, and posing one or two comments or questions on what you've read. These should be posted each week by midnight Sunday to the class discussion board. Be sure each time to include your name and which reading assignment you are reporting on. Feel free to read others' and respond to them politely on the discussion board.

Reading reports will count for about 5% of your final grade. You may miss one without penalty, but only one.

Exams
There will be one midterm exam and a two-part final. One part will be taken in class on the last day of the summer quarter. The other will be a take-home graded entirely on your writing. The midterm and the final will each be worth about 30% of your final grade. We'll discuss these in more detail when the time comes.

If you know in advance that you will have to miss an exam, let me know as soon as possible. I may or may not allow you to schedule a make-up, depending on how good a reason you have. If something disasterous happens to you, like a fire or automobile accident or family emergency, that forces you to miss an exam, contact me as soon as possible to set up a make-up. I will want to see some kind of written confirmation that forces beyond your control were involved.

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