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

TENTATIVE SYLLABUS - The reading and homework assignments are SUBJECT TO CHANGE

Math 315 Elementary Analysis Winter 2015

Syllabus Version 3 as of 17 May 2015

  • MATH 315 CRN 14660. Meets Monday, Tuesday, Wednesday, Friday.
  • Office Hours:  Monday, Wednesday, Friday 09:00-10:00 or by appointment.
  • Text: Ross, Elementary Analysis: the theory of calculus any edition.
  • Organization. Homework is probably the most important activity in the course in terms of helping you internalize the material. Homework will be due each Tuesday on the material of the previous week. The Monday class period will be a discussion section for the homework to be due the subsequent day. The last 20 minutes will be devoted to a quiz.
  • Grades:
  • 100 points Homework and Quiz Average (The 2 lowest scores from the combined list of homework and quiz scores will be dropped)
  • 100 points Exam #1 28 January 2015 (Week 4)
  • 100 points Exam Exam #2 Wednesday 25 February 2015 (Week 8)
  • 200 points Final Exam 10:15 Wednesday 18 March 2015
  • An incomplete can be assigned when the quality of work is satisfactory but a minor yet essential requirement of the course has not been completed for reasons acceptable to the instructor (NOTE: this grade requires a contract to be completed). According to faculty legislation, final exams may not be given early under any circumstances. Your final grade will be assigned on the basis of the total point score of 500 points. Any student getting at least a B on the final will receive at least a C- in the course; no student can pass the course unless they receive a grade of D or better on the final exam. You must bring your photo ID to all exams. You may bring a 3x5 inch index card with any formulas on it to any exam or quiz if you wish. Similarly, you may bring with you a hand held graphing calculator to any exam or quiz if you wish.
  • Teaching Associate: Ekaterina Puffini
  • See Academic Calendar

    Assignments (Tentive and subject to change. Page numbers are from first edition. The problems are uniquely identified by their number (e.g. 1.12))

    Course objective The course serves as a transition between the computationally oriented calculus sequences (Math 251/2/3 and Math 281/2) and some of the more theoretically oriented 400 level courses (the analysis sequence Math 413/4/5 and the complex variables sequence Math 412/3 come to mind as exemplars). More importantly, it serves as an entry into proof based mathematics supplementing the course on proof theory (Math 307). The course will begin with an introduction to the basics - natural numbers, rational numbers, real numbers. A rigorous treatment of limits (sequential limits, monotone sequences, cauchy sequences, subsequences, limit points, lim sup, lim inf etc) will be given. A brief introduction to metric spaces will be given (compactness, connectedness, etc). Alternating series and integral tests will be discussed. Continuity, compactness, uniform continuity, and limits of functions will be discussed. If time permits, power series and L'Hospital's rule will be treated. At this stage in their mathematical education, students should be familiar with the mechanics of calculus. What this course will stress are the rigorous foundations of the subject - there will be lots of epsilon-delta proofs.

    Learning Outcomes Students must be able to demonstrate an understanding of the nature of mathematical proof by proving various assertions concerning limits. They should be able to not only calculate but prove their answer for various limits (sequential limits, monotone sequences, cauchy sequences, subsequences, limit points, lim sup, lim inf etc). They should be able to give proofs related to compactness, connectedness, etc. as well as to compute and prove the correctness of the calculations using the alternating series test, the integral test, and other tests. They should be able to give proofs that deal with continuity, compactness, uniform continuity, and limits of functions. What is crucial is the ability to give rigorous proofs of the epsilon-delta sort.

    Mathematics Department Undergraduate Grading Standards November 2011 There are two important issues that this grading policy recognizes.

    Rubric for applied courses: Modeling, in mathematical education parlance, means the process of taking a problem which is not expressed mathematically and expressing it mathematically (typically as an equation or a set of equations). This is usually followed by solving the relevant equation or equations and interpreting the answer in terms of the original problem.

    Rubric for pure courses:

    Many courses combine pure and applied elements and the rubrics for those courses will have some combination of elements from the two rubrics above. Detailed interpretation of the rubrics depends on the content and level of the course and will be at the discretion of instructors. Whether to award grades of A+ is at the discretion of instructors.

    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 studentsŐ 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

    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.

    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:
    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 CouncilŐs 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

    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 spun 17 May 2015 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