This one-year sequence Honors Mathematics I-II (Math 203-204) is designed for first year students with a strong background in calculus technique. It aims to give students a rigorous understanding of single and multivariable calculus and basic linear algebra, together with their theoretical underpinnings. Along the way, students will be introduced to the language and methods of modern mathematics, with a strong emphasis on proofs.
The prerequisite for enrollment is a score of "5" on the AP Calculus Exam (BC version). If you are one of these students and are interested in a solid theoretical foundation in calculus for future study, possibly as a major in mathematics, then you might consider the one-year sequence Math 203-4. Both courses are 4 units, meeting each week on MTThF. The class will be "medium-sized" rather than "large-lecture" with an enrollment cap somewhere around 45.
In the first semeser, the course will use a classic and challenging textbook (Apostol, Calculus, vol 1); it will start at the beginning of calculus and do a careful treatment of topics, taking advantage of the fact that students already know how to do the standard Calculus I & II calculations. Although students go "back to the beginning," those who complete both Math 203-204 will have covered the material through Calculus III in a rigorous way. They will also have covered a significant part of introductory linear algebra and have developed some ability in reading and writing proofs. On the recommendation of the instructor, students who do well should be able to replace one or two intermediate courses usually taken by math majors with more advanced courses. They will be in a position for a stronger math major and will not have fallen behind: in fact, they may be a course or two more advanced than others by the end of the freshman year. You can see a list of the topics Math 203 will cover in the WUSTL Course Listings online.
Many students who have been very successful in high school calculus (including many who earned a "5" on the BC exam) will still find the regular Calculus III course (Math 233) a better fit for them. Math 203-204 is a more theoretical treatment and of more interest to students who enjoy mathematics and logical reasoning for their own sake. A student who begins with the standard Calculus III course will still be able to complete a strong major in mathematics if desired.
A student who takes Math 203 in the fall but not Math 204 in the spring will NOT have completed an equivalent of Calculus III, although s/he will have received a solid theoretical treatment of Calculus I-II topics and some new ideas as well. But we do recommend that students who enroll in Math 203 should also be planning to take Math 204.
Students who are hesitant about signing up for an intensive "Honors Mathematics" course should remember that for the first week of the semester, a switch into Calculus III (Math 233) is still possible. There is a section of Calculus III (Math 233) that meets in the same hour as Math 203, so the switch will probably not disrupt the rest of your class schedule.
For 2015-2016, Math 203-4 will be taught by a popular instructor, Professor Xiang Tang. You can learn more about Professor Tang on his webpage. This syllabus from the Fall 2015 version of the course should give you some idea about the content. If you have further questions, feel free to send an email to Professor Tang.