THIS SYLLABUS WAS MODIFIED ON MARCH 24, 2020,
IN RESPONSE TO THE COVID-19 PANDEMIC.
For announcements and updates regarding the transition to online course delivery,
please see the Announcements page.
The world in which we live today could not exist without the explosion in mathematical knowledge which has occurred since the Renaissance. Not only does mathematics make modern technology possible, but mathematical ideas have profoundly changed our views of the structure of the world itself. The ideas which today are grouped under the heading of Calculus lie at the center of this transformation; although some of them can be traced back to Archimedes, the subject is usually considered to have been developed by Newton and Leibniz in the seventeenth century, and its success in solving problems such as planetary motion led to the modern idea of the universe as a complex, but predictable, machine.
In the two semesters of Honors Calculus, MATH 221/222, we will cover material equivalent to the standard three-semester calculus sequence, but our goal is to gain a richer understanding of the material, both of the fundamental concepts and of their use in solving real-world problems. Accordingly, we will study calculus largely by solving realistics and challenging problems, both in class and in smaller work groups. Some of this work will be done by hand, and some using a computer system such as Geogebra or Desmos. A sound knowledge of algebra and trigonometry is required for the course. The key concepts we will cover in the first semester are:
- vectors and vector functions;
- sequences and series;
- functions of several variables, partial derivatives;
- multiple integrals.
(Note that while we will study all of these topics, we may not study them in the listed order.)
Beginning on March 30, we will conduct the class online, largely through the Canvas course management system. In particular, we will hold interactive sessions using the Collaborate Ultra software within Canvas. During these sessions, I will try to keep lecturing to a minimum, and devote the time to discussion and problem solving. As a result, you will be expected to read the textbook in a timely fashion, as necessary to participate in the class discussions. In order to help you with understanding the readings, I will also post brief summaries of the textbook sections you are being asked to read, and appropriate links to online videos. When I assign reading, I will often ask you to e-mail me, again in a timely fashion, with one or more questions you have about the reading. I will review those e-mails before the session and organize the session accordingly. I will also save those e-mails; they will be used at the end of the semester as evidence of your good faith effort to complete the remaining work of the course, and will count towards the homework portion of your grade. In particular, responding to these question requests will help to ensure that your final grade for the course will not be lower than your current grade.
All class information (homework, class cancellations, etc.) will be posted in Canvas, and also on this website, https://sites.uwm.edu/kevinm/math-222-honors-calculus-ii/. You are responsible for any posted information, so please check one or other of these sites (preferably Canvas) frequently.
Your grade for the course will be based on the following factors:
- Homework In addition to the textbook (and possibly other) readings, you will be assigned written homework regularly, some of which you will be expected to hand in. 20%.
- Class participation You will be expected to contribute to the Collaborate Ultra discussions, and to other class activities, such as responding to requests for questions on the readings. (If you feel that participating in any part of the class will be difficult for you under current circumstances, please contact me to discuss alternative arrangements. 15%.
- Projects You will complete two projects during the semester, in project groups of 2 or (preferably) 3. These projects will consist of extended applications of the material we study in class. You will be given 3 weeks to complete each project. Project 1 will be worth 10% of your grade; Project 2 will be worth 15%. 25%.
- Exams There will be two exams: a midterm and the final exam. The midterm exam will be given at approximately week 7 of the semester (you will be given at least one week’s notice of the exact date). The final exam will be a Take-home exam, due on Wednesday, May 13. Each exam will be worth 20% of your grade. 40%.
Please note that this computation has changed from that announced at the start of the semester: there are now 2 projects instead of 3, with the second project being worth 15%, and class participation has been increased from 10% to 15%. In compensation for changing the rubric in the middle of the semester, and in hope of relieving some anxiety over your grade under a course arrangement that you did not sign up for, I am instituting the following policy:
I have computed your grades as of today (March 24). I will compute your final grade at the end of the semester, and provided you have made a good-faith effort to complete the course, as measured by attendance at the Collaborate Ultra sessions, responses to e-mail question requests, and homework submissions, you will be given the better of the two grades for the course.
If any part of this policy bothers you (for example, if it is going to be hard for you to attend Collaborate Ultra sessions at our usual class time), please contact me to discuss alternative arrangements.
Average Time Investment
The amount of time that an average student should expect to spend on this class is as follows:
- Classroom time (face to face instruction, including Collaborate Ultra): 75 hours
- Time taking exams (midterm, final exam): 15 hours
- Time completing reading and other homework assignments: 150 hours
- Time for preparation and study for exams: 10 hours
Total number of hours: 250.
Students with disabilities
If you feel you are a student with a disability, please feel free to contact me early in the semester for any help or accommodation you may need.
You should keep yourself informed of important dates in the University calendar.
The Secretary of the University has a page dedicated to university policies for religious observances, grade appeal procedures, military service and other matters. You should also familiarize yourself with the information on the Dean of Students Office webpage concerning proper student conduct at the university, both academic and non-academic misconduct. You will be held responsible for
the information and policies contained at these links.
Finally, please note that I reserve the right to make changes to this syllabus in the event of a
disruption to normal classroom activities, or other needs that may arise during the semester.