Math 51 lectures will be devoted to developing a mixture of the underlying concepts and theory, along with examples and review. Assigned homework problems will NOT be worked out in lecture, although at times some similar "daily discussion problems" will be worked out.
College mathematics courses are much harder than high school courses, and the expectations of the professors are much higher. A rule of thumb is that you should spend two to three hours working outside of class for each in-class hour. Since Math 51 meets six hours and forty minutes each week, this means you should expect to spend 13-20 hours outside of class working on the course material, studying the textbooks, the notes, and working on problems, perhaps even more than those assigned.
In order to be certain of doing well on examinations, it is important that you truly understand the material, and not just memorize certain mechanical techniques. Over 900 students at Stanford complete Math 51 each year. Several hundred of these students go on to study advanced topics in mathematics, statistics, physics, computer science, engineering, economics, and other fields. The Math 50 series courses are designed to make that possible, but a student who just gets by in a basic course (in any subject) by memorizing as needed to get through exams, will probably not be successful at more advanced levels down the road.
Read and take notes on the chapter associated to the exercises before completing them. Reading math takes longer than reading fiction. Be prepared to spend some time studying each section, with pencil and paper nearby to take notes, write down questions, or fill in gaps in the steps given in the book.
Write up neat solutions to homework, not a collection of scrap work that resulted in the right answer. Be critical of your own solutions: Is each step clearly explained? Is the logic sound? Most homework problems will be calculations, but students will also be asked to give some proofs. A proof must be a logical, sequential argument, with no holes, gaps, or errors. To write a satisfactory proof, you must use exact definitions.
It is a very good idea to learn the definitions of terms as they come up in the course. In mathematics, probably more than in any other subject, new ideas are built on and depend on previous ideas. If you fall behind in understanding definitions it can be almost impossible to learn and understand the ideas later on in the course. Don't let that happen! Try to spend some time comprehending the new definitions that come up in each section of the textbook. Homework will also help with this.
Office hours of both the TAs and Professors are an opportunity to discuss difficulties you are having with concepts and homework problems. You will get much more out of coming to office hours if you have spent time beforehand trying to do the problems. All students may go to the office hours of any of the Professors or TAs. These are set at a wide variety of days and times.
We do allow and encourage students to work with each other, and the course staff, in the preliminary stages of completing homework assignments. However, each student must then write up in his or her own words the actual solutions submitted for grading. To simply copy solutions from someone else is an Honor Code violation. Stanford's Honor Code and Fundamental Standard are taken very seriously. By Math Department policy, any student found to be in violation of the Honor Code on any assignment or exam in this course will receive a final course letter grade of NP.
In addition to the office hours of Professors and TAs, Stanford Summer Tutor Program (STP) offers FREE tutoring and academic skills coaching to students enrolled in Stanford's Summer Quarter; just drop in. Math tutoring is held in the Organic Chemistry Building, and the weekly schedule is posted here.