# MATH 112

Welcome to the home page for MATH 112 at the University of California, Riverside, in the second Summer Session of 2003. I am Toby Bartels, the instructor. You can email me at toby+s3w@math.ucr.edu. The class meets in Watkins 1101 Monday through Thursday from 8:00 to 9:30. My office hours are in Surge 263 Monday through Thursday from 10:00 to 12:00. Everything is in the morning -- and I don't like it any more than you do.

This web site will be updated from time to time, so if you want information that's most up to date, then be sure to check back here again. Any important changes will be in the announcements, so at least check there. Of course, I'll also announce things in class, so you can ignore this web site completely if that's what you want.

The course also appears on UCR's Blackboard site. I will use that site for three things:

• Sending announcements to you by email;
• Maintaining a discussion board; and

If your email address on Blackboard (also under Student Tools), is missing or wrong, then you won't get announcements by email, but they'll still show up on both that site and this site. Note that the Blackboard site requires Javascript to work.

## Introduction to the course

Discrete mathematics, as the name suggests, is mathematics that is unconcerned with the continuity properties of the real line. I like to think of it as that branch of mathematics that has nothing at all to do with calculus. As such, it covers very different material from what you may be used to from other math classes. In the past half century, discrete mathematics has had a great deal of application to computer science, and this course is intended to prepare for those applications. Nevertheless, the material is math, not CS.

Discrete mathematics is also called "Finite Mathematics"; in fact, that's the official title for this course. I think that this name refers to the absence of calculus' infinite limit processes. But don't assume that all of the mathematical objects that we'll be dealing with are finite. In particular, we will cover recursion, a concept which inherently contains a potential infinity.

## Prerequisites

The formal prerequisites for this course are a term of differential calculus and a term of C++. We will not be using calculus (that's exactly what discrete mathematics is not about), but some level of familiarity with college mathematics is necessary, and UCR just doesn't offer any lower-level math courses except calculus. We also won't be using the particular features of C++, but familiarity with a programming language will be useful. Also, I'll assume that students can follow C-style code like this example, which I'll use to present algorithms.

## Books

The required book for this course is Schaum's Outline of Discrete Mathematics, by Seymour Lipschutz and Marc Lipson, 2nd edition (1997), published by McGraw-Hill. This should be available at the bookstore, or you can search for it online.

The optional book for this course is 2000 Solved Problems in Discrete Mathematics, by Seymour Lipschutz, published (1991) by McGraw-Hill. This should be available at the bookstore, or you can search for it online.

The alternate book for this course is Discrete Mathematics and its Applications, by Kenneth H. Rosen, 4th edition (1998), published by McGraw-Hill. If you already have this book, then you don't have to buy the Lipschutz & Lipson. But this book is much more expensive.

A book not recommended for this course is Schaum's Easy Outline of Discrete Mathematics. This is an abridgement of the required text, but it doesn't contain all of the material that we'll be studying.

## Syllabus

The topics to be covered include propositional and predicate logic, operations on sets, methods of proof, induction and recursion, the pigeonhole principle, counting with binomial coefficients, recurrence equations (the discrete version of differential equations), graphs and trees, equivalence relations, and partially ordered sets.
• Week 1: Logic and sets
• Week 2: Proofs
• Week 3: Counting
• Week 4: Relations
• Week 5: Graphs and review
• August 29: Final exam, 7:30 to 9:30

There is a more detailed schedule.

Strictly speaking, there is no curve, so you are not competing against your fellow students. So I encourage you to study together and learn from each other! However, if grades don't turn out as I expect, then I'll consider whether an assignment was more difficult than I intended and adjust the grades accordingly.

Numerically, I will grade harshly -- it's hard to get 100% on any assignment. On the other hand, the correspondence between numerical grades and letter grades is nicer than most math courses:

• [100%, ∞): A+
• [93%, 100%): A
• [86%, 93%): A-
• [79%, 86%): B+
• [71%, 79%): B
• [64%, 71%): B-
• [57%, 64%): C+
• [50%, 57%): C
• [43%, 50%): C-
• [36%, 43%): D+
• [29%, 36%): D
• [21%, 29%): D-
• [0, 21%): F

Here, "[x%, y%)" means «at least x% but less than y%». There is no rounding; an average of 49.99% is not enough for a C.

There will be 4 projects worth 10% each, 4 homework assignments worth 5% each, and 1 examination worth 40%. There may also be occasional quizzes, but these won't contribute to your grade. The final exam is August 29 Friday, and it starts at 7:30, not 8:00, so don't be late!

## A typical class day

Each day, I will lecture on the material for that day. At the end of the lecture, I'll assign some homework problems. Homework is always due the following Tuesday. The beginning of each class (about 15 minutes) will be devoted to solving problems about the previous day's material; please participate in the discussion! You should look at homework each day, even though it's not due until the following Tuesday, so that you can ask questions about it the next day. Depending on the available time, I might give quizzes occasionally. The purpose of these would be to help you see how well you're doing; they won't count towards your grade. Project lists will be handed out each week; the projects are due the following Tuesday.

## Resources

Some good places to learn about mathematics on the World Wide Web include:
• PlanetMath, a free encyclopaedia of mathematics written by mathematicians;
• MathWorld, an encyclopaedia of mathematics written by astrophysicist Eric Weisstein;
• Wikipedia, a free encyclopaedia of everything written by anybody that shows up, which has fairly good coverage of many mathematics topics.

This web page was written in 2003 and 2004 by Toby Bartels. Toby reserves no legal rights to it.

The permanent URI of this web page is `http://tobybartels.name/MATH112/2003/`.