MATH 247 Discrete Math

MATH 247-01 Discrete Mathematics
Syllabus for Spring 2016

Mon, Wed, & Fri, 9:00 – 9:50am

325 Gildemeister Hall

Instructor: Dr. Eric Errthum Winona Email Username: eerrthum Office: 205 Gildemeister Hall Office Hours: See homepage. Or by appointment on any day.

Text:   “Discrete Mathematics” by zyBooks.com
                        1) Create a zybooks.com account, 2) Use code WinonaMath247Spring2016, 3) Click “Subscribe” to enter payment info ($48)
            AND
            “Applied Discrete Structures” by Al Doerr and Ken Levasseur.
                        A free pdf of the book can be downloaded from: http://faculty.uml.edu/klevasseur/ADS2_zips/ADS_V2-0.pdf
            AND
            Other materials will also be available on D2L Brightspace.

Calculator: You are allowed at most times to use a calculator, but you must show work. At times you will be prohibited from doing specific calculations on your calculator.
You are not allowed to use your cell phone, laptop, or any other device capable of electronic communication in place of a calculator.

Prerequisite: MATH140 – Applied Calculus or MATH212 – Calculus I. (Though you can probably get by with a strong Pre-Calc background.)

Course Website: http://course1.winona.edu/eerrthum/math247

About This Course: This course is designed to fill students in on the side of mathematics that they missed out on as they worked toward calculus. In contrast to Calculus where it is essential that the real numbers have the property of being arbitrarily close, the objects studied in this course – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Areas of application included digital circuits, design optimization, general problem solving, etc.

Expectations: Students who complete this course with a passing grade are expected to be able to demonstrate the following skills: (i) Mastery of prerequisite material (mostly basic algebra/pre-calc), (ii) Create arguments using tables, pictures, and/or examples, (iii) Compute in a variety of discrete systems including logic, sets, sequences, modular arithmetic, graphs, and trees, (iv) Find optimal solutions on graphs and trees, (v) Communicate mathematical reasoning clearly.

Grading:        Textbook Activities (scaled as needed)                   100 points------ 14.3%
                        Oral Homework (scaled as needed)                         100 points------ 14.3%
                        Written Homework (scaled as needed)                   150 points------ 21.4%
                        Midterms (2 @ 100 points)                                      200 points------ 28.6%
                        Final                                                                         150 points------ 21.4%
                                                                                                     --------
                                                                                                         700 points total

Grades: A = 90% (630 pts), B = 80% (560 pts), C = 70% (490 pts), D = 60% (420 pts). There will be no curving of individual assessments.

Homework: Homework will be completed in three ways:

Textbook Activities: According to the schedule below, Sections of the zyBook text should be read before lecture and all Participation and Challenge questions should be completed before the indicated lecture.

Oral Homework: According to the schedule below, on Homework Days students will be chosen randomly to present solutions to problems from the oral homework assigned since the last homework day. Most Oral Homework problems are out of the “Applied Discrete Structures” book. On Homework days students will be graded a 0, 1, or 2 out of 2 corresponding to their level of preparedness (not necessarily correctness). When presenting a solution, you should be prepared to answer questions clarifying your work. It is not acceptable to write out a whole solution, but then when asked about a particular step to say “I don’t know.” To me this indicates you copied the homework from someone else without understanding it.

Written Homework: The written portion of the homework is due the period after a Homework Day. This work should be written nicely or typed, stapled, and presented in order. Each readable problem will be graded out of 2 corresponding to its level of correctness and clarity.

Exams: There will be two in-class midterm exams. Exam dates are tentative until officially announced in class. The final exam will contain a part that is a third midterm exam and a part that is a comprehensive final exam. The final exam is tentatively scheduled for Tuesday, May 3, 8:00am – 10:00am.

D2L Brightspace: Many course materials can be found on D2L Brightspace including homework problems, study materials, and approximate grades. If at any point during the semester you would like to know your exact grade, please email the instructor.

