<commit_before>---
layout: class
title: "MATH 260: Discrete Mathematics, Fall 2022"
catalog-desc: "An introduction to proof based mathematics through the study of key areas of discrete mathematics."
semester: f22
---

*{{ site.data.policies.syllabus_deviation_v2 }}*

* TOC
{:toc}

## Logistics

* Class Meetings: MTWF 10:00 AM - 10:50 AM in CSB 380
* Instructors: <NAME>
  * Office: {{ site.data.me.office }}
  * Zoom Room: {{ site.data.me.zoom }}
  * Website: <a href="{{ site.url }}">{{ site.url }}</a>
  * Email: <a href="mailto:{{ site.email }}">{{ site.email }}</a>
  * Office Hours: {{ site.data.semesters[page.semester].office_hours }}
* Website: <a href="{{ site.url }}{{ page.url }}">{{ site.url }}{{ page.url }}</a>
* Credits: 1 course credit
* Prerequisites: An ACT MATH subscore of 22+ or QRAC120.
* Feedback: At any time during the course you can use
  [this]({{ site.data.semesters[page.semester].feedback_form }}) to provide
  anonymous suggestions, criticism, praise, etc.

## Content

### Description
An introduction to proof-based mathematics through the study of key
areas of discrete mathematics. This course serves as an introduction
to higher-level mathematics and advanced coursework in math. Students
will hone their mathematical reasoning skills, learning to express and
work with precise mathematical definitions. A strong emphasis is
placed on developing the skills necessary to communicate mathematical
results.

Topics covered in this course include the the core definitions and
theorems from set theory, mathematical logic, and combinatorics.  In
this context students will explore ideas such as mathematical
induction, functions, and relations and the proof techniques of direct
proof, contrapositive proof, proof by contradiction, and disproof.

### Sources

The course textbook will be:

* <NAME>. _Book of Proof_. 3rd Edition. Licensed under CC BY
  ND. Available
  [here](http://www.people.vcu.edu/~rhammack/BookOfProof/). ISBN:
  978-0-9894721-2-8.

## Assessment

### Assignments and Workload
The weekly workload for this course will vary by student and by week
but should be about 12 hours per week on average. The following table
provides a rough estimate of the distribution of time over different
course components for a 16 week semester, as well as detailing the
type, amount, and relative value of all assignments.

| Category      | Amount | Final Grade Weight  | Time/Week (Hours) |
|---------------|--------|---------------------|-------------------|
| Lectures      | 41     | 10% (Participation) | 2.5               |
| Problem Sets  | 35--45 | 35%                 | 6                 |
| Reading/Study | -      | -                   | 3.5               |
| Exams         | 5--8   | 55%                 | -                 |
|---------------|--------|---------------------|-------------------|
|               |        |                     | 12                |

Much of the material builds on previous material; hence, exams are
naturally cumulative. Each exam is weighted equally.

Your lowest 3 problem set scores will be dropped, i.e., your final
problem set grade is the average of all except the two smallest. Your
lowest exam score is also dropped.

### Grading

Your participation grade is based on a variety of activities. During
class I will often make use of the [Socrative](https://socrative.com)
app, so you'll need to install this on your phones. Participating in
Socrative questions and with in-class group activities is required for
a decent participation grade; an A includes asking questions either in
class or in office hours.

An additional portion of your participation grade is based on your
problem set *presentations*. Every day that a problem set is due, one
or more students will be randomly selected to present their solution
to a portion of the assignment. You will be graded based on
*preparation* and the thoroughness of your explanations, NOT on
correctness, although you should of course strive for
correctness. Students taking late days will be required to leave the
classroom during these presentations. You must inform me *BEFORE*
class if you are taking late days to avoid being randomly selected to
present. Otherwise, if you are randomly selected to present but have
not done the assignment, you will receive a 0.

Your final grade is based on a weighted average of particular
assignment categories. You can estimate your current grade based on
your scores and these weights. You may always visit the instructor
outside of class to discuss your current standing. Assignments and
final grades use a standard grading scale shown below and will not
be curved except in rare cases when deemed necessary by the
instructor.

