## Milestone Course in the Mathematical Sciences, MATH 250X, Spring 2015

This is the home page and first day handout for MATH 250X, meeting Fridays, 2:30pm -- 4:20pm, in CBC C116.  My name is Dr. Arthur Baragar, my office is CDC-1016, and I can be reached at (702) 895-0378. Important information announced in class will also be posted on WebCampus. The prerequisite for this course is MATH 182 (Calculus II), and the co-requisite is a linear algebra class (MATH 330 or MATH 365).

Purpose: To see interesting mathematical results that are now accessible to the students; to see interesting results that introduce the students to subjects they will see in future courses, notably Differential Equations (MATH 427), Real Analysis (MATH 457), and Abstract Algebra (MATH 453); to explore topics that are beyond the scope of their senior level courses; and to think about and participate in the communication of mathematics. Prerequisite: MATH 182. Co-requisite: Either MATH 330 or MATH 365. Recommended co-requisite: MATH 283.

Text: There is no textbook. I hope to provide lecture notes.

Sylabus (for half the course): The following are our expected topics:
• What is pi? The number pi is defined as the ratio of the circumference of a circle to the diameter of the circle. We have been told that pi = 3.14159265 ..., and that "we" know pi to thousands of digits. That knowledge cannot be experimental -- we cannot get that many digits of accuracy by taking measurements of circumferences and diameters. So how do we know what pi is?
• How far away is the moon? Using our collective knowledge and some calculus, we will calculate the distance from the Earth to the Moon.
• The hanging chain problem. In this lecture, we set up the differential equation that models the shape of a cable suspended between two points.
• What is the motion of a pendulum? In this lecture, we set up and solve the differential equation that models the motion of a pendulum.
• Different infinities, Cantor's diagonal argument, and the continuum hypothesis.
• The Cantor set and pathological examples.
• Modern cryptography.
• Construction of the regular 17-gon.
• Elliptic curves.

Term project (the other half):

For the term project, students, working in pairs or groups of three, are expected to produce a mathematical presentation in a modern media (e.g. youtube, or interactive or animated webpage). While mathematical content is expected to be correct and non-trivial, the emphasis will be on communicating that content. Students will investigate a topic and decide how to best convey that topic to an audience. Early in the course, students will look for and present inspirational examples (see, for example, youtube videos by Vi Hart). Some time before mid-semester, each group will present a rough (hand drawn) storybook mock up of what they hope their finished product will look like.

Office Hours: If you need to see me, please look for me during the office hours posted below, or please make an appointment.

• Monday, Tuesday, and Wednesday, 1:00pm -- 2:00pm,
• ... or by appointment

Office hours begin the second week of classes.

Other Important Dates:  (See the UNLV calendar for more details.)

• January 20th:  Instruction and late registration begin.
• January 26th:  Final date for late registration, course additions, changes, or fee payment (with late penalty).  Last day to inform me of absences due to religious holidays.  Last day to drop a course without it showing up on transcripts.
• February 16th (Monday):  Presidents' Day recess.
• March 30th -- April 4th:  Spring break.
• May 4th -- 9th:  Study Week.
• May 11th -- 16th:  Final examinations.

University required announcements:

Academic Misconduct – “Academic integrity is a legitimate concern for every member of the campus community; all share in upholding the fundamental values of honesty, trust, respect, fairness, responsibility and professionalism. By choosing to join the UNLV community, students accept the expectations of the Academic Misconduct Policy and are encouraged when faced with choices to always take the ethical path. Students enrolling in UNLV assume the obligation to conduct themselves in a manner compatible with UNLV’s function as an educational institution.”

An example of academic misconduct is plagiarism: “Using the words or ideas of another, from the Internet or any source, without proper citation of the sources.” See the “Student Academic Misconduct Policy” (approved December 9, 2005) located at: http://studentlife.unlv.edu/judicial/misconductPolicy.html.

Copyright – The University requires all members of the University Community to familiarize themselves and to follow copyright and fair use requirements. You are individually and solely responsible for violations of copyright and fair use laws. The university will neither protect nor defend you nor assume any responsibility for employee or student violations of fair use laws. Violations of copyright laws could subject you to federal and state civil penalties and criminal liability, as well as disciplinary action under University policies. To familiarize yourself with copyright and fair use policies, you are encouraged to visit the following website: http://www.unlv.edu/committees/copyright/.

Disability Resource Center (DRC)–  It is important to know that over two-thirds of the students in the DRC reported that this syllabus statement, often read aloud by the faculty during class, directed them to the DRC office.

The Disability Resource Center (DRC) coordinates all academic accommodations for students with documented disabilities. The DRC is the official office to review and house disability documentation for students, and to provide them with an official Academic Accommodation Plan to present to the faculty if an accommodation is warranted. Faculty should not provide students accommodations without being in receipt of this plan.

UNLV complies with the provisions set forth in Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, offering reasonable accommodations to qualified students with documented disabilities. If you have a documented disability that may require accommodations, you will need to contact the DRC for the coordination of services. The DRC is located in the Student Services Complex (SSC), Room 137, and the contact numbers are: Voice (702) 895-0866, TDD (702) 895-0652, fax (702) 895-0651. For additional information, please visit:http://studentlife.unlv.edu/disability/.

Religious Holidays Policy -- Any student missing class quizzes, examinations, or any other class or lab work because of observance of religious holidays shall be given an opportunity during that semester to make up missed work. The make-up will apply to the religious holiday absence only. It shall be the responsibility of the student to notify the instructor no later than the last day at late registration of his or her intention to participate in religious holidays which do not fall on state holidays or periods of class recess. This policy shall not apply in the event that administering the test or examination at an alternate time would impose an undue hardship on the instructor or the university which could not be avoided.   http://catalog.unlv.acalog.com/content.php?catoid=1&navoid=44&bc=1

Tutoring  -- The Academic Success Center (ASC) provides tutoring and academic assistance for all UNLV students taking UNLV courses.  Students are encouraged to stop by the ASC to learn more about subjects offered, tutoring times and other academic resources.  The ASC is located across from the Student Services Complex, #22 on the current UNLV map. Students may learn more about tutoring services by calling (702) 895-3177 or visiting the tutoring web site at:  http://academicsuccess.unlv.edu/tutoring/

UNLV Writing Center – The following statement is recommended for inclusion in course syllabi:

One-on-one or small group assistance with writing is available free of charge to UNLV students at the Writing Center, located in CDC-3-301. Although walk-in consultations are sometimes available, students with appointments will receive priority assistance.

Appointments may be made in person or by calling 895-3908. The student’s Rebel ID Card, a copy of the assignment (if possible), and two copies of any writing to be reviewed are requested for the consultation. More information can be found at: http://writingcenter.unlv.edu/

“Just forward it.”  It is recommended that all students accept Rebelmail, either directly by logging on, or by forwarding it to another monitored email account.  Please see details on how to access your Rebelmail at http://oit.unlv.edu/sites/default/files/forms/Rebelmail_2009_Flyer.pdf or http://rebelmail.unlv.edu/