Peter B Gilkey
202 Deady Hall,1-541-346-4717 (office phone) 1-541-346-0987 (fax) email:
Mathematics Department, University of Oregon, Eugene Oregon 97403 USA

Math 639 Spring 2018 CRN 33521

  • Office Hours:  Monday, Wednesday, Friday 0900-0950 or by appointment.
  • Meets MUWF 10:00-10:50 in Deady 104.
  • Text: The text is should be available for free from any UO location (i.e. IP address) from Morgan and Claypool Aspects of Differential Geometry I and Aspects of Differential Geometry II. These locations should let you down load the pdf file automatically; you don't need to sign in or anything. Let Gilkey know if you have troubles. This is part of the Synthesis Lectures on Mathematics and Statistics and the authors are Gilkey, Park, and Vazquez-Lorenzo. (Since the UO subscribes to Morgan & Claypool, any UO Student or Faculty Member can download the PDF file for free). If after trying the PDF file you really want a hard copy, you can either order one direct from Morgan & Claypool or AMAZON.COM. But I suggest you work with the PDF file first.
  • Organization. Homework is probably the most important activity in the course in terms of helping you internalize the material. There will be 9 homeworks; each homework will be due each Monday on the material of the previous week.
  • If you are a student with a documented disability please meet with me soon to discuss your needs. If you have not already requested a notification letter from Disability Services outlining recommended accommodations, please do so soon.
  • Grades:
  • There will be weekly homework assignments -- a total of 9 in all. They will be graded. At the end of the quarter, the lowest 2 homework scores will be dropped and an average computed of the remaining 7 homeworks. Your final course grade will be based on this average. There will not be any exams in the course; in a course in differential geometry I believe it is fairest to base the grade on the homeworks where you have a chance to think about the material at leisure and not on a timed exam where there is no opportunity to go into the material in some depth.
  • Teaching Associate: Ekaterina Puffini. Additional information: Academic calendar.

  • Academic dishonesty

    Academic Misconduct: The University Student Conduct Code (available at defines academic misconduct. Students are prohibited from committing or attempting to commit any act that constitutes academic misconduct. By way of example, students should not give or receive (or attempt to give or receive) unauthorized help on assignments or examinations without express permission from the instructor. Students should properly acknowledge and document all sources of information (e.g. quotations, paraphrases, ideas) and use only the sources and resources authorized by the instructor. If there is any question about whether an act constitutes academic misconduct, it is the students’ obligation to clarify the question with the instructor before committing or attempting to commit the act. Additional information about a common form of academic misconduct, plagiarism, is available at see also

