FUNDAMENTALS OF SET THEORY

Name: FUNDAMENTALS OF SET THEORY
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MATH 570

과목 설명

Introduces the basic concepts of Set Theory including: Set-theoretical paradoxes and means of avoiding them, sets, relations, functions, orders and well-orders, proof by transfinite induction and definitions by transfinite recursion, cardinal and ordinal numbers and their arithmetic, construction of the real numbers, the axiom of choice and its consequences.

선수과목

(MATH 234 and MATH 467 ) or (MATH 341 , MATH 375 , MATH 421 or MATH 521 ) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

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평점

2.89

-3.7% 과거 데이터 대비

수료율

77.78%

-11.31% 과거 데이터 대비

A 비율

33.33%

-1.52% 과거 데이터 대비

학급 규모

10.77% 과거 데이터 대비

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유사 과목

FOUNDATIONS OF MATHEMATICS

MATH 770

First-order logic syntax and semantics, Completeness and Compactness Theorems, Lowenheim-Skolem Theorem, computable and computably enumerable sets, Incompleteness Theorem, axioms of Zermelo-Fraenkel set theory with choice, ordinal and cardinal arithmetic.

INTRODUCTION TO DISCRETE MATHEMATICS

COMPSCI/MATH 240

Basic concepts of logic, sets, partial order and other relations, and functions. Basic concepts of mathematics (definitions, proofs, sets, functions, and relations) with a focus on discrete structures: integers, bits, strings, trees, and graphs. Propositional logic, Boolean algebra, and predicate logic. Mathematical induction and recursion. Invariants and algorithmic correctness. Recurrences and asymptotic growth analysis. Fundamentals of counting.

MODEL THEORY

MATH 776

Review of compactness and some consequences. Quantifier elimination with examples. The omitting types theorem. Categoricity. Baldwin-Lachlan theory. Strongly minimal and o-minimal theories. Saturated models. Morley's theorem. Familiarity with the topics in a basic Foundations course such asMATH 770is strongly recommended.

ANALYSIS I

MATH 521

The real numbers, elements of set theory, metric spaces and basic topology, sequences and series, limits, continuity, differentiation, integration, sequences and series of functions, uniform convergence.

SET THEORY

MATH 771

Martin's Axiom, Suslin and Aronszajn trees, diamond principle, absoluteness and reflection, constructible universe, and one-step forcing constructions. Familiarity with the topics in a basic Foundations course such asMATH 770is strongly recommended.