## Fall-2011. Math 104 (ccn 54281): Introduction to Analysis

Instructor: Alexander Givental
Lectures:
MWF 9-10, room: 4 Evans
Room change: 740 Evans, starting Mon, Aug 29 - no food or drink allowed!
• Office hours: M 1:00-3:00 p.m., in 701 Evans
• Textbook author: W. Rudin
• Textbook title: Principles of Mathematical Analysis, McGrow Hill, 3rd edition.
• Syllabus: Chapters 1-7.
• Grading: 40% Homework, 20% Midterm, 40% Final.
• HW: Weekly homework assignments are posted to this web-page, and your solutions are due on Friday in class.
Typically your homework will be returned to you in a week from the due date with some of the problems graded by our reader.
• Academic honesty policy: All exams are closed books / closed notes. In homework, while it is recommended that you work on your own, no form of collaboration is prohibited. So, one can discuss problems with others, read books, use electronic sources, hire tutors, etc. However, any use of outer sources must be acknowledged in the submitted solution. Failure to acknowledge the use of someone else's ideas is commonly known as academic plagiarism.
• Midterm Exam: Friday, October 14; Chapters 1-3.
• Final Exam: Thursday, Dec 15, 7-10 p.m.

#### HOMEWORK

HW1, due by Fri, Sep 2: Solve exercises 5, 8, 9, 13, 14 of Chapter 1.
HW2, due by Fri, Sep 9: Solve exercises 2, 12, 17, 18 of Chapter 1, and prove the following
Theorem. For any distinct real numbers x and y, there is a rational number r that lies between them. Find explicitly a rational number that lies between the square root of 10 and the number pi (the famous 3.14....)
HW3, due by Fri, Sep 16: Solve Exercises 2,3,4,10,11 of Chapter 2.
Here is a youtube link found by Irina Titova, a student in our class, where Hilbert's Hotel is mentioned.
HW4, due by Fri, Sep 23: Solve exercises 6, 8, 12, 14, 15 of Chapter 2.
HW5, due by Fri, Sep 30: Solve exercises 19d, 20, 21c of Chapter 2, and exercises 1, 2 of Chapter 3.
HW6, due by Fri, Oct 7: Solve exercises: 4, 5, 16, 20, 23 of Chapter 3.
HW7, due by Fri, Oct 14: Solve exercises: 6,7,8,9,10 of Chapter 3.
HW8, due by Fri, Oct. 21: Solve exercises: 1,3,4,6,7 of Chapter 4.
HW9, due by Fri, Oct. 28: Solve exercises: 8, 10, 11, 13, 21 of Chapter 4.
HW10, due by Fri, Nov. 4 Solve exercises: 14, 15, 18 of Chapter 4, and exercises 1, 13 of Chapter 5.
HW11, due by Mon, Nov. 14. Solve exercises: 2, 5, 9, 22 of Chapter 5, and also compute the limit of (x/tan(x))ยดยดยดยด (the fourth derivative), as x -> 0.
HW12, due by Fri, Nov. 18. Solve exercises: 2, 4, 5, 6, 8 of Chapter 6.
HW13, due by Mon, Nov. 28. Solve exercises: 1,2,3,8,9 of Chapter 7.
HW14, due by Fri, Dec. 2. Solve exercises: 15,16,18 of Chapter 7.
HW15, due by Fri, Dec. 9. Solve exercises: 14,19,20,22,24 of Chapter 7.