CSc 245 (Introduction to Discrete Structures) Syllabus
Spring 2008
[Catalog] == [Personnel] == [Resources] == [Outline] == [Dishonesty] == [Grades] == [Class Policies] == [University Policies] == [Caveat]
General Catalog Information:
| Description: | An introduction to mathematical concepts for Computer Science. Topics include first-order logic and logical arguments, proof techniques with an emphasis on mathematical induction, sets, relations and functions, properties of integers, counting methods, probability, and recurrences. Weekly laboratory. | ||||||||||||||||||||||||||||
| Lecture: | Mondays, Wednesdays, and Fridays, 2:00 p.m. - 2:50 p.m., CHVEZ 110. | ||||||||||||||||||||||||||||
| Recitations: | Here are the section times and locations: | ||||||||||||||||||||||||||||
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| Honors students (those enrolled in the "H" sections) also attend a additional 4:00 p.m. - 4:50 p.m. meeting every Monday in G-S 805. | |||||||||||||||||||||||||||||
| See the Personnel section, below, for section leader contact info. | |||||||||||||||||||||||||||||
| Each recitation section is lead by an undergraduate section leader (SL). We require attendance at the weekly section meetings to give you the opportunity to work on more examples that tie in with the lecture topics, to allow you to ask questions about things you saw in recent lectures that you didn't fully understand, and to allow us to offer clarifications on homework and programming exercises. Other things will happen in section, too, such as returning and reviewing homework assignments. | |||||||||||||||||||||||||||||
| Prerequisite(s): | Math 110 (College Algebra), Math 111 (Plane Trigonometry), and a grade of B or better in either CSc 127B (Intro. to CS, 2nd Semester) or CSc 227 (Program Design and Development). | ||||||||||||||||||||||||||||
| In particular, you are expected to know and be able to apply the basics of algebra and trigonometry, and how to write Java programs that include basic data structures (arrays, linked lists, and binary trees) | |||||||||||||||||||||||||||||
| Credits: | 4 | ||||||||||||||||||||||||||||
| Final Exam: | Friday, May 9, 2008, 2:00 p.m. - 4:00 p.m. The final is required, is comprehensive, and will be given on this date at this time. Make your travel plans accordingly. |
Class Personnel:
| Name | Office | Phone | Fax | Office Hours | ||
|---|---|---|---|---|---|---|
| Instructor | Lester I. McCann, Ph.D. | G-S 809 | mccannl@acm.org | 621-3498 | 621-4246 | T 2-4pm; W 3:30-4:30pm; F 3-4pm |
| SL | Jude Nelson | G-S 737 | jnelson@cs.arizona.edu | ----- | 621-4246 | R 3-4pm; F 12-1pm |
| SL | Robert Stout | G-S 737 | robert@cs.arizona.edu | ----- | 621-4246 | R 11:30am - 12:30pm, 2-3pm |
| SL | Joe Thomas | G-S 737 | jthomas@cs.arizona.edu | ----- | 621-4246 | R 4-5pm; F 10-11am |
| SL | Susan Evans | G-S 737 | susan@cs.arizona.edu | ----- | 621-4246 | R 1-2pm; F 1-1:50pm |
Each of the SLs has successfully completed this class (or its equivalent) and is paid by the Department of Computer Science to help me help you learn the material. In addition to leading a section (or two) each week, they grade homeworks and quizzes, do the bulk of grading on the exams, let me know what topics seem to be especially baffling to the students, and even hold office hours in their offices or our Commons room (G-S 737). I expect that you'll find your section leader to be a valuable resource.
Please keep in that that it is possible to meet with each us outside of office hours. Contact us to make an appointment.