Late/Missed Work: Late homework or missed exams will result in a score of zero. Make-up exams before the time of the normal exam will be given at the discretion of the instructor. If you miss class, it is your responsibility to obtain notes and assignments from fellow students. If you have an unavoidable absence, please inform the instructor beforehand.

Academic Dishonesty: Any type of academic dishonesty (cheating, copying, using a solutions manual to do homework, finding solutions online, etc.) will result in failure and will be reported to school authorities. If you are having trouble with an assignment, please see the instructor first.

Study Groups: Students are allowed to form study groups for the course. However, students are strongly encouraged to work on the homework individually first. All students must put homework solutions into their own words.

Note: This syllabus is subject to change if deemed necessary by the instructor.

Tentative Schedule of Events – Math 247

(subject to change)

Week Beginning	Monday	Wednesday	Friday
1/11	Introductions	Before Class (in zyBook): Sections 1.1, 1.2, 1.3 Introduction to Sets Set operations and Venn Diagrams After Class (in pdf): Oral HW: (§1.1, pg 14) 1 – 5 Oral HW: (§1.2, pg 19) 1, 4abc, 5, 7 Written HW 1: located in D2L	Before Class: Sections 1.4, 1.5 Larger Sets Binary Representation After Class: Oral HW: (§1.3, pg 22) 2, 4, 6 Oral HW: (§1.4, pg 25) 2, 4, 6, 8
1/18	NO CLASS MLK Day	Before Class: Section 1.9 Summation Notation After Class: Oral HW: (§1.5, pg 27) 1, 2bcd, 8, 9, 10	Homework Day
1/25	Before Class: Sections 2.1, 2.2 Written HW 1 Due Logic Propositions and Operations Truth Tables After Class: Oral HW: (pg 51) 2, 3 Oral HW: (pg 53) 2 Written HW 2: located in D2L	Before Class: Sections 2.3, 2.4 Equivalence and Implication Laws of Logic After Class: Oral HW: (pg 56) 2ab, 4, 6 Oral HW: (pg 59) 2	Homework Day
2/1	Before Class: Section 2.5 Written HW 2 Due Digital Logic Gates and Circuits After Class: Oral HW: Finish Circuits Handout Written HW 3: located in D2L	Before Class: Proof by Venn Diagram and Proofs of DeMorgan’s Law Proof on Sets with Venn Diagrams and Tables After Class: Oral HW: (pg 83) 1ac, 2ac, 4ab (Note: Use Venn Diagrams and/or Tables for Proofs)	Before Class: Creating Examples with Venn Diagrams (video) Creating Counterexamples with Venn Diagrams (video) Proof on Sets with Venn Diagrams and Tables, cont. After Class: Oral HW: Finish Proof Handout
2/8	Homework Day	Written HW 3 Due Before Class: Sections 3.1, 3.2 Propositions over a universe Quantifiers After Class: Oral HW: (pg 65) 2, 4	Before Class: Sections 3.3, 3.4, 3.5 Quantifiers, cont. After Class: Oral HW: (pg 72) 2, 4, 6, 8
2/15	Homework Day	Written HW 3.5 Due Review	Exam I
2/22	Before Class: Section 4.1, 4.2, 4.3 Sequences & Recursion After Class: Oral HW: (OralHWSequences in D2L) 13, 15, 16, 17, 18, 24, 25-32	Before Class: Finite Differences (Part 1) Finite Differences (Part 2) Finite Difference Methods After Class: Oral HW: (247FiniteDiffHW in D2L) 1abcde, 2	Before Class: Sections 4.7, 4.8 Mathematical Induction After Class: Oral HW: (pg 70) 1 – 5
2/29	Homework Day	Before Class: Section 4.10 Written HW 4 Due Solving Linear Recurrences (Homogeneous Cases) After Class: Oral HW: (LinearRecursionOral in D2L or “Exploring further exercises” at end of zyBook section 4.10) All of them	Before Class: Sections 5.1, 5.2 Division Algorithm Factorizations After Class: Oral HW: Handout (also in D2L)
3/7	SPRING BREAK No Class
3/14	No Class	Homework Day	Written HW 5 Due Before Class: Sections 5.3, 5.4 Floor and Ceiling Functions Modular Arithmetic Oral HW: 247OralModularArith.pdf found in D2L
3/21	Before Class: TBD Solvability of Systems of Integral Equations Oral HW: Complete handout	Homework Day	Review
3/28	Exam II	Before Class: Sections 6.1, 6.2, 6.3 Relations and digraphs After Class: HW: (pg 108) 1-4 (pg 111) 1-6	Before Class: Sections 6.4, 6.5, 6.7 Properties of Relations Closures and Reductions Partial Orders After Class: HW: (pg 115) 2, 3, 4, 5, 6, 9, 10bc (For #3 also give transitive closures and anti-symmetric reductions)
4/4	Before Class: Section 6.9 and Max-Flow / Min Cuts Equivalence Relations Weighted Graphs Max Flow – Min Cuts / Ford-Fulkerson Algorithm HW: Handout (Written HW 7)	Homework Day	Written HW 6 Due Before Class: Sections 7.1, 7.2, 7.3 Intro to Graph Theory Graph Properties Graph Isomorphism After Class: HW: 247OralGraphIntro (found in D2L)
4/11	Before Class: Sections 7.4, 7.5 Graph Connectedness Paths and Cycles Eulerian and Hamiltonian Cycles After Class: HW: (pg 205) 2, 4, 6	Written HW 7 Due Before Class: TBD Shortest Paths / Dijkstra’s Algorithm After Class: HW: 247WrittenHWPaths (found in D2L)	NO CLASS Spring Break Day
4/18	Homework Day	Written HW 8 Due Before Class: Sections 7.6, 7.7 Play this Game Planar Graphs Graph Coloring After Class: Oral HW: Planar (found in D2L) Part 1: 1abc, 2, 4, 5abcdef, 10b Part 2: 2, 3, 5ab, 6, 8b, 10ab, 19	Before Class: Sections 8.1, 8.2, 8.3 Trees Applications of Trees Properties of Trees After Class: HW: 247OralTrees (found in D2L)
4/25	Before Class: Sections 8.5, 8.6 Minimum Spanning Trees Prim’s Algorithm After Class: HW: 247WrittenHWMinTrees (found in D2L)	Homework Day	Written HW 9 Due Review

