You've attended all the seminars, gone to Freshman Advising, read the Course
Catalogue, and you still have no idea what math class you're really supposed
to take this year. Selfdetermination is great most of the time, but sometimes
you just want someone to tell you what to do. Here, compiled from the
comments of members of the class of 2006, is an honest assessment of the
freshman math offerings. Note: These opinions are not compiled by the Mathematics department and are intended only as guidance. Exceptions to the generalizations stated below are fairly frequent. When in doubt, ignore your misgivings and talk to the Math Head Tutor. Worst comes to worst, the advice is lousy, but the Head Tutor is then to blame, not you. 
A thorough treatment of multivariable calculus and linear algebra with reallife applications. Assigned problems (especially in 21a) use numbers more often than not, and proofs are limited to nonrigorous examples (basically commonsense proofs). Class meets three hours per week, and homework usually takes three to six hours per week to complete. Many sections are taught by graduate students, which means that it is possible to switch sections (and thus instructors) if necessary, but there may be little contact with professors. This sequence is a very efficient way to learn calculus and linear algebra, but the lack of proofs does not imply that the classes are easy. These courses have ranged from very reasonable (Fall 2002) to hard (Fall 2001). 
You should take this class if one or more of these describes you:

A class that covers linear algebra and multivariable calculus while also teaching proofwriting, starting with the basics. Problems still use numbers but also employ the formal terminology of advanced mathematics. Class meets three hours per week, and problem sets can take anywhere from five to fifteen hours per week. Students usually complete problem sets by working in groups a night or two before the sets are due; many students find that working in a group of similarlyabled peers turns out to be one of the most rewarding aspects of this class. This class is always taught by a faculty member; in previous years, the instructor has been someone who enjoys teaching and explains things well. It is not, in principle, supposed to be as homework intensive as Math 25. 
You should take this class if one or more of these describes you:

A rigorous treatment of multivariable calculus, linear algebra, and introductions to other topics in advanced mathematics. This class is a springboard to the study of advanced math; the class thoroughly covers its topics but moves very quickly, and examples tend to be theoretical instead of concrete. Class meets three hours per week and homework can take from seven to fifteen hours per week to complete. The course is taught by a professor; previous instructors have varied greatly in teaching ability and prestige. A previous knowledge of proofs, linear algebra, or multivariable calculus is helpful, but not necessary. However, being 'gungho' about mathematics is a definite prerequisite. 
You should take this class if one or more of
these describes you:

This is probably the most difficult undergraduate math class in the country; a variety of advanced topics in mathematics are covered, and problem sets ask students to prove many fundamental theorems of analysis and linear algebra. Class meets three hours per week, plus one hour of section, and problem sets can take anywhere from 24 to 60 hours to complete. This class is usually small and taught by a wellestablished and prominent member of the faculty whose teaching ability can vary from year to year. A thorough knowledge of multivariable calculus and linear algebra is almost absolutely required, and any other prior knowledge can only help. Students who benefit the most from this class have taken substantial amounts of advanced mathematics and are fairly fluent in the writing of proofs. Due to the necessity of working in groups and the extensive amount of time spent working together, students usually meet some of their best friends in this class. The difficulty of this class varies with the professor, but the class often contains former members of the International Math Olympiad teams, and in any event, it is designed for people with some years of university level mathematical experience. In order to challenge all students in the class, the professor can opt to make the class very, very difficult. 
You should take this class
if one or more of these describes you:

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