Discrete Mathematics -- Mathematics 574


Frank Thorne - Spring 2012


University of South Carolina

      Instructor  
      Frank Thorne  
  Office     LeConte 400G  
  E-mail     thornef [at] mailbox.sc.edu  
  Office hours   Mon/Thu 3:30-4:30, Tue 10:00-11:00

Course information and learning outcomes:

Students will master foundational concepts in discrete mathematics, including: set theory, logic, proof techniques (induction, contradiction, and others), and elementary combinatorics (counting techniques).

  • Text : Susanna Epp, Discrete Mathematics: Introduction to Mathematical Reasoning, brief edition. You can buy it from Amazon here, for over $30 less than the campus bookstore is charging.

    Update: The bookstore doesn't even have it (??!) despite the fact that I requested it six weeks ago, and the manager has not responded to my inquiries. Please buy the book online.

  • Lectures : LeConte 405, Tues/Thurs, 2:00-3:15.

  • Exam schedule :

    Exam 1: February 9, in class. Solutions.

    Exam 2 (with solutions) March 22, in class.

    Practice Exam 3, with solutions.

    Final Exam: Wed., May 2, 9:00 am - 12:00 noon.

  • Finals Period Office Hours/Review Session:

    As settled by popular vote, there will be a review session on Sunday, April 29 in the usual room, from 7:00 until around 9:00. Bring questions.

    Office Hours: Mon., April 23 and Tue., April 24, 1:30-2:30. Monday and Tuesday, April 30-May 1, times TBD (requests welcome!)

  • Homework :

    WARNING. I assign a lot of homework.

    The homework is intended to take 6-8 hours a week (which is a lot of effort). Please count on making a consistent effort to do well in this class! Note that starting the night before will not be good enough. If homework takes you more than 8 hours on any given week then please let me know.

    (Grading details, TBA)

    There will be a few bonus problems on each homework, each worth one or two points, up to a maximum score of 11/10 on each week's homework. The bonus homework is intended to let you skip some (not all) of the more routine exercises if you feel like attempting something more difficult.

    Some homework solutions.

  • Grading :

    WARNING. You will be graded both on correctness and on quality of exposition. Indeed, a major focus of Math 574 is the ability to communicate mathematical ideas clearly. The standard is that someone who doesn't know the answer should be able to easily follow your work. In particular, please write in complete English sentences where appropriate (in particular, where writing proofs.) Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

    Exams will have a variety of questions. Some questions will be chosen directly from the homework assignments, and most will at least be similar to homework problems.

    Grading scale: A = 90+, B+ = 85+, B = 78+, C+ = 73+, C = 66+, D = 52+.

    Please note that my grading scale is more generous than the usual 10-point scale. However, I am a (slightly) stricter grader than most. This is intended to balance out.

      Grade component     % of grade  
      Two in-class exams     20% x 2  
      Final exam:     35%  
      Homework:     25%  

  • Contacting me : Please contact me if you have any questions about the course, about my expectations, about my lectures, about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my job to help you succeed. The best ways to get help are to come to office hours (no appointment necessary) or to e-mail me (I will almost always reply within 24 hours). If neither of these work for you then please e-mail me to set up an appointment.

  • Feedback : This is my first time teaching Math 574 at the University of South Carolina. I would be grateful to receive any and all feedback. If your feedback is critical and you would like to be anonymous, consider signing up for a Yahoo or Gmail account and e-mailing from there (I will cheerfully respond).

  • Make-up policy :

    If you have a legitimate conflict with any of the exams it is your responsibility to inform me at least a week before the exam. Late homework will be accepted once per student, up to a week late; after that, no late homework please except in case of emergency.

    Academic honesty and attendance are expected of all students.

    Calculators will not be needed, and they will not be permitted on exams.

  • Lectures and homeworks :

    The following schedule is a rough outline of what we will cover. Subject to change. Homework assignments will be added here as the term goes on.

    Jan. 10-12: Sets, relations, and functions (Ch. 1.1-1.3)

    * Homework 0, due Friday, January 13, by 5:00. (Please note the special instructions.)

    Jan. 17-19: Introduction to logic (Ch. 2.1-2.3)

    * Homework 1, due Friday, January 20, by 5:00.

    Jan. 24-26: Introduction to logic (Ch. 2.1-3.4)

    * Homework 2, due Friday, January 27, by 5:00.

    Jan. 31-Feb. 2: The logic of quantified statements (Ch. 3.1-3.4)

    * Homework 3, due Friday, February 3, by 5:00.

    Feb. 7: Methods of proof (Ch. 4.1-4.6)

    Feb. 9: Midterm Examination 1

    Feb. 14-16: Methods of proof (cont.) (Ch. 4.1-4.6)

    * Homework 4, due Friday, February 17, by 5:00.

    Feb. 21-23: Proof by induction (Ch. 5.1-5.4)

    * Homework 5, due Friday, February 24, by 5:00.

    Feb. 28-Mar. 1 Induction (Ch. 5)

    * Homework 6, due Friday, March 2, by 5:00.

    Mar. 6-Mar. 8 Spring Break!

    Mar. 13-15 Introduction to set theory (Ch. 6.1-6.4, 7.2)

    * Homework 7, due Monday, March 19, by 5:00.

    Mar. 20 More on set theory; exam review

    Mar. 22 Midterm Examination 2

    Mar. 27-29 Counting and probability (Ch. 9)

    * Homework 8, due Monday, April 2, by 5:00.

    Apr. 3-5 Counting and probability (cont.) (Ch. 9)

    * Homework 9, due Friday, April 6, by 5:00.

    Apr. 10-12 Counting and probability (cont.) (Ch. 9)

    * Homework 10, due Monday, April 16, by 5:00.

    Apr. 17-19 Counting and probability (cont.) (Ch. 9)

    Final exam: May 2, 9:00 am-12:00 pm.