# MATH 570: Fundamentals of Set Theory | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_570)

## Dataset

### revision

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## course

### run id

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### semester

1272

### observed at

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### course id

MATH 570

### course uid

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### catalog version id

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### course number

570

### subjects

* MATH

### title

FUNDAMENTALS OF SET THEORY

### description

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.

### requirements text

(MATH 234and467) or (MATH 341,375,421or521) or graduate/professional standing or member of the Pre-Masters Mathematics (Visiting International) Program

### credit offering ids

None recorded.

### llm job id

enrich-f516c4d3e82cfe326b4f5f54

### llm output id

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### llm model revision

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### llm task version

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### llm search status

valid

### llm summary

Covers set theory fundamentals, transfinite methods, cardinal/ordinal arithmetic, and real number construction.

### llm topics

* Set-theoretical paradoxes.
* Sets, relations, functions, orders, and well-orders.
* Cardinal and ordinal numbers.
* Axiom of choice and consequences.

### llm skills

* Transfinite induction and recursion.
* Construction of real numbers from set-theoretic foundations.
* Cardinal and ordinal arithmetic.

### llm assumed background

* Foundational set theory, logic, and proof techniques.
* Multivariable calculus and linear algebra.

### llm search phrases

* set theory axioms
* transfinite induction
* cardinal arithmetic
* real number construction
* axiom of choice consequences

### llm requirements status

valid

### llm student summary status

valid

### llm experience status

valid

### catalog variants

None recorded.

### student summary

#### context hash

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#### course id

MATH 570

#### current instructors

None recorded.

#### difficulty workload

Historical reviews of Uri Andrews: The course content closely follows the textbook, with a moderate difficulty level rated at 3 out of 5.

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#### errors

None recorded.

#### historical context

Historical instructor Uri Andrews is described as an awesome lecturer who makes set theory and logic engaging through insights and humor. Reviewers note the course follows the textbook closely, making him a strong choice for a solid undergraduate introduction to the subject.

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#### offered

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#### profile hash

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#### quick take

Historical reviews of Uri Andrews: Uri Andrews provides a solid undergraduate introduction to set theory and logic, making lectures worthwhile through his insights and humor.

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Recent recorded grades — Fall 2020: 3.42 GPA, 75.0% A/AB (n=12 letter grades); Fall 2022: 2.89 GPA, 44.4% A/AB (n=18 letter grades); Fall 2025: 3.65 GPA, 80.0% A/AB (n=10 letter grades).

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#### student experience

Historical reviews of Uri Andrews: Students find lectures engaging due to the instructor's jokes and t-shirts, though the curriculum is primarily textbook-driven.

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#### teaching history

URI ANDREWS is recorded teaching in Fall 2016. Recorded history may be incomplete and does not establish a future schedule.

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#### term name

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#### version

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#### notes

* Fixed missing node references for condition nodes n3 and n4.
* Updated evidence strings for n1 and n2 to exactly match source substrings as required by validation.
* Ensured condition nodes n3 and n4 preserve verbatim source text and include the required 'evidence' property.
* Set condition field for n3 and n4 to the verbatim source substring.

#### root

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#### status

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### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