    Ethical Standards

    From the President's Office 2 May 2014: The University of Oregon is a community of scholars dedicated to the highest standards of academic inquiry, learning, and service. We are also committed to the highest standards of ethics as we work to fulfill our mission. We all share responsibility for ensuring that we conduct our transactions in ways that are ethical, honest, and reflect sound fiduciary practices. To accomplish this, it is important that all UO employees review, understand, and consistently practice the standards included in the following laws, rules, and policies including:
  • Child Abuse Under the Oregon Child Abuse Reporting Statutes, all UO employees have a duty to make a report to the Oregon Department of Human Services or a law enforcement agency when they have reasonable cause to believe any child with whom the employee comes in contact has suffered abuse or that any person with whom the employee comes in contact has abused a child. For instances that relate to UO authorized activities, UO employee are to report to the University of Oregon Police Department. For purposes of this reporting responsibility, a "child" is any "unmarried person who is under 18 years of age" and "abuse" includes, but is not limited to: assault of a child; physical injury to a child caused by other than accidental means; any mental injury to a child caused by cruelty to a child; rape of a child; sexual abuse; sexual exploitation; Š negligent treatment or maltreatment of a child; threat of harm to a child; buying or selling of a child; allowing a child on the premises where methamphetamine is being manufactured; and unlawful exposure to a controlled substance that subject a child to risk of harm. The duty of employees of public universities to report incidents of child abuse applies at all times, not just to those incidents occurring during working hours or on campus. For this purpose, university employees include all faculty and staff members, student workers, graduate teaching fellows, and temporary employees.
  • Under the law, reports must be made to the local office of the Department of Human Services or to a law enforcement agency in the county where the employee making the report is located at the time of the contact. Failure to report when required to do so is a Class A violation. Persons who make reports in good faith are immune from liability for making the report. For instances that relate to UO-authorized activities, UO employees are expected to make the report immediately to the UO Police Department at 541-346-2919. Karen Logvin, Director of Work/Life Resources in Human Resources, 541-346-2962,, is the initial point of contact for further questions related to the reporting of child abuse. In addition, you will find additional information and resources regarding mandatory reporting of child abuse and neglect at "
    1. ORS Chapter 244, which codifies ethics and conflict of interest policies that you are required to follow as you conduct University of Oregon business. See the guide for public officials here.
    2. The Oregon University System (OUS) has a responsibility to prevent and detect fraud, waste, and abuse and to hold accountable those who engage in it. The OUS Fraud, Waste, and Abuse policy sets forth guidelines for reporting known or suspected fraud, waste, or abuse within any OUS institution.
    3. If you are aware of fraud, waste, or abuse occurring at the UO or within the OUS, matters can be reported to campus management, OUS Internal Audit Division, or OUS Financial Concerns Hotline. Additional information is also available on the UO Business Affairs and UO vice president for finance and administration webpages.
    4. The OUS information security policy and UO information security policy set forth your responsibilities relating to the security of electronic information systems and confidentiality of data. A more comprehensive listing of state laws and rules that guide our operations is available here.
    5. The UO will continue a similar focus on these important issues under our new governance structure. We will communicate any changes to reporting protocols after July 1. We are all responsible for understanding and complying with ORS 244, applicable government regulations and policies. We also have a responsibility to raise compliance and ethics concerns through established channels. I appreciate your commitment to integrity and honesty, as it is an essential element in maintaining an ethical and secure UO workplace environment for everyone.

    Statement on Final Exams

  • 1. In the week preceding final examination during fall, winter, and spring terms: No examination worth more than 20% of the final grade will be given, with the exception of make-up examinations. No final examinations will be given under any guise. No work that will be evaluated for grades/credit will be due unless it has been clearly specified on the class syllabus within the first two weeks of the term.
  • 2. Take-home examinations will be due no earlier than the day of the formally assigned final examination for the class in question.

    This action clarifies and extends earlier faculty legislation (1911 Faculty Assembly archives) prohibiting the giving of final examinations earlier than officially scheduled.

    In addition, you should be aware of the Faculty Advisory Council's statement on students with multiple exams:

    Examination schedules are listed each term in the Time Schedule. Students who are scheduled to take more than three examinations within one calendar day may take the additional examination(s) as makeup examination(s) later in the examination week. The instructor(s) of record for the course(s) beyond the third examination, counting in the order the examination(s) are scheduled, will arrange for (a) makeup examination(s).

    The following procedures were approved by the Undergraduate Council to address rare circumstances of competing exam times. Students with examination conflicts may contact the Office of Academic Advising for assistance.

    In the case of two examinations scheduled at the same time, the course with the largest enrollment must provide an alternate examination. For conflicts between regular courses and combined examinations, the combined examination course must provide the alternate examination. For combined examinations with conflicts, the largest combined enrollment course must provide the alternative examination.

    Questions and concerns regarding this policy should be directed first to the relevant instructor, then the department head, and finally the dean if necessary. You may also find reference to the policy on the Academic Affairs website. If additional input is needed, please contact

    Title IX

    Under Title IX, I have a duty to report relevant information. The UO is committed to providing an environment free of all forms of prohibited discrimination and sexual harassment, including sexual assault, domestic and dating violence and gender-based stalking. Any UO employee who becomes aware that such behavior is occurring has a duty to report that information to their supervisor or the Office of Affirmative Action and Equal Opportunity. The University Health Center and University Counseling and Testing Center can provide assistance and have a greater ability to work confidentially with students. Note: UO employees also have a duty to report child abuse. For those classes and/or processes in which students have historically reported information regarding child abuse, the language can be expanded to provide that notice as well by adding the following statement: All UO employees are required to report to appropriate authorities when they have reasonable cause to believe that any child with whom they come in contact has suffered abuse or any person with whom they come in contact has abused a child.
  • Discrimination and Discriminatory Harassment: Oregon law requires that all university employees with credible evidence that any form of prohibited discrimination by or against students, faculty members, staff members, or visitors to our campus is occurring have a duty to report that information. "Prohibited discrimination" includes: Discrimination on the basis of age, disability, national origin, race, marital status, religion, gender, gender identity, gender expression or sexual orientation; and Discriminatory harassment, including all forms of sexual harassment. Reports are to be made to the employee’s supervisor or to the Office of Affirmative Action and Equal Opportunity (OAAEO) at 541-346-3123; or via email to the Office of Affirmative Action and Equal Opportunity. Any UO supervisor who has been notified of credible evidence that prohibited discrimination is occurring has a duty to report that to the OAAEO. Penelope Daugherty, Director of OAAEO and Title IX Coordinator, 541-346-2971,, is the contact person for questions about the duty to report discrimination and discriminatory harassment.

