Home » Discrete-Fall2014

# Category Archives: Discrete-Fall2014

## Discrete Mathematics: Homework for Fall 2014

The homework assignments are organized according to their due date. You should assume that the homework problems are from Krussel’s text, unless there is a specific link to a pdf. Please report any issues back to Iva.

**Week 1**: NONE

**Week 2**:

Homework due Monday, Sept 8th:

- Chapter 1, Section 1, Problems 4, 5, 6, 8, 9, 11, 14.

- Chapter 1, Section 2, Problems 5, 6, 9, 13.

- Chapter 1, Section 3, Problems 11, 15, 16.

Homework due Thursday, Sept 11th:

- Chapter 1, Section 3, Problems 7a), 7c), 8, 10, 13 along with 6 and 12.

**Week 3**:

Homework due Monday, Sept 15th:

- Chapter 2, Section 1, Problems 4, 5, 6, 7, 8, 9a) from the textbook. In addition, prove Proposition 5, Lemma 6 and Corollary 7 from the

__class handout__. Here are some guidelines for

__writing mathematical proofs__which you might find helpful.

Homework due Thursday, Sept 18th:

- Chapter 2, Section 2, Problems 2, 3, 11, 12, 13, 14, 15.

**Week 4**:

Homework due Monday, Sept 22nd:

__Extra problems__on primes and composites, and the following

__worksheet__.

Homework due Thursday, Sept 25th:

- Chapter 2, Section 3, Problems 1, 7, 8, 12, 14, 16, 21.

**Week 5**:

Homework due Monday, Sept 29th:

__Problems__on strong induction.

- Chapter 5, Section 1, Problems 1, 2a), 2b), 2c), 3a), 4, 5, 6, 9 (see sample problem

__here__), 11.

Homework due Thursday, October 2nd:

- Chapter 2, Section 4: Problems 1, 3, 5, 7, 9.

- Chapter 2, Section 5: Problems 1, 3, 4, 7, 8, 9.

**Week 6**:

Homework due Monday, October 6th:

Homework due Thursday, October 9th:

- FALL BREAK! Plus, Iva is giving a

__seminar__.

**Week 7**:

Homework due Monday, October 13th:

- NONE

Homework due Thursday, October 16th:

- Chapter 3, Section 1: Problems 3, 6, 9, 10, 12, 13, 14, 15.

- Chapter 3, Section 2: Problems 1, 2, 12, 13, 14.

**Week 8**:

Homework due Monday, October 20th:

- Homework on

__Boolean algebra__.

- Chapter 3, Section 3:

__Quantifier homework__.

Homework due Thursday, October 23rd:

- Chapter 4, Section 1: Problems 2 (skip 2e)), 3, 4, 5.

- Chapter 4, Section 2: Problems 2, 3, 4, 8.

- Chapter 4, Section 3: Problem 1, parts a), b), c), d).

**Week 9**:

Homework due Monday, October 27th:

- Homework on

__proof writing in set theory__.

Homework due Thursday, October 30th:

- Homework on

__Cartesian product__.

**Week 10**:

Homework due Monday, Nov 3rd:

- Chapter 6, Section 1, Problems 6, 7, 8.

- Chapter 6, Section 2, Problems 7, 8, 9, 10, 11, 12.

- More homework on

__equivalence classes__.

Homework due Thursday, Nov 6th:

- Chapter 6, Section 3:

__Homework on functions__

**Week 11**:

Homework due Monday, Nov 10th:

- Chapter 6, Section 4, Problems 2, 3, 4, 5.

- Chapter 6, Section 5, Problems 1, 2, 5, 6, 7, 9, 10.

Homework due Thursday, Nov 13th: NONE

**Week 12**:

Homework due Monday, Nov 17th: NONE

Homework due Thursday, Nov 20th:

- Chapter 8, Section 1, Problems 1, 2, 3, 10, 11, 14.

**Week 13**:

Homework due Monday, Nov 24th:

- Chapter 8, Section 2, Problems 1, 5, 6, 7.

