Foundations

Course Information

Course: Foundations of Mathematics, math 221.
Professor: Tom Linton, 312 B Central Hall, campus phone (641) 628-5264, email: lintont@central.edu.
Office Hours: 9 AM Mon, Fri, 1 PM Tues, 3 PM Wed, or by appointment.
Class Meets: 8:00 to 8:50 AM MWF in Central Hall 308.
Text: Mathematical Structures for Computer Science, 4th Edition, by Judith Gersting.
Technology: We may utilize Mathematica (or other software) on occassion. The class web page is located at the URL http://www.central.edu/homepages/lintont/classes/spring03/foundationsframeset.html and information relevant to this course may come via email. You should check your email and the class web page on occasion.
Final Exam: Tuesday May 6, 8 AM, 308 Central Hall.

Class Overview Foundations is a course that examines the mathematics of logic and proof as well as structures (sets, relations, functions, graphs, trees) encountered in many computer science and mathematics courses. We will study the precise language of mathematics and develop sophiscated techniques for counting objects in mathematics and computer science.

Goals and Objectives By the end of this class you will be able to:

learn advanced technical material in almost any area of mathematics or computer science;
critically analyze written arguments and have a decent understanding of elementary logic and basic proof techniques;
understand at a deeper level several of the basic structures in mathematics such as sets, trees, and functions;
develop well designed and logically sound algorithms;
understand the basic principles of counting, such as combinations, permutations, and countable versus uncountable.

American Disabilities Act 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.

Grades Grades, based on the letter, or A, A-, B+, B, B-, . . . system, will be based on a curve of the total points in the class. The curve used will be the traditional 100-93 A, 92-90 A-, 89-88 B+, etc. (or an easier curve). The breakdown of the points in the class is given below. There is no extra credit for this class. You are encouraged to work together on group assignments (including homework), but copying answers of others (including those in the back of the text) will result in no credit. Working together does NOT mean copying someone else's solution, in fact, a good rule to always follow is:

When you require help on a problem, you should only have your helper
look at what you have done, and give you advise. You should never look at what they have done.

Exams We will have three midterm exams (100 points each). These exams will most likely follow our completion of chapters 1, 2, and 3. We will also have a cumulative (150 point) final exam on Tuesday, May 6 at 8 AM.

Homework, Quizzes, and Activities I will assign and collect homework problems on a regular basis (one assignment from each section we cover). Recording "just the answer" will receive little or no credit. You should show and/or explain your work on all assignments for this class. You are encouraged to work together on homework assignments, but this does NOT mean copying the work of others nor answers from a solution set. Homework is probably the most important component of this course. Problems will be assigned each day and designated as either board problems or hand-in problems. Solutions to the board problems will be presented (by you, at the board) at the beginning of the next class period. Each student should attempt to do several board problems during the semester, as these will be counted in your homework grade. We may do a few in-class activities throughout the semester (where new concepts are introduced, or old notions are examined in more detail). Most of these activities will be done in groups, and all will contain questions similar to homework problems. We may have a few (3 to 5) announced quizzes. There will be roughly 350 points for this portion of your grade.

Participation You are expected to be in class each day. If you miss a day of class, you are still responsible for the materials-activities completed that day. You are expected to participate in class discussions, ask questions, and to be engaged in the day to day actions of the class. There will be 50 associated with your class participation.

Late Assignments and academic dishonesty

Late homework, activities, and projects will be penalized by 10% each lecture they are late, up to the date I return the graded assignments. Once I have returned an assignment (normally this will occur one or two class periods after I collect it), you will no longer receive credit for handing in that assignment. I am fairly flexible about giving exams at alternate times, BUT you should definitely warn me before the exam is missed, and plan on taking it early rather than late. Quizzes missed due to absences can NOT be made up. You are responsible for all of the material covered in class each day, even if you are not present.