{{ site.data.policies.gradescale_std_v1 }}

You are always welcome to challenge a grade that you feel is unfair or
calculated incorrectly. Mistakes made in your favor will never be
corrected to lower your grade. Mistakes made not in your favor will be
corrected. *Basically, after the initial grading your score can only
go up as the result of a challenge.*

## Policies

* **Late Assignments**: {{ site.data.policies.late_days_v4 }}

* **Academic Dishonesty**: {{ site.data.policies.cheating_v1 }}

* **Collaboration**: {{ site.data.policies.collab_v1 }}

* **Electronic Devices**: {{ site.data.policies.electronics_v1 }}

* **General Expectations**: {{ site.data.policies.expectations_v1 }}

## Schedule
The following *tentative* calendar should give you a feel for how work is
distributed throughout the semester. Assignments and events are listed
in the week they are due or when they occur. *This calendar is subject
to change based on the circumstances of the course*.

Sections marked with an asterisk (*) may be skimmed.

{: .schedule}
| Date                  | Topic/Reading                                | Assignment                                   |
| :-------------------- | :--------------------:                       | --:                                          |
| Wed 08/24 (Week 1)    | Logistics, Sets (1.1)                        |                                              |
| Fri 08/26             | Products (1.2), Subsets (1.3)                | PS01: §1.1 (2,6,14,20,26,30,36,48)           |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 08/29 (Week 2)    | Set Operations I (1.4-1.5)                   | PS02: §1.2 (2,4,12,20), §1.3 (6,10,12,14)    |
| Tue 08/30             | Presentations/Examples                       |                                              |
| Wed 08/31             | Set Operations II (1.6-1.7)                  | PS03: §1.4 (2,8,10,14,18) §1.5 (2,4abcfg,8)  |
| Fri 09/02             | Indexed Sets (1.8, 1.9\*)                    | PS04: §1.6 (2,6), §1.7 (4,8)                 |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/05 (Week 3)    | Statements, And,Or,Not (2.1-2.2)             | PS05: §1.8 (2,4,6,8)                         |
| Tue 09/06             | Exam Review                                  |                                              |
| Wed 09/07             |                                              | PS06: §2.1 (4,6,8,10), §2.2 (2,4,8,10)       |
| Fri 09/09             | Exam 1 (Ch. 1)                               |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/12 (Week 4)    | Conditionals (2.3-2.4)                       |                                              |
| Tue 09/13             | Exam 1 Solutions                             |                                              |
| Wed 09/14             | Truth Tables, Equivalence (2.5-2.6)          | PS07: §2.3 (2,4,6,10), §2.4 (2,4)            |
| Fri 09/16             | Quantifiers (2.7)                            | [PS08](./ps08)                               |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/19 (Week 5)    | English to Logic (2.8-2.9)                   | PS09: §2.7 (2,6)                             |
| Tue 09/20             | Exercises                                    |                                              |
| Wed 09/21             | Negation & Inference (2.10-2.12)             | PS10: 2.9 (2,6)                              |
| Fri 09/23             | Multiplication Principle (3.1-3.2)           | PS11: §2.10 (2,4)                            |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/26 (Week 6)    | Exam Review                                  |                                              |
| Tue 09/27             | Exam 2 (Ch. 2)                               |                                              |
| Wed 09/28             | Addition/Subtraction/Permutations (3.3-3.4)  |                                              |
| Fri 09/30             | Counting Subsets (3.5-3.6)                   | PS12: §3.2 (4,6,10), §3.3 (4,8), §3.4 (4,12) |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/03 (Week 7)    | Direct Proof (4.1-4.3)                       | PS13: §3.5 (6,8,12), §3.6 (4,8)              |
| Tue 10/04             | Exercises                                    |                                              |
| Wed 10/05             | Cases (4.4-4.5)                              |                                              |
| Fri 10/07             | Proof by Contrapositive (5.1-5.3)            | PS14: §4 (2,6,14)                            |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/10 (Week 8)    | Exam Review                                  | PS15: §5 (8,12,20)                           |
| Tue 10/11             | Exam 3 (Ch. 3,4,5)                           |                                              |
| (Wed 10/12)           | (Fall Break)                                 |                                              |
| (Fri 10/14)           | (Fall Break)                                 |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/17 (Week 9)    | Exam 3 Solutions                             |                                              |
| Tue 10/18             | Proof by Contradiction (6.1)                 |                                              |
| Wed 10/19             | More Proofs by Contradiction (6.2-6.4)       |                                              |
| Fri 10/21             | Proving Non-Conditional Statements (7.1-7.4) | PS16: §6 (2, 8, 10)                          |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/24 (Week 10)   | Practice Exam Solutions                      | PS17: §7 (2, 10, 16)                         |
| Tue 10/25             | Exercises/Review                             |                                              |
| Wed 10/26             | Exam 4 (Ch. 6,7)                             |                                              |
| Fri 10/28             | Proofs with Sets (8.1-8.2)                   |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/31 (Week 11)   | 8.3                                          |                                              |
| Tue 11/01             |                                              |                                              |
| Wed 11/02             | 8.4                                          |                                              |
| Fri 11/04             | 9.1-9.3                                      |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 11/07 (Week 12)   | 10.1                                         |                                              |
| Tue 11/08             | Exam 5 (Ch. 8,9)                             |                                              |
| Wed 11/09             | 10.2-10.3                                    |                                              |
| Fri 11/11             | 10.4,10.5\*                                  |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 11/14 (Week 13)   | 11.1-11.2                                    |                                              |
| Tue 11/15             |                                              |                                              |
| Wed 11/16             | 11.3-11.4                                    |                                              |
| Fri 11/18             | 11.5-11.6                                    |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 11/21 (Week 14)   |                                              |                                              |
| Tue 11/22             | Exam 6 (Ch. 10,11)                           |                                              |<commit_msg>260 sched<commit_after>---
layout: class
title: "MATH 260: Discrete Mathematics, Fall 2022"
catalog-desc: "An introduction to proof based mathematics through the study of key areas of discrete mathematics."
semester: f22
---

