Syllabus

CMPS/MATH 2170: Discrete Mathematics Spring 2019

Note this page and syllabus is common for all sections including:

- Bert Lindenhovius: CMPS-2170-01 and MATH-2170-01
- Nicholas Mattei: CMPS-2170-02 and MATH-2170-02

We will attempt to run these courses in parallel but attendance for lectures and labs must be in the sections for which you have signed up.

This course is an introduction to several areas of mathematics that are particularly useful in computer science. The following topics will be covered:

- Propositional and predicate logic
- Set theory
- Mathematical induction and recursion
- Number theory
- Counting
- Discrete probability
- Graphs?

Upon completion of the course, successful students will be able to:

- establish the logical equivalence of two mathematical statements;
- use rules of inference to construct proofs;
- prove theorems using proof by contraposition, proof by contradiction, and mathematical induction;
- understand the definitions and operations of sets, functions, and sequences;
- understand recursive definitions and model with recurrence relations;
- understand basic number theory and its applications in cryptography;
- apply basic counting techniques;
- find the distribution of a discrete random variable;
- understand conditional probability and Bayes' theorem.

http://www.nickmattei.net/cmps2170-spring-2019/

Instructor: Bert Lindenhovius

- Email: alindenh@tulane.edu
- Office: Stanley Thomas 314
- Office Hours: MW 1100 - 1200, and by appointment.

- Lectures: MWF 1000 - 1050 in Stanley Thomas Hall 302
- Labs: R 1400 - 1515 in Norman Mayer Building 118

Instructor: Nicholas Mattei

- Email: nsmattei@tulane.edu
- Office: Stanley Thomas 303E
- Office Hours: MW 1500 - 1600, and by appointment.

- Lectures: MWF 1200 - 1250 in Stanley Thomas Hall 302
- Labs: R 1700 - 1815 in Stanley Thomas Hall 302

Teaching Assistant: Aram Bingham

- Email: abingham@tulane.edu
- Office: Gibson Hall 309E
- Office Hours: WF 1100 - 1200, and by appointment.
- Aram will be instructing both lab times above.

This schedule is subject to change.