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          "difficulty": 4.71,
          "quality_count": 7,
          "difficulty_count": 7
        },
        "course_4aa5bbed0c86993f5f0dc832": {
          "review_count": 1,
          "quality": 3,
          "difficulty": 4,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_3f55e55b94f0e0724493de53": {
          "review_count": 2,
          "quality": 3,
          "difficulty": 3.5,
          "quality_count": 2,
          "difficulty_count": 2
        },
        "course_fa53f4954bab469b5d4c4fe3": {
          "review_count": 1,
          "quality": 3,
          "difficulty": 4,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_63c43e7ac8225e2773df74d8": {
          "review_count": 1,
          "quality": 1,
          "difficulty": 5,
          "quality_count": 1,
          "difficulty_count": 1
        },
        "course_6bc496e4640fd08f71e1b041": {
          "review_count": 2,
          "quality": 1.5,
          "difficulty": 5,
          "quality_count": 2,
          "difficulty_count": 2
        }
      },
      "bayesian_quality": 2.3336015219859463,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 2.843,
      "graded": 1712,
      "counts": [
        400,
        271,
        386,
        204,
        251,
        148,
        52
      ],
      "sections": 50
    },
    "instructor_url": "/instructors/STEFFEN_LEMPP"
  },
  {
    "instructor_uid": "instructor_e0fb56b7bae68763eeb2fd33",
    "source": "madgrades",
    "source_instructor_id": "5178712",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "JUN LE GOH",
    "email": null,
    "first_observed_at": "2026-09-06 23:14:58.172943+00:00",
    "last_observed_at": "2026-09-07 15:55:43.033547+00:00",
    "ratings": {
      "review_count": 17,
      "quality": 3.24,
      "difficulty": 3.94,
      "quality_count": 17,
      "difficulty_count": 17,
      "profile_id": "rmp:2526934",
      "source_url": "https://www.ratemyprofessors.com/professor/2526934",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:29:29.569922+00:00",
      "courses": {
        "course_9a1a7bf1933981bcbaca47ac": {
          "review_count": 14,
          "quality": 2.86,
          "difficulty": 4,
          "quality_count": 14,
          "difficulty_count": 14
        },
        "course_63c43e7ac8225e2773df74d8": {
          "review_count": 2,
          "quality": 5,
          "difficulty": 3.5,
          "quality_count": 2,
          "difficulty_count": 2
        }
      },
      "bayesian_quality": 3.4668571802954573,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 3.329,
      "graded": 650,
      "counts": [
        230,
        181,
        137,
        49,
        31,
        15,
        7
      ],
      "sections": 9
    },
    "instructor_url": "/instructors/JUN_LE_GOH--instructor_e0fb56b7bae68763eeb2fd33"
  },
  {
    "instructor_uid": "instructor_1078565b279a801a06f86832",
    "source": "madgrades",
    "source_instructor_id": "6492122",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "MANLIO VALENTI",
    "email": null,
    "first_observed_at": "2026-09-06 23:14:58.172943+00:00",
    "last_observed_at": "2026-09-07 15:55:43.033547+00:00",
    "ratings": {
      "review_count": 3,
      "quality": 3.67,
      "difficulty": 3,
      "quality_count": 3,
      "difficulty_count": 3,
      "profile_id": "rmp:2872255",
      "source_url": "https://www.ratemyprofessors.com/professor/2872255",
      "match_basis": "exact_name",
      "observed_at": "2026-09-07 16:21:24.542748+00:00",
      "courses": {
        "course_63c43e7ac8225e2773df74d8": {
          "review_count": 3,
          "quality": 3.67,
          "difficulty": 3,
          "quality_count": 3,
          "difficulty_count": 3
        }
      },
      "bayesian_quality": 3.6610311161274747,
      "prior_mean": 3.6596857835465957,
      "prior_weight": 20
    },
    "grade_statistics": {
      "gpa": 2.948,
      "graded": 97,
      "counts": [
        36,
        10,
        20,
        6,
        13,
        6,
        6
      ],
      "sections": 5
    },
    "instructor_url": "/instructors/MANLIO_VALENTI"
  },
  {
    "instructor_uid": "instructor_8cf924023df1ff56004e1ca1",
    "source": "madgrades",
    "source_instructor_id": "6803789",
    "identity_basis": "source_id",
    "identity_status": "source_identified",
    "name": "ISABELLA SCOTT",
    "email": null,
    "first_observed_at": "2026-09-06 23:14:58.172943+00:00",
    "last_observed_at": "2026-09-07 15:55:43.033547+00:00",
    "grade_statistics": {
      "gpa": 3.478,
      "graded": 228,
      "counts": [
        123,
        40,
        30,
        18,
        11,
        4,
        2
      ],
      "sections": 3
    },
    "instructor_url": "/instructors/ISABELLA_SCOTT--instructor_8cf924023df1ff56004e1ca1"
  }
]
```

### grades