    I am a student directed employee. Students experiencing any form of prohibited discrimination or harassment, including sex or gender based violence, may seek information on,,, or or contact the non-confidential Title IX office (541-346-8136), AAEO office (541-346-3123), or Dean of Students offices (541-346-3216), or call the 24-7 hotline 541-346-SAFE for help. I am also a mandatory reporter of child abuse.

    Any student who has experienced sexual assault, relationship violence, sex or gender-based bullying, stalking, and/or sexual harassment may seek resources and help at To get help by phone, a student can also call either the UO’s 24-hour hotline at 541-346-7244 [SAFE], or the non-confidential Title IX Coordinator at 541-346-8136. From the SAFE website, students may also connect to Callisto, a confidential, third-party reporting site that is not a part of the university. Students experiencing any other form of prohibited discrimination or harassment can find information at or or contact the non-confidential AAEO office at 541-346-3123 or the Dean of Students Office at 541-346-3216 for help. As UO policy has different reporting requirements based on the nature of the reported harassment or discrimination, additional information about reporting requirements for discrimination or harassment unrelated to sexual assault, relationship violence, sex or gender based bullying, stalking, and/or sexual harassment is available at Discrimination & Harassment. Specific details about confidentiality of information and reporting obligations of employees can be found at Mandatory Reporting of Child Abuse UO employees, including faculty, staff, and GEs, are mandatory reporters of child abuse. This statement is to advise you that your disclosure of information about child abuse to a UO employee may trigger the UO employee’s duty to report that information to the designated authorities. Please refer to the following links for detailed information about mandatory reporting: Mandatory Reporting of Child Abuse and Neglect.

    The instructor of this class, as a Student Directed Employee, will direct students who disclose sexual harassment or sexual violence to resources that can help and will only report the information shared to the university administration when the student requests that the information be reported (unless someone is in imminent risk of serious harm or a minor). The instructor of this class is required to report all other forms of prohibited discrimination or harassment to the university administration.

    Safe Ride is an assault prevention shuttle that works to provide free, inclusive, and accessible alternatives to traveling alone at night for UO students, faculty, and staff. We are a schedule-ahead service and riders can (1) call once we open to schedule a ride with a dispatcher or (2) leave a voicemail on the day of their ride request. We do not call riders ahead of time to confirm due to capacity constraints, but riders are always welcome to call us to double-check that their ride was scheduled. We are a feminist, ‘for-the-students/by-the-students’ organization and operate out of the Women’s Center in EMU 12F. Operating hours: Spring term Summer term Fall/Winter term Sunday - Thursday | 7p - midnight Friday + Saturday | 7p - 2a Sunday - Thursday | 9p - midnight Friday + Saturday | 9p - 2a Sunday - Thursday | 6p - midnight Friday + Saturday | 6p - 2a Policy and rules: 1. We are a schedule-ahead service, we do not call ahead, and we can only wait for riders for 5 minutes at their pick-up time and location. 2. We only give rides to groups of 3 or less to prioritize groups that are at higher risk. 3. We are a free service and do not accept tips.

    To rest on the blue of the day, like an eagle rests on the wind, over the cold range, confident on its wings and its breadth.

    Web page updated on 2 April 18 by Peter B Gilkey 202 Deady Hall, Department of Mathematics at the University of Oregon, Eugene OR 97403-1222, U.S.A. Phone 1-541-346-4717 of Deady Spider Enterprises