Final Exam (Exam III + Comprehensive)

Tuesday, May 3

8:00am – 10:00am

Welcome to college math!

If this is your first math class taken in college, there are some important things you need to know. College math classes are run very differently from high school math classes. On the surface it may seem they are similar as you listen to the lecture and take notes, but there are significant underlying differences. Knowing these ahead of time can help you make the most of this coming semester.

#1: College math classes generally stay on the schedule in the syllabus. If there is one day allotted to the topic that is probably all of the class time that will be spent on it, even if “most” of the students “don’t get it.”

#2: It is expected that you will read the text and do the problems in order to learn the material, even if no one checks up on you. The instructor might never collect the homework, but that doesn’t mean it doesn’t affect your grade.

#3: You will sometimes be responsible for material in the textbook that is not covered in class. If there is a text reading and/or homework problems covering a concept that was not discussed in class, you are still expected to learn it. If you don’t understand it, make an appointment with your instructor for help.

#4: Some material is covered only in class, is not in the textbook, and may not have any homework problems on it. If you miss class, you may miss content that you are responsible to know. If you have an unavoidable absence, be sure to get the notes and any announcements from a classmate.

#5: There will be test questions that don’t look “just like the homework.” In college, you are expected to focus on learning the concepts, not just memorizing how to do certain types of problems. These concepts can – and will – appear in very different forms on tests and quizzes.

