Department of Mathematical Sciences,
Northern Illinois University

## MATH 206 Spring 2011

| Catalogue description | Prerequisite | Instructor | Course Objectives | Syllabus | Withdrawal | Grading | Homework Assignments | Exam Schedule | Sample Exams | Spring Break | Final Exam | Calculators | Text | Handouts | Special Handouts | Resources on the web | Academic Conduct | CAAR Statement | Some advice |

PREREQUISITE: Math 110 or Satisfactory performance on the Placement Exam

Office: Watson Hall 344 (later Watson Hall 355)
Email: richard@math.niu.edu
Phone: 753-1835
Office Hours: Mon and Wed 2-3, Wed 4-5, Thurs 2:30-3:30
• To understand and connect concepts of discrete mathematics with real world problems and other scientific disciplines, especially computer science.
• To value mathematics and develop an ability to communicate mathematics, both in writing and orally.
• To develop mathematical reasoning and to understand the basic tools of elementary combinatorics, number theory, and graph thoery.
• To attain computational facility and an ability to analyze and develop efficient algorithms.

SYLLABUS: The course will cover most of Chapters 1-5 of the text.

• 1.4 Algorithms and their Efficiency
• 2. Sets, Equivalence Relations
• 3. Coding Theory:
Congruence, Euclidean Algorithm, Encryption, Decryption, Error Correction
• 4. Graphs:
Paths, Circuits, Shortest Path, Coloring Problems, Directed Graphs, Multigraphs
• 5. Trees:
Spanning Trees, Depth-first search, Breadth-first search, Rooted Trees, Binary Trees

WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course is Friday, March 11

GRADING: Grades will be assigned on the basis of 500 points, as follows:

2 hour exams worth 100 points each
Quizzes 100 points total
Homework 100 points total
Final exam 100 points (
The curve will be at least as generous as
A: 85%
B: 75%
C: 60%
D: 50%
HomeWork I Due 1/28
1.4 page 33: 1 - 21 odd
2.1 page 45: 1 - 27 odd
HomeWork II Due 2/11
2.2 page 52: 2, 6, 10, 12, 18, 20, 24, 25, 26, 31
POW Handout: Section 1, Binary Numbers, page 7: 1 - 8
POW Handout: Section 2, Tic-Tac-Toe Code, page 10: 1 - 3
HomeWork III Due 2/18
POW Handout: Section 3, Pails of Water Problem, page 14: 1 - 6
POW Handout: Section 4, Clock Arithmetic, page 17: 1 - 5
HomeWork IV Due 2/25 (not collected)
POW Handout: Section 5, Secret Codes, page 21: 1 - 5
HomeWork V Due 3/4 (not collected)
1.1 PERT, page 8-9: 5, 8, 9, 12, 17, 18
HomeWork VI Due 3/11
4.1 pages 161-4: 1, 4, 6, 9, 13, 15, 18, 19, 21, 22, 23, 28, 30, 42, 44
HomeWork VII Due 3/25
4.2 pages 176-181: 10, 18, 20, 22, 24, 26, 28, 30, 31, 32, 33, 34, 41
HomeWork VIII Due 4/1
4.3 pages 190-193: 2, 4, 6, 12, 16, 17
HomeWork IX Due 4/8
4.4 pages 199-202: 2, 4, 6, 11, 12, 17, 23, 24, 25, 28, 33
Show that the 7 triples of the Fano Plane cannot be bi-colored
HomeWork X Due 4/15 (not collected)
4.5 pages 212-217: 8, 12, 17, 18, 23, 24, 26, 40, 42, 48, 68
Venn Diagram Handout
HomeWork XI Due 4/22
5.1 pages 234-237: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 17, 18, 26
HomeWork XII Due 4/29
5.2 pages 248-253: 3, 4, 8, 9, 10, 12, 16, 18, 20, 22, 24, 34, 39, 41
5.3 pages 263-266: 2, 12, 20, 22, 24, 25, 26, 27, 28
HomeWork XIII Due 5/5 (not collected)
5.4 pages 271-274: 2, 3, 4, 6, 8, 12, 17, 18, 20, 21, 24, 25, 28, 30, 32
5.5 pages 284-287: 2, 4, 6, 16, 22, 28, 36, 42, 46, 50, 52, 54, 58, 64
12 Pennies Problem: Find the bad penny in 3 weighings
Test 1 Friday Feb 25
1.4 Alorithms
2.1 Sets
2.2 Equivalence Relations
POW Handout, Section 1, Binary Numbers
POW Handout, Section 2, Tic-Tac-Toe Error Correcting Code
POW Handout, Section 3, Pails of Water Problem and the Euclidean Algorithm
POW Handout, Section 4, Clock Arithmetic and Congruences
POW Handout, Section 5, Secret Codes

