MATH 3000.001 Real Analysis I

Fall 2014

Instructor: Dr. Kiko Kawamura

Email:

Website:

Office/Office Hrs: GAB 433, MTWR: 11am-noon, TR: 1-2pm

Course Meets: CURY 110 MWF: 1:00-1:50pm

Textbooks: Analysis with an Introduction to Proof by Steven R. Lay (5th edition)

Prerequisite: Math 1720 or equivalent

Course Description:

A better title for this course might be” how to think like a mathematician”. This class will be considerably different than any previous math class you have taken (most likely). Unlike your previous classes, there are not many important mathematical “facts” to learn from this class. Generally, we will NOT be learning any computational “rules”. Instead, the important part of this class is teaching you how to communicate in a mathematically precise fashion and prove mathematical statements; in a sense, you are learning a language and you cannot expect to speak it by tying to pick it up the day before you need it. It takes considerable effort and practice. You will recognize some of the ideas presented in this class from your calculus courses, but we will look at them in a different way than you did in calculus.

By the end of the semester, you should be familiar with mathematical proofs of various types including proof by induction, direct proof, proof by contradiction, proof using the completion axiom, existence proof, and uniqueness proof. Furthermore, you will be able to construct proofs using these techniques. The real analysis you will learn include basic cardinality proofs, axioms of the real numbers, the concepts of open and closed subset of the real numbers, continuous functions and compact sets. You will learn how to put these ideas together to prove the Intermediate Value Theorem and the Extreme Value Theorem from calculus.

Grading Scheme:

Exams (best 2/3)– 40%

Homework (after dropping three lowest grades)–20%

Quiz/Class work(after dropping three lowest grades) - 20%

Comprehensive final exam - 20%

Grades: A 90%-100%, B 80% - 89%, C 70% - 79%, D 60% - 69%, F below 60%

Class Attendance:

Required. Attendance and participation are significant part of your grade since this course is more an experience than a set of material to be learned. More than fiveabsences may lower your grade.

Exams: The following schedule is tentative and is subject to capricious changes in case of extracurricular events deemed sufficiently important to the upper administration.

Three Exams:Exam 1: September 26(Friday)

Exam2: October 29(Wednesday)

Exam3: November 24 (Monday)

Comprehensive Final Exam: Friday, December 12, 11:00am-1:00pm!

Code of Conduct: Students are expected to be respectful of others at all times. This includes keeping talk and other noise to a minimum while a lecture is in progress or an exam is being taken. Any student being disruptive may be dismissed from the class meeting. Cheating will NOT be tolerated and anyone found guilty of cheating may receive and F for the course.

HomeworkPolicy:

  • Homework will be assigned from the book and handouts. Soon after class each day the homework assignments will be posted on blackboard in the course content tab. The reading assignments are to be completed by the beginning of class on the days indicated. The class discussion will focus on the reading assignment.
  • You are expected to turn in neatly written homework. If the grader has trouble reading the homework, then the homework will be returned with a zero.
  • When computing the final grade, I will drop the three lowest homework before computing the average. I have this policy in case you get sick, have a family emergency, etc., during the semester. You will still be responsible for the material in such assignments during the examinations. Because of this policy, I will NOT give any extensions on homework assignments, nor will I accept late assignments for any reason whatsoever.

Tutoring:

  • If you are having trouble, please make full use of my office hours. Working together with other students is also a good way to get help, but just be sure you are also able to work alone when it comes time to take the tests. This course tends to be difficult for most students. From personal experience, believe me that you will ultimately benefit far more by struggling with a problem than you will by having a solution presented to you. I highly recommend you start the homework early and think about a troubling problem for at least a day before seeking help.
  • Math 3000 is not one of the courses eligible for math lab tutoring; however, there is a specialized tutoring sessions offered by UNT graduate students as follows. The location is GAB 440A (the small room inside of the Math Lab).

Cory Krause / Tuesday and Thursday: from 12:30-1:30pm
Chris Allen / Fridays from 1-4pm
Angela Berardinelli / Tuesdays from 1:30-3:30pm and Wednesdays from 2-3pm

Make-up Policy: NO MAKE-UP examsand quizzes WILL BE GIVEN. An exam may be taken prior to the scheduled date. I request a week’s notice for this accommodation via email. In the event of a schedule conflict with a university function, dental/physician’s appointment, wedding, formal, etc., you must take the exam early. If you do not take a scheduled exam, a zero will be recorded. Two best grades of exams will be used to determine the final grade.

When computing the final grade, I will drop the three lowest quiz grades before computing the average. I have this policy in case you get sick, have a family emergency, etc., during the semester.

Again, NO MAKE-UP exams and quizzes WILL BE GIVEN FOR ANY REASON EVER.

