# Department of Mathematics

## FAQ: Honors Calculus, MATH 16100-16200-16300

#### Q: What am I getting into if I register for Honors Calculus?

A: The course is a theoretical treatment of the mathematics underlying the main theorems of calculus. We will begin with the axioms for an ordered field, learn to prove theorems using these axioms (why is 0 times any number 0, for example), and work with the concept of completeness in the real number system. These are probably unfamiliar topics to you, and that's normal. These are concepts that are not covered in high school calculus and are only mentioned in the Math 15100 courses. In the first quarter of 160's, we move through the epsilon-delta limit definition, to the proofs of the Intermediate and Mean Value Theorems. In the second quarter we develop the Riemann integral, prove the Fundamental Theorem(s) of Calculus, and begin work with infinite sequences and series. The third quarter deals with complex valued functions and additional topics once we finish the text.

#### Q: How much math do I REALLY need to have taken to be prepared for this class?

A: Your performance on the placement test reflects your preparation, and you just need to be willing to work, etc. Here's a word from a former 16100 student: "Everyone comes from a different math background. It might be a bit much, but I know some people get pretty intimidated when they're hearing others talking about the linear algebra and calc 3 classes they've been taking at 'X local university'. The point is, if you placed into the class, you're ready to try it."

#### Q: How much time does it really take?

A: Most students find that spending 10 hours per week on the course in addition to attending classes will do the trick. However, there may be times, especially at the beginning, when it takes longer to understand how to do problems. Homework is hard, the problems are challenging. It helps to form study groups for working through the problems, but of course, you'll write up all your solutions on your own.

#### Q: How much homework?

A: This varies from section to section, but it can be substantial. It is also different from what you're used to doing as math homework. Quite often, a homework score of 16/30 on a 30-point problem set may be the best score in the class. We assign difficult problems to challenge you, but understand that you will not be able to do all the problems perfectly, or even at all sometimes!

#### Q: What about taking 2 honors courses at the same time, such as honors calculus with either honors chem. Or honors physics?

A: Some students find this is doable, but some find it too much work and stress. Our advice is to start with any honors courses you want to try, see how you feel the first week, and then maybe drop into a regular level in the course that seems to be more trouble. Talk to upper-class students who have tried this.

#### Q: Is there a difference between the sections?

A: For most, it is only the time that they meet for lectures. Sections 30 and 50 are each a horse of a different color: see the additional sheet.

#### Q: What are the grading policies? Wouldn't it be better to get an A in 15100 than a B in 16100?

A: Faculty recognize that this is an honors course and agree that, unless someone really works at it (by not attending classes, or turning in homework), the lowest grade assigned in 16100 will be a C- (a signal that you should return to regular calculus, by the way). Most grades are in the range from A to B-. One student says: "this is a challenging but rewarding class and has benefits for your education far beyond the grade you get."

#### Q: What if I can't do the homework?

A: There are lots of ways to get help, including office hours, problem sessions, fellow students, and being active in the class itself. Here's a thought from a former 16100 student: "the one thing that I think you should stress is the various sources of help - office hours, appointments, and above all, asking questions in class. I remember well the tense atmosphere in the first couple days of class, and then when you said, 'you guys can ask questions, you know'; the entire class breathed a collective sigh of relief."

#### Q: What can I do if I'm in over my head?

A: There are many sources of support for this class as listed in the previous answer. Again, from a former student: "I think the support network for the 160s is really important for people who are worrywarts like me." You may always exercise the option of dropping down a level if necessary.

#### Q: How do I drop to a lower level course?

A: If you want to drop down to the 15100 or 15200 or 15300 course you placed into, see Diane Herrmann to do a course change. While such a change is permitted through the 5th week of the quarter, it is advisable to make up your mind around the time of the first exam, and not before. If you bail out too quickly, you may never know if you were in the right place all along. Talk to your instructor before you panic and make a move. You may think you're doing badly, judging by homework scores, when you may be doing just fine compared to your fellow students.

#### Q: If I have AP credit, why should I give that up to start calculus over again?

A: Think of your AP experience as preparation for a new, more theoretical introduction to analysis, instead of something you'll be repeating here at Chicago. While your AP course prepared you to do calculations well, it did not give you the tools for the kind of thinking that you'll need in honors calculus. Testimony from a former 16100 student, not a math major: "Reasons to do it and lose AP credit include personal challenge and learning a whole new way of approaching math."

#### Q: Many of the students I talk to who placed into honors calculus have had BC calculus. I've only had AB (or I had IB, or I had a calculus course that wasn't AP or IB). Does this matter?

A: If you've had a calculus course already and have learned enough to place into honors calculus, the particular version of calculus you had should not matter. Even AP classes differ in terms of what they cover and in how much depth. There will be topics that you may need to review more than some of the other students, but usually that doesn't prove to be a substantial hurdle.

#### Q: If I placed into 20300 and have credit for a whole year of math, is there any reason to consider taking 16100 instead?

A: If you have not yet had any preparation in proof techniques, you may find analysis (Math 20300) a little daunting. In addition, if you elect to begin with 20300 this year, you will not have a chance to take Honors Analysis, Math 20700. Some students give up a year of credit to take Math 16100-16200-16300 their first year, and learn enough about proof to be qualified to take Honors Analysis in their second year. Here's a thought from a former 16100 student: "Personally, I have no doubt that I benefited from taking 160s first, because it served as a kind of stepping stone between regular high school calculus and Analysis." Another student said: "A second year told me that in her analysis class, those who had taken Math 160s had a much easier time learning the concepts and in the end, usually got higher grades than those who didn't. Math 160s really is a great stepping-stone to analysis. Otherwise, there's a big jump in there that a lot of people have trouble with." Such students may find the new sections 30 or 50 particularly appealing. See the sheet!

#### Q: I'm not a math major and have no intention of being a math major. Why would I even consider taking the class?

A: First, this course builds on knowledge you have acquired through your high school mathematics courses, and this can be a satisfying way to use all that stuff. More important, this is a course about a certain way of thinking and doing mathematics. It's a way of stretching your brain and trying something new, challenging, and interesting. We don't assume everyone taking the class is intending to be a math major. In addition, if you are majoring in a subject that requires a second year of mathematics (physics or econ for example), this course is the best preparation for analysis, the second year sequence in mathematics. Another thought from a former student about this question: "I would add, because it's fun. Honors Calc. was the first math class that I *really* enjoyed, and the satisfaction I derived from successfully completing a tricky problem or problem set was great indeed. Plus classes were enjoyable as well, which added to the experience." Here's even more from another student: "I had a lawyer comment to me this summer when I mentioned that I might go to law school, that not nearly enough lawyers learn to think logically. Therefore, he was very glad I had taken an advanced math class and hopefully had learned to think that way."

More questions? See Diane Herrmann in Eckhart 212 or John Boller in Ry 354.