Introduction to Mathematical Analysis
Mathematics · 3 hrs Lecture
Offered: Fall/Winter Only, Every Year
MATH-3101 prerequisites
14 courses appear in this chain, up to 6 levels deep. 7 are needed whichever route you take: MATH-1103 → MATH-1104 → MATH-1201 → MATH-1401 → MATH-2105 → MATH-2106 → MATH-2405
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Where MATH-3101 counts
Counts toward 4 more as one option among several, not as a course you must take:
Read from the departments' own calendar pages, where 50 of 208 programs are only partly machine-readable, so treat these as a minimum rather than the full list. Confirm with an academic advisor.
Description
This course provides a careful treatment of the basic concepts of mathematical analysis including properties of the real numbers, countable and uncountable sets, the topology of metric spaces including compactness, connectedness, sequence/series convergence, continuity, and complete metric spaces. Rigorous proofs of the Heine-BoreI theorem, the extreme value theorem, and the intermediate value theorem are given. Other topics studied include differentiation, Riemann-Stieltjes integration, normed linear spaces, uniform convergence and the Stone-Weierstrass theorem, and Fourier analysis.
Requisite courses
MATH-2405(3) and MATH-2106(3), and MATH-2203(3) or MATH-2221(3) [prerequisite(s)].
From the 2026-27 undergraduate calendar. Always verify details on WebAdvisor or with an academic advisor before registering.