START WORKING NOW: The best way to ensure you pass this course is to work consistently throughout the semester. In mathematics courses topics always build one upon the other making it very difficult to catch up later if you fall behind. If you need to pass this course because it is your last semester, your financial aid depends on it, your scholarship depends on it, or your parent/guardian has threatened to harm you in some manner then do yourself a favor and start studying right away. I will not entertain any pleas for extra credit or offers to do additional work at the end of the semester.

Disability Accommodations: The University of North Texas makes reasonable academic accommodation for students with disabilities. Students seeking accommodation must first register with the Office of Disability Accommodation (ODA) to verify their eligibility. If a disability is verified, the ODA will provide you with an accommodation letter to be delivered to faculty to begin a private discussion regarding your specific needs in a course. You may request accommodations at any time, however, ODA notices of accommodation should be provided as early as possible in the semester to avoid any delay in implementation. Note that students must obtain a new letter of accommodation for every semester and must meet with each faculty member prior to implementation in each class. For additional information see the Office of Disability Accommodation website at You may also contact them by phone at 940.565.4323.

The Student Evaluation of Teaching Effectiveness (SETE) is requirement for all organized classes at UNT. This short survey will be made available to you at the end of the semester, providing you a chance to comment on how this class is taught. I am interested in feedback from students as I work to continually improve my teaching. I consider the SETE o be an important part of your participation in this class.

Course Outline:

Meeting 1 – Introduction to the course

Meeting 2 – Topology of R (Section 3.4)

Meeting 3, 4 – Set Theory (Section 1.2)

Meeting 5, 6 – Logic (Section 1.1)

Meeting 7 – Quantifiers (Section 1.2)

Meeting 8, 9, 10, 11, 12 – Topology of R (Section 3.4)

Meeting 13 – Axioms of R (Section 3.2)

Meeting 14, 15, 16– Completion Axiom (Section 3.3)

Meeting 17 – Relations (Section 2.2)

Meeting 18, 19 – Functions (Section 2.3)

Meeting 20, 21, 22, 23–Continuous functions (Section 5.2)

Meeting 24 – Proof of Intermediate Value Theorem (Section 5.3)

Meeting 25, 26, 27, 28 - Compact sets (Section 3.5)

Meeting 29 – Proof of Extreme Value Theorem (Section 5.3)

Meeting 30, 31, 32 – Proof by Induction (Section 3.1)

Meeting 33– Cardinality (Section 2.4)

Course Calendar Fall 2014 (Tentative)

MONDAY / TUESDAY / WEDNESDAY / THURSDAY / FRIDAY
8/25
Meeting 1 / 8/26 / 8/27
Meeting 2 / 8/28 / 8/29
Meeting 3
9/1
LABOR DAY
University closed / 9/2
MATH LAB OPENS for the semester / 9/3
Meeting 4 / 9/4 / 9/5
Meeting 5
9/8
Meeting 6 / 9/9 / 9/10
Meeting 7 / 9/11 / 9/12
Meeting 8
9/15
Meeting 9 / 9/16 / 9/17
Meeting 10 / 9/18 / 9/19
Meeting 11
9/22
Meeting 12 / 9/23 / 9/24
Review / 9/25 / 9/26
Exam 1
9/29
Meeting 13 / 9/30 / 10/1
Meeting 14 / 10/2 / 10/3
Meeting 15
10/6
Meeting 16 / 10/7 / 10/8
Meeting 17 / 10/9 / 10/10
Meeting 18
10/1
Meeting 19 / 10/14 / 10/15
Meeting 20 / 10/16 / 10/17
Meeting 21
10/20
Meeting 22 / 10/21 / 10/22
Meeting 23 / 10/23 / 10/24
Meeting 24
10/27
Review / 10/28 / 10/29
Exam 2 / 10/30 / 10/31
Meeting 25
11/3
Last day to drop a course with consent of instructor
Meeting 26 / 11/4 / 11/5
Meeting 27 / 11/6 / 11/7
Meeting 28
11/10
Meeting 29 / 11/11 / 11/12
Meeting 30 / 11/13 / 11/14
Meeting 31
11/17
Meeting 32 / 11/18 / 11/19
Meeting 33 / 11/20 / 11/21
Last day for an instructor to drop a student with a grade of “WF” for non-attendance
Review
11/24
Exam 3 / 11/25 / 11/26
Review for the final / 11/27
Thanksgiving
University Closed / 11/28
Thanksgiving
University Closed
12/1
PRE-FINAL WEEK
Review for the final / 12/2
PRE-FINAL WEEK / 12/3
PRE-FINAL WEEK / 12/4
PRE-FINAL WEEK / 12/5
READING DAY
NO CLASSES
4:00 pm – MATH LAB CLOSES for the semester
12/8
FINALS WEEK / 12/9
FINALS WEEK
/ 12/10
FINALS WEEK / 12/11
FINALS WEEK / 12/12
FINALS WEEK
Final exam : 11am-1pm

I reserve the right to change this schedule as necessary throughoutthe semester. You are responsible for being aware of any changes I announce in class.