**Spring 2015. MATH4351. Section 001. (CRN 27550) **

**Instructor:** Luan Thach Hoang

Office: MA 208.
Phone: (806) 834-3060
Fax: (806) 742-1112

Email address: *luan.hoang@ttu.edu*

Homepage: *http://www.math.ttu.edu/~lhoang/*

Office hours: TR 10:00 am - 11:30 am

**Time and Classroom:** TR 2:00 pm - 3:20 pm Mathmematics Building 013

**Course website:**
*http://www.math.ttu.edu/~lhoang/2015Spr-M4351/*

Updates about the course and other related announcements will be posted on this webpage.

**Prerequisite:** MATH 4350.

**Text:** *Introduction to Real Analysis,* 4th edition by R. G. Bartle and D. R. Sherbert, published by Wiley & Sons, Inc., and Chapter 11 of *Methods of Real Analysis* by Goldberg, 2nd ed., available from CopyTech

**Course Description:** This course covers theory of differentiation and integration, sequences and series of functions, introdution to measure theory, and multi-variable calculus. Students are expected to present rigorous proofs. This is a writing intensive course.

**Course Outline:**

- Review, supplementaries
- Chapter 6 - Differentiation
- Chapter 7 - The Riemann integral
- Chapter 8 - The Riemann integralSequences of fuctions
- Chapter 9 - Infinite series
- Chapter 11 - A glimpse into topology
- Chapter 11 from Goldberg
- Multi-variable calculus

**Expected Learning Outcomes:** Students learn how to think and reason abstractly in the context of analysis, and learn how to write correct and clear mathematical arguments in this context. There will be a heavy emphasis on proofs, especially epsilon-delta proofs. Concepts and skills to be mastered by the students include but are not limited to: L’Hospital’s Rules, Taylor’s Theorem, the Riemann integral, sequences of functions, infinite series, introduction to the topology of the line, introduction to Lebesgue measure and integration, and fundamentals of multi-variable calculus.

**Methods of Assessment of Learning Outcomes:** Assessment of
the learning outcomes will be achieved through homework assignments, writing excercises,
two midterm exams, and a final exam.

**Homework Assignments:** Written homework will be assigned
weekly and will be collected in class. Each is worth of 100 points.

**Writing Exercises:** Writing exercises will be assigned
weekly and will be collected in class. Each is worth of extra 10 points added to the homework grades.

**Grading Policy:** Homework will count for 30% of the grade.
The lowest score of homework will be dropped. There will be two
midterm exams in class, each will count for 20% of the grade. The
final exam will count for 30% of the grade. All in-class exams are
closed-book. No make-up exams are given unless legitimate documents
for excuses are presented to the instructor at least a week in
advance. Grading Scale: A: 90%-100%, B: 80%-89%, C: 70%-79%, D:
60%-69%, F: below 60%

**Attendance Policy:** Students must go to lectures and
attendance will be taken. If you miss no more than four lectures, a
bonus of three points will be added to your final grade.

**Examination Schedule:**

Midterm 1: Thursday, February 26.

Midterm 2: Thursday, April 9.

FINAL EXAM: 4:30 p.m. - 7:00 p.m., Thursday, May 7, 2015, Room MA 013.

**Critical Dates:**

Jan. 14: Classes begin.

Jan. 19: Martin Luther King Jr. Day. Holiday.

Jan. 30: Last day for student-initiated drop on MyTech without academic penalty.

Mar. 14 - 22: Spring Break.

Apr. 6: No classes.

Apr. 29 - May 5: No exams.

May 5: Last day of classes.

**Academic Misconduct:** Academic dishonesty is intolerable and
will be punished to the full extent allowed by the University policy.

**Civility in the Classroom:** Texas Tech University endeavor
to foster a classroom climate of mutual respect among students and
between students and teacher. Students are expected to maintain a
classroom environment that is conducive to learning. In order to
assure that all students have the opportunity to gain from time spent
in class, unless otherwise approved by the instructor, students are
prohibited from engaging in any other form of distraction. Students
must * attend class on time and are not allowed to leave the
class before the end of the hour* without authorization.
During class time students are not allowed to eat, smoke, drink
alcohol, text, chat, sleep, play games, read newspapers, wear
earphones, play with smart phones or tablets, etc. Please put silent
mode to all your electronic devices. Inappropriate behavior in the
classroom shall result, minimally, in a request to leave class.

**Students with Disabilities:** Any student who because of a
disability may require special arrangements in order to meet course
requirements should contact the instructor as soon as possible. *I
would appreciate hearing from anyone who has a disability that may
require special accommodations. I am sure we can work out whatever
arrangements are necessary. Please see me during my office hours.*
Student Disability Services office is in 335 West Hall (phone:
806-742-2405).

**Advice:** Come to class regularly, work on homework problems.
Ask questions in class and get help from the instructor during the
office hours. Since a lot of material will be covered, students have
to master them quickly and do not wait too late until the midterms or
the final exam. Students are encouraged to give feedbacks to the
instructor during the semester.

*NOTE:* When needed, the instructor will communicate with the
students using their TTU email addresses. At the beginning of the
semester, the instructor will send an email to confirm the students'
email addresses. If a student does not receive this message by the
time of the second class, he/she must contact the instructor
immediately.