I understand you're looking for information about . This is a specific, upper-division course, and I want to give you a thorough, accurate breakdown.
MATH 327 is a rite of passage for UW math majors. It’s the moment you stop being a calculator and start becoming a mathematician.
The course begins by dismantling the intuition you built in calculus. In calculus, you dealt with "continuous" functions as those you could draw without lifting a pencil. In Math 327, you learn that intuition is dangerous. math 327 uw
| Component | Weight | |-----------|--------| | Weekly homework | 20–25% | | Two midterms (in class) | 20–25% each | | Final exam (cumulative) | 30–35% | | Quiz section participation/quizzes | 5–10% |
This problem tests: understanding of convergence definition, proof by contradiction, and epsilon choice. I understand you're looking for information about
Diving into convergence, Cauchy sequences, and the Bolzano-Weierstrass Theorem.
| Week | Topics | |------|--------| | 1 | – Quantifiers, negation, basic set operations, functions, injectivity/surjectivity. | | 2 | The Real Numbers – Axioms of an ordered field, completeness axiom, supremum/infimum, Archimedean property. | | 3 | Sequences I – Definition of convergence, epsilon-N proofs, uniqueness of limits, boundedness. | | 4 | Sequences II – Monotone Convergence Theorem, subsequences, Bolzano-Weierstrass Theorem. | | 5 | Cauchy Sequences – Definition, Cauchy Criterion for convergence, completeness of R. | | 6 | Limits of Functions – Epsilon-delta definition, sequential criterion for limits, limit laws. | | 7 | Continuity – Definition, combinations of continuous functions, continuity on intervals (Intermediate Value Theorem). | | 8 | More Continuity – Extreme Value Theorem, uniform continuity (introduction). | | 9 | Differentiation – Definition of derivative, derivative rules, Carathéodory’s formulation (sometimes). | | 10 | Mean Value Theorem & Applications – Rolle’s theorem, MVT, Cauchy MVT, L’Hôpital’s rule, Taylor’s theorem with remainder. | It’s the moment you stop being a calculator
Understanding the least upper bound property and why the "completeness" of real numbers matters.