Math 327H: Honors Introduction to Analysis
Fall 2018
| Instructor: | Kristen Hendricks |
| Office: | D320 Wells |
| Office Hours: | M 11:20-12:20, W 3-4, Th 9-10 |
| E-Mail: | hendricks at math .msu .edu |
Location and Time
MWF 10:20-11:10 in A316 Wells Hall.Content
Real analysis is the study of the continuum of real numbers and other structures in mathematics constructed from the continuum. In this course, we will discuss some basic notions of logic, real and complex numbers, metric topology, sequences and series, real valued functions, continuity, differentiation, and integration. Some of these topics are familiar from calculus; however, our focus in this course is on theory rather than computation.Prerequisites
Approval of the department. Also, an interest in learning about the theoretical underpinnings of calculus and a willingness to work on challenging homework problems.
Textbook and Reading
W. Rudin, Principles of Mathematical Analysis. Third Edition. We will cover Chapters 1-6 of this textbook. There are also some helpful supplemental materials for the first few weeks of class posted below. Reading assignments will be distributed in advance of each weeks’ lectures. You will get the most out of lecture if you read the text before coming to class.
Attendance Policy
Attendance is not mandatory. However, you are very strongly encouraged to come to lecture. Lecture will often feature additional examples to complement those in the text, opportunities to briefly discuss the material with your classmates, and other useful things reading the textbook cannot provide.
Homework
Homework will be assigned weekly and due at the beginning of Friday’s lecture. There will be eleven homeworks. (There will not be a homework due the week of Thanksgiving, or the weeks that an exam is due.) No late homework will be accepted. Homework will not be accepted electronically. However, your lowest homework score will be dropped when computing your grade.
Typically three homework problems will be graded carefully, and some points will be given for completeness of the rest of the assignment. To receive full credit, a solution must be written out in clear prose. (This means that a solution should usually take the form of a paragraph of text.) Solutions that are incompletely or unclearly exposited will not receive full credit even if it appears that the mathematical content is correct.
You are encouraged to work in groups on your homework – this is generally beneficial to your understanding and helps you learn how to communicate clearly about mathematics. However, you must write up all solutions yourself. Moreover, since crediting your collaborators is an important element of academic ethics, you should write down with whom you worked at the top of each assignment. You must also cite any sources you use other than the lecture or the textbook (other textbooks, a blog about analysis, a useful Wikipedia article, etc.)
Exams
There will be two take-home exams during the semester. One will be assigned October 12 and due at the beginning of class on October 19. One will be assigned November 30 and due at the beginning of class December 7. There will not be a final exam.
Grading
Grades will be computed as follows:
The semester grades may be higher than the grading scale below, but they will definitely not be any lower.
Supplemental Reading
Homeworks
Homework 1 (Due September 7)Solutions
Homework 2 (Due September 14)Solutions
Homework 3 (Due September 21)Solutions
Homework 4 (Due September 28)Solutions
Homework 5 (Due October 5)Solutions
Homework 6 (Due October 12) All problems from Rudin, so no solutions.
Homework 7 (Due October 26)Solutions
Homework 8 (Due November 2)Solutions
Homework 9 (Due November 9)Solutions
Exams
Exam 1 (Due October 19)Solutions
Exam 2 (Due December 7)Solutions
Challenge Problems These problems are optional, and have no relationship with your grade.
On a related theme, you may also enjoy Polya and Szego's Problems and Theorems in Analysis II, available through SpringerLink.
(Also, you can find a copy of Manturov et al's Selected Problems in Real Analysis in the Advance Track lounge, C313. Let me know if you are having any trouble accessing it.)