Math 441 - Real Analysis

Shippensburg University - Spring 2025

  • Instructor: Paul Taylor
  • Phone: 477-1705
  • email: pttaylor (at) ship.edu
  • Lectures: MCT251-TR, 12:30-1:45
  • Office Hours: MCT281 - M 1:00-2:00, T 11:00-12:00, W 1:00-2:00, R 11:00-12:00, F 1:00-2:00
  • Textbooks:
  • M. H. Protter and C. B. Morrey, A First Course in Real Analysis, 2nd Ed, Springer Undergraduate Texts in Mathematics
  • W. F. Trench, Introduction to Real Analysis, online at: http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF
  • Course Web Page: http://webspace.ship.edu/pttaylor/441/441home.html
    •
  • Homework Problems
  • Homework Solutions
    •
    TOPICS OUTLINE
  • Real numbers and open and closed sets (including axioms)
  • Limits and continuity (including limits with epsilon-delta)
  • Sequences of real numbers and functions (including Bolzano-Weierstrass, Cauchy sequences, Heine-Borel)
  • Derivatives
    •
    STUDENT EXPECTATIONS
  • This is a proof intensive course. Students will be required to write clear, accurate, detailed mathematical proof.
  • Attend every class period.
  • If there is a concept with which you need extra help, or if you find yourself falling behind, tell me about it. Come to office hours for extra help, or send me an email explaining your concerns. The sooner the better.
    •
    GRADE WEIGHTING
    Your numerical grade for the course will be out of 500. The points are assigned as follows:
  • 100 points - Homework
  • 125 points - Midterm Exam 1
  • 125 points - Midterm Exam 2
  • 150 points - Final Exam
    •  Your total points will be converted to a letter grade according to the following scale:

    Letter Grade

    A

    A-

    B+

    B

    B-

    C+

    C

    D

    F

    Point Total

    465-500

    450-464

    435-449

    415-434

    400-414

    375-399

    325-374

    250-325

    less than 250
    HOMEWORK
    Homework problems will be posted online for most classes. Each Thursday, you are required to submit the completed homework from the previous week. Only some of the problems you submit will be graded. Your grade on each homework will be out of 10 points, 6 points determined by the graded problems and 4 points determined by the completeness of the non-graded problems. You will lose 1 point from the non-graded portion for each non-graded problem left blank.
    After the homework is due, solutions to all problems will be posted on the class website. No late homework will be accepted.
    EXAMS
    There will be two midterm exams. Material covered will be announced in class and on this web page. The tentative dates are Thursday, February 20 and Thursday, March 27. If you anticipate a conflict with any of these dates, you must inform me at least one week in advance, or no accommodations will be given.
    The final exam will be longer and contain problems from the entire course.
    EXTRA CREDIT
    You can earn extra credit for participating in certain mathematical enrichment activities.  You can receive a maximum of 10 points of extra credit.
  • You receive 2 points for attending the seminar and writing a paragraph containing some of your thoughts on the seminar. Your paragraph must be sent to Dr. Taylor by email prior to the next class period. Attending conferences and presenting in seminars or conferenes qualify for these points.
  • You receive 2 points for submitting a solution for the Problem Solving Contest. Your solution must be submitted before the deadline for the problem. Your solution need not be correct, but it must represent a strong effort (as determined by Dr. Taylor).
  • You receive 8 points for participating in the Mathematical Contest in Modeling (MCM).
    •
    POLICY REGARDING MISSED WORK
    If you are going to miss an exam or a homework deadline, inform me beforehand as soon as possible and at least one week in advance. We will then be able to arrange an alternate test time or deadline.
    If you miss a homework deadline because of sudden, unexpected reasons, inform me as soon as possible by email.
    ACADEMIC DISHONESTY It is the policy of Shippensburg University to expect academic honesty. Students who commit breaches of academic honesty will be subject to the various sanctions outlined in the Undergraduate Catalog.
    OFFICE OF ACCESSIBLE RESOURCES Shippensburg University welcomes students with disabilities into all of the University's educational programs and strives to make all learning experiences as accessible as possible.  Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Office of Accessibility Resources (OAR) to discuss specific needs.  OAR is located in Mowrey Hall 252 and can be reached by phone at (717) 477-1364 or via email at oar@ship.edu. The office�s website is www.ship.edu/oar.