Week | Date | Topic | Link |

1 | 1/14 | Course Overview, Propositional Logic (§1.1) | |

1/16 | Propositional Logic 2 (§1.1, 1.2) | ||

1/17 | Lab 1: Quiz 1 and Homework 1 Distributed | ||

1/18 | Propositional Logic 3 (§1.3, 12.2) | ||

2 | 1/21 | MLK - No Class | |

1/23 | Predicate Logic 1 (§1.4) | ||

1/24 | Lab 2: Quiz 2, Homework 1 Collected, Homework 2 Distributed | ||

1/25 | Predicate Logic 2 (§1.5), Inference 1 (§1.6) | ||

3 | 1/28 | Inference 2, Proofs 1 (§1.6, 1.7) | |

1/30 | Proofs 2 (§1.7, 1.8) | ||

1/31 | Lab 3: Quiz 3, Homework 2 Collected, Homework 3 Distributed | ||

2/1 | Proofs 3 (§1.8) | ||

4 | 2/4 | Proofs 4 (§1.8) | |

2/6 | Sets (§2.1) | ||

2/7 | Lab 4: Quiz 4, Homework 3 Collected, Homework 4 Distributed | ||

2/8 | Sets (§2.1) | ||

5 | 2/11 | Set Operations (§2.2) | |

2/13 | Set Operations / Functions ((§2.2, 2.3) | ||

2/14 | Lab 5: Quiz 4, Homework 4 Collected, Homework 5 Distributed | ||

2/15 | Functions | ||

6 | 2/18 | Functions | |

2/20 | Cardinality | ||

2/21 | Lab 6: Quiz 5, Homework 5 Collected, Homework 6 Distributed | ||

2/22 | Cardinality | ||

7 | 2/25 | Review for Midterm | |

2/27 | Midterm Exam in Class - Logic, Proofs, Sets | ||

2/28 | Lab 7: Homework 7 Collected | ||

3/1 | Sequences | ||

8 | 3/4 | Spring Break - No Class | |

3/6 | Spring Break - No Class | ||

3/7 | Spring Break - No Class | ||

3/8 | Spring Break - No Class | ||

9 | 3/11 | Induction | |

3/13 | Induction | ||

3/14 | Lab 8: | ||

3/15 | Induction | ||

10 | 3/18 | Strong Induction | |

3/20 | Recursion | ||

3/21 | Lab 9: | ||

3/22 | Recursion | ||

11 | 3/25 | Division and Primes | |

3/27 | Primes | ||

3/28 | Lab 10: | ||

3/29 | CGD | ||

12 | 4/1 | Euclid’s Algorithm | |

4/3 | Congruences | ||

4/4 | Lab 11: | ||

4/5 | Congruences | ||

13 | 4/8 | Counting | |

4/10 | Pigeonhole Principle | ||

4/11 | Exam 2: In Lab. | ||

4/12 | Permutations and Combinations | ||

14 | 4/15 | Permutations and Combinations | |

4/17 | Intro to Probability | ||

4/18 | Lab 12: | ||

4/19 | Good Friday - No Class | ||

15 | 4/22 | Easter Monday - No Class | |

4/24 | Independence, Random Variables | ||

4/25 | Lab 13: | ||

4/26 | Expected Value | ||

16 | 4/29 | Last Class - Review for Midterm | |

5/4 | Final Exam: 1300 - 1700 |

Kenneth H. Rosen, Discrete Mathematics and Its Applications, 7th edition, McGraw-Hill, 2012. Older editions of the book contain most of the covered material, but not all. Students are responsible for identifying the differences.

- Homework - 30%
- Quizzes - 10%
- Midterm - 25%
- Final Exam - 35%

The weighted average will determine your letter grade roughly as follows: A >= 90%; B >= 80%; C >= 70%; D >= 60%; F < 60% +/- grades will be given for borderline cases.

All grades will be posted on Canvas.

Students are required to attend all classes and labs unless they are ill or prevented from attending by exceptional circumstances and with a valid excuse note. Students are responsible for notifying instructors about absences that result from serious illnesses, injuries, or critical personal problems. Students with frequent absences will be removed from the course according to university policy.

Homework will be assigned in most weeks and will be due at the beginning of Thursday labs. All homework assignments will be posted on the course webpage one week before the due date. You may discuss homework problems with your classmates. However, what you turn in must be your own. You may not read another classmate’s solutions or copy a solution from the web. There will be no late homework allowed. Requests for a homework extension (with a valid reason) must be given to the instructor before the homework is due.

Part of your Homework grade (5%) will be determined by working and presenting problems and homework solutions in the lab sections.

Attendance in the labs is required. There will be short quizzes in most of the labs. No make-up quizzes will be allowed, but the two lowest quiz scores will be dropped.

During lab each week we will:

- Hand in homework that is due that week.
- Take a short quiz.
- Ask questions and present problems from the homework.
- Group time to work on next week’s homework.

Exams

There will be a midterm and a final exam. Both will be closed-book and closed-notes, but you will be allowed to bring a cheat sheet to each exam (one letter page single-sided -- must be hand-written!). The final exam will be comprehensive. Missing an exam will result in a grade of zero. A request for a make-up exam must be given to the instructor prior to the exam date (documentation may be required).

This course will follow Tulane's Code of Academic Conduct. Cheating will be reported to the Associate Dean of Newcomb-Tulane College. Discussion is encouraged. However, what you turn in must be your own. You may not read another classmate’s solutions or copy a solution from the web.

Please silence your cellphones during class. If you want to use a laptop or other device with a large screen for note taking please sit in the back rows of the classroom -- it’s distracting to other students https://www.scientificamerican.com/article/students-are-better-off-without-a-laptop-in-the-classroom/

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