현재 이 사이트는 활발히 개발 중입니다. 문제를 발견하시면 신고해 주세요! - 문제 신고하기

COMPUTABILITY THEORY

MATH 773
과목 설명

Turing degree and jump, strong reducibilities, arithmetic hierarchy, index sets, simple and (hyper)hypersimple sets, easy forcing arguments in computability theory, finite and infinite injury, Friedberg-Muchnik and Sacks Splitting Theorem, Sacks Jump and Sacks Density Theorems, computable ordinals. Familiarity with the topics in a basic Foundations course such asMATH 770is strongly recommended.

선수과목

Graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

충족 요건

This course does not satisfy any prerequisites.

학점

미보고

개설 시기

미보고

평점
3.21

-7.02% 과거 데이터 대비

수료율
100%

8% 과거 데이터 대비

A 비율
42.86%

-34.5% 과거 데이터 대비

학급 규모
7

46.91% 과거 데이터 대비

Cumulative Grade Distribution

강사 (2026 Summr)

다음 사이트의 평점순으로 정렬 Rate My Professors

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 THEORY OF COMPUTING

COMPSCI 520

Basics about the notion, capabilities, and limitations of computation: elements of finite automata and regular languages, computability theory, and computational complexity theory. Additional topics include context-free grammars and languages, and complexity-theoretic cryptography.

COMPUTATIONAL COMPLEXITY

COMPSCI 710

Study of the capabilities and limitations of efficient computation. Relationships between models representing capabilities such as parallelism, randomness, quantum effects, and non-uniformity; and models based on the notions of nondeterminism, alternation, and counting, which capture the complexity of important problems. Knowledge of the theory of computation is strongly encouraged, such asCOMP SCI 520.

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.

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.