Discrete Mathematical Structures
Math 2513
Summer Semester 2005

• The final exam (and last day of class) will be on Monday, July 25.
  As promised here are solutions to the first two problems from Exam 2.

• For Friday, July 22 we will not have an in-class problem but instead the problem will consist of the following, to be turned in at class on Friday: Read the document titled Some Guidelines for Constructing and Writing Proofs and answer the following:
  1. Which one or two of the guidelines do you think is the most important and/or personally significant (explain)?
  2. Which one or two of the guidelines do you think is least important or confusing (explain)?
  3. List at least one, but preferably two, additional guidelines that you think could be included.

• Here are copies of the first exam, second exam and third exam.

• Homework Assignments will be posted at this web site. Students should check regularly for updates.

• Solutions to Class Problems:
  • Monday, July 18
  • Thursday, July 14
  • Wednesday, July 13
  • Tuesday, July 12
  • Monday, July 11
  • Friday, July 8
  • Thursday, July 7
  • Wednesday, July 6
  • Tuesday, July 5
  • Tuesday, June 28
  • Monday, June 27
  • Friday, June 24
  • Thursday, June 23
  • Wednesday, June 22
  • Tuesday, June 21
  • Monday, June 20
  • Thursday, June 16
  • Wednesday, June 15
  • Tuesday, June 14
  • Monday, June 13
  • Friday, June 10
  • Thursday, June 9
  • Wednesday, June 8

• Here are some Guidelines for Proofs which may help you to approach constructing and writing proofs in a systematic fashion.
  Above all, in this course students should learn to equate effective mathematical writing with good common sense reasoning. To achieve this it is best to avoid the overuse of special logical symbols whenever possible in mathematical writing. Unfortunately, our course textbook is not always a good model for common sense explanations. For example, compare the book's proof in Example 10 starting at the bottom of page 89 with the much preferable and easier to read alternate proof of Example 10.

• The Course Information Sheet includes information about how the class will be conducted.

• Important Class Policy: During each class (except for exam classes) there will be a 10-minute Class Problem. This problem may be completed either directly before the class starts at 10:30 AM, or directly after the class ends at 11:30 AM. If you choose to work the problem before class then you must arrive prior to 10:20 AM to do this--if you arrive later, then you will need to work the problem at the end of class instead. Students may start working the problem at 10:15 or slightly earlier.

• 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).

• Old Exam Archive:
  Looking at some old exams may help to prepare for this semester's course. However the topics that were included, as well as the order in which they were presented, may be different:
  • Spring 2005: Exam1 and some solutions
  • Fall 2004: Exam 1 from the Fall 2004 course and some answers
  • Spring 2005: Exam2 with answers
  • Fall 2004: Exam 2 with answers
  • Spring 2005: Exam 3 with answers
  • Fall 2004: Exam 3
  • Fall 2004: Final Exam

• 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.
  • Seymour Lipshutz, Discrete Mathematics, Schaum's Outline Series: This book doesn't have much information on constructing mathematical proofs but it has a lot of worked and unworked problems involving set theory, functions, relations and many other topics from discrete mathematics.
  • 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, Summer 2005