Some will have enough previous experience to complete problem sets in a few hours, such as those who have participated extensively in math competitions, but most should expect to work a minimum of 10-15 hours on assignments with high probability, there will be at least one problem set that takes 20+ hours. The beginning of the semester will be an adjustment, but eventually, you will become comfortable with these sorts of questions.įor the students who choose to enroll in 215, it will likely be their most demanding and time-consuming course that semester. A central goal of the course is to build your familiarity with this style of math. applying the root or ratio test, though both make an appearance in the course). does the following series converge?), but even these will go far beyond basic approaches (e.g. A few questions will be more computational in nature (e.g. Rarely will your teacher stop to address the best way to handle a particular class of problems. Lectures follow a common pattern: the professor presents a theorem, supplies a proof or sketch of a proof, and discusses the significance of the result. There are some recurring techniques that you will learn to apply, but homework and exams will require you to maneuver a little differently in each instance. In 215, you will never have a problem this routine. High school math typically involves applying and sometimes slightly modifying a procedure that the teacher has previously demonstrated. First-hand Account of MAT 215įor most students, MAT 215 will be the first course they take in rigorous mathematics. Read more about the introductory courses on the math department website. Update (2019): The fast track is called MAT 216/218, and Gunning’s notes have also been published in the form of a book. The fast track uses Professor Gunning’s notes, which can be found on: The fast track refers to the combination of 215/217/218 integrated in a single year. The regular track refers to the combination of 215 in the fall and 217 in the spring. In short, there will be two sections of math 215/217. The other section, which we will call the regular section, will complete 215 in the fall, 217 in the spring, and students are expected to take 218 in the fall of the following academic year. One section which we will call the fast track will cover the material of 215/217/218 in one year, thus completing all three introductory courses. Students start in MAT215 together during the fall, but will be split into two sections after two to three weeks. The resulting changes in the course structure are significant. One section will introduce students to proofs more fully and gradually, while the other will assume experience with proofs and launch right into the material. To accommodate both of these groups, the math department will be splitting up MAT 215 into two sections. Some incoming math majors will have already seen and done proofs, while others will have not. The math department has recently seen its enrollment rise, which entails an increasing diversity in levels of preparation. MAT 218 concludes with a surprisingly elegant generalization of the fundamental theorem of calculus called Stokes’ Theorem. The course briefly touches on the subject of manifolds, i.e., smooth surfaces, which are important in fields such as topology, differential geometry, and Lie theory. In particular, linear algebra turns out to play a significant role, especially the space Rn and the determinant. Though some of the material at the beginning of MAT 218 might look familiar, fairly soon analysis in several variables takes on a flavor of its own. MAT 218 is in a sense a continuation of MAT 215: it generalizes the concepts of limits, differentiation, and integration from one to multiple dimensions. The majority of the course is spent studying linear transformations between vector spaces and their close relatives, matrices. One example of this is the set of n-tuples of real numbers. The most basic mathematical object this course deals with the vector spaces, a structure whose elements can be added and multiplied by scalars. MAT 217 is a course in linear algebra, a subject at the foundation of almost all branches of pure and applied math. See below for a first-hand description of MAT 215. The remainder of the course is spent on developing the theory of limits, differentiation, integration, sequences, and series. The course starts by addressing the question: what are real numbers? It then introduces its students to important topological preliminaries such as open and closed sets, compactness, and completeness. The goal of MAT 215 is to build the theory of analysis from the ground up, teaching students to think rigorously along the way.
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