# MATH 561: Differential Geometry | UW–Madison

[View on UW Courses](https://uwcourses.com/courses/MATH_561)

## Dataset

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

### repository

twangodev/uwcourses

### schema version

6

### importer version

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### observed at

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### built at

2026-09-10T23:19:01.870283+00:00

### courses

8951

### current instructors

5754

### limited

false

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### term

1272

### departments

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| --------- | ----- |
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| ASIANAM   | 28    |
| ASTRON    | 38    |
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| HDFS      | 41    |
| HEBR-BIB  | 13    |
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| HISTORY   | 233   |
| HISTSCI   | 56    |
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| ILS       | 43    |
| INFOSYS   | 9     |
| INTEGART  | 7     |
| INTEGSCI  | 22    |
| INTER-AG  | 18    |
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| INTEREGR  | 16    |
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| MEDPHYS   | 39    |
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| MILSCI    | 16    |
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| MS\&E     | 59    |
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| NAVSCI    | 20    |
| NE        | 44    |
| NEURODPT  | 11    |
| NEUROL    | 7     |
| NEURSURG  | 4     |
| NTP       | 11    |
| NURSING   | 111   |
| NUTRSCI   | 65    |
| OBS\&GYN  | 18    |
| OCCTHER   | 39    |
| ONCOLOGY  | 14    |
| OPHTHALM  | 5     |
| OTM       | 43    |
| PATH      | 34    |
| PATH-BIO  | 29    |
| PEDIAT    | 26    |
| PHARMACY  | 31    |
| PHILOS    | 77    |
| PHMCOL-M  | 11    |
| PHMPRAC   | 45    |
| PHMSCI    | 60    |
| PHYASST   | 37    |
| PHYSICS   | 88    |
| PHYSIOL   | 3     |
| PHYTHER   | 37    |
| PLANTSCI  | 52    |
| PLPATH    | 35    |
| POLISCI   | 192   |
| POPHLTH   | 58    |
| PORTUG    | 33    |
| PSYCH     | 101   |
| PSYCHIAT  | 22    |
| PUBAFFR   | 54    |
| PUBLHLTH  | 23    |
| RADIOL    | 11    |
| REALEST   | 41    |
| RELIGST   | 90    |
| RHABMED   | 9     |
| RMI       | 24    |
| RP\&SE    | 102   |
| S\&APHM   | 17    |
| SCANDST   | 73    |
| SLAVIC    | 89    |
| SOC       | 149   |
| SOCWORK   | 87    |
| SOILSCI   | 46    |
| SPANISH   | 83    |
| SRMED     | 21    |
| STAT      | 94    |
| STDYABRD  | 52    |
| STS       | 8     |
| SURGERY   | 25    |
| SURGSCI   | 33    |
| THEATRE   | 91    |
| URBRPL    | 60    |
| UROLOGY   | 5     |
| ZOOLOGY   | 89    |

## course

### run id

20260907T155543-ce3781c4

### semester

1272

### observed at

2026-09-07 15:55:43.033547+00:00

### record version id

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### course id

MATH 561

### course uid

course\_a133a953d2fc593f17f887bf

### catalog version id

8c630ee0762d4b6bf686d579a75164a9f1e4aceb4acb0a99c86252dfe7d0b851

### course number

561

### subjects

* MATH

### title

DIFFERENTIAL GEOMETRY

### description

Theory of curves and surfaces by differential methods.

### requirements text

(MATH 320,340,341,345, or375) and (MATH 322,341,376,421,467, or521), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate)

### credit offering ids

None recorded.

### llm job id

enrich-f516c4d3e82cfe326b4f5f54

### llm output id

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### llm model

nvidia/Qwen3.6-35B-A3B-NVFP4

### llm model revision

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### llm task version

14

### llm search status

valid

### llm summary

MATH 561 covers the theory of curves and surfaces using differential methods.