- Chapter 8, Section 3, Problems 1, 2, 5, 6.

Homework due Thursday, Nov 27th: THANKSGIVING BREAK!

**Week 14**:

Homework due Monday, Dec 1st:

- Chapter 8, Section 4, Problems 4, 5 and problems from

__this sheet__.

Homework due **FRIDAY**, December 5th:

- Chapter 8, Section 4, Problem 8.

- Chapter 8, Section 5, Problems 1, 2, 6, 7 and problems from

__this sheet__.

## Discrete Mathematics: Syllabus for Fall 2014

**Textbook**

We will use the manuscript *Discrete Mathematics (and Other Stuff) * by Prof. John M. Krussel of Lewis and Clark College; it is available in our college bookstore. Do note that some of the course content will not be directly based on the textbook material. At times, you will be expected to rely on your lecture notes.

**Homework**

Most lectures will be followed by a homework assignment, which will be posted online. Generally speaking, homework assigned on Monday and Tuesday will be due the following Thursday while the homework assigned on Thursday and Friday will be due the following Monday. Assignment which would be due on the Thanksgiving Day will in fact be due the following Monday. Each homework assignment will contribute to the course grade through the letter grade for the relevant educational goal (please follow __this link__ for details).

**Late or missed assignments**

I understand that you might find yourself in a situation where you cannot complete a homework assignment on time. You will *nevertheless* be expected to turn in what you have by the due date and *immediately* inform me about your situation. Assuming you are making a good faith effort to stay current in the class, you will be given an opportunity to make up an incomplete assignment.

**Exams and such**

There will be two in-class exams, one quiz, and a comprehensive final exam, each of which will contribute to the course grade through the letter grade for the relevant educational goal (please follow __this link__ for details). In-class exams will take place on Tuesday, October 7th and Friday, November 14th; the quiz will be on Monday, December 8th.

**Essay**

In the spirit of good liberal arts education and the fourth educational goal for this class (please follow __this link__ for details) students will be expected to develop an ability to discuss the practice of mathematics in non-technical terms. In relation to this, the students will be given a brief essay assignment at the end of the course. The essay will be due on our last day of class; late essays will only be accepted in the case of medical emergency or the like. More or less, the essay will be worth 5% of the course grade. (See below for details.)

**Grading scheme**

For each rubric under __Educational Goals__ you will receive a letter grade determined by your performance on the corresponding portion(s) of exams/quizzes, homework assignments and/or the essay. In addition, a certain portion of your grade will correspond to the effort you put into participating and staying current in the class; students with a substantial number of class absences and/or late assignments can expect a slightly lowered course grade. The final course grade will be a weighted average of the above:

- Goal 1: 35%

- Goal 2: 35%

- Goal 3: 20%

- Goal 4: 5%

- Participation: 5%

For the description of letter grades please refer to our College Catalog. Please note that a professor has a right to withdraw a student for the reasons of non-attendence. * I reserve the right to fail any student who exhibits an extreme inability to construct a logical argument on the final exam. I also reserve the right to boost the course grade of any student who presents an impressive amount of progress throughout the semester.*

## Discrete Mathematics: Educational Goals

**Goal 1:**

To develop skills needed in order to read, write, recognize and appreciate a (good) mathematical proof. The corresponding assessment will be based on student performance on the two in-class exams, the final exam, and select homework assignments.

**Goal 2:**

To develop fluency in using basic logic and set theory, including the language of functions and relations. The extent to which this goal is achieved will be determined by student performance on the second in-class exam, the final exam, and select homework assignments.

**Goal 3:**

To gain familiarity with certain areas of mathematics which could be labeled as being “discrete”: combinatorics, number theory, graph theory. The extent to which this goal is achieved will be assessed by means of the first in-class exam, the final exam, the graph theory quiz, and select homework assignments.

**Goal 4:**

To situate the practice of mathematics within its larger intellectual and social context. The corresponding assessment will rely on student essays at the end of the semester.