    In order to receive consideration for reasonable accommodations, you must provide documentation and participate in an intake meeting.  If the documentation supports your request, the Office of Accessibility Resources will provide you with an Accommodation Notification Form.  OAR encourages you to share your notification form with your instructors and discuss your accommodations with them as early in your courses as possible. You must submit a request for a new notification form each semester that you request accommodations.
    CAS ADVISING CENTER The College of Arts & Sciences Advising Center (CASA): located in DHC 216, CASA is a walk-in office that offers several types of academic support, from advice and help on time management, test anxiety, and study skills to discussions about what major might be right for you. You can email (casa@ship.edu) or call (717-477-1150) to set up a time to meet with a success coach or faculty advisor.
    TITLE IX

    Shippensburg University of Pennsylvania and its faculty are committed to assuring a safe and productive educational environment for all students. To comply with the requirements of Title IX of the Education Amendments of 1972 based on the 2020 Regulations and the university’s commitment to offering supportive measures in accordance with the 2020 regulations issued under Title IX, Shippensburg University of Pennsylvania requires faculty members to report incidents of sexual violence shared by students to the university's Title IX Coordinator, Dr. John Burnett [JABurnett@ship.edu] or [Title9@ship.edu]. The only exceptions to the faculty member's reporting obligation are when incidents of sexual violence are communicated by a student during a classroom discussion, in a writing assignment for a class, or as part of a university-approved research project. Faculty members are obligated to report sexual violence or any other abuse of a student who was, or is, a child (a person under 18 years of age) when the abuse allegedly occurred to the person designated in the university’ Protection and Supervision of Minors on Campus Policy. 

    Information regarding the reporting of sexual violence and the resources that are available to victims of sexual violence are available on the Office of Human Resources website:  

    https://www.ship.edu/about/offices/hr/title_ix_statement/

    Reports may be made to the following individuals:

    Dr. John Burnett                            Nipa Browder                                    Jennifer Milburn                                         Trejon Dinkins

    Title IX Coordinator                        Deputy Title IX Coordinator               Deputy Title IX Coordinator                       Deputy Title IX Coordinator

    Office of Human Resources          Office of Human Resources               Housing/ResLife/Conferences                    Retention and Student Succes

    Old Main 106-A                             Ph: 717-477-1124                             Ph:  717-477-1904                                      Ph: 717-477-1123   x3027

    Shippensburg, PA 17257               Email:  Nbrowder@ship.edu       Email:  JSMilburn@ship.edu               Email:  TADinkins@ship.edu

    771-477-1323    

    Cell:  724-317-6415

    Email:  JABurnett@ship.edu                                                              Alix Rouby                                             Mary Burnett           

                                                                                              Deputy Title IX Coordinator                       Deputy Title IX Coordinator

                                                                                              Career Center                                            International Programs

                                                                                                                      Ph:  717-477-1595                                     Ph:  717-477-1279

                                                                                                                      Email:  AJRouby@ship.edu                        Email:  MEBurnett@ship.edu

     

     

     

     

    Link for the online reporting form: (This is for reporting an issue, not making a formal complaint)

    https://cm.maxient.com/reportingform.php?ShippensburgUniv&layout_id=3

    Link for the Formal Complaint form:

    https://cm.maxient.com/reportingform.php?ShippensburgUniv&layout_id=21

    Link for campus resources:

    https://www.ship.edu/about/offices/hr/title_ix_statement/resources/

    Last modified: Jan 14, 2025
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