### llm topics

* Curves and surfaces
* Differential methods

### llm skills

* Applying differential methods to study curves and surfaces

### llm assumed background

* Linear algebra and multivariable calculus
* Partial differential equations

### llm search phrases

* differential geometry
* curves and surfaces
* differential methods
* MATH 561
* graduate mathematics

### llm requirements status

needs\_review

### llm student summary status

valid

### llm experience status

valid

### catalog variants

None recorded.

### student summary

#### context hash

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#### course id

MATH 561

#### current instructors

None recorded.

#### difficulty workload

Historical reviews of Ruobing Zhang: The final exam is described as extremely difficult and tough graded, with some formulae considered obvious by the instructor. One reviewer regretted not dropping the course after the midterm.

```json
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      "type": "review"
    }
  ]
}
```

#### errors

None recorded.

#### historical context

Historical reviews of Ruobing Zhang: Ruobing Zhang is described as an outstanding mathematician with engaging lectures, but his course is extremely difficult and poorly graded. Reviewers report that the final exam is exceptionally tough and the material often lacks clarity, leading some students to drop the class.

```json
{
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      "source_instructor_id": "rmp:3065186",
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      "review_date": "2025-05-08 20:37:30 +0000 UTC",
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}
```

#### offered

false

#### profile hash

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#### quick take

Historical reviews of Ruobing Zhang: Ruobing Zhang's MATH 561 is a challenging graduate-level course that may not suit students without a strong pure math background. Reviews indicate significant frustration with the final exam's difficulty and grading.

```json
{
  "citations": [
    {
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      "review_date": "2025-04-22 01:50:53 +0000 UTC",
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      "run_id": "20260907T155543-ce3781c4",
      "source_instructor_id": "rmp:3065186",
      "source_review_id": "UmF0aW5nLTQwOTk4MjMx",
      "source_url": "https://www.ratemyprofessors.com/professor/3065186",
      "type": "review"
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    {
      "instructor_name": "Ruobing Zhang",
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}
```

Recent recorded grades — Spring 2024: 3.23 GPA, 61.5% A/AB (n=13 letter grades); Spring 2025: 3.45 GPA, 71.4% A/AB (n=21 letter grades); Spring 2026: 3.50 GPA, 76.2% A/AB (n=21 letter grades).

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```

#### student experience

Historical reviews of Ruobing Zhang: Students report that the course did not cover materials stated in the first class. The instructor's teaching style can be confusing, with unclear derivations of formulae.

```json
{
  "citations": [
    {
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```

#### task hash

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#### teaching history

MUSTAFA KALAFAT is recorded teaching in Spring 2010. Recorded history may be incomplete and does not establish a future schedule.

```json
{
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}
```

RUIFANG SONG is recorded teaching in Spring 2014. Recorded history may be incomplete and does not establish a future schedule.

```json
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      "run_id": "20260907T155543-ce3781c4",
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      },
      "table": "section_grades_latest",
      "term_id": "1144",
      "type": "grade"
    }
  ]
}
```

RUOBING ZHANG is recorded teaching in Spring 2025. Recorded history may be incomplete and does not establish a future schedule.

```json
{
  "citations": [
    {
      "course_id": "MATH 561",
      "run_id": "20260907T155543-ce3781c4",
      "section_number": 1,
      "source_course_id": "ba3943cc-ecb5-3d2a-bb73-4ac4433fd0b6",
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      "table": "section_grades_latest",
      "term_id": "1254",
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}
```

#### term id

1272

#### term name

2026 Fall

#### version

2

### requirements

#### nodes

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]
```

#### notes

* MATH 376, MATH 421, MATH 467, MATH 521 are mentioned in requirements\_text but are not in linked\_courses. They are preserved as course nodes with verbatim evidence substrings, but status is needs\_review due to missing canonical references.

#### root

n0

#### status

needs\_review

### instructors

None recorded.

### offerings

None recorded.

### sections

None recorded.

