Course Syllabus for Math 241: Honors Calculus III (Fall 2013)


Calculus is the mathematics of quantities that vary in time, with a wealth of applications to many different branches of science. It's also a marvelous synthesis of algebra and geometry, tying together pretty much everything you learned in high school math, and serving as a bridge to higher mathematics.

In Math 241, we'll take a more in-depth study of calculus than is offered in Math 231, with more of a focus on the rigorous underpinnings of the subject: not just what's true, but why it's true. Also, since the class is small (fewer than 20 students), class discussions can play a big role in helping you learn to view the material from many different angles, and you'll get more direct contact with a faculty member.

You'll also learn the answer to the questions: What do you get when you mate a mountain-climber and a mosquito? And: Why do pirates like polar coordinates?

You can view an MP4 or two, excerpted from a video interview that I gave in 2013, in which I described the Honors Calc sequence.

I want all of you to succeed in this class; below you will find some tips for how you can help make this happen.


Course overview (the lecture notes for the first day; these notes will probably answer most of your questions about the structure of the course)

Lecture-by-lecture reading assignments (subject to change)

Lecture notes

Homework problems and solutions

Some past students have found these notes (created by Paul Dawkins of Lamar University) to be helpful.


Professor James Propp

Email: JamesPropp at gmail dot com (note: I also have a James_Propp account but I don't read it very often).

Phone: (978) 934-2438. Please note that I do not listen to my voicemail very often. To check whether the university is closed because of weather, call (978) 934-2121.

Fax: (978) 934-3053 (“Attn: James Propp”).

Office: Olney 428C.

Consultation Hours: Mondays, Wednesdays, and Thursdays, 1-2.
Meetings at times other than my office hours can be arranged by appointment; see me after class, call me on the phone, or send me an email message.

Suggestions about how the course is being run are welcome at any time. If something isn't working for you, please don't wait until the end of the semester to tell me!


Meeting times: Mondays, Wednesdays, Thursdays, and Fridays, 12:00 to 12:50 p.m.

Meeting place: Olsen 403.

Prerequisites: Honors Calculus II, or the equivalent.

Expectations: You're expected to attend classes, do the reading in advance, ask questions, and make serious attempts to answer questions raised by me or by other students during class. If you miss a class, it's your responsibility to make sure you obtain all information (course material, assignments, changes in exam dates, etc.) presented that day.


James Stewart, Essential Calculus: Early Transcendentals (2nd edition), 2012. A copy of this book, and a copy of the 1st edition, are at the reserve desk at Lydon Library, linked to the course number 92.141. (On the other hand, the Stewart book Calculus: Early Transcendentals --- note the absence of the word ``Essential'' --- is structured differently and cannot be used as a textbook for this class.)

During the Fall semester, we'll cover Chapters 10 through 13.


Course grades

Course grades will be based on three numbers: your Homework score, your score on the in-class Midterm, and your score on the Final. Your average score for the course will be computed as a weighted average of your Homework, Midterm, and Final scores in which the highest of the three scores is assigned weight 40% and the other two scores are assigned weight 30%. (For instance, if your highest score was on the Midterm, your average score for the course would be 30% of your Homework score plus 40% of your Midterm score plus 30% of your Final score.) Since this is an Honors class with challenging problems, the scheme for computing letter-grades is on the lenient side, and is determined from your weighted average score according to the following table:

Average [85, 100) [82, 85) [80, 82) [75, 80) [72, 75) [70, 72)
Grade A A- B+ B B- C+

Average [65, 70) [62, 65) [60, 62) [55, 60) [0, 55)
Grade C C- D+ D F

(I may raise your grade above what's shown in the table if your class participation is strong: one more reason to come to class. Also, coming to office hours counts as a form of class participation.)

Exam dates: Midterm TBA; final exam TBA.

Exam Policy

It's important that everyone take the same exams under the same conditions for maximum fairness and reliability of testing. I therefore don't give makeup exams unless you have a valid reason for missing the scheduled exam (for example, illness or a religious holiday), and I don't allow extra time on exams unless you have a note from Disability Services (see below). If you have to miss a scheduled exam, please let me know ahead of time if at all possible; I'm much more likely to be sympathetic if you call me the morning of the exam and say “I have the flu and can’t take the exam” than if you come in two days after the exam and say “I missed the exam. When can I take a makeup?”

You may not use a cell phone in any way during an exam.

Use of calculators is prohibited during exams.

You can always reschedule an exam that falls on a day that is a religious holiday for you, but you must make these arrangements ahead of time.


Tips on Preparing for Exams

  • Start studying for an exam at least one week ahead of time.
  • Begin by reviewing the homework problems for the sections that will be covered on the exam. Make sure you know how to solve each problem. If you can't solve a particular problem, make a note of the problem number and move on to the next problem; you can go back to the problem later with a fresh head (yours or someone else’s!).
  • You can test your knowledge by trying odd-numbered problems for which the answer is given at the back of the book.
  • Try the review problems that appear at the end of each chapter.
  • Ask me or someone else for help on any homework problem that gave you trouble, then try to solve a similar problem from the textbook.
  • Get a good night’s sleep the night before the exam. You'll perform better if you are fresh and able to think clearly.

