## General Information

• In-class versus on-line. There is almost universal agreement that taking an online class is harder than taking a regular class covering the same material. You may be wondering if you should take this class on-line or in-class. We offer both versions. The two versions cover the same material. The same (add, drop, withdraw...) deadlines apply to both versions. Main advantages of the in-class sections include: regular personal contact with the instructor and fellow students, a regular opportunity to ask questions, and regular presentation of the material by an actual person. The main advantage of the on-line course is that you can work on it on your own schedule, and wherever it is convenient (literally anywhere on the planet). However, you should be aware that taking the online version is likely harder than taking the in class version, and you need to be prepared to work on your own.

The main requirements for taking the on-line version are

• Availability of an internet browser such as Netscape or Internet Explorer.

• Your ability and willingness to use e-mail.

• Your ability to print postscript or pdf files. (This is not essential but highly desirable.)

• The University also charges an extra fee for the administration of the course.

• Instructor: Cynthia S. Bestvina; JWB 115; 801-581-3901; cbestvin@math.utah.edu
E-mail is best. You can email me to make an appointment to visit me in my office or to skype me.

• Course Contents: The essence of Algebra is to use variables instead of numbers. This enables us to set up and solve word problems, and to construct a link between formulas and pictures which in turn much amplifies our problem solving ability. You don't need to understand all that follows, but for your information here is a list of the topics we will cover:

• Manipulation of algebraic expressions such as (a+x)2 =a2 + 2ax + x2.

• Solution of linear equations such as 3x+2 = 5   -->   x = 1.

• Solution of quadratic equations such as x2-5x+6 = 0   -->   x=2   or    x=3.

• Solution of linear systems such as 2x+3y = 8    and    3x-y =1    -->    x= 1    and   y=2.

• The concept of a function.

• The Cartesian coordinate system and the graphs of equations and functions.

• Grading: There will be 16 WeBWorK based home work assignments counting 2% each, 2 one hour exams counting 18% each, and a final exam counting 32%. The exams will be organized by the University on-line administration. The WeBWorK home-works will be due Fridays at 11:59pm.

• Grading is based on a Fixed Scale:

 > 90% > 85% > 80% > 75% > 70% > 65% > 60% > 55% > 50% > 45% > 40% else A A- B+ B B- C+ C C- D+ D D- F
• Make ups: You will have one week for each home work, and the purpose of the home work is to help you learn by doing problems, and benefiting from the instant feedback. If you miss a home work you miss the experience. Therefore there will be no make-ups for home work. Exams will be arranged in a very flexible manner by the U of U on-line administration. However, if you have to miss an exam for a legitimate reason, then talk to me, preferably before, but no later than a week after the exam. I will add the weight of what you missed to the weight of your final. Thus effectively you will get the same percentage on the missed test as you will on the final. That's reasonable since the final is comprehensive. Any make-up or substitute for the final exam itself will be an oral exam, and will be available only in exceptional circumstances.

• Calculators: Calculators are great tools, but at this level it is crucial to acquire arithmetic and algebraic proficiency that does not depend on the crutch of a calculator. That's why for in-class tests (including the final) calculators are prohibited. Of course you can use calculators for the home work.

• University versus High School Classes. Some mathematics (essentially Intermediate Algebra through Calculus, and some basic statistics) are taught at High Schools as well as at a University like this one. There are two main differences between classes on the same subject taught at a University or a high school. The University class is faster paced, and at a University there is no supervision of your learning by the teacher. I will frequently make suggestions about how you should go about it, but you are in charge of your learning. This is a difference in philosophy, not a matter of not caring. I measure my success by seeing how much students in this class learn, but I assume you are fully responsible and capable to make the best of what this class has to offer. I'd be pleased to talk with you about ways of maximizing your success. Don't hesitate to contact me if I can be of assistance.

• What it Takes: Taking any math class is a serious enterprise that requires your commitment, time, and energy. Obviously, we are all busy, and there are many competing claims to our attention, all of which are legitimate. So it's not a moral problem if you don't have enough time to dedicate to this class. But it is a fact of life that understanding new mathematics takes a great deal of time and effort, and if you are not prepared to spend that time and effort you will not understand the mathematics. As a guide-line you should count on spending a total of about 12 hours per week on this class, approximately and on average. Moreover, you should be able to spend that time in good sized chunks without distractions. If you are unable to spend that kind of time, you are better off taking Intermediate Algebra during another semester when you do have the time.

• I'm not a math person. Many people feel they are intrinsically unable to learn mathematics. This feeling is usually sincere, but it's also irrational, a poor excuse, and unnecessarily self-limiting. You may not be able to make mathematics your career, but anybody can study mathematics successfully. If you follow the suggestions given here in the next few paragraphs you will succeed!

• Make sure you have the prerequisites: Mathematics proceeds in a logical sequence, and you can't understand new mathematics if you don't understand what underlies it. For this class this means you must understand basic arithmetic, including the arithmetic of fractions, equalities, and inequalities. You should also have seen the concept of using variables instead of numbers, and you should understand the basic conventions of arithmetic precedence, and the use of parentheses. The latter seems to be the greatest stumbling block in using WeBWorK and we will review and discuss this issue in some detail.