Information Resources:
| Homepage: | http://www.cs.arizona.edu/classes/cs245/spring08/ |
| Textbook: | Discrete Mathematics and its Applications (Rosen), 6th ed., McGraw-Hill, 2007, is the required text. Its corresponding web site is also worth a look. You may find other books to be useful purchases. A more complete collection of solutions to the odd-numbered end-of-chapter exercises is available in the form of the Student Solutions Guide (Rosen), McGraw-Hill, 2007. Some students find How To Prove It 2/e (Velleman), Cambridge, 2006, to be helpful with learning how to construct proofs. |
Course Objectives and Expected Learning Outcomes:
| Topics and Subtopics | Sections In Text | Sample Learning Objectives |
|---|---|---|
| 1. Mathematical Review | ||
| a. Associative, Commutative, and Distributive Laws | Lecture | • Correctly apply to given operators and domains |
| b. Fractions | Lecture | • Know how to algebraically manipulate fractions |
| c. Congruences and the Modulo Operator | 3.4, Lecture | • Understand the relationship between them |
| d. Exponents and Logarithms | Lecture | • Knowledge of and ability to use basic identities |
| e. Factoring Quadratics and the Quadratic Formula | Lecture | • Be able to factor quadratic polynomials |
| • Use the quadratic formula to solve quadratic equations | ||
| f. Laws of Inequalities | Lecture | • Be able to correctly merge inequalities |
| g. Summation and Product Notation | 2.4, Lecture | • Evaluate summations and products of sequences |
| h. Number Systems | 3.6, Lecture | • Work with and convert between number systems |
| 2. Logic | ||
| a. Background | Lecture | • Distinguish mathematical and philosophical logic |
| b. Propositions | 1.1 | • Identify propositions in natural language |
| • Use logical operators to construct compound propositions | ||
| • Evaluate propositions | ||
| c. Conditional Propositions | 1.1 | • Construct inverses, converses, and contrapositions |
| • Translate to and from conversational English | ||
| d. Application of Equivalences | 1.2 | • Simplify expressions via application of equivalences |
| 3. Quantification | ||
| a. Predicates | 1.3 | • Distinguish predicates from propositions |
| b. Universal Quantification | 1.3, 1.4 | • Convert U.Q. between logic and English |
| c. Existential Quantification | 1.3, 1.4 | • Convert E.Q. between logic and English |
| d. Evaluating Quantified Expressions | 1.3, 1.4 | • Determine the veracity of such expressions |
| e. "Exactly n" Expressions | 1.4, Lecture | • Convert such expressions to and from logic notation |
| 4. Arguments | ||
| a. Arguments | Lecture | • Distinguish inductive and deductive reasoning |
| 1.5, Lecture | • Distinguish valid and sound arguments | |
| b. Rules of Inference | 1.5 | • Know the basic rules of inference |
| • Use the rules of inference to construct valid arguments | ||
| • Recognize common fallacious arguments | ||
| 5. Proofs of "p implies q" | ||
| a. Background | 1.6 | • Know the purpose of proofs |
| b. Direct Proofs | 1.6, 1.7 | • Read and construct such proofs |
| • Recognize Proof by Cases as a form of direct proof | ||
| • Distinguish good proofs from bad | ||
| c. Proof by Contraposition | 1.6 | • Read and construct such proofs |
| d. Proof by Contradiction | 1.6 | • Read and construct such proofs |
| e. Disproving Conjectures | 1.7, Lecture | • Show how to demonstrate that a conjecture is false |
| 6. Sets | ||
| a. Properties | 2.1, 2.2 | • Know the basic characteristics of sets |
| b. Set Operators | 2.1, 2.2 | • Demonstrate knowledge of set operator behavior |
| • Use set identities appropriately | ||
| c. Set Cardinality | 2.4, Lecture | • Know the definition |
| 7. Matrices | ||
| a. Scalar and Matrix Products | 3.8 | • Demonstrate ability to compute both types |
| b. Miscellaneous | 3.8, Lecture | • Know basic matrix properties and relevant applications |
| 8. Relations | ||
| a. Binary Relations | 8.1 | • Know how they are distinguished from other types |
