This course continues 110.415 Honors Analysis I, with an emphasis on the fundamental notions of modern analysis. Topic here include functions of bounded variation, Riemann-Stieltjes integration, Riesz representation theorem, along with measures, measurable functions, and the lebesgue integral, properties of Lp- spaces, and Fourier series.

Text book: Real Analysis, by Carothers, Cambridge, ISBN:9780521497565

Liming Sun Krieger 222 lsun at math.jhu.edu

Junyan Zhang Krieger 211 jzhan182@math.jhu.edu

Time: MW 01:30-02:45PM

Location: Bloomberg 172, Homewood Campus

Office Hour: T 10:00am-11:30am and Th 4:00-5:00pm or by appointment

Section 1: T 01:30 PM - 02:20 PM Krieger Laverty

Final: 50%

Midterm: 25%

Homework: 25% overall

Homework’s due date will be announced explicitly. All homework must be handed in hard copy at the beginning of section class. The two lowest homework will be dropped.

There will be one in-class midterm. First one is placed on 3/13. The final examination given at 5/1 in the last class.

No late homework

No cell phone or computer in the class

You are expected to attend every class. The course will pick up its pace gradually. As such, it will be very easy to fall behind, even from missing a single class. Please do not be late for the lecture and recitation.

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the “Statement on Ethics” at the Ethics Board website for more information.

Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at two weeks prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.

**Week 1: 1/28 & 1/30 Chapter 11 The space of continuous functions**

\(\hspace{1.5cm}\) Homework 1: chapter 11, #45 #46 #47 #48 #60 #61 #64 #65

**Week 2: 2/4 & 2/6 Chapter 14 The Riemann-stieltjes integral**

\(\hspace{1.5cm}\) Homework 2: Chapter 6 of Rudin: #1 #2 #3 #5 #6 #7 #8

**Week 3: 2/11 & 2/13 Chapter 14 The Riemann-stieltjes integral**

\(\hspace{1.5cm}\) Homework 3: Chapter 6 of Rudin: #10:(a), (b), (c), #11 #12

**Week 4: 2/18 & 2/20 Chapter 15 Fourier Series**

\(\hspace{1.5cm}\) Homework 4: Chapter 15: #1 #2 #6 #7

**Week 5: 2/25 & 2/27 Chapter 15 Fourier Series**

\(\hspace{1.5cm}\) Homework 5

**Week 6: 3/4 &3/6 Chapter 16 Lebesgue outer measure**

**Week 7: 3/11 & 3/13 First midterm**

\(\hspace{1.5cm}\) Homework 6: Chapter 15: #9 #11 Chapter 16: #5 #7 #9 #13

**Week 8: Spring Break**

**Week 9: 3/25 & 3/27 Chapter 16 Lebesgue outer measure **

**Week 10: 4/1 & 4/3 Chapter 16 Lebesgue outer meansure**

\(\hspace{1.5cm}\) Homework 7: Chapter 16: #40 #43 #44 #48 #52 #53(i) (ii)

**Week 11: 4/8 & 4/10 Chapter 17 Measurable functions**

\(\hspace{1.5cm}\) Homework 8: Chapter 16: #62 #68 #78 Chapter 17: #4 #5 #6 #7 #18

**Week 12: 4/15 & 4/17 Chapter 17: Measurable functions**

\(\hspace{1.5cm}\) Homework 9: Chapter 17: #29 #31 #35 #46 #48 #50

**Week 13: 4/22 & 4/24 Chapter 18: The Lebesgue Integral**

\(\hspace{1.5cm}\) Homeowork 10: Chapter 18: #4 #6 #9 #12 #14 #17

**Week 14: 4/29 & 5/1 Chapter 18: The Lebesgue Integral**

\(\hspace{1.5cm}\) Suggested Homework: #22 #23 #27 #36 #40 #46 #47

\(\hspace{1.5cm}\) Final exam

**Final exam 5/1**