  • Tips on Taking Exams


  • Read every question on the exam before you start working. This will give you a feel for how long the exam is and how you should pace yourself. It'll also give your subconscious mind a chance to start working on the questions.
  • If you're not sure what a question means, please ask me. I'm trying to see how well you know the material, not to trick you with ambiguous wording.
  • Show as much of your work as possible, in as clear a way as possible. Even if you get the wrong answer, I'll try to award you as much partial credit as I feel I can conscientiously give you, but it's hard for me to do this if you don't show your thought-processes.
  • Look at the point value of each question. Obviously, it's more important to do well on the questions that count the most than the ones that count the least.
  • It's generally best to do the easiest problem first, then the next easiest, and so on. You don't have to do the problems in the order they appear on the exam.
  • If you get stuck on one question, move on to the next. Come back later to the question that is giving you trouble.
  • Be aware of how much time you have left. Don't spend too much time on a single question. It's generally better to get partial credit on every question than full credit on a small number of questions.
  • If you have extra time, use it to check your work! Better still, if there's more than one natural approach to the problem, try to solve the problem with a different method; this can be a better way to catch mistakes than just re-reading your calculations. If you get the wrong answer with one approach but the right answer with the other approach, I'll give you nearly full credit (especially if you speculate intelligently on where you might have made an error).
  • If you get an answer that doesn't make sense but don't have time to trace where your error came from, don't just cross out your answer; explain why you think the answer you got looks wrong, and you may get some extra points for having good instincts.
  • Never be afraid to ask for extra paper. (If you want to write on the reverse side of a page, please write “see other side”.)


    Typically there'll be one homework assignment per week, due one week after it is assigned. (We may deviate from this schedule at the beginning of the term and around the time of the midterm.)

    In order for you to understand the material in this course, it's extremely important that you do the assigned homework problems. Working with your classmates can be a great help, and I strongly encourage it, subject to certain provisos (see below). I also urge you to ask questions about any problems that give you trouble.

    Homework will usually be due each week on Friday (except during the week of an exam). Your grade will be based on clarity as well as correctness, so neatness, grammar, and punctuation should not be neglected. Harder problems will in general be worth more points. You are required to include an estimate of how much time you spent on each and every assigned problem; this will help me assess which of the problems are the harder ones. (I reserve the right to throw out a problem entirely if it turns out to be too hard.)

    Barring unusual circumstances, late homeworks will not be accepted.

    Each student will be allowed to skip two assignments without penalty; additional skipped homeworks will only be permitted if a valid excuse is presented, preferably ahead of time rather than afterwards. Don't use up your “free skips” too early in the semester! If you skip just one assignment, your lowest homework score gets dropped. If you don't skip any assignments, your two lowest homework scores get dropped.

    While you can discuss the exercises with classmates, the work you hand in should be your own write-up and not copied from someone else. When leaving a joint homework-solving session, don't carry away anything that doesn't fit in your own brain. Also, you must acknowledge who you worked with. (If you didn't work with anyone, please write “I worked alone on this assignment”.)

    Academic honesty in homeworks is expected. (E.g., if you use web-resources or tutors or collaborators of any kind, the role of their contribution must be acknowledged; you won't receive a lower grade for using such resources, but if the grader and I feel you're relying on them too heavily, we may require you to change your way of doing homework.) My expectations for appropriate ways of doing the homework will be discussed in class; in case you are in any doubt about what is expected, it is your responsibility to contact me for clarification. See the UMass Lowell catalogue for a definitive statement of UMass Lowell's academic honesty policy.

    It is not required that you submit your solutions in LaTeX, but if you are planning to be a mathematician, scientist, or engineer, it's never too early to learn! LaTeX is free software that lets you typeset formulas about as fast as you can write them (with some practice). Composing your homework in LaTeX will help you pay attention to your communication of mathematics, and make it much easier to edit your work as you go along. There will be an initial hump of getting started, but after a couple of problem sets, using LaTeX will become quite natural. You'll probably still want to draw your diagrams and figures free-hand, but knowing how to write equations in LaTeX is a life-skill that will serve you well in later courses in which homeworks involve fewer pictures and more formulas.

    Also, if you want to use Mathematica as an aid to your learning, check out Effective Fall 2011, students will be able to download Mathematica as part of the campus license, so using it for classes will be more convenient than in the past. You shouldn't use Mathematica as a substitute for being able to do the work yourself the old-fashioned way, but it's a great way to check your work. Also, Mathematica features many demonstrations (see that can bring course material to life in a vivid way.

    You will be expected to fill out a time sheet that tells me how much time you spent on each problem (rounded to the nearest minute, or the nearest five minutes; there's no need to be super-precise). This helps me improve the course from year to year by spreading out the work-load more evenly from week to week. Points may be deducted from students who repeatedly fail to submit legible time sheets.

    Many students find it profitable to read the solutions to all the problems in the current assignment (posted on the web each week). Even if you got a problem correct, you may learn something from reading the posted solution, such as an alternate approach to the problem or a good clear way to express the main ideas.


    Regular attendance is expected. It is not part of the grading scheme, but it may be used to adjust grades upward in the event of a borderline grade. Class participation that shows that you have read the assigned material may also be helpful in borderline cases.


    If you have any special needs, e.g., you need more time on exams because of a disability, I'll do my best to accomodate you. Please notify me at least two weeks in advance.