University of Connecticut

Advanced Calculus

An accelerated program 

This four-course sequence, Math 2141QMath 2142QMath 2143QMath 2144Q,  designed to recognize the developments in the advanced math high school curricula or college calculus and, using that as a starting point, continue mathematical training in the spirit of higher level mathematics and theoretical science and engineering.

Among the paths into advanced mathematics, both for its own sake and for its utility in other disciplines, Advanced Calculus places the greatest emphasis on understanding and proofs of key ideas.

Students are assumed to have learned most standard calculus computations in high school, Math 1131Q-1132Q or Math 1151Q-1152Q; for that reason, students taking Math 2141 retain their AP calculus and ECE calculus credit. For non-math majors, successful completion of the sequence will satisfy the requirements for a minor in mathematics.

The initial course (Math 2141) differs from the standard AP Calculus curriculum in that little attention will be devoted to routine drill and more attention given to theory and a deeper level of understanding. Throughout the sequence, the order of the material covered will be substantively different from standard calculus courses such as our 1131Q-1132Q-2110Q-2410Q or 1151Q-1152Q-2130Q-2420Q sequences. Starting with series, drill will be included but the emphasis on thinking rather than memorization is retained.

Analysis or advanced calculus courses cover much of the same material as do calculus courses but the different point of view makes that kinship virtually unrecognizable to people who have only taken skill-oriented math courses. The theoretical point of view is essential to advanced study in mathematics and is a fundamental need for people planning careers involving theoretical science and engineering. Indeed, the emphasis on theory is accompanied by practice in how to “learn from one’s mistakes.” Since quality experimental work rarely succeeds on the first try, one must gain insight from previous tries in all of these areas.

The second edition of Apostol’s Calculus, Vol. 1 (ISBN: 9780471000051) will be the text for the first two semesters.

The sequence requires serious effort and mathematical talent. It is designed as a course for entering freshmen and also for sophomores who have taken calculus at the university. The freshmen who have taken calculus in high school should have grades which are the equivalent of a 4 or 5 on the AP AB-calculus exam and a score of over 700 on the Math SAT.  Registration for Math 2141 requires permission of either of the instructors; their names will be available either on the Mathematics Department website or on PeopleSoft.

If you think you are interested in, and qualified for, the sequence, please contact either of the instructors before or during registration or during the week before classes. For more information, you might want to read an informal discussion of Advanced Calculus.

The prequisite for any of the subsequent courses is its predecessor or permission of the instructor. Each semester of this sequence is 4 credits. It may be taken for honors credit but is open to any qualified student.