| b. Properties | 8.1, 8.5, 8.6 | • Identify reflexive, symmetric, antisymmetric, and transitive relations |
| • Identify partial and total orders, and equivalence relations | ||
| c. Representations | 8.3 | • Be able to work with linear and matrix forms |
| 9. Functions | ||
| a. Definitions | 2.3 | • Know the basic properties |
| b. Types | 2.3 | • Identify injective, surjective, and bijective functions |
| 10. Integers | ||
| a. Prime Numbers | 3.5 | • Learn the Fundamental Theorem of Arithmetic |
| b. GCD and LCM | 3.5 | • Define them and their properties |
| 11. Sequences and Strings | ||
| a. Sequences | 2.4 | • Know the basic terminology and properties |
| • Understand the connection with summation notation | ||
| b. Strings | 2.4, Lecture | • Know the basic terminology and properties |
| c. Countability | 2.4 | • Distinguish countable, countably infinite, and uncountable |
| 12. Mathematical Induction | ||
| a. Principle of Mathematical Induction | 4.1 | • Understand why induction works |
| b. Weak and Strong Induction | 4.1, 4.2, Lecture | • Understand the distinction |
| • Construct and understand such proofs | ||
| 13. Counting | ||
| a. Pigeonhole Principle | 5.2 | • Appreciate its utility |
| b. Product and Sum Rules | 5.1, 7.5 | • Recognize when each applies |
| • Generalize to Principle of Inclusion-Exclusion | ||
| c. Permutations | 5.3, 5.5, 5.6 | • Know that order matters |
| • Generalize to counting with indistinguishable objects | ||
| d. Combinations | 5.3 - 5.6 | • Distinguish from permutations |
| • Generalize to counting with indistinguishable objects | ||
| • Learn connection to (and applications of) binomial coefficients | ||
| 14. Recursive Algorithms | ||
| a. Properties of Algorithms | 3.1 | • Know the characteristics of a complete algorithm |
| b. Recursive Algorithms | 4.3, 4.4 | • Review components of such algorithms |
| c. Structural Induction | 4.3, 4.4 | • Proving correctness of recursive algorithms |
| 15. Recurrence Relations | ||
| a. Definition | 7.1 | • Connect recurrence relations to recursive algorithms |
| b. Solving Recurrence Relations | 7.2, Lecture | • Solutions for Linear Homogeneous RRs |
| • Solutions via 'Find the Pattern' | ||
| • Approximate solutions with the Master Theorem | ||
| 16. Finite Probability | ||
| a. Basics | 6.1 | • Learn terminology and notation |
| b. Conditional Probability | 6.2 | • Learn relationship to event independence |
| c. Probabilistic Reasoning | 6.1, Lecture | • Recognize connection to logical arguments |
Topics may be added, removed, or reordered as time and circumstances dictate.
Academic Dishonesty (i.e., Cheating):
| See Also: | • The Department of Computer Science Course Policy on Collaboration: http://www.cs.arizona.edu/policies/collaboration.html |
| • The University of Arizona Code of Academic Integrity: http://dos.web.arizona.edu/uapolicies/cai1.html | |
| • The Arizona Board of Regents list of Prohibited Conduct: http://www.abor.asu.edu/1_the_regents/policymanual/chap5/chapter_v.htm#5-303 | |
| • The Arizona Board of Regents Student Code of Conduct: http://www.abor.asu.edu/1_the_regents/policymanual/chap5/chapter_v.htm#5-308 |
Most, if not all, assignments in this class will be individual assignments, to be worked on outside of class. All individual work assigned to you in this class is to be completed only by you. It is not acceptable for you to `borrow' (a.k.a. steal, copy, coerce, etc.) solutions or parts of solutions from other people or have other people write part or all of your solutions for you. However, it IS acceptable (and encouraged!) for students to help one another understand the assignment requirements and to help one another track down logic errors in exercises. In short, do your own work, but feel free to discuss difficulties with each other. Of course, you may always ask me or a SL for help, but don't expect that we'll just hand you solutions; we'll make you work for them.