*{{ site.data.policies.syllabus_deviation_v2 }}*

* TOC
{:toc}

## Logistics

* Class Meetings: MTWF 10:00 AM - 10:50 AM in CSB 380
* Instructors: <NAME>
  * Office: {{ site.data.me.office }}
  * Zoom Room: {{ site.data.me.zoom }}
  * Website: <a href="{{ site.url }}">{{ site.url }}</a>
  * Email: <a href="mailto:{{ site.email }}">{{ site.email }}</a>
  * Office Hours: {{ site.data.semesters[page.semester].office_hours }}
* Website: <a href="{{ site.url }}{{ page.url }}">{{ site.url }}{{ page.url }}</a>
* Credits: 1 course credit
* Prerequisites: An ACT MATH subscore of 22+ or QRAC120.
* Feedback: At any time during the course you can use
  [this]({{ site.data.semesters[page.semester].feedback_form }}) to provide
  anonymous suggestions, criticism, praise, etc.

## Content

### Description
An introduction to proof-based mathematics through the study of key
areas of discrete mathematics. This course serves as an introduction
to higher-level mathematics and advanced coursework in math. Students
will hone their mathematical reasoning skills, learning to express and
work with precise mathematical definitions. A strong emphasis is
placed on developing the skills necessary to communicate mathematical
results.

Topics covered in this course include the the core definitions and
theorems from set theory, mathematical logic, and combinatorics.  In
this context students will explore ideas such as mathematical
induction, functions, and relations and the proof techniques of direct
proof, contrapositive proof, proof by contradiction, and disproof.

### Sources

The course textbook will be:

* <NAME>. _Book of Proof_. 3rd Edition. Licensed under CC BY
  ND. Available
  [here](http://www.people.vcu.edu/~rhammack/BookOfProof/). ISBN:
  978-0-9894721-2-8.