#6: At times you will be expected to be able to explain why a problem is done a certain way in addition to being expected to do the problem. As you work on problems in class and on homework, don’t be satisfied with getting the correct answer; ask yourself why that method is logical, and how you could explain that logic to someone else.

#7: Most importantly, you are responsible for your own learning. If you attend class faithfully, get the notes and announcements if you have an unavoidable absence, read the text, do the homework and question yourself (as in #6), and still don’t understand something, it is up to you to get the extra help you need. Visit the instructor during office hours or make a special appointment to ask questions, form a study group, etc. There are many resources and people willing and happy to help, but you need to take the initiative and seek out the help you need.

Good luck on a happy and successful semester!

Commitment to Inclusive Excellence

WSU recognizes that our individual differences can deepen our understanding of one another and the world around us, rather than divide us. In this class, people of all ethnicities, genders and gender identities, religions, ages, sexual orientations, disabilities, socioeconomic backgrounds, regions, and nationalities are strongly encouraged to share their rich array of perspectives and experiences. If you feel your differences may in some way isolate you from WSU’s community or if you have a need of any specific accommodations, please speak with the instructor early in the semester about your concerns and what we can do together to help you become an active and engaged member of our class and community.

Campus Resources

Student Support Services, Krueger Library 219, 457-5465 www.winona.edu/studentsupportservices/
Inclusion and Diversity Office, Kryzsko Commons Room 236, 457-5595 www.winona.edu/inclusion-diversity/
Access Services, Maxwell 314, 457-5878 www.winona.edu/accessservices/
Counseling and Wellness Services, Integrated Wellness Complex 222, 457-5330 www.winona.edu/counselingcenter/
GLBTA Advocate, contact Counseling and Wellness Services for name and number of the current Advocate
Advising Services, Maxwell 314, 457-5878 www.winona.edu/advising/
Tutoring Services, Krueger Library 220, 457-5680 http://www.winona.edu/tutoring/
Writing Center, Minné Hall 348, 457-5505 www.winona.edu/writingcenter/
Math Achievement Center, Tau 313, 457-5370 http://www.winona.edu/mathematics/mac/

Details about Campus Resources

Two good places to help you find resources of all kinds on campus are Student Support/Campus Services and the Inclusion and Diversity Office. Both offices are dedicated to helping students of all races, ethnicities, economic backgrounds, nationalities, and sexual orientations. They can facilitate tutoring and point you to a wide range of resources.
If you have a disability, the Access Services office can document it for your professors and facilitate accommodations. If you have a documented disability that requires accommodation, please contact Access Services as soon as possible.
College can be very stressful. Counseling offices on both campuses are here to help you with a wide range of difficulties, ranging from sexual assault, depression, and grief after the loss of a loved one to stress management, anxiety, general adjustment to college, and many others.
The GLBTA Advocate can direct people to GLBT resources on and off campus. In addition, the advocate is responsible for documenting homophobic and transphobic incidents on campus and working with the appropriate channels to get these incidents resolved.
To find out about web registration, placement tests, program requirements and support tools to help students succeed, visit the Advising Services office and website for answers to all your questions!
On the Rochester campus, the UCR Learning Center provides help with both the development and the writing of papers.
On the Winona campus, for help with understanding the concepts of a particular class or understanding the requirements of an assignment, Tutoring Services offers three types of tutoring: drop-in appointments, 1-on-1 tutoring, and group sessions. You can visit them in the Library (220) or go on-line and use TutorTrac to schedule a session.

For help specifically with writing and the development of papers, the English department has a Writing Center that is staffed by trained graduate students pursuing their Master’s degree in English. The Writing Center is located in Minné Hall 348. You can make an appointment on the sign-up sheet on the door or call 457-5505.
For help specifically with understanding math concepts and solving math problems, the Math Achievement Center (MAC) is staffed with friendly undergraduate tutors who will help you work through difficult material. The MAC is located in Tau 313 and provides free tutoring for all students in math, statistics, or math education courses. The center is open Mon-Fri, and Sunday evening.

The Standard Disclaimer applies.