```json
[
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 570",
    "course_uid": "course_e9cad4922428a06d854a5cf9",
    "term_id": "1172",
    "term_name": "Fall 2016",
    "instructors": [
      "Uri Andrews"
    ],
    "a": 7,
    "ab": 4,
    "b": 4,
    "bc": 2,
    "c": 3,
    "d": 1,
    "f": 0,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 21,
    "source_aliases": [
      "MATH 570"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 570",
    "course_uid": "course_e9cad4922428a06d854a5cf9",
    "term_id": "1192",
    "term_name": "Fall 2018",
    "instructors": [
      "STEFFEN LEMPP"
    ],
    "a": 4,
    "ab": 3,
    "b": 0,
    "bc": 1,
    "c": 3,
    "d": 1,
    "f": 1,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 13,
    "source_aliases": [
      "MATH 570"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 570",
    "course_uid": "course_e9cad4922428a06d854a5cf9",
    "term_id": "1212",
    "term_name": "Fall 2020",
    "instructors": [
      "JUN LE GOH"
    ],
    "a": 5,
    "ab": 4,
    "b": 0,
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    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
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    "total": 13,
    "source_aliases": [
      "MATH 570"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 570",
    "course_uid": "course_e9cad4922428a06d854a5cf9",
    "term_id": "1232",
    "term_name": "Fall 2022",
    "instructors": [
      "MANLIO VALENTI"
    ],
    "a": 6,
    "ab": 2,
    "b": 5,
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    "c": 1,
    "d": 4,
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    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
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    "total": 18,
    "source_aliases": [
      "MATH 570"
    ]
  },
  {
    "run_id": "20260907T155543-ce3781c4",
    "semester": "1272",
    "observed_at": "2026-09-07 15:55:43.033547+00:00",
    "course_id": "MATH 570",
    "course_uid": "course_e9cad4922428a06d854a5cf9",
    "term_id": "1262",
    "term_name": "Fall 2025",
    "instructors": [
      "Isabella Scott"
    ],
    "a": 6,
    "ab": 2,
    "b": 1,
    "bc": 1,
    "c": 0,
    "d": 0,
    "f": 0,
    "satisfactory": 0,
    "unsatisfactory": 0,
    "credit": 0,
    "no_credit": 0,
    "passed": 0,
    "incomplete": 0,
    "no_work": 0,
    "not_reported": 0,
    "other": 0,
    "total": 10,
    "source_aliases": [
      "MATH 570"
    ]
  }
]
```

### statistics

#### gpa

3.128

#### graded

74

#### counts

* 28
* 15
* 10
* 6
* 8
* 6
* 1

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_e9cad4922428a06d854a5cf9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_e9cad4922428a06d854a5cf9-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_e9cad4922428a06d854a5cf9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_e9cad4922428a06d854a5cf9-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_e9cad4922428a06d854a5cf9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_e9cad4922428a06d854a5cf9-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_e9cad4922428a06d854a5cf9-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_e9cad4922428a06d854a5cf9-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.1283783783783785

#### count

74

#### university

##### size

2863

##### gpa Percentile

5

##### count Percentile

37

##### median Count

103

##### histogram

| range   | count | current |
| ------- | ----- | ------- |
| 0.0–0.4 | 0     | false   |
| 0.4–0.8 | 0     | false   |
| 0.8–1.2 | 0     | false   |
| 1.2–1.6 | 0     | false   |
| 1.6–2.0 | 0     | false   |
| 2.0–2.4 | 0     | false   |
| 2.4–2.8 | 7     | false   |
| 2.8–3.2 | 229   | true    |
| 3.2–3.6 | 785   | false   |
| 3.6–4.0 | 1842  | false   |

#### departments

