Mathematics 3000.002 Syllabus
Fall 2014
Course Description: Introduction to mathematical proofs through real analysis. Topics include sets, relations, types of proofs, continuity and topology of the real line.
Course Objective: By the end
of the semester you should be very familiar with mathematical proofs of various
types including proof by induction, direct proof, proof by contradiction, proof
using the completion axiom, existence proofs, and uniqueness proofs.
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 subsets 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.
Prerequisite: Math 1720 or equivalent
Book: Analysis with an Introduction to Proof by Steven R. Lay (5th Edition)
Professor: Neal Brand
Office: GAB 417B M 2:00-2:50,
T 9:00-11:30, W 4:00-4:50, Th 9:00-11:30, F 1:00-1:50 and by appointment.
Please use these hours to ask questions of your instructor. Do not just
drop in at other times since your instructor will most likely be busy with
other responsibilities. If you need to see your instructor at another
time, make an appointment in advance.
Grading: Grades are based on three regular exams, homework, quizzes, a notebook and a final. The homework is worth a total of 100 points, each exam is worth 100 points, the quizzes are worth a total or 100 points, the notebook is worth 100 points, and the final is worth 200 points. This gives you a total of 800 possible points. To earn an A it is sufficient to make a total of 720 points, 640 for a B, 560 for a C, and 480 for a D. You are also required to complete the on-line course evaluation described below.
Course Evaluation: The SETE website will be open April 14 to May 4 for you to evaluate the course. You are required to complete an evaluation of the course sometime during the open period. Your instructor will not receive any other information that would link you to your specific answers or comments. The university, the mathematics department, and your instructor take your course evaluation input very seriously.
Homework: Homework will be assigned from the book and handouts. The assignments will be posted on the web. 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.
Exams: The exams will be in class and most likely they will be given on Abraham Lincoln’s 215th birthday (February 12), the day before Paul Erdos’ birthday (March 26) and Felix Klein’s birthday (April 25). The final exam is scheduled for the day after Audrey Hepburn’s birthday (Monday May 5 at 10:30).
Web Page: From the UNT home page follow through the links through the College of Arts and Sciences, the Mathematics Department and Neal Brand's home page to find the Math 3000 home page. You will find homework assignments, and other information concerning this class at that site. The URL is http://www.math.unt.edu/~brand/CLASS/3000/2014Spring/3000.htm .
Extra Credit: Do not expect to be able to do extra credit work to help your grade either before or after the final exam. There will be no extra credit for this course other than perhaps an extra problem on an exam. Please do not ask for extra credit work to help your grade. Your best bet to help your grade is to do the required work at the time it is assigned. For this class it is particularly important to keep up with what is done in class each day.
Cell Phones: Although not forbidden, the use of cell phones or other electronic devices to text, talk, browse or anything else not related to this class is strongly discouraged. (If you need to talk on your phone, go outside the room!) Their use is distracting to the user, other students and the instructor. It is essential to pay close attention and focus while in class in order to follow the logic and flow of the lecture and classroom discussion.
Disabilities: 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 http://www.unt.edu/oda. You may also contact them by phone at 940.565.4323.
Cheating: No cheating will be tolerated. Cheating includes receiving help from anyone or anything that is not specifically allowed on an exam, final, or project. For example, calculators are not allowed on exams and using one would constitute cheating. On the other hand, you are encouraged to work together on the regular homework assignments as long as everyone participates and no one just copies the answers. Anyone caught cheating will receive an F for the course. Furthermore, a letter will be sent to the appropriate dean. I expect no cheating in this class. (See the UNT website on academic dishonesty: http://www.vpaa.unt.edu/academic-integrity.htm.)
Last Comment: Anything on this syllabus is subject to change at the discretion of the instructor.