MATH 451 - Advanced Calculus I
Section: 101
Term: SP 2009
Subject: Mathematics (MATH)
Department: LSA Mathematics
Requirements & Distribution:
Credit Exclusions:
No credit granted to those who have completed or are enrolled in MATH 351.
Waitlist Capacity:
Advisory Prerequisites:
Previous exposure to abstract mathematics, e.g. MATH 217 and 412.
Other Course Info:
F, W, Sp.
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
May not be repeated for credit.
Primary Instructor:

This course has two complementary goals: (1) a rigorous development of the fundamental ideas of calculus, and (2) a further development of the student's ability to deal with abstract mathematics and mathematical proofs. The key words here are "rigor" and "proof"; almost all of the material of the course consists in understanding and constructing definitions, theorems (propositions, lemmas, etc.) and proofs. This is considered one of the more difficult among the undergraduate mathematics courses, and students should be prepared to make a strong commitment to the course. In particular, it is strongly recommended that some course which requires proofs (such as MATH 412) be taken before MATH 451. Topics include: logic and techniques of proof; sets, functions, and relations; cardinality; the real number system and its topology; infinite sequences, limits, and continuity; differentiation; integration, and the Fundamental Theorem of Calculus; infinite series; and sequences and series of functions. There is really no other course which covers the material of MATH 451. Although MATH 450 is an alternative prerequisite for some later courses, the emphasis of the two courses is quite distinct. The natural sequel to MATH 451 is 452, which extends the ideas considered here to functions of several variables. In a sense, MATH 451 treats the theory behind MATH 115-116, while MATH 452 does the same for MATH 215 and a part of MATH 216. MATH 551 is a more advanced version of Math 452. MATH 451 is also a prerequisite for several other courses: MATH 575, 590, 596, and 597.

MATH 451 - Advanced Calculus I
Schedule Listing
101 (LEC)
TuWF 9:00AM - 11:00AM
NOTE: Data maintained by department in Wolverine Access. If no textbooks are listed below, check with the department.

ISBN: 9780387904597
Elementary analysis : the theory of calculus, Author: Kenneth A. Ross., Publisher: Springer Corr. 10. 1998
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