Plagiarism (which includes working together on an individual assignment, or editing someone else's work and turning it in with your name on it), or copying answers from other people or books without citing the source is a serious offense and will result in no credit for the work and possibly more serious punishment (failing the class, placing a letter in your file, and withdrawl from school are possibilities). It is OK to discuss your answers with other groups on group assignments, but the work you turn in must be your own, not a modified version of someone else's work.

Central College's Academic Honesty Policy
"Academic dishonesty is defined as behavior that is inappropriate for academic pursuits, including plagiarizing, cheating and other such dishonest activities. Some examples of misconduct are

presenting other's work as your own: copying homework or test answers from other students, unauthorized collaboration on class activities, using unauthorized materials in a test, having someone else write your paper or test,
improper computer usage: inappropriate or illegal use of computers, including such things as pirating of programs or files, unauthorized access to files or passwords, altering records, and/or damaging programs
plagiarism and/or misuse of ideas from other sources: deliberately using or adopting materials, ideas, or images produced by another person and taking credit for them, regardless of the format in which they originally appeared, including books, journals, web pages, video or audio recordings, and/or computer files, accessing or using privileged information without authorization, quoting, paraphrasing, and/or copying materials without footnoting or proper attribution, using privileged information without authorization.

Depending on the nature of the offense, the penalty for academic dishonesty ranges from permission to redo the project (if plagiarism was inadvertent), failing the project, to failing the course. A second offense is grounds for dismissal from Central College."

Class Materials

In class activity on introduction to formal proofs.
Chapter 1 rules for proof sequences (gif file)

Schedule Relevant information will be added to this schedule as we progress through the semester. An up to date version is available on line at http://www.central.edu/homepages/lintont/classes/spring03/foundations/index.htm#schedule. The board problem assignments are in bold.

Week	Dates	Section(s)	Assignment
1	1-13 to 17	1.1	1.1#1,2,7,10, 6,8abc,11abcfg,16,17
2	1-20 to 24	1.2, 1.3	1.2#2,3,5,9,11 17,22,25,31,37
3	1-27 to 31	1.3, 1.4	1.3# 1,3,7,9cde 4be,10abhjkl,12cef,13,16bd (due 1-31)
4	2-3 to 7	1.4	1.4 (no board problems) #1,3,5,6,10,12,14,19,23,24 Due Wed 3-5 Intro to proofs Rules from chp 1.
5	2-10 to 14	exam 1
6	2-17 to 21	2.1,2.2	2.1#1,2,4,7,11, 15,16,20,24,31,35,47 due Fri 2-21
7	2-24 to 28	2.2, 2.4	2.2 #2,6,12,24 11,16,27,39,41,55,63 due Fri 2-28
8	3-3 to 7	2.3, 2.4, 2.5	2.4# 2,5,8,10,14 18,28,33,34,41,53,65,69 due Mon 3-17 2.3# 5,7,8 due Fri 3-7
	Spring Break
9	3-17 to 21	3.1, 3.2	3.1 # 2,5,7,9,10agijn,12 #16,17,18,23,35,43,56aef,59cef due Fri 3-21
10	3-24 to 28	3.2	exam 2 3.2 # 4,5,12,16,22 46,47,48,49,50,61,63
11	3-31 to 4-4	3.3, 3.4	3.3# 1,4,7,11,15,18,20 3.4# 1,6,8,14,17,19 #28,32,39,40,41,42,43,46,53, 60,64,66,68 due Wed 4-9
12	4-7 to 11	3.5	3.5 #1dgh,3,5,8,11 #13,16,17
13	4-14 to 16	4.1	4.1# 2,3,6,8,9abcgh #15,19,20,21,33,34,35,37
14	4-21 to 25	4.1
15	4-28 to 5-2	4.4	4.4# 1,2,5,6,8abc,11 #19,20,21,23 chapter 3 and 4 practice
17	Tuesday May 6	8 AM	Cumulative Final Exam