| Office: | Padelford C-528 |
| Office Hours: | Fridays 3:30-5:30 after that |
| TA, email and Office Hours: | Roy Han, royhan[_a_t_]math.washington.edu, Mondays 4-6, office PDL C-8K |
| Classroom: | LOW
113 |
| Hours of Instruction: | MWF 11:30-12:20 |
| Textbook: | Principles of Mathematical Analysis 3rd Ed, by
W. Rudin. NOTE: The role of the textbook is to serve as a reference for material covered in class, and so any alternative will also do, so long as it covers what we will be covering (see "Material Covered" below). Rudin is quite expensive, but is one of the best analysis textbooks available. Alternatives books (that are cheaper, although perhaps with dated font and alternate notation and proofs) include Rosenlicht and Apostol, the latter being available on reserve at the math library along with Rudin (please avoid using Kenneth Ross' book). These books are also good for finding extra practice problems. Consult me if you're unsure about whether a book will be sufficient for the course. |
| Material Covered: |
The general aim of the 424/425/426 series is to reconstruct
calculus from more basic principles, carefully handling some
of the results and assumptions that were taken for granted
(for example, what is a real number). We'll first start by
introducing the basics of set theory (ordered sets,
cardinality). Assuming the existence of the integers and
rational numbers, we will use this as the basis for
rigorously constructing the real numbers. After this, we'll
introduce metric spaces (geometry of abstract sets when all
you know are distances between points). We'll talk about
several important properties and results for abstract metric
spaces (compactness, perfect sets, connectivity...) but with
particular emphasis on understanding Euclidean space.
Finally, we'll study sequences, series, and continuity
(which may be familiar to some, but hopefully will be more
challenging). Additional subjects may be covered if time
permits. |
| Homework and reading: | Each week I will assign a list of problems along with a
due date on this webpage (not all problems will be from the
textbook). Students are responsible for checking the
homepage regularly for new assignments, turning assignments
in at their respective due dates, and checking for changes
to the homework (throughout the week I may add or correct
problems or change the due date). No late assignments will
be accepted. Insha'allah, your homework will be graded and
handed back at the end of class within a week. Not all
problems will be graded, so for additional feedback on your
skills, come to office hours. In addition, I will assign the relevant reading for the week. These will consist of sections from the book as well as my own lecture notes. My lectures will not be identical with the text book, so the lecture notes are intended to supplement the material and explain content and notation not present in the book. Please forgive the inevitable and prolific typos and errors in my notez, and let me know if you spot any. For these weekly assignments, see the bottom of the page. |
| Recommended problems: | Not all problems in the textbook are relevant to the
material we are covering, and some are infeasibly difficult.
Below, however, I will recommend relevant problems from the
book. For adequate practice with the material, you should
attempt all of these plus all problems provided in the
lecture notes.
|
| Exams: | There will be two midterms (tentatively on October 23 and November 22 respectively) and a final exam ( Wednesday, December 11, 2013, 2:30-4:20 pm, LOW 113). There are no make-up exams. |
| Grading: | Homework is worth 30% (the lowest homework is dropped),
the maximum of your two midterm scores is worth 30%, and the
final exam is worth 40% of your final grade. Final grades
will be based upon overall class performance. |
| Calculators: | No calculators may be used on quizzes or exams. |
| Week 1: |
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| Week 2: |
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| Week 3: |
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