The class policy on cheating is simple: If we determine that your work was turned in by another student, or we determine that you turned in the work of another person or persons, all students involved will receive at minimum a zero on that entire assignment. Additional sanctions are possible should additional information come to light. The CS department exchanges information about academic integrity violations with the office of the Dean of Students. If you have a history of violations, the penalty is likely to be much worse than just a zero on the assignment. Multiple violations in this class will result in a failing course grade at minimum. We take academic dishonesty very seriously, as you should be able to tell; we expect you to take it just as seriously.
If you are not familiar with them, please take the time to read the references linked above. Ignorance of the policies is not an acceptable excuse for their violation. For your convenience, here is the section of the University's Code of Academic Integrity entitled "Prohibited Conduct":
| Conduct prohibited by the Code consists of all forms of academic dishonesty, including, but not limited to: cheating, fabrication, facilitating academic dishonesty, and plagiarism as set out and defined in the Code of Conduct, ABOR Policy 5-308-E.10 and F.1; submitting an item of academic work that has previously been submitted without fair citation of the original work or authorization by the faculty member supervising the work; modifying any academic work to obtain additional credit in the same class unless approved in advance by the faculty member; failure to observe rules of academic integrity established by a faculty member for a particular course; and attempting to commit an act prohibited by this Code. Any attempt to commit an act prohibited by these rules shall be subject to sanctions to the same extent as completed acts. |
The bottom line: Do your own work. If you have any doubts, please come talk to me -- before you do anything you might regret.
Grades and Grading:
| Section Attendance | = | 4 | % | |
| Homeworks | = | 20 | % | total |
| Quizzes | = | 16 | % | total |
| 3 Midterm Exams | = | 45 | % | total |
| Comprehensive Final Exam | = | 15 | % | |
| Total | = | 100 | % |
I use the common 90-80-70-60 grading scale. It's possible that final grade cutoffs will be lowered a little (from 90% to 88.5% for the bottom of the 'A' range, for example) but they will never be raised. I make such determinations only at the end of the term, after the final exam has been graded.
You will be expected to regularly attend your weekly section meetings. To help encourage you to do so, your SL will be taking attendance each week. Hopefully, you will find the sections to be useful enough that you won't need the encouragement.
The idea behind the homework assignments is to help you get more hands-on experience with the material as preparation for the exams. Clearly, it is in your best interest to work as many problems as possible, not just the ones assigned as homework.
Expect to complete 9-11 homework assignments during this course. Most homeworks will be due a week from the date on which they are assigned. If there is a week without a homework, probably there is an exam lurking.
For the most part, the homework assignments in this class are ``written'' (which includes electronic composition), although you can expect that we'll ask you to program a little bit, too, now and then. When programs are required, you can use the Gould-Simpson 228 or 930 labs, or your own equipment, as the situation permits.
We expect your written work to have your answers clearly marked, to include sufficient detail to enable us to follow your reasoning, and to be legible so that we can easily read your words, understand your explanations, and decipher your diagrams. Difficulties in any of these areas will likely result in a loss of points. This isn't high school; you are preparing yourselves for careers, and you need to get in the habit of preparing your work in a professional manner. Here's another way to look at it: Make it easy for us to see that you know your stuff.
You are encouraged (but, at least initially, not required) to learn and use the scientific document preparation package LaTeX 2e to typeset your homework submissions. Not only will this help you produce readable answers, you will be ready for future classes and research papers that require the use of this tool. LaTeX 2e tutorials and samples will be provided.
On the due date, turn in what you have accomplished, whether or not it is complete. If you feel that you deserve an extension of the due date based on exceptional circumstances, contact me and I will consider your request.
Each problem will be worth a certain number of points. A complete, correct, and legible answer will receive full credit. We will award partial credit to incomplete and/or semi-legible answers when appropriate. If you feel that your homework was graded improperly, please contact your SL to discuss your concerns.
