It can be difficult to plan which mathematics courses to take and when. It’s hard to know which courses are most important, and choosing the right times to take each class can be difficult, as well. Here we will try to help you make informed choices about what courses you need.
If you are not a math major:
Your first goal should be the successful completion of Calculus I and II. Math 106 and 107 (Calculus for Biological and Social Sciences) and Math 108 and 109 (Calculus for Engineering and Physical Sciences) are equally challenging sequences. Students needed only Calculus I and II often take 106 and 107, because they are geared to teach the last math you will need. Students intending to continue to Calculus III and Differential Equations will probably find 108-109 more agreeable. Honors variants of these courses will teach more theory and detail, and will make it easier to understand higher mathematics later. But they also will teach fewer applications, so they may not be appropriate for engineers regardless of ability.
After completing Calculus I and II, you may continue to Calculus III, Linear Algebra, and Differential Equations. These three may be taken in any order that fits your schedule, but the listed order is most common.
If you are a math major:
Your first focus will probably be calculus, unless you enter with lots of experience already. We recommend that you take the honors variants whenever possible, because it will prepare you better for higher mathematics, but this is certainly not required. As an entering student, you will probably go into Calculus II, then Linear Algebra, followed by Calculus III. Or perhaps Calculus III followed by Linear Algebra.
The courses 401 (Abstract Algebra) and 405 (Analysis I) are the only two courses absolutely required for all majors. In these courses, you will learn the foundations of modern mathematics, and advanced techniques of proof. Because they are so important, you should take them as soon as you are ready. But because they are fairly difficult, it could be hard to take them too early or to take them simultaneously. Honors Calculus III and Honors Linear Algebra should definitely be enough preparation for both courses. Ask your adviser if you’re not sure whether you’re ready.