Colorado State University, Pueblo
Math 421 — Advanced Calculus I — Fall 2009

Here is a shortcut to the course schedule/homework page.

Lectures: MTWF 11-11:50pm in PM 116      Office Hours: MWF 9-10am in PM 248

Study group: T 9-10am and &Theta 11-12am, outside PM 248. This is an informal get-together of students who are interested in talking about the class and current assignments, in which I will participate.

Instructor: Jonathan Poritz     Office: PM 248     E-mail:
Phone: 549-2044 (office — any time); 337-1210 (cell) and 473-8928 (home) (both for emergencies only, please)

Text: Understanding Analysis, by Stephen Abbott. Please bring it to class every day.

Prerequisites: Math 307 and three additional upper division math courses.

Content: We will cover most of Chapters 1-7 of the textbook, along with various other additional topics as time and interest allow. At one level, the theme of all of this work is to work carfully with the concept of taking a limit, in the context of numbers, sequences, series, functions, etc. At another, the point of course might be explained as to revisit many of the ideas, definitions and techniques of the standard Calc I and II class and to do them all very carefully and solidly. There could be very much a "so you thought you understood that a while ago, but what about this?", really with an idea of tearing down the house in order to expose its lack of foundations, then to build those foundations and rebuild the house (or start rebuilding). For example, we will start the term with the question "Are you sure you know what the real numbers are?"

Academic integrity: Mathematics is more effectively and easily learned — and more fun — when you work in groups. However, all work you turn in must be your own, and any form of cheating is grounds for an immediate F in the course for all involved parties.

Students with disabilities: The University abides by the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973, which stipulate that no student shall be denied the benefits of education "solely by reason of a handicap." If you have a documented disability that may impact your work in this class for which you may require accommodations, please see the Disability Resource Coordinator as soon as possible to arrange accommodations. In order to receive this assistance, you must be registered with and provide documentation of your disability to the Disability Resource Office, which is located in the Psychology Building, Suite 232.

Your activity: This may be one of your first classes in which the primary goal is for you to understand and create proofs, not calculations or algorithms. It is expected that you will take several steps into the subculture of academic mathematics, which has its own characteristic ways of speaking, listening, reading, writing, and discourse, some of which are more than two thousand years old, while most of the rest are at least several decades or centuries old... and yet they are tremendously powerful and efficient. In fact, an argument could be made that they underlie in a fundamental way the scientific method and the whole project of modernism itself. It is for this reason that we will spend a fair bit of time discussing and practicing these metamathematical processes both in class and in work you do at home. In particular:

Grades: Your total homework points will be scaled to be out of 200. Both midterms will be graded out of 100, while the final will be out of 150. Group activities, worksheets, your notesbooks and classroom participation will together count for 50 points. This means that the maximum possible course points are 600. Letter grades will then be calculated in a way no more strict than the old "90-100% is an A, 80-90% a B, etc." system, based on your total points. (Note that by Math Department policy, there will be no +'s or -'s on final course grades.) On test days, attendance is required -- if you miss a test, you will get a zero as score; you will be able to replace that zero only if you are regularly attending class and have informed me, in advance, of your valid reason for missing that day.

The MFAT: Students are required to take the MFAT (Major Field Achievement Test) to obtain a grade in Math 421. It will be given at a date and time to be determined, near the end of the term.

Contact outside class: Over the years I have been teaching, I have noticed that the students who come to see me outside class are very often the ones who do well in my classes. Now correlation is not causation, but why not put yourself in the right statistical group and drop in sometime? I am always in my office, PM 248, during official office hours. If you want to talk to me privately and/or cannot make those times, please mention it to me in class or by e-mail, and we can find another time. Please feel free to contact me for help also by e-mail at, to which I will try to respond quite quickly (usually within the day, often much more quickly); be aware, however, that it is hard to do complex mathematics by e-mail, so if the issue you raise in an e-mail is too hard for me to answer in that form, it may well be better if we meet before the next class, or even talk on the telephone (in which case, include in your e-mail a number where I can reach you).

A request about e-mail: E-mail is a great way to keep in touch with me, but since I tell all my students that, I get a lot of e-mail. So to help me stay organized, please put your full name and the course name or number in the subject line of all messages to me. Also, if you are writing me for help on a particular problem, please do not assume I have my book, it is often not available to me when I am answering e-mail; therefore, you should give me enough information about the problem so that I can actually help you solve it (i.e., "How do you do problem number n on page p" is often not a question I will be able to answer).

Jonathan Poritz (