Skip to main content

Math 414

Mathematics 414: Analysis I



Scott Hansen
office: Carver 494
telephone: 294-8171
Office Hours: Hansen homepage
Comments, Assignments


Basic Analysis , by Jiri Lebl. This is available free online from the link Basic Analysis.
I may also refer at times to the book by W. Trench available for free online: Introduction to Real Analysis



Math 201 ... but the more math the better. For many students, this is a very difficult course if you have not had other upper division courses.


Class meetings.

MWF 11-11:50 in Carver 118


Course Topics:

We will review main points of Chapter 1 and then cover much of the material in Chapters 2-6 of Lebl. At times I'll refer to Trench book (see above link) The topics are:

  • Chapter 1: Review of Real Numbers, Axioms of real number system
  • Chapter 2: Limits, Bolzano-Weierstrauss Theorem, Cauchy sequences, sequences and series
  • Chapter 3: continuity, extreme value theorems, monotone functions
  • Chapter 4: Differentiation, Mean Value Theorem, Taylor's Theorem, inverse function theorem
  • Chapter 5: Integration theory
  • Chapter 6: Sequences of functions

The point of this course is to understand in depth the real number system. Many basic properties of calculus that you are already familiar with will be proved. However, along the way a number of additional theorems of calculus that should be new to most people will be covered, if not proved. A very important part of the course is to develop an ability to write clear and correct proofs. Not only is this a necessary skill for people planning on teaching mathematics, but it also seems to be the best way to gain a deep understanding of calculus, which is necessary to gain before attempting to learn higher level forms of calculus used in Science, Math and Engineering.



are basically useless for this course.

Course Policy

The course grade is based upon about 250 total points: Quizzes and homework: approximately 40 percent, two mid-term exams: (20 percent each), and final exam (20 percent). Tentatively, Test 1 and Test 2 are scheduled Feb. 14 and April 3. (Any channges will be announced obout two weeks in advance.)

Due to the high amount of theory, I have a grade scale that is more spread-out than usual. The grade borderlines for A - B- C - D will be 85-70-55-45.


REVISED Course Policy

Due to Covid 19, the above policy is revised to the following: Test 2 is cancelled. There will continue to be assigned HW, and there will be a final take home exam that covers all material beyond Test 1 material. The course grade is based 60 percent HW, 20 percent Test 1, 20 percent Final Exam. We can continue to do Practice problems, but this will be explained on Canvas.


Homework and quizzes:

I'll assign many problems to work on. Most of these will be "practice problems" that will not be collected, but may be discussed in class or be problems we do as a group on the board. Other problem sets are to be turned in and graded. You will have about 5 or 6 turn-in homework sets and about 4 or 5 quizzes over the course of the semester. Late homework will be downgraded. After I go over it in class it will no longer be accepted for any credit. Quizzes will be announced at least 1 class period in advance. If you can not be in class for a quiz, and let me know in advance I will try to work out a way to give a make up quiz. If you miss a quiz without letting me know in advance, there will be no make-up quiz.


Practice Problems:

Most fridays will include some time to solve practice problems on the board. All students are required to do at least 2 practice problems (3 points each), and will receive extra credit (2 points) for additional practice problems that are worked, up to a maximum of 6 points EC.


Regular attendance is considered an important part of the course. Therefore excessive unexcused absences - missing 3 or more weeks of class time- may result in a grade reduction. If you have to miss more than a few classes for legitimate reasons, please inform me of the circumstances in advance if possible.

My Webpage Policy

The classroom is always the primary source of information. For convenience, I will try to regularly post the assignments, important comments on the course webpage, but from time to time, I make some typo or get something wrong. So please correct me if you think I have something posted incorrectly. (When in doubt, go with what was stated in class, until you hear otherwise.)



Students With Disabilities

Iowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at, by contacting SAS staff by email at, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.

More information about disability resources in the Mathematics Department can be found at (Make sure you memorize that link).

Last updated 1-11-2020,