To help you do better on future homeworks, your SL will be offering "interactive grading." Here's how it works. Most homeworks will be constructed to be worth 45 points initially. If your score is below 35, you may set up a meeting with your section leader so that the two of you can discuss your difficulties with the exercises and (hopefully) correct them. At the end of the meeting, your section leader will give you an additional 5 points on the assignment.
If your score is 35 or better, your section leader will automatically add the 5 points onto your score. This prevents you from being penalized for doing well. The true maximum that can be earned on most homework assignments is 50 points.
In this class, the late policy is simple. Homework assignments are due no later than five (5) minutes into class on the due date. (That is, if the class starts at 1:00, the assignment is due at 1:05.) No late assignments will be accepted (although exceptions may be granted in exceptional circumstances). If you know you are going to be absent on the due date, be sure to get your solutions turned in early; in such cases, you may submit your solutions electronically, by FAX, by carrier pigeon, etc., just so long as they arrive in time and are complete and legible.
I am planning to give 11 or 12 unannounced quizzes, of which only your best 8 scores will be counted. Why about 12? I like to average one quiz per non-exam week of the semester. This means that there will be weeks with no quiz, but there may be weeks with multiple quizzes. The quizzes will not be on predictable days of the week but are usually given at the end of the class period.
I will not be giving any make-up quizzes. Why not? Of the 11 or 12 quizzes I anticipate giving, only your best 8 quiz scores will count. This gives you multiple opportunities to have an off-day or to miss a quiz for whatever reason without it hurting your quiz total.
The use of calculators is NOT permitted on quizzes unless warranted by special circumstances.
Exam formats will be fairly consistent throughout the semester. Exams will consist primarily of short answer and problem-solving questions, but code-writing questions are also possible. The use of calculators or any other electronic devices is NOT permitted on exams unless warranted by special circumstances.
I expect all students to take the exams at the announced exam times. I give make-up exams only in extreme circumstances. I decide if a circumstance is "extreme." For example, being in a documented car accident on the way to the exam is likely to count as an extreme circumstance. Circumstances that are not considered to be extreme include losing a cell phone, breaking up with a significant other, forgetting to set/heed an alarm clock, having a runny nose, etc. Please be aware that missing a midterm exam isn't necessarily a disaster; see below.
I will schedule a midterm when I feel that we've reached a suitable point in the lecture material. Midterms will focus on the material covered in class, on the homeworks, and by the programs since the time of the previous midterm (or the start of the term in the case of the first midterm). As new material in this class usually builds upon the old, you should expect that your knowledge of material covered by previous exams will be necessary for success on subsequent exams.
Regrade Requests: After midterm exams are graded, they will be returned to you and you may keep them. We will also review the exam, either in class or in section. If you feel that your exam was graded improperly, prepare a brief memo that explains which problems concern you and why. Within one week of the date on which the exam was returned to the class/section, submit your exam (not a copy) and the memo to me. I will regrade the entire exam, paying particular attention to the problems you highlighted in the memo. Because errors in grading can cause scores to be too high as well as too low, it is possible that your grade will go down as a result of the regrade. Be sure to review your entire exam before you ask for a regrade.
The final exam will be given at the time stated in the class schedule. (I have also placed it near the beginning of this syllabus. If you see that I have listed the exam time incorrectly, please let me know.) The final will be comprehensive and will have a format similar to that of the midterms. If you miss the final under less than extreme circumstances, you will receive a score of zero for the final.
At the end of the semester, I will replace your lowest midterm exam score with a percentage-equivalent copy of your final exam score, but only if the final score is higher than at least one of your midterm scores. (Thus, this is a potential bonus but never a penalty.) I do this to reward you for demonstrating an improved mastery of the material over the course of the semester. However, it can also help you if you should miss a midterm because your car broke down, your alarm clock didn't go off, you had a disfiguring zit, or any other non-extreme quirk of fate. Please note that should you miss multiple midterms under sub-extreme circumstances, you will definitely get a zero for those additional missed midterms.
If room capacity permits, leave a seat vacant between you and your neighbor. If need be, we will reseat students before or even during an exam to maintain an honest evaluation environment for all students.
