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Math 237: Discrete Structures (Fall 2017)
Contents
Syllabus
Download the course syllabus here. The syllabus contains essential information about the course (textbook, prerequisites, course description, material covered, etc.).
Textbook
The official textbook for this course is: Discrete Mathematics (7th edition), authored by Richard Johnsonbaugh, published by Pearson. See this link for the full reference.
Note: Although we will use the 7th edition, getting the 8th edition is also fine. You may also get a digital version of the book.
Class time and location & Office hours
Class time and location:
Monday: 10:00am11:20am, Smith Hall B24
Wednesday: 10:00am11:20am, Smith Hall B24
Office hours:
Monday: 1:152:15pm, Smith Hall 308
Wednesday: 2:303:30pm, Smith Hall 308
Course policies
Grading policy
Your overall grade for the course will be a precise combination of:
 Your global quiz grade $G_1$. There will be about 9 quizzes in the semester. Each quiz grade will be automatically scaled to a grade /100, and at the end all the quiz grades, dropping the lowest two, will be averaged to a global quiz grade.
 Your global midterm grade $G_2$. There will be two midterm exams, whose grades will be automatically scaled to grades /100, and then averaged to a global midterm grade.
 Your final exam grade $G_3$. There will be one final exam, whose grade will also be automatically scaled to a grade /100.
The formula for your overall grade $G$ for the course will be: $G = c_1 G_1 + c_2 G_2 + c_3 G_3$, where the coefficients $c_1$, $c_2$ and $c_3$ will be around $c_1 = 35\%$, $c_2 = 30\%$ and $c_3 = 35\%$. These coefficients may be subject to marginal change.
Finally, you will be assigned a letter grade for the course depending only on your overall grade $G$, according to the following table:
Overall grade  Letter grade 

90% ≤ G ≤ 100%  A 
80% ≤ G < 90%  B+ 
70% ≤ G < 80%  B 
60% ≤ G < 70%  C+ 
50% ≤ G < 60%  C 
40% ≤ G < 50%  D 
0% ≤ G < 40%  F 
Note: There will be no exceptions to the grading policy described above.
Attendance & Excused absence policy
Attendance is mandatory: you are required to attend every class.
If you must miss a class for a legitimate reason, you are required to inform me as soon as possible and provide documentation for your absence. If you miss a midterm exam, there will not be automatically a makeup exam if the reason of absence is not serious or the notice is too short. There will be no makeup quizzes, even if you miss a quiz with a valid reason of absence.
Textbook vs Lecture notes
Although we will follow the outline of the textbook very closely, your lecture notes should always be your primary source of information. You can only be expected to know the contents of the lectures, unless you are explicitely asked to review specific segments of the textbook. Nevertheless, the textbook is a great secondary source of information and will be the main source of problems, which are of the utmost importance.
Calculator
You will never need to use a calculator in this course. Calculators will not be allowed during quizzes or exams.
General advice
Our goal is to provide all the resources necessary for you to succeed and learn great mathematics in the process, regardless of your background coming in. Nevertheless, you may find this course very challenging. Attending every class is absolutely necessary to meet the challenge but in no way will it be sufficient. The key to your success rests on yourself: it will require hard work, including hours of study, lots of problem solving, and your active involvement in learning both in and outside of the classroom. Of course, you will be assisted in your efforts, and I encourage you to reach me as often as you need.
Contact
My email is brice@loustau.eu. I encourage you to write with any questions.
My office is 308 in Smith Hall. You are welcome during office hours (see above), you may also see me outside of office hours by appointment (first send me an email).
Course schedule
For general important dates in the semester, see the academic calendar here.
Refer to the course schedule below very regularly. It contains among other things the homework assignments and the past quizzes and exams.
This course schedule is only tentative: it is very much subject to change. Always refer to last version online, and make sure that you refresh the page.
Date  Topic  Homework assignment  Special 

Wed 09/05 
Discussion of course policies Introduction to the course Chapter 1: Sets and Logic 1.1 Sets 
First day of class  
Mon 09/11 
1.1 Sets 
Review lecture notes 1.1 Review exercises 115 

Tue 09/12      Last day to drop a course without a "W" grade 
Wed 09/13 
1.2 Propositions 1.3 Conditional Propositions and Logical Equivalence 
Review lecture notes 1.1 Exercises: 148, 5793, 95 

Mon 09/18 
1.4 Arguments and Rules of Inference 1.5 Quantifiers 1.6 Nested Quantifiers 
Review lecture notes 1.2 Exercises: All 1.3 Exercises: All except 74, 75 
Quiz #1 Quiz #1 Solutions 
Wed 09/20 
1.5 Quantifiers 
Review lecture notes 1.4 Exercises: 117 

