Real Analysis I
Mathematics · 3 hrs Lecture
Offered: Fall Or Winter, Every Year
MATH-2405 prerequisites
2 courses appear in this chain, up to 2 levels deep. 1 is needed whichever route you take: MATH-1401
Part of this course's requisite text couldn't be parsed into structure, so the chain below may be incomplete. The full wording is under “Requisite courses”.
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Minimum grade of C in both MATH-1104
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Where MATH-2405 counts
Counts toward 3 more as one option among several, not as a course you must take:
Read from the departments' own calendar pages, where 71 of 141 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 lays the theoretical foundation of single-variable calculus by providing a careful introduction to several fundamental concepts of analysis on the real line, and it provides a gateway to more advanced studies in analysis, topology and set theory. Topics covered include: functions acting on sets; countable and uncountable sets; suprema and infima; properties of the real numbers including completeness, the Archimedean property and density of the rational numbers in the real numbers; sequence convergence, monotone sequences, subsequences, the Bolzano-Weierstrass theorem and Cauchy sequences; limits of functions; continuous functions including proofs of the extreme and intermediate value theorems.
Requisite courses
Minimum grade of C in both MATH-1104 and MATH-1401 [prerequisite(s)].
From the 2026-27 undergraduate calendar. Always verify details on WebAdvisor or with an academic advisor before registering.