## Assessment

### Assignments and Workload
The weekly workload for this course will vary by student and by week
but should be about 12 hours per week on average. The following table
provides a rough estimate of the distribution of time over different
course components for a 16 week semester, as well as detailing the
type, amount, and relative value of all assignments.

| Category      | Amount | Final Grade Weight  | Time/Week (Hours) |
|---------------|--------|---------------------|-------------------|
| Lectures      | 41     | 10% (Participation) | 2.5               |
| Problem Sets  | 35--45 | 35%                 | 6                 |
| Reading/Study | -      | -                   | 3.5               |
| Exams         | 5--8   | 55%                 | -                 |
|---------------|--------|---------------------|-------------------|
|               |        |                     | 12                |

Much of the material builds on previous material; hence, exams are
naturally cumulative. Each exam is weighted equally.

Your lowest 3 problem set scores will be dropped, i.e., your final
problem set grade is the average of all except the two smallest. Your
lowest exam score is also dropped.

### Grading

Your participation grade is based on a variety of activities. During
class I will often make use of the [Socrative](https://socrative.com)
app, so you'll need to install this on your phones. Participating in
Socrative questions and with in-class group activities is required for
a decent participation grade; an A includes asking questions either in
class or in office hours.

An additional portion of your participation grade is based on your
problem set *presentations*. Every day that a problem set is due, one
or more students will be randomly selected to present their solution
to a portion of the assignment. You will be graded based on
*preparation* and the thoroughness of your explanations, NOT on
correctness, although you should of course strive for
correctness. Students taking late days will be required to leave the
classroom during these presentations. You must inform me *BEFORE*
class if you are taking late days to avoid being randomly selected to
present. Otherwise, if you are randomly selected to present but have
not done the assignment, you will receive a 0.

Your final grade is based on a weighted average of particular
assignment categories. You can estimate your current grade based on
your scores and these weights. You may always visit the instructor
outside of class to discuss your current standing. Assignments and
final grades use a standard grading scale shown below and will not
be curved except in rare cases when deemed necessary by the
instructor.

{{ site.data.policies.gradescale_std_v1 }}

You are always welcome to challenge a grade that you feel is unfair or
calculated incorrectly. Mistakes made in your favor will never be
corrected to lower your grade. Mistakes made not in your favor will be
corrected. *Basically, after the initial grading your score can only
go up as the result of a challenge.*

## Policies

* **Late Assignments**: {{ site.data.policies.late_days_v4 }}

* **Academic Dishonesty**: {{ site.data.policies.cheating_v1 }}

* **Collaboration**: {{ site.data.policies.collab_v1 }}

* **Electronic Devices**: {{ site.data.policies.electronics_v1 }}

* **General Expectations**: {{ site.data.policies.expectations_v1 }}

## Schedule
The following *tentative* calendar should give you a feel for how work is
distributed throughout the semester. Assignments and events are listed
in the week they are due or when they occur. *This calendar is subject
to change based on the circumstances of the course*.

Sections marked with an asterisk (*) may be skimmed.

