# MATH 112

Welcome to the home page for MATH 112 at the University of California, Riverside, in the second Summer Session of 2004. I am Toby Bartels, the instructor. You can email me at `toby+s4w@math.ucr.edu`. The class meets in Watkins 1101 on Monday through Thursday afternoons from 1:00 to 2:30. My office hours will be in Surge 263, on Monday mornings from 10:30 to 12:00 and on Tuesday, Wednesday, and Thursday afternoons from 3:00 to 4:30. You can also meet with me by appointment.

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.

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 (which is also listed 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

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 believe that this name is meant to refer to the absence of calculus's 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. (Beginning next fall, this will change with the creation of MATH 11. You are the last class under the old system.) We also won't be using any particular features of C++, but familiarity with a programming language will be useful.

## Books

The recommended book for this course is Schaum's Outline of Discrete Mathematics, by Seymour Lipschutz and Marc Lipson, 2nd edition (1997), published by McGraw-Hill. The alternate book 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 Lipschutz & Lipson. But Rosen is much more expensive. Both of these books are available at the UCR bookstore.

There is also a supplementary handout on Rules of Inference.

## Syllabus

The topics to be covered include:
• divisibility, congruences, and counting;
• sets, relations, and functions;
• graphs and trees;
• logic and proof; and
• induction, recursion, and recurrence relations.
We will cover items in roughly this order, which is different from the order of the books. However, material from earlier in the course will be used later in the course as examples; for example, divisibility is an example of a binary relation.

## Assignments

Each day, I will lecture on the material for that day. At the beginning of the next day, I'll assign some homework problems. Homework is always due one week after it is handed out. The homework will also be available online. The beginning of each class (about 15 minutes) will be devoted to answering questions; please participate in the discussion! You should look at homework each day, even though it's not due for a week, so that you can ask questions about it.

Project lists will be handed out each week; the projects are due one week after they are handed out. The projects will also be posted online.

Strictly speaking, there is no curve, so you are not competing against your fellow students. 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 (40% in total), daily homework assignments worth 20% in total, and 1 examination worth 40%.

## Final exam

The final exam was August 27 Friday afternoon from 1:30 to 3:30. Here is the Mock Final, handed out the last week:

And here is the actual Final Exam itself:

## 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 good coverage of many mathematics topics.

This web page and the exams linked from it were written in 2003 and 2004 by Toby Bartels. Toby reserves no legal rights to them.

Although the page has been preserved in its original form, the exams linked from it have been converted to DjVu using Any2DjVu; they can be viewed on almost any operating system using DjVuLibre.

The permanent URI of this web page is `http://tobybartels.name/MATH112/2004/`.