Mon 09/25  1.6 Nested Quantifiers 
Review lecture notes 1.5 Exercises: 167 
Quiz #2 Quiz #2 Solutions 
Wed 09/27 
Chapter 2: Proofs 2.1 Proofs and Counterexamples 2.2 More Proof Methods 
Review lecture notes 1.6 Exercises: 192 

Mon 10/02 
2.1 Proofs and Counterexamples 2.2 More Proof Methods 
Review lecture notes Exercise given in class 
Quiz #3 Quiz #3 Solutions 
Wed 10/04 
2.2 More Proof Methods 
Review lecture notes 2.1 Exercises 615, 1927, 4454 

Mon 10/09  2.4 Mathematical Induction 
Review lecture notes 2.2 Exercises 1, 68, 12, 15, 16, 18, 21, 2227, 30, 32, 33, 3739, 43, 48 
Quiz #4 Quiz #4 Solutions 
Wed 10/11 
2.4 Mathematical Induction Chapter 3: Functions 3.1 Relations and Functions 
Review lecture notes 2.4 Exercises 19, 14, 2126, 28 

Mon 10/16    List of topics 
EXAM #1 EXAM #1 Solutions 
Wed 10/18  3.1 Relations and Functions 
Review lecture notes 

Mon 10/23 
3.1 Relations and Functions 3.2 Sequences and Strings 
Review lecture notes Exercise given in class 3.1 Exercises 15 (except the part about the inverse function), 1031, 5152, 8288, 98103 
No quiz 
Wed 10/25 
3.2 Sequences and Strings 3.3 Relations 
Review lecture notes Exercises given in class 3.1 Exercises 15, 3247, 6270, 9097 

Mon 10/30 
3.3 Relations 3.4 Equivalence Relations 
Review lecture notes 3.2 Exercises 182, 116122, 124, 129131 
Quiz #5 Quiz #5 Solutions 
Wed 11/01 
3.4 Equivalence Relations 3.5 Matrices of Relations 3.6 Relational Databases 
Review lecture notes 3.3 Exercises 155, (5659) 

Mon 11/06 
Chapter 4: Algorithms 4.1 Introduction 4.2 Examples 4.3 Analysis of Algorithms 
Review lecture notes Exercises given in class 3.4 Exercises 120, 24, 27, 28 
Quiz #6 Quiz #6 Solutions Last day to drop a course with a "W" grade 
Wed 11/08 
4.2 Examples 4.3 Analysis of Algorithms 
Review lecture notes 4.1 Exercises 5, 912, 14 4.2 Exercises 47, 14, 19 

Mon 11/13   
Review lecture notes 4.3 Exercises 128, 3334, 6061 List of topics 
EXAM #2 EXAM #2 Solutions 
Wed 11/15 
4.4 Recursive Algorithms Chapter 7: Recurrence relations 7.1 Introduction 
Review lecture notes  
Mon 11/20 
7.2 Solving Recurrence Relations 7.3 Analysis of Algorithms 
Review lecture notes 4.4 Exercises 1, 5, 6, 9, 12, 13 7.1 Exercises 117, 5657, (70) 
No quiz 
Wed 11/22      Class cancelled follows a Friday schedule 
    Thanksgiving recess 11/23  11/26 

Mon 11/27 
7.3 Analysis of Algorithms: complexity of selection sort Chapter 6: Counting methods 6.1 Basics 
Review lecture notes Problem given in class 7.2 Exercises 1114, 27, (2932) 
Quiz #7 Quiz #7 Solutions 
Wed 11/29 
6.1 Basics 6.2 Permutations and Combinations 
Review lecture notes Homework problems given in class 7.3 Exercises 2839 6.1 Exercises 412, 1516, 3137, 4460 

Mon 12/04 
6.2 Permutations and Combinations (6.7 Binomial coefficients and Combinatorial identities) 6.8 The pigeonhole principle 
Review lecture notes 6.1 Exercises 412, 1516, 2027, 3137, 4460, 86, 87, 90, 91 6.2 Exercises 113, 2529, 3338, 4041, 4347, 6064 
Quiz #8 Quiz #8 Solutions 
Wed 12/06 
Chapter 5: Number theory 5.1 Divisors 
Review lecture notes Homework problems given in class 6.7 Exercises 1, 2, 22 6.8 Exercises 14, (6), 78 

Mon 12/11 
5.2 Representations of Integers and Integer Algorithms (5.4 The RSA PublicKey Cryptosystem) 
Review lecture notes Homework problem given in class 5.1 Exercises 133 
Quiz #9 Quiz #9 Solutions 
Wed 12/13  Review session 
Review lecture notes 5.2 Exercises 141 

Mon 12/18  FINAL EXAM  List of topics 
FINAL EXAM Time: 11:45  2:45pm Location: Smith B24 