Math 110:
Discovering in Mathematics

   Department of Mathematics and Computer Science
   Hobart and William Smith Colleges

   Spring 2014.

   Instructor:  David J. Eck  (
   Monday, Wednesday, Friday, 3:00--3:55 PM
        Room Stern 304.

About The Course and the Textbook

There are at least two reasons to study mathematics: because it is beautiful and because it is useful. In many cases, it is both. We will try to see mathematics in both aspects in this course.

You might have encountered mathematics mainly as a set of rules, formulas, and techniques for solving certain types of problems. Memorizing rules and applying them is an aspect of useful mathematics at it most boring. Understanding why the rules work how they were discovered, on the other hand, can reveal some of the beauty of math.

This course is called "Discovering in Mathematics." The intent is that you will learn about how mathematics is discovered and maybe do some discovery of your own by working on problems that require creative thought and ingenuity rather than mechanical rule-following. The hope is that you will get to experience mathematics the way mathematicians do, at least to some extent.

The textbook for the course is The Heart of Mathematics: An Invitation to Effective Thinking, Fourth Edition, by Edward Burger and Michael Starbird. We will cover various topics from this textbook, and not always in the order in which they occur in the book. I will assign readings and homework exercises from the book, and you will sometimes work in class on exercises from it. You will not need the textbook for the first two days of class, but it's a good idea to bring the it with you to every class after that.

I do not have a definite schedule of topics for the course. We will start with some material from Chapter 2, on numbers, and from Chapter 3, on infinity. It is likely that we will then jump to parts of Chapter 8, on probability. Where we go from there will depend on how the course is going and on what people in the class are interested in.

Math 110 satisfies the Colleges' "Quantitative Reasoning" goal.

About Assignments and Academic Integrity

An assignment will be collected on the majority of class days. Some assignments will be graded. Some will be "low-stakes". Low-stakes assignments are given a check (serious effort), check-plus (serious effort with especially good writing, insight, or analytic depth), or check-minus (not at the expected level). A low-stakes assignment that is not completed is much worse than a check-minus.

There will be a variety of assignments. Some done in class, some started in class and finished for homework, and some done entirely outside of class. For some group assignments, I will ask everyone in the group to turn something in; for others, will ask for something from the group as a whole.

For most assignments, you are encouraged to work on the assignment with other people in the course. However, the work that you turn in should be your own, and you should never simply copy someone else's work. Some assignments might ask you to work on your own, and you should be careful to follow such instructions. For some essays, it will be useful to consult on-line or print sources; you should be careful to give proper credit to any sources that you use, just as you would for any writing project. If you have questions about academic integrity requirements for any assignment, please ask!

Mathematics Colloquia

The Department of Mathematics and Computer Science sponsors several colloquium talks every semester. They are usually scheduled at 4:15 or 4:45 PM. I expect several of this semester's talks to be about mathematics. It would be a good experience for you to attend these talks. To encourage you to attend at least one of them, you can get 1.5 points of extra credit on your final grade for the course for attending one of the mathematics talks.

Talks will be announced in class and by email. If you attend a talk, be sure to let me know that you are there!

Tests and Final Exam

There will be three in-class tests in addition to a final exam. The tests will be given on Friday, February 14, Wednesday, March 12, and Monday, April 14. The final exam will take place during the officially scheduled exam time for the course, which is Sunday, May 11, at 1:30 PM. The final exam will not be much longer than the in-class tests and will count for the same number of points. It will concentrate on material from the last part of the course, but will in addition have one or two general essay questions about the course as a whole.

A part of each test will be solving problems that test your knowledge of facts and techniques—the sort of thing that you would likely think of as typical math problems. However, a larger part of the test will be essay questions about the terms and concepts that have been discussed in class.


Your numerical grade for the course will be determined as follows:

First test:               15 points
Second test:              15 points
Third test:               15 points
Final exam:               15 points
Graded assignments:       20 points
Low-stakes assignments:   20 points

For the low-stakes assignment, I will scale your grade so that the average grade for the class on those assignments is 85.

The numerical average might then be adjusted up somewhat because of attendance at a math colloquium or a very high level of class participation. It might be adjusted down if you have missed an excessive number of classes.

Letter grades are assigned as follows: 90-100: A; 80-89: B; 60-79: C; 55-69: D; 0-54: F. Grades near a cutoff get a + or -.

Attendance, Etc.

I assume that you understand the importance of coming to class, and I expect you to try to be present every day. I will not take attendance at every class. When I do, it will most often be by returning assignments. However, I will pay attention to absences, and if I notice that you are missing too many classes, it will affect your grade. I will warn you if you are in danger of that happening.

If you miss an in-class assignment, a test, or the final exam without an extremely good excuse, you will receive a grade of zero. If you think you have an excuse for missing a test, please discuss it with me, in advance if possible. If I judge that your excuse is reasonable, I will -- depending on the circumstances -- either give you a make-up test, or I will average your other grades so that the missing grade does not count against you. If at all possible, please do not miss the final exam!

Although it should not need to be said, I expect you to maintain a reasonable level of decorum in class. This means that there is usually no eating or drinking in class. Cell phones are turned off. There is no walking in and out of the room during lecture.

Disability Statement from the CTL

Disability Accommodations: If you are a student with a disability for which you may need accommodations, you should self-identify and register for services with the Coordinator of Disability Services at the Center for Teaching and Learning (CTL), and provide documentation of your disability. Disability related accommodations and services generally will not be provided until the registration and documentation process is complete. The guidelines for documenting disabilities can be found at the following website:

Please direct questions about this process or Disability Services at HWS to David Silver, Coordinator of Disability Services, at or 315-781-3351.

Office Hours, E-mail, WWW

My office is room 313 in Lansing Hall. My office phone extension is 3398. I am on campus most days, and you are welcome to come in anytime you can find me there. I will announce office hours and post them on my office door and on the course web page as soon as my schedule is determined, but note that your office visits are certainly not restricted to my regular office hours!

My e-mail address is E-mail is good way to communicate with me, since I usually answer messages within a day of receiving them.

The home page for this course on the World Wide Web is located at This page will contain a weekly guide to the course and links to lab worksheets. You will want to bookmark this page. This courses does not use Canvas.