Miscellaneous Class Policies:
The instructor and the SLs will attempt to reply to email from students within 24 hours. This means that if you wait until the evening before an assignment is due to send a question to your SL, you may not get a reply before the due date and time. There's a classic sentence that covers this: A failure to plan on your part does not constitute an emergency on our part. We want to help, but like you, we have tasks other than email that require our attention.
There will be no opportunities for extra credit points. Use your time to concentrate on doing well on the assigned work. If your grade in this class is important to you, start taking this class seriously now, not just after you do poorly on the first exam. Additional late days for assignments may be offered as incentives under special circumstances.
| See Also: | • Accommodation of Religious Observance and Practice: http://dos.web.arizona.edu/uapolicies/ouap4.html#religion |
All holidays or special events observed by organized religions will be honored for those students who show affiliation with such religions. Absences pre-approved by the UA Dean of Students office will be honored. No matter the reason for missing class, the student is always responsible for the missed material.
| See Also: | • Audit Policy: http://catalog.arizona.edu/2007-08/policies/audit.htm |
If you are auditing this class, you may attend lecture and you may attend your assigned weekly section. You can turn in programs and homeworks only if your SL agrees to accept them. You may not take exams.
Miscellaneous University Policies:
| See Also: | • Spring 2008 Dates and Deadlines: http://www.em.arizona.edu/datesDeadlines/datesDeadlines.aspx?t=081 |
If you find yourself thinking about dropping this (or any other) class, first make sure that that's what you really want to do. Chatting with me, your SL, or your academic adviser may help. If you drop within the first four weeks of the semester, there will be no notation on your transcript; it will be as though you'd never enrolled. During the fifth through the eighth weeks, a drop will be recorded on your transcript. You will receive a "WP" (withdrawn passing) only if you were passing the class at the time of your drop. After the eighth week, dropping becomes a challenge, because you need to explain to me and to your dean why you were unable to drop the class during the first half of the semester.
| See Also: | • Office of Curriculum and Registration Grading Policy Manual: http://www.registrar.arizona.edu/gradepolicy/incomplete.htm |
| • UA General Catalog's Grades and the Grading System: http://catalog.arizona.edu/2007-08/policies/grade.htm |
The university's course catalog contains all of the details about incompletes, but here's the key sentence:
| The grade of I may be awarded only at the end of a term, when all but a minor portion of the course work has been satisfactorily completed. |
To qualify for an incomplete, a student must have maintained a passing grade for the class until the term is nearly complete, and then, due to an unusual and substantiated cause beyond the student's control, the student is unable to complete the class work. In short, you can't get an "I" just because you aren't happy with your grade.
| See Also: | • UA Disability Resource Center Information for Students: http://drc.arizona.edu/learn/index.html |
| • UA SALT Center: http://www.salt.arizona.edu |
The university and the Disability Resource Center (DRC) have asked all instructors to include the following text in class syllabi:
| If you anticipate issues related to the format or requirements of this course, please meet with me. I would like us to discuss ways to ensure your full participation in the course. If you determine that formal, disability-related accommodations are necessary, it is very important that you be registered with Disability Resources (621-3268; drc.arizona.edu) and notify me of your eligibility for reasonable accommodations. We can then plan how best to coordinate your accommodations. |
Additional help is available from the UA Strategic Alternative Learning Techniques (SALT) Center. SALT provides fee-based services for students with various learning disabilities.
Under the guidelines of the Rehabilitation Act of 1973 and the Americans with Disability Act of 1990, students are obligated to notify the school that they need accommodation.
| See Also: | • UA Policy on Threatening Behavior by Students: http://policy.web.arizona.edu/~policy/threatening.pdf |
If you're upset with me or any of the SLs, please talk directly with us about your concerns. The university takes a very dim view of antisocial behaviors on campus.
Caveat:
The above schedules, policies, and procedures are subject to change. Whenever possible, changes will be announced to the class before the on-line version of this document is altered.