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 Fall 2013 CRN 14660

Syllabus Version 2 as of 2 September 2013

  • MATH 315 CRN 14660. Meets Monday, Tuesday, Wednesday, Friday in 306 Deady from 10:00 to 10:50
  • 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 Wednesday 23 October 2013 (Week 4)
  • 100 points Exam #2 Wednesday 20 November 2013 (Week 8)
  • 200 points Final Exam 10:15 Monday, December 9, 2013.
  • 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

    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 on 3 September 2013 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