```json
[
  {
    "subject": "MATH",
    "comparison": {
      "size": 73,
      "gpaPercentile": 25,
      "countPercentile": 29,
      "medianCount": 173,
      "histogram": [
        {
          "range": "0.0–0.4",
          "count": 0,
          "current": false
        },
        {
          "range": "0.4–0.8",
          "count": 0,
          "current": false
        },
        {
          "range": "0.8–1.2",
          "count": 0,
          "current": false
        },
        {
          "range": "1.2–1.6",
          "count": 0,
          "current": false
        },
        {
          "range": "1.6–2.0",
          "count": 0,
          "current": false
        },
        {
          "range": "2.0–2.4",
          "count": 0,
          "current": false
        },
        {
          "range": "2.4–2.8",
          "count": 2,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 25,
          "current": true
        },
        {
          "range": "3.2–3.6",
          "count": 19,
          "current": false
        },
        {
          "range": "3.6–4.0",
          "count": 27,
          "current": false
        }
      ]
    }
  }
]
```

### terms

#### 1172

##### term

1172

##### gpa

3.142857142857143

##### count

21

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1192

##### term

1192

##### gpa

2.769230769230769

##### count

13

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1212

##### term

1212

##### gpa

3.4166666666666665

##### count

12

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1232

##### term

1232

##### gpa

2.888888888888889

##### count

18

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

#### 1262

##### term

1262

##### gpa

3.65

##### count

10

##### departments

| subject | comparison |
| ------- | ---------- |
| MATH    |            |

### benchmarks

#### all

##### school

###### size

2863

###### gpa

3.66186519788458

###### top Share

81.98473215341427

###### count

103

##### MATH

###### size

73

###### gpa

3.4467058069937333

###### top Share

68.35289849299923

###### count

173

#### terms

##### 1172

###### school

###### size

991

###### gpa

3.465129042641772

###### top Share

69.42600667567366

###### count

67

###### MATH

###### size

36

###### gpa

3.098601909983034

###### top Share

48.67573746500224

###### count

66

##### 1192

###### school

###### size

1077

###### gpa

3.50327634323125

###### top Share

72.44641925727845

###### count

67

###### MATH

###### size

39

###### gpa

3.1003216533236415

###### top Share

50.01588968281552

###### count

99

##### 1212

###### school

###### size

1111

###### gpa

3.5856416028074487

###### top Share

77.58926748660845

###### count

68

###### MATH

###### size

41

###### gpa

3.3211331103538813

###### top Share

59.85093623917685

###### count

87

##### 1232

###### school

###### size

1216

###### gpa

3.575457431972425

###### top Share

77.33712216234007

###### count

66

###### MATH

###### size

43

###### gpa

3.2486774162409366

###### top Share

56.56203211471963

###### count

69

##### 1262

###### school

###### size

1320

###### gpa

3.628825763035853

###### top Share

80.21118846327654

###### count

70

###### MATH

###### size

43

###### gpa

3.2481769276584003

###### top Share

56.325967864851854

###### count

81

## instructor Trends

```json
[
  {
    "uid": "instructor_94ccac6a4bdcb82edf344586",
    "name": "URI ANDREWS",
    "count": 21,
    "terms": [
      {
        "term": "1172",
        "count": 21,
        "sections": 1,
        "gpa": 3.142857142857143
      }
    ]
  },
  {
    "uid": "instructor_1078565b279a801a06f86832",
    "name": "MANLIO VALENTI",
    "count": 18,
    "terms": [
      {
        "term": "1232",
        "count": 18,
        "sections": 1,
        "gpa": 2.888888888888889
      }
    ]
  },
  {
    "uid": "instructor_cdebe12f82db274ba9d0eda3",
    "name": "STEFFEN LEMPP",
    "count": 13,
    "terms": [
      {
        "term": "1192",
        "count": 13,
        "sections": 1,
        "gpa": 2.769230769230769
      }
    ]
  },
  {
    "uid": "instructor_e0fb56b7bae68763eeb2fd33",
    "name": "JUN LE GOH",
    "count": 12,
    "terms": [
      {
        "term": "1212",
        "count": 12,
        "sections": 1,
        "gpa": 3.4166666666666665
      }
    ]
  },
  {
    "uid": "instructor_8cf924023df1ff56004e1ca1",
    "name": "ISABELLA SCOTT",
    "count": 10,
    "terms": [
      {
        "term": "1262",
        "count": 10,
        "sections": 1,
        "gpa": 3.65
      }
    ]
  }
]
```

## following

None recorded.