{: .schedule}
| Date                  | Topic/Reading                                | Assignment                                   |
| :-------------------- | :--------------------:                       | --:                                          |
| Wed 08/24 (Week 1)    | Logistics, Sets (1.1)                        |                                              |
| Fri 08/26             | Products (1.2), Subsets (1.3)                | PS01: §1.1 (2,6,14,20,26,30,36,48)           |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 08/29 (Week 2)    | Set Operations I (1.4-1.5)                   | PS02: §1.2 (2,4,12,20), §1.3 (6,10,12,14)    |
| Tue 08/30             | Presentations/Examples                       |                                              |
| Wed 08/31             | Set Operations II (1.6-1.7)                  | PS03: §1.4 (2,8,10,14,18) §1.5 (2,4abcfg,8)  |
| Fri 09/02             | Indexed Sets (1.8, 1.9\*)                    | PS04: §1.6 (2,6), §1.7 (4,8)                 |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/05 (Week 3)    | Statements, And,Or,Not (2.1-2.2)             | PS05: §1.8 (2,4,6,8)                         |
| Tue 09/06             | Exam Review                                  |                                              |
| Wed 09/07             |                                              | PS06: §2.1 (4,6,8,10), §2.2 (2,4,8,10)       |
| Fri 09/09             | Exam 1 (Ch. 1)                               |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/12 (Week 4)    | Conditionals (2.3-2.4)                       |                                              |
| Tue 09/13             | Exam 1 Solutions                             |                                              |
| Wed 09/14             | Truth Tables, Equivalence (2.5-2.6)          | PS07: §2.3 (2,4,6,10), §2.4 (2,4)            |
| Fri 09/16             | Quantifiers (2.7)                            | [PS08](./ps08)                               |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/19 (Week 5)    | English to Logic (2.8-2.9)                   | PS09: §2.7 (2,6)                             |
| Tue 09/20             | Exercises                                    |                                              |
| Wed 09/21             | Negation & Inference (2.10-2.12)             | PS10: 2.9 (2,6)                              |
| Fri 09/23             | Multiplication Principle (3.1-3.2)           | PS11: §2.10 (2,4)                            |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 09/26 (Week 6)    | Exam Review                                  |                                              |
| Tue 09/27             | Exam 2 (Ch. 2)                               |                                              |
| Wed 09/28             | Addition/Subtraction/Permutations (3.3-3.4)  |                                              |
| Fri 09/30             | Counting Subsets (3.5-3.6)                   | PS12: §3.2 (4,6,10), §3.3 (4,8), §3.4 (4,12) |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/03 (Week 7)    | Direct Proof (4.1-4.3)                       | PS13: §3.5 (6,8,12), §3.6 (4,8)              |
| Tue 10/04             | Exercises                                    |                                              |
| Wed 10/05             | Cases (4.4-4.5)                              |                                              |
| Fri 10/07             | Proof by Contrapositive (5.1-5.3)            | PS14: §4 (2,6,14)                            |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/10 (Week 8)    | Exam Review                                  | PS15: §5 (8,12,20)                           |
| Tue 10/11             | Exam 3 (Ch. 3,4,5)                           |                                              |
| (Wed 10/12)           | (Fall Break)                                 |                                              |
| (Fri 10/14)           | (Fall Break)                                 |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/17 (Week 9)    | Exam 3 Solutions                             |                                              |
| Tue 10/18             | Proof by Contradiction (6.1)                 |                                              |
| Wed 10/19             | More Proofs by Contradiction (6.2-6.4)       |                                              |
| Fri 10/21             | Proving Non-Conditional Statements (7.1-7.4) | PS16: §6 (2, 8, 10)                          |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/24 (Week 10)   | Practice Exam Solutions                      | PS17: §7 (2, 10, 16)                         |
| Tue 10/25             | Exercises/Review                             |                                              |
| Wed 10/26             | (No class)                                   |                                              |
| Fri 10/28             | Exam 4 (Ch. 6,7)                             |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 10/31 (Week 11)   | Proofs with Sets (8.1-8.2)                   |                                              |
| Tue 11/01             | 8.3                                          |                                              |
| Wed 11/02             | 8.4                                          |                                              |
| Fri 11/04             | 9.1-9.3                                      |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 11/07 (Week 12)   | 10.1                                         |                                              |
| Tue 11/08             | Exam 5 (Ch. 8,9)                             |                                              |
| Wed 11/09             | 10.2-10.3                                    |                                              |
| Fri 11/11             | 10.4,10.5\*                                  |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 11/14 (Week 13)   | 11.1-11.2                                    |                                              |
| Tue 11/15             |                                              |                                              |
| Wed 11/16             | 11.3-11.4                                    |                                              |
| Fri 11/18             | 11.5-11.6                                    |                                              |
| :-------------------- | :--------------------:                       | ---------------------:                       |
| Mon 11/21 (Week 14)   |                                              |                                              |
| Tue 11/22             | Exam 6 (Ch. 10,11)                           |                                              |
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