`toby+s5w@math.ucr.edu`

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The class meets in Sproul 2351
on Monday through Thursday mornings from 9:40 to 11:10.
My office hours will be in Surge 263,
on Mondays through Thursdays from 11:30 to 1:00.
You can also meet with me by appointment;
you can make an appointment by email or whenever you see me.
In fact, you should feel free to drop by my office at any time;
I might not be there,
and I might not have time when you come even if I *am* there,
but your odds are good, so give it a shot!

This web site will be updated from time to time, so if you want to look up up-to-date information, then check online. 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
- Keeping track of your grades (under Student Tools).

There is a myth, which I've found prevalent among undergraduates, that mathematics study is a linear progression: arithmetic, algebra, geometry, trigonometry, calculus, and so on. This is almost entirely false; mathematics is a web of ideas, all related but in different ways, and the traditional high school curriculum in the United States is simply one way to organise it. This traditional curriculum is geared towards calculus; it focuses on the ideas needed for calculus, which in turn is needed for the engineering that was central to the American economy (and the Cold War) half a century ago.

The curriculum could equally well pass from algebra to logic (including proofs), modular arithmetic, algorithms, graph theory, and (instead of calculus) abstract algebra. This is a curriculum of discrete mathematics, which is needed for computer science, systems engineering, logistics and management engineering, and similar endeavours. In another 50 years, MATH 11 may simply be the remedial class for students that didn't learn what they should have in high school; while MATH 9 (calculus) will be special material required only for biology and economics majors.

Another useful book is
2000 Solved Problems in Discrete Mathematics,
by Seymour Lipschutz alone (1991), again published by McGraw-Hill.
This book is a companion
to the Lipschutz & Lipson textbook mentioned above.
As its title says, it contains 2000 solved problems,
so you can use it for practice or extra study.
I should also warn you *not* to get
Schaum's *Easy* Outline of Discrete Mathematics.
This is an abbreviation of Lipschutz & Lipson,
and it doesn't cover enough material to be a textbook for this course.

You can buy books online usually cheaper than at the bookstore (but then there are shipping delays):

- Get Rosen (textbook) online;
- Get Lipschutz & Lipson (textbook) online;
- Get Lipschutz (problem book) online.

There have also been two supplementary handouts on rules of inference. The first one covers material that's not (completely) in either book but which you are still responsible for knowing:

The second one gives templates (in diagrammatic form) for the various rules of inference; this material is pretty idiosyncratic (although I've based it on the teaching of Paul Taylor, a theoretical computer scientist in England), so you won't be required to know it. Nevertheless, it may help you to use the rules of inference to find proofs:- Week 1: Logic, proofs, and algorithms;
- Week 2: Sets, functions, and relations;
- Week 3: Natural numbers, induction, and recursion;
- Week 4: Divisibility, arithmetic algorithms, and counting;
- Week 5: Equivalence relations, partial orders, and review.

Each week (except the last), I will also assign a project that is due one week later. These projects ask you to write an essay (of a few pages) about a topic related to the class material. You'll have a choice of topics, and you'll probably need to do research outside of the class lecture. The projects will also be posted online.

For both homework and projects,
I encourage you to talk with your fellow students.
In my class, this is *not* cheating!
*However*, the final result that you turn in to me
must be your own work, written by you in your own words.
Do *not* turn in anything that you copied from another person
(except for properly cited quotations),
and do *not* let other students copy from what you plan to turn in.

Numerically, I will grade harshly —it's hard to get 100% on any single assignment. On the other hand, the correspondence between numerical grades and letter grades is nicer than most math courses (especially at the low end):

- [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

There will be 4 projects worth 10% each (40% in total), daily homework assignments worth 20% in total, and 1 examination worth 40%.

- 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 handouts linked from it were written between 2003 and 2005 by Toby Bartels. Toby reserves no legal rights to them.

Although the page has been preserved in its original form, the handouts 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/MATH11/2005/`

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