1. Contact Information
  2. Prerequisites
  3. Course Description and Credit Hours
  4. Required Texts
  5. Course Objectives
  6. Student Learning Outcomes
  7. Other Course Materials
  8. Outline Of Topics
  9. Exams and Assignments
  10. Grading Policy
  11. Policy on Missed Exams and Coursework
  12. Attendance Policy
  13. Notification of Changes
  14. Custom Sections
  15. Statements on Academic Misconduct
  16. Statement On Disability Accommodations
  17. Severe Weather Protocol
  18. Pregnant Student Accommodations
  19. Religious Observances
  20. UAct Statement

Discrete Mathematics

MATH 301-004Spring 2018 | 3 Credit Hours

Lecture

Shibin Dai

Contact Information

UA Campus Directory:

Office Hours: MWF 10:00-11:00, W 4:00-5:00, F 2:00-3:00.

Prerequisites

UA Course Catalog Prerequisites:

MATH 125 or MATH 145

Course Description

Course Description and Credit Hours

An introduction to mathematical logic and proof within the context of discrete structures. Topics include basic mathematical logic, elementary number theory, basic set theory, functions, and relations. Writing proficiency is required for a passing grade in this course. A student who does not write with the skill normally required of an upper-division student will not earn a passing grade, no matter how well the student performs in other areas of the course.

Required Texts

Required Texts from UA Supply Store:
  • EPP(VP) / DISCRETE MATHEMATICS W/APPL (Choose One)
  • EPP(VP) (RENTAL) / (RENTAL) DISCRETE MATHEMATICS W/APPL (RENTAL)
  • EPP (EBOOK) / DISCRETE MATHEMATICS WITH APPLICATIONS (Choose One)

Course Objectives

This course will discuss formal and informal logic and present applications to selected topics in discrete mathematics. This is primarily a course in mathematical thinking. Selected areas include number theory, set theory, and probability theory. Other topics may be introduced as time allows. Students will be expected to understand the notion of mathematical proof and to write their own proofs in these areas.

Student Learning Outcomes

 Students will be able to determine the validity of a compound statement, its

  • converse, inverse, and contrapositive

 Students will be able to write proofs using various techniques, including

  • direct proof

  • proof by contradiction

  • proof by mathematical induction

  • proof by contrapositive

  • proof by division into cases

 Students will be able to prove properties of sets, including

  • equality and containment of sets

  • set identities

  • partitioning of sets through equivalence relations

 Students will be able to prove theorems related to the partitioning of sets through

  • equivalence relations.

 Students will be able to prove theorems related to properties of functions, including:

  • Surjectivity

  • Injectivity

  • Bijectivity

  • Inverses

  • Compositions

Other Course Materials

None

Outline of Topics

The course will include the following topics:

 Logic of Compound Statements (2.1-2.3)

 Logic of Quantified Statements (3.1-3.4)

 Elementary Number Theory and Methods of Proof (4.1-4.7)

 Sequences, Mathematical Induction, and Recursion (5.1-5.4, 5.6, 5.7)

 Set Theory (6.1-6.3)

 Functions (7.1-7.3)

 Relations (8.1-8.3)

Exams and Assignments

Homework will be assigned each week, and will be posted on blackboard.

Exam 1: Wednesday 02/07

Exam 2: Wednesday 03/07

Exam 3: Wednesday 04/11

Final:11:30 am -2:00 pm, Friday 05/04

Grading Policy

Homework: 10% (Two of the lowest homework scores will be dropped)

3 in class exams: 60% (20% each)

Comprehensive final exam: 30%

[97, 100)

A+

[87, 90)

B+

[77,80)

C+

[67,70)

D+

[0,60)

F

[93,97)

A

[83,87)

B

[73,77)

C

[63,67)

D

[90,93)

A-

[80,83)

B-

[70,73)

C-

[60,63)

D-

Policy on Missed Exams and Coursework

There will be no extensions of the deadline for homework, unless there are documented legitimated reasons.

A makeup exam may be given in the following cases subject to verification: a medical emergency, a University-sponsored event, a religious event, or a family emergency. A makeup exam should be scheduled at least one week in advance, unless it is due to emergency situations. You must present the documentation either before the exam or as soon as you return to class.

Attendance Policy

Class attendance is required. Class participation is strongly encouraged. Students are solely responsible for any work missed during an absence.

Notification of Changes

The instructor will make every effort to follow the guidelines of this syllabus as listed; however, the instructor reserves the right to amend this document as the need arises. In such instances, the instructor will notify students in class and/or via email and will endeavor to provide reasonable time for students to adjust to any changes.

Statement on Academic Misconduct

Students are expected to be familiar with and adhere to the official Academic Misconduct Policy provided in the Online Catalog.

Statement On Disability Accommodations

Contact the Office of Disability Services (ODS) as detailed in the Online Catalog.

Severe Weather Protocol

Please see the latest Severe Weather Guidelines in the Online Catalog.

Pregnant Student Accommodations

Title IX protects against discrimination related to pregnancy or parental status. If you are pregnant and will need accommodations for this class, please review the University’s FAQs on the UAct website.

Religious Observances

Under the Guidelines for Religious Holiday Observances, students should notify the instructor in writing or via email during the first two weeks of the semester of their intention to be absent from class for religious observance. The instructor will work to provide reasonable opportunity to complete academic responsibilities as long as that does not interfere with the academic integrity of the course. See full guidelines at Religious Holiday Observances Guidelines.

UAct Statement

The University of Alabama is committed to an ethical, inclusive community defined by respect and civility.  The UAct website (www.ua.edu/uact)  provides extensive information on how to report or obtain assistance with a variety of issues, including issues related to dating violence, domestic violence, stalking, sexual assault, sexual violence or other Title IX violations, illegal discrimination, harassment, hate or bias incidents, child abuse or neglect, hazing, threat assessment, retaliation, and ethical violations or fraud.