• Make sure you do not fall behind: This is the most important suggestion on this page! If you miss just one key idea you will not properly understand what we are doing and your subsequent time and effort will be wasted. Saving two hours today may result in wasting days and weeks later. So before doing the WeBWorK home work read the relevant sections of the textbook and the pertinent web pages. Make sure you understand the subject. If there is a problem on the homework that you are unable to solve or where you do not fully understand the question and the answer, do not allow yourself to be satisfied with only a partial understanding of the issues. Go back over the relevant material, and go on only after everything makes sense to you.

• Seek Help: Work with friends or study partners. Soon after the class starts I will distribute a list of participants, including e-mail addresses, phone numbers, and suitable study times. Then it will be up to you to contact your class mates and arrange times to get together. It's OK if you and your partner or partners have different levels of experience or ability. One of you will benefit from explaining something and the other from having something explained again in a different way. Use our free tutoring service in the Math Center. You are welcome to ask me questions by phone, e-mail, or by just dropping by.

• Focus on understanding the subject rather than memorizing recipes for doing simple things. You understand a piece of mathematics if you can explain it in terms of simpler mathematics, you can make multiple logical connections between different facts and concepts, and you can figure out how to apply the mathematics to solve new problems. Too much teaching of mathematics is directed towards memorizing and rehearsing the application of simple recipes to narrow classes of problems. Focusing on the underlying connections and learning how to figure things out is vastly more efficient and empowering than trying to memorize countless formulas.

• You can learn mathematics only by doing mathematics. The main purpose of the WeBWorK assignments in this class is to give you a guided opportunity to learn by doing. But you have to go beyond that! Which and how many additional exercises you should do depends on your background, your current understanding, and your interests. Rather than giving you a list of exercises I believe you are better served by your picking the exercises yourself and me giving you just some general guidelines. The best way to find good exercises is to make them up yourself, but there are also a great many exercises in the textbook, ranging from very simple problems letting you practice just one specific technique to quite sophisticated and deep questions.

• Always Check your Answers: Everybody makes mistakes, and you simply have to recognize that fact and guard against it. You should always check your answers. The answers to odd numbered problems are in the book, but that should not discourage you from working even numbered problems or making up your own. You can check your answers by computing the same result in different ways, by checking for plausibility and consistency, or by using more specific techniques such as substituting in the original function or equation, drawing a graph, or making sure that physical units are consistent. (For example, if your analysis calls for adding two seconds to a square foot then something must have gone wrong.) One major checking technique deserves it own paragraph:

• Hostile Testing: No, this phrase does not refer to the testing we inflict upon our students! It means that you approach your answer with the expectation that it's wrong and you try to prove that it is wrong. That way, if you fail, then maybe your answer is actually correct! Apply the same attitude to your textbook and to what your teacher tells you. You are more likely to find errors, and you end up processing what you read or hear with a much higher degree of awareness and effectiveness.

• Language: Part of learning mathematics is learning the language of mathematics, and mastering the language is essential for understanding mathematics and communicating it to your peers and others. Make a habit of having your textbook and a standard dictionary handy, and when there is a word you don't understand figure out what it is before you read on. This will cost you some time at the moment but in the long run it will save you time, and it will help you understand the subject much better. It will also make you a more effective problem solver and communicator.

• How to Work: You are probably familiar with a mode of mathematics teaching that goes like this: Here is how you solve a quadratic equation, now go and solve problems 1--100 in your textbook. This is not productive because it turns home work into a chore that needs to be gotten over with, but that is neither enjoyable nor useful. It is much better to solve only a few problems but to go about them deliberately and carefully, with an eye towards noticing what the problem teaches you, and a determination to solve the problem correctly and to understand every detail of it. It is also important to organize your work in such a way that you can go back and see what you did and figure out what you did wrong. When you see my office you will notice that I am not a neatness freak, but in doing mathematics careful and deliberate neatness actually saves you time and enhances your learning experience. Watch what I write on the board and arrange your work similarly.

• How to take Exams: There is only one fundamental way to prepare for an exam: make sure you understand the material. Rather than worrying about what specific problems might or might not be on the test, just make sure the mathematics covered by the test make sense to you, following the suggestions above. Here are some more suggestions specifically with respect to exams:

• Cramming does not work. That is particularly true in mathematics. Instead study steadily throughout the semester, and relax and do something fun the day or the night before the exam.

• It seems that there is always someone who is late for an exam. It may be a trite thing to say, but there is no benefit in being late! Make sure you come to the exam on time and unflustered by having to rush and worry. Just allocate a little more time to your commute than you would normally.

• When you actually receive the exam, relax, and read all the instructions and all the problems, before you start working on any of them.

• Then do those problems that are easy or obvious. Not only does that give you a good start but also it may teach you or remind you of something that's useful for the other problems. There is rarely a good reason to do the problems in exactly the sequence in which they appear on your piece of paper.

• If you get stuck put that problem aside and return to it after you are done with the more tractable problems.

• When you are through and there is time left, don't leave! Instead, check your answers and make sure they are correct. You've spent a lot of time and money getting to the stage where you are taking that exam, and a lot is riding on it. Being able to correct a mistake you made far outweighs the benefits of being able to spend 20 minutes more on whatever else you like to do.

• Even if you feel you don't understand a question, or several questions, at all, don't just leave. Write what you do understand and spend all the time you have available trying to figure out even those problems that appear hopeless.

• After the exam go over the answers as soon as they are available. The exam is not an end in itself, you are here to learn the subject, and reading and thinking about problems you have just wrestled with is extremely helpful in this process.

• Study-Guide: I highly recommend that you check out the detailed on-line study guide written by Peter Alfeld of the Mathematics department here at the University of Utah.