Math 221 -- Foundations of Mathematics

Spring, 2004 -- Allen Hibbard

text: Discrete Mathematics with Proof (Gossett)

COURSE DESCRIPTION: Although the discipline of discrete mathematics has many interesting topics, the fundamental goal of this course is to prepare one for advanced, junior/senior-level courses. In other words, we want to give you the foundation needed to prepare you for more abstract and/or difficult mathematics and computer science courses.

Specifically, the topics that are important for both mathematics and computer science majors include the following: set theory, logic, introduction to proof and the axiomatic approach, introduction to the theory of algorithms, functions and relations, counting, recursion, graphs and trees, and combinatorics. You may note that these topics roughly reflect the chapter titles of chapters 2-4, 12, 5, 7, 10, 11, and 8, respectively. This is roughly the outline of how we will proceed with the course. Time permitting, we will also venture into parts of chapters 6 and 9 (probability and models).

For some of you, it may come as a harsh realization that mathematics is more than working with numbers and solving equations and that computer science is more than programming code. Both disciplines have an abstract nature to them and require and introduction to learning how to think at a higher level. This course is meant to help you do so. Therefore, it is very important to give this course your best and build that good foundation for your future courses to build upon.

YOU CAN NOT AFFORD TO GET BEHIND IN THIS CLASS! PLEASE get help from me or your classmates when you encounter difficulties. Attending class with regularity and a willingness and desire to learn will help you greatly.

TEXT: This book was very intentionally written with the student in mind. The author has tried hard to make it readable to the reader who is still learning to read sophisticated material. It is of utmost importance that you learn to read advanced mathematics and computer science books and this books is intended to help you in this process. There are many Quick Check sections sprinkled throughout the text. Do them! Also, read through the examples and material trying to anticipate and make sure that you understand each step. Each chapter ends with abundant review material. Take advantage of what is given! Read the book and enjoy.

HOMEWORK: I say this in every class: One can not learn mathematics in a passive state; one must be an active participant. To this end, homework will be regularly assigned. This will consist primarily of exercises from the text, though there will be other assignments as well. There will be an attempt to regularly collect problems from the text and have specific exercises graded. An announcement that homework will be collected may or may not occur. (Typically, however, I assign it on day n, review any questions on the exercises on day n+1, and then collect it on day n+2.) Diligently doing your homework pays off with big dividends at quiz and test time! The exercises are not simply a collection of routine drill problems, but many require serious thought and reflection on the concepts presented in the text; give it your best by thoroughly reading before trying the problems. You are encouraged to work together on homework from the text, but each should submit one's own individual work. Homework constitutes 10% of your final grade.

QUIZZES: There will be an attempt to be give quizzes about once per week and may be possibly unannounced. These will be short in nature and cover relatively recent material. There will be NO makeup for missed quizzes! However, the lowest score will be dropped. Quizzes constitute 15% of your final grade.

TESTS: There will be 3 major tests occurring roughly every four weeks, scheduled on 2/20, 3/31, and 4/30. You would benefit by beginning your study for each test at least one week in advance. Tests constitute 60% of your final grade.

FINAL: There will be a final exam, which will be cumulative in design as well as incorporating material since the last exam. This will constitute the remaining 15% of your final grade.

GRADES: Based on the scores weighted as above, a letter grade will then be awarded as delineated below, though other factors such as attendance, participation, effort and trends may also play a (minor) role.

A : [93, 100] A- : [90, 93) B+ : [88, 90) B : [82, 88)
B- : [80, 82) C+ : [78, 80) C : [72, 78) C- : [70, 72)
D+ : [68, 70) D : [62, 68) D- : [60, 62) F : [0, 60)

OFFICE HOURS: I will be available (almost) every day from 8:00-9:00 and 10:00--10:50 in room 133 in Vermeer Science Center. If this time is not convenient, please feel free to make an appointment for a different time. I am usually available in the afternoons, though it can not be guaranteed. If you wish to see me any time outside of the "guaranteed" office hours, for your sake, prearrange it or give me a call to see if I am free. My phone number is 5133; leave a message if I don't answer. You can also e-mail me at

NOTE: Central College abides by interpretations of the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973 that stipulates no student shall be denied the benefits of an education “solely by reason of a handicap.” Disabilities covered by law include, but are not limited to, learning disabilities, hearing, sight or mobility impairments, and other health related impairments. If you have a documented disability that may have some impact on your work in this class and for which you may require accommodations, please see me and Nancy Kroese, Director of Student Support Services and Disability Services Coordinator, (x5247) so that such accommodations may be arranged.