Exams

There will be two midterm exams (evening exams) and a final exam (comprehensive). Exam dates will be announced here at least two weeks in advance.

Final Exam

Scheduled on Thur, Dec 18, 8:00–10:00am in HAAS G066.

As before, you will be permitted to bring a copy of the book [R] to the exam. No other books or notes will be allowed (particularly, the copy of [R] that you bring should not contain any notes, but highlights are fine.)

The exam will be comprehensive, i.e., covering all material in the course. We will have  two review sessions for the final (Wed, Dec 10 and Fri, Dec 12).

[Additional Practice Problems for Final Exam]

Final Score

Your final score is going to be calculated by the following scheme:

Final Score =(1/3) FE + (7/30) ME1+ (7/30) ME2+(1/5) HW

where FE, MEi, HW are the scores (in %) for Final Exam, Midterm i, Homework

Midterm Exam 2

Scheduled on Thur, Nov 20, 8:00–9:30pm in LWSN B155.

The exam will cover Chapters 3 (starting with Series), 4, 6, 7 (up to and not including Equicontinuos Families of Functions)

You will be permitted to bring a copy of the book [R] to the exam. No other books or notes will be allowed (particularly, the copy of [R] that you bring should not contain any notes, but highlights are fine.)

The class on Mon, Nov 24 will be cancelled to compensate for the evening exam.

We will have a review on Wed, Nov 19, in class.

[Midterm Exam 2 Practice Problems]

[Midterm Exam 2 Solutions]

Midterm Exam 1

Scheduled on Thur, Oct 9, 8:00–9:30pm in MA175 (evening exam)

The exam will cover Chapters 1, 2, 3 (up to and not including Series) from [R].

You will be permitted to bring a copy of the book [R] to the exam. No other books or notes will be allowed (particularly, the copy of [R] that you bring should not contain any notes, but highlights are fine.)

We will have a review on Wed, Oct 8, in class.

[Midterm Exam 1 Practice Problems]

[Midterm Exam 1 Solutions]

Course Log

Here you can find the information on the material already covered in the course or planned to be covered in the next few lectures.

Planned

• Fri, Dec 12: Review for Final
• Wed, Dec 10: Review for Final

Covered

• Mon, Dec 8: 8.3-8.5
• Fri, Dec 5: 8.1
• Wed, Dec 3: 7.32
• Mon, Dec 1: Midterm 2 Overview, 7.30-7.31
• Fri, Nov 28: No class (Thanksgiving)
• Wed, Nov 26: No class (Thanksgiving)
• Mon, Nov 24: No class (cancelled because of evening exam)
• Fri, Nov 21: 7.26-7.29
• Wed, Nov 19: Review for Midterm 2
• Mon, Nov 17: 7.25-7.26
• Fri, Nov 14: 7.19-7.24
• Wed, Nov 12: 7.17-7.18
• Mon, Nov 10: 7.11-7.12, 7.14-7.16
• Fri, Nov 7: 7.1-7.10
• Wed, Nov 5: 6.17, 6.19-6.22
• Mon, Nov 3: 6.12-6.16
• Fri, Oct 31: 6.8-6.11
• Wed, Oct 29: 6.2-6.7
• Mon, Oct 27: 4.28-4.34, 6.1
• Fri, Oct 24: 4.22-4.27
• Wed, Oct 22: 4.13-4.20 
• Mon, Oct 20: 4.8-4.9, 4.11
• Fri, Oct 17: 4.1-4.7, 4.10
• Wed, Oct 15: Midterm 1 Overview, 3.38-3.46
• Mon, Oct 13: No class (October break)
• Fri, Oct 3: No class (cancelled because of evening exam)
• Wed, Oct 8: Review for Midterm 1
• Mon, Oct 6: 3.33-3.40
• Fri, Oct 3: 3.26-3.32
• Wed, Oct 1: 3.20-3.25
• Mon, Sep 29: 3.17-3.19
• Fri, Sep 26: 3.13-3.16
• Wed, Sep 24: 3.6-3.12
• Mon, Sep 22: 3.3-3.6
• Fri, Sep 19: 2.47, 3.1-3.2
• Wed, Sep 17: 2.44-2.46
• Mon, Sep 15:2.37-2.42
• Fri, Sep 12: 2.27, 2.31-2.32, 2.34-2.35
• Wed, Sep 10: 2.18, 2.20-2.27
• Mon, Sep 8: 2.13-2.16, 2.18, 19
• Fri, Sep 5: 2.1-2.12
• Wed, Sep 3: 1.23, 1.35-1.38
• Mon, Sep 1: No class (Labor Day)
• Fri, Aug 29: 1.19-1.21
• Wed, Aug 27: 1.10-1.18
• Mon, Aug 25: 1.1-1.9

Homework Assignments

There will be weekly homework assignments. The exact due dates and assignments will be posted here, at least one week prior to deadline.

