General Information
The central difference between Calculus and Algebra is the notion of change. Whereas the letters x,y,z, etc. are used to represent "unknowns" in Algebra, in Calculus they are interpreted as "variables": all situations are viewed as changing (potentially or actually), and the purpose of the Calculus is to be able to make predictions based on the laws of change of the variables.
In order to succeed in Calculus you must be proficient in Algebra, for once the principles of Calculus are applied, the steps toward solution of a problem are algebraic. Many of the ideas of Calculus are based on geometry. A strong background in this subject trigonometry is important. You are urged to take the diagnostic test (download the pdf file from the 1210 online home page) to check for this proficiency. You should complete with ease about 80% of the problems in part I of the diagnostic test.
Given proficiency in geometry, algebra, trigonometry, and a willingness to think in terms of changing rather than static images, you should do well in Calculus. To succeed in an online course, you must also be strongly self-motivated and prepared to work on your own until the topics are mastered. Such independent study, particularly when you must begin by thinking in a way different from the way of Algebra, is a challenge. Online, it is you who must provide the motivation, search for the subtleties, and notice the pitfalls; they will not be presented to you. Having said this, I welcome you to this challenge and will provide as much assistance as possible in this context. I wish you well!
There are three major components to this course:
Assignments. There are 13 sets of 8-16 problems each, to be done on the web using a facility called WebWork. When you submit an answer, you are informed whether or not it is correct. You may redo the problem as often as needed until the closing date. Webwork keeps track of your scores. Your total on assignments counts 26% toward your final grade.
Notes provide a survey of the topics of the course, illustrative examples, and descriptions of methods for solving problems. These lead to the "Practice Problems" and Solutions, pdf files which can be accessed from the Syllabus page. It is strongly recommended that you do these problems, for they are typical of problems in the assignments and examinations. Try to do the problem first, and then compare your work with the solution in the "Answers".
Here is a suggested guide for doing the work of the course. 1. Read the textbook. 2. Read the notes and work the illustrative examples. 3. Do the recommended exercises from the textbook and the practice problems from the notes and compare your work with the given answers. 4. Then go to the Webwork assignments and try to do the first problem. If you get stuck, follow the links. When you understand the problem, submit the answer, and go to the next problem, working through the assignment in this way. At the end of the assignment, return to the problems not yet completed, and repeat this process.
Examinations. There will be two midterm examinations, each counting for 20% of the final grade, and a comprehensive final examination, counting 34% (and finally, WebworK assignments make up the remaining 26%). There is a page on the course website, Past Examinations, from which you can download sample problems and actual past examinations for this course. You may use graphing calculators on the exams, but no notes. Remember that you are graded on the work that you show; just giving the answer is insufficient.
All exams are administered through Distance Education. Instructions on how to register for your exams are located on Distance Education's Online Independent Study webpage (link to http://continue.utah.edu/distance/online.html).
Instructor:
Cynthia Shipley Bestvina, JWB 307, 581-8338, cbestvin@math.utah.edu.
E-mail contact is best way to reach me. I will attempt to answer your emails as quickly as possible, but please allow one business day to be safe.
Text. The text for the course is
Calculus, by Varberg, Purcell and Rigdon, Prentice-Hall, Eighth edition.
The online notes by Prof. Hugo Rossi cover all the material for the course and are strongly recommended to supplement the text. (Professor Rossi's notes are available on the Course Information page.)
Grading Policy
Assignment total 26%
Exam II 20%
Final Exam 34%
______________________
Total 100%
The following scale will be used to determine your course grade:
A 93-100 C 70-74
A- 90-92 C- 65-69
B+ 87-89 D+ 60-64
B 83-86 D 55-59
B- 80-82 D- 50-54
C+ 75-79 E below 50
NOTE: Independent Study policy requires that you pass the final examination in order to pass the class. When you complete this course, your grade ñ whether passing or failing ñ will be recorded with the University of Utah Registrar.
Calculators. You are encouraged to use calculators in this class. Keep in mind however, that it is possible to do every routine calculus problem by pushing a few buttons. Thus, you should anticipate that at least half the problems on examinations will require some complex thinking without the use of calculators and you will be required to show all work on all problems.
Mathematics Center. For University of Utah campus student, The Benny Rushing Mathematics Center (RMC) between LCB and JWB on President's Circle offers study and meeting space, a computer lab, and tutoring services, all free of charge. For more information call Angie Gardiner at 585-9478, send her e-mail at gardiner@math.utah.edu, or visit her in the Center.
General Comments about Online Mathematics Courses
In-class versus online. You may still be wondering if you should take this class online or in-class. The two versions cover the same material. The 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 your own schedule, and wherever it is convenient (literally anywhere on the planet). The main requirements for taking the online version are availability of an internet browser such as Netscape, Safari, Mozilla, or Internet Explorer, your ability and willingness to use e-mail almost daily, and your ability to view/print postscript or pdf files.
About Studying and Learning Mathematics
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.
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. Anybody who has the mathematical prerequisites can study mathematics successfully. Here are some hints for success:
Do your course work regularly and don't fall behind. If you have difficulty with a particular concept, don't set it aside for later; confront it and conquer it. Seek help, from me, from the study center, or from your peers.
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 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. Mathematics at this level is about connections, not about isolated truths or techniques. You can only make those connections by doing complex problems. Always Have High Expectations! Take the time with each problem to fully understand it and to think about what kind of answer to expect. There is only one 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. Cramming does not work. Go over the past exams, check on points that seem fuzzy to you, and then relax with confidence. Confidence level- even if by hypnotic suggestion - is a better predictor of success on exams than late hour cram sessions with the ensuing tensions.