Intro Modern Analysis I · Mathematics
How to prove basic calculus concepts (differentiability, continuity, etc) from a rigorous perspective.
The first 6 chapters of Rudin's analysis pretty closely: Properties of real numbers, basic topology and metric spaces, sequences and series, continuity, differentiation, integration.
Prerequisites:MATH UN1202MATH V1202or the equivalent, andMATH V2010. The second term of this course may not be taken without the first.Prerequisites:MATH UN1202or the equivalent, andMATH UN2010. The second term of this course may not be taken without the first. Real numbers, metric spaces, elements of general topology, sequences and series, continuity, differentiation, integration, uniform convergence, Ascoli-Arzela theorem, Stone-Weierstrass theorem
Proof based review of single variable calculus as well as sequences and series of functions.
set theory, compact, series, differentiable and integrable
The fundamentals of modern mathematics - analysis.
Basics of Real Analysis. Fairly rigorous and proof heavy
Very Manageable. The weekly problem sets have 4-5 mandatory questions but generally only 1 or 2 require substantial effort. He also provides optional practice problems on every problem set that are great for studying from (Hint Hint).
An unreasonable amount: 9 homeworks of 10 problems each. some required topology textbooks, others were just painfully long. One was 11 pages for me. The exams literally require that you've seen and remembered the proofs elsewhere, they don't test your knowledge of a process taught by him but of a process either taught in topology or something completely unrelated to analysis (what was his stuff on commutative maps?) or your memory of a proof from some topology book or a half a page long proof in rudin.
Weekly psets, midterm and final, standard grading for the math department (idk if that makes sense), similar workload to other courses of that nature (I.e. similar to intro to modern algebra)