10. Due, Fri, Dec 5: [R], pp. 165-171: 16, 18, 19, 20, 21
    [Solutions]
9. Due Mon, Nov 17: [R], pp. 165-171: 1, 2, 5, 8, 10
   [Solutions]
8. Due Fri, Nov 7: [R], pp.138-142: 2, 5, 6, 11, 12, 17
   [Solutions]
7. Due Fri, Oct 31: [R], pp.98-102: 6, 18, 20, 21, pp.138-142: 1, 4
   [Solutions]
6. Due Wed, Oct 22: [R], pp.78-82: 10, 11(a,b), pp.98-102: 2, 4, [18 - this problem is postponed]
   [Solutions]
5. Due Mon, Oct 6: [R], pp.78-82:  4, 5, 7, 16(a-b), 19
   [Solutions]
4. Due Fri, Sep 26: [R], pp.43-45: 19(a-d), 20; pp.78-82: 1, 20, 21, 23
   [Partial Solutions]
3. Due Fri, Sep 19: [R], pp.43-45: 12, 14, 15, 16, [17 – this problem will not be graded]
   [Partial Solutions]
2. Due Fri Sep 12: [R], pp.22–23: 16; pp.43-45: 2, 4, 5, 7(a-b), 9 (a-f)
   [Solutions]
1. Due Wed Sep 3: [R], pp.22–23: 4, 5, 6(a-d), 7(a-f)
   [Solutions]

Announcements

• 11/11/14: Midterm Exam 2 is scheduled on Thur, Nov 20, 8:00–9:30pm in LWSN B155. For more information see Exams page.
• 9/21/14: Midterm Exam 1 is scheduled on Thur, Oct 9, 8:00–9:30pm, in MATH 175. For more information see Exams page.
• 8/19/14: Welcome to MA50400 course webpage!

Course Information

Time and Place: MWF 11:30am–12:20pm in REC 113

Instructor: Arshak Petrosyan

Office Hours: MWF 9:30-10:30, or by appointment, in MATH 610

Textbook: [R] W. Rudin, Principles of mathematical analysis, Third edition, McGraw-Hill, New York, 1976

Homework will be collected weekly on Wednesdays. The assignments will be posted on this website at least one week prior the due date.

Exams: There well be two midterm exams (evening exams) and a comprehensive final exam (covering all material). The exact time and place will be specified at least two weeks in advance.

Description: Completeness of the real number system, basic topological properties, compactness, sequences and series, absolute convergence of series, rearrangement of series, properties of continuous functions, the Riemann-Stieltjes integral, sequences and series of functions, uniform convergence, the Stone-Weierstrass theorem, equicontinuity, and the Arzela-Ascoli theorem.

Syllabus:
Chapter 1. The Real and Complex Number System

• Real number system - (Emphasize inf, sup)
• Extended real number system
• Euclidean spaces

Chapter 2. Basic Topology

• Finite, countable and uncountable sets
• Metric spaces (Only a few special examples)
• Compact sets

Chapter 3. Numerical Sequences and Series

• Convergent sequences
• Subsequences
• Cauchy sequences
• $\limsup x_n$ and $\liminf x_n$
• Series
• Series with many terms (comparison test)
• Absolute and conditional convergence
• Rearrangements

Chapter 4. Continuity

• Limits of functions
• Continuous functions
• Continuity and compactness
• Intermediate Value Theorem

Chapter 6. The Riemann-Stieltjes Integral

• Definition and existence
• Properties
• Integration and differentiation

Chapter 7. Sequences and Series of Functions

• Uniform convergence
• Uniform convergence and continuity
• Uniform convergence and integration
• Uniform convergence and differentiation
• Equicontinuous families of functions
• Stone-Weierstrass Theorem

Optional Topics

• Sets of Lebesgue measure zero
• Characterization of Riemann integrable functions bounded and continuous a.e.
• Differentiability a.e. of monotone functions