SAMPLE EXAMS: [WORK IN PROGRESS] You may wish to look at some first exams from previous semesters to see the level of analysis we expect students to be able to carry out.
Exam 1
Exam 3 (NOT READY) Please note that different instructors assign different exams, so that a certain raw score on one test might be comparable to a very different score on another.
Caution: These exams are from a different semester. The subject matter was comparable, but the text, the audience, the instructor, and the testing environment may have been different from what you will face. The testing points in the syllabus also vary from semester to semester. Please remember in addition that tests cannot be comprehensive; therefore, there are topics not on this test for which the students were - and you will be - responsible for studying in prepartion for the your own test.

SPRING BREAK: Spring Break is from Saturday March 12 through Sunday March 20. All classes are cancelled during this week.

FINAL EXAM: The Final Exam is scheduled for the last day of classes, Thursday, May 5, 2011. Class will meet during the final exam period to review the results of this exam. These periods depend on your section:

Section 1: Wed, May 11, noon - 1:50
Section 2: Mon, May 9, 4 - 5:50

Note: The course changes and the exams change. Our goal is to help you learn the material in Calculus, not specifically to prepare you for the final exam. We may choose to assess your command of these ideas rather differently this semester, should the opportunity arise.

CALCULATORS: Students are asked to have a graphing calculator with roughly the capabilities of the TI-83. You will find this useful for investigating the concepts of the class, so you can experiment with additional examples. You may also want to verify parts of your homework calculations.

Graphing calculators will be allowed on all exams and quizzes, although most, if not all, of the questions can be answered without it. Calculators on cell phones or other devices which can communicate to external devices are not allowed on tests or quizzes.

TEXT: Discrete Mathematics (5th. ed.), by Dossey, Otto, Spence, Vanden Eynden (publ. by Pearson Addison-Wesley)

Discrete Mathematics: An Introduction to Mathematical Reasoning, Brief Edition, by Susanna S. Epp, Brooks/Cole
Discrete Mathematics with Applications, Fourth Edition, by Susanna S. Epp, Brooks/Cole
Discrete Mathematics, Second Edition, by Richard Johnsonbaugh, Pearson/Prentice Hall
Discrete Mathematical Structures, Sixth Edition, by Kolman, Busby, Ross, Pearson/Prentice Hall
Discrete Mathematics with Graph Theory, Third Edition, by Goodaire and Parmenter, Pearson/Prentice Hall
Computers, Codes, and Pails of Water
Vocabulary List for Graphs
Hamiltonian Cycles and the Proof of Ore's Theorem
Dijkstra's Shortest Path Algorithm
Fano Plane Problem
Binary Numbers and Venn Diagrams
Understanding Mathematics: a study guide, from the University of Utah
"Symbolic calculators" on-line which will compute derivatives and integrals.

ACADEMIC CONDUCT: Academic honesty and mutual respect (student with student and instructor with student) are expected in this course. Mutual respect means being on time for class and not leaving early, being prepared to give full attention to class work, not reading newspapers or other material in class, not using cell phones or pagers during class time, and not looking at another student's work during exams. Academic misconduct, as defined by the Student Judicial Code, will not be treated lightly.

CAAR STATEMENT: If you have specific physical, psychiatirc, or learning disabilities and require accomodations, please let your instructor know early in the semester so thatyour learning needs may be appropriately met. You will need to provide documentation of your disability to the CAAR (Center for Access Ability Resources) Office located in the Health Services Building, 4th floor.

ADVICE: Perhaps the single most important factor in your success in this course is your study habits . Think of learning math as "working out" in the gym. Study at least 3 times per week; do not wait until the day before the exam. Learn mathematics like you would learn a language. Work on the concepts until they make sense. Don't just memorize facts and then forget them a few weeks later. You will need to know this stuff for Calc III and other courses. Master each homework problem - beyond just getting a correct answer. Be on the lookout for mistakes in algebra and trig. Always come to class! While you're there, listen, think, and ask questions.

Last update: Feb 18, 2011