You should use office hours (for all your classes) as an ongoing resource to address questions or difficulties that were not addressed in class.  Knowing your professor is also a great motivator and a good way to get advice on courses and other education and career related decisions.

Objectives:  Mathematics is an important part of a broad education, is used in all science and many social science fields, and is crucial in thinking logically and critically.  Mathematical literacy includes not only mastering various technical principles but also developing the ability to use the precise language of mathematics to justify assertions, both of which can help you both in your future career and in daily decisions.  Learning these skills can be difficult and frustrating at times.  But solving a problem, constructing a rigorous argument, and expressing solutions clearly are all rewarding processes that contribute to becoming a well educated and well rounded person.

This course focuses on logic and rigorous methods of proof in the context of discrete mathematics.  Most importantly, since this course serves as a transition to theoretical upper division courses in mathematics and certain courses in computer science, you will learn to construct and write rigorous arguments as precise proofs.  Such skills are essential in mathematics and useful for programming, daily reasoning, and effective communication in other fields.  Along the way you will use and learn math that is discrete in nature.  Discrete mathematics not only includes beautiful proofs and unsolved problems, but is also a very active area of recent research, in part due to its applications to computer technologies (such as secure communication and efficient data storage).  Unfortunately we will only have time to barely scratch the surface of this important and growing field.  Specific topics will be chosen from number theory, set theory, and combinatorics, each of which deserve their own course.  By the end of this course you should:

• Be fluent in the fundamental notions of logic, use of quantifiers, and methods of proof.
• Be able to analyze the validity of statements and arguments.
• Be aware of the crucial need for clear, precise terms and proofs and be able to write rigorous proofs using such clarity and precision.
• Be familiar with some foundational results and techniques and able to construct proofs of basic results in number theory, set theory, combinatorics, and related topics.

Materials: The text is Discrete Mathematics with Applications, 3rd Edition, by Epp.  We will cover parts of Chapters 1-10, but the parts and chapters we skip are important material worth learning on your own.

Prerequisites: The official prerequisite for this course is Math 160 or Math 170.  Perhaps more important is the need to be careful and precise in explaining arguments, to focus attention on details and methods of proof, and to apply consistent hard work throughout the semester.  As stated in the undergraduate catalog, you must earn a C- or better in this course before using it as a prerequisite for another math course.

Format and Evaluation
Class time will include a mixture of brief lectures and cooperative group work.  I expect you to prepare for each class.  You are responsible for material covered in all class sessions regardless of whether you have reason to be absent.

Homework will be from two lists of problems.  The beginning of class will be spent meeting with other students to compare your answers to problems from the first list and answering any resulting questions.  Solutions to these may at times be turned in for a score of 0, 1, or 2 based solely on effort.  Thus you should prepare for each class by reading and thinking about the material marked on the calendar for that day, attempting the homework problems on the first list, and jotting down any questions you have.  Solutions to problems on the second list will be written up in final form and turned in for comments and a grade roughly once a week.  The calendar with lists of homework problems and due dates will be posted and updated as the semester progresses on the class web page, http://www.isu.edu/~krilcath/m287Fa04.html.

Studying together and discussing problems are encouraged, after you have worked hard on the material or problem yourself, since this can be a very effective and rewarding way to learn mathematics.  You will find such sessions most useful if you write up solutions yourself.  Answers in the book or a study guide are also most valuable when used after completing a problem.

Quizzes, given roughly once per week, will require you to write 1-3 definitions of key terms in the course.  Exams will be closed book in-class exams.  Each will include some questions modeled directly on problems in the text and some problems that involve applying familiar concepts in new situations. If an emergency requires you to miss an exam, you should contact me or have someone else contact me before the exam if at all possible and must provide documentation.  The final date is firm, so please mark it down now.

Grades of A, B, C, D will be guaranteed by earning overall percentages of 90%, 80%, 70%, 60%.  Cutoffs for +/- will be determined at the end of the semester, but will be within 3 percentage points of these values.

Philosophy: All of you have the potential to succeed in this course and hard work counts for a great deal.  I continue to learn by expanding my knowledge of mathematics and its connections with other subjects, by doing original research, by understanding more about learning and teaching, and by working to teach in ever more effective ways.  I expect you will deepen your knowledge of mathematics and its applications, will learn to formulate questions that lead you to construct your own understanding of mathematics, and will know more about the process of learning, solving problems, and writing proofs after you complete this course.  The most important skill you gain during a college education is the ability to learn independently.

Accommodations: Our program is committed to all students achieving their potential.  If you have a disability or think you have a disability (physical, learning, hearing, vision, or psychiatric) that may need a reasonable accommodation, please contact the ADA Disabilities & Resource Center, Room 123 Graveley Hall, 282-3599 as soon as possible.