Discrete Mathematical Structures
Math 2513
Spring Semester 2005

• The Final Exam will take place on Friday morning May 13 at 8:00 AM. It will cover the material that has been covered on Exams 1--3 as well sections 6.1 and 6.2. Many of the exercises at the end of these sections are recommended for study---a good set to start with might be the following
  • Section 6.1, page 409: 3, 4, 7, 8, 23, 24, 40
  • Section 6.2, page 423: 2, 4, 11, 19, 21--26, 28
  During finals week I will hold my usual office hours on Monday afternoon 3:30-4:30 PM, and also on Wednesday 5:00-6:00 PM. We will have a Review Session in PHSC 1105 on Wednesday April 11 from 3:30 to 4:30 PM. During the review session we will focus on discussing problems from sections 6.1 and 6.2, and other questions that you have. Here is a copy of the final exam from last semester (however we did cover some different topics this semester).

• Answers to the third exam are now available and here is a copy of the exam 3 re-retest. Here is an old third exam (the last problem on this is one that we haven't covered yet). Problems 2 and 6 from exam 2 of last semester (posted below) are also relevant for this test.

• There will be a curve of five points added to each students score on the second exam. Here are some solutions to the second exam. One of the problems consisted of Problem 20 on page 75 (or a portion of it), here is a discussion of a similar problem. The second exam from last semester (with answers) covered somewhat different material (for example, we have not yet discussed problems like numbers 2 and 3) but may be useful to study.

• Homework Assignments will be posted at this web site. Students should check regularly for updates. Assignments will generally be due once a week during the semester.

• The Class Problems will be posted here:
  • March 31 Problem.
  • March 24 Problem.
  • March 1 Problem with solution.
  • February 24 Problem with solution.
  • February 22 Problem.
  • February 3 Problem.
  • January 27 Problem. Notice that the definition of substring was changed to allow the empty string to be considered as a substring of a bit string. With this change, the answers are
    1. There are three bit strings of length 3 that do not occur as substrings: 000, 100 and 010
    2. The set A has 22 elements.

• Here are some Guidelines for Proofs which may help you to approach constructing and writing proofs in a systematic fashion.

• Exam1 and Solutions to Exam 1 are now available on-line.

• Here is a Course Information Sheet.

• Exam 1 from the Fall 2004 course may be useful to study. To review the concept of function, I would recommend looking at any of exercises 1 through 33 in section 1.8 (on page 108) of Rosen's book. Here are some answers from last semester's exam.

• Catalan and his numbers: The Catalan Numbers were named after a Belgian mathematician Eugene Catalan: you can find out about him by looking at his biography at the St. Andrews Biographies of Mathematicians web site. You can also see some of the different interpretations of the Catalan numbers or find more information by entering the first few Catalan numbers {1, 1, 2, 5, 14, 42, ...} at the On-Line Encyclopedia of Integer Sequences web site (this site contains an extensive database of interesting sequences of integers).
  On February 25, Dr. Edward Brandt from the OU Health Sciences Center was honored with one of the College of Arts & Sciences Distinguished Alumni Awards. Professor Brandt, who earned an undergraduate degree in mathematics at the University of Oklahoma in 1954, has had a distinguished career in medicine and biostatistics, specializing in health policy and administration. He will present a talk entitled "A Look at the Healthcare System in Oklahoma" on Thursday, February 24 at 3:30 PM in the Scholar's Room of Oklahoma Memorial Union. Dr. Brandt is an amazing model for career accomplishments that can be attained starting with a strong foundation in mathematics. Students in the class can earn extra credit for the course by attending the lecture and submitting a brief 3 or 4 paragraph summary of Professor Brandt's talk and personal reactions to it.

• Course Bibliography:
  • Kenneth Rosen, Discrete Mathematics and Its Applications (5th edition), McGraw-Hill, 2003: The course textbook.
  • George Polya, How To Solve It, Anchor Books, 1957: A classic book discussing methods of solving mathematical problems and constructing mathematical arguments.
  • Daniel Solow, How To Read and Do Proofs: An introduction to mathematical thought processes, Wiley, 1990: One of a number of elementary books discussing how to create and analyze a mathematical argument. This type of book is very highly recommended for students who have not written mathematical proofs before.
  • Alan Levine, Discovering Higher Mathematics: Four habits of highly effective mathematicians, Academic Press, 2000: Another book that discusses how to approach mathematical arguments.
  • Antonella Cupillari, The Nuts and Bolts of Proofs, Wadsworth, 1989. Another example of a book that discusses how to approach mathematical arguments and has lots of examples.
  • Colin Adams, Joel Hass and Abigail Thompson, How to Ace Calculus: The streetwise guide, W.H. Freeman, 1999: Amusing observations on surviving the Calculus I course, also contains many valuable nuggets for dealing with any undergraduate mathematics course.
  • Raymond Wilder, Introduction to the Foundations of Mathematics, John Wiley & Sons: If you would like a reference that provides a firm axiomatic foundation of set theory (including, for example, discussions of Russell's Paradox), I recommend this book. I'm not certain if it is currently in print but it shouldn't be too difficult to locate a copy in the library.

Math 2513, Spring 2005