### grade instructors

```json
[
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### grades

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```

### statistics

#### gpa

3.374

#### graded

227

#### counts

* 117
* 39
* 28
* 15
* 15
* 10
* 3

### grade conflicts

None recorded.

### evidence

#### history

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course\_a133a953d2fc593f17f887bf-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/history/course_a133a953d2fc593f17f887bf-0.json)

#### traces

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course\_a133a953d2fc593f17f887bf-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/traces/course_a133a953d2fc593f17f887bf-0.json)

#### reviews

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course\_a133a953d2fc593f17f887bf-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/reviews/course_a133a953d2fc593f17f887bf-0.json)

#### results

* [/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course\_a133a953d2fc593f17f887bf-0.json](https://uwcourses.com/data/e243353dcb7d79b7247ced91d69443ef4c2a6349/results/course_a133a953d2fc593f17f887bf-0.json)

### revision

e243353dcb7d79b7247ced91d69443ef4c2a6349

## context

### all

#### term



#### gpa

3.3744493392070485

#### count

227

#### university

##### size

4223

##### gpa Percentile

17

##### count Percentile

60

##### median Count

160

##### 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 | 11    | false   |
| 2.8–3.2 | 317   | false   |
| 3.2–3.6 | 1197  | true    |
| 3.6–4.0 | 2698  | false   |

#### departments

```json
[
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    "comparison": {
      "size": 104,
      "gpaPercentile": 40,
      "countPercentile": 53,
      "medianCount": 209.5,
      "histogram": [
        {
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          "current": false
        },
        {
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          "current": false
        },
        {
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          "range": "2.4–2.8",
          "count": 6,
          "current": false
        },
        {
          "range": "2.8–3.2",
          "count": 24,
          "current": false
        },
        {
          "range": "3.2–3.6",
          "count": 25,
          "current": true
        },
        {
          "range": "3.6–4.0",
          "count": 49,
          "current": false
        }
      ]
    }
  }
]
```

### terms

#### 1074

##### term

1074

##### gpa

2.9375

##### count

16

##### departments

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

#### 1084

##### term

1084

##### gpa

3.55

##### count

10

##### departments

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

#### 1104

##### term

1104

##### gpa

3.8636363636363638

##### count

11

##### departments

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

#### 1114

##### term

1114

##### gpa

3.3461538461538463

##### count

13

##### departments

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

#### 1124

##### term

1124

##### gpa

3.772727272727273

##### count

11

##### departments

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

#### 1144

##### term

1144

##### gpa

3.25

##### count

8

##### departments

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

#### 1154

##### term

1154

##### gpa

3.269230769230769

##### count

13

##### departments

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

#### 1164

##### term

1164

##### gpa

4

##### count

7

##### departments

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

#### 1184

##### term

1184

##### gpa

4

##### count

13

##### departments

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

#### 1194

##### term

1194

##### gpa

2.4615384615384617

##### count

26

##### departments

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

#### 1204

##### term

1204

##### gpa

3.45

##### count

20

##### departments

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

#### 1224

##### term

1224

##### gpa

3.75

##### count

12

##### departments

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

#### 1234

##### term

1234

##### gpa

3.4583333333333335

##### count

12

##### departments

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

#### 1244

##### term

1244

##### gpa

3.230769230769231

##### count

13

##### departments

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

#### 1254

##### term

1254

##### gpa

3.4523809523809526

##### count

21

##### departments

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

#### 1264

##### term

1264

##### gpa

3.5

##### count

21

##### departments

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

### benchmarks

#### all

##### school

###### size

4223

###### gpa

3.6603685131516563

###### top Share

81.92901702798027

###### count

160

##### MATH

###### size

104

###### gpa

3.4936279020570664

###### top Share

72.47110546960288

###### count

209.5

#### terms

##### 1074

###### school

###### size

695

###### gpa

3.3616924722887376

###### top Share

63.22509110105764

###### count

69

###### MATH

###### size

17

###### gpa

2.821339129045922

###### top Share

38.66654769268061

###### count

133

##### 1084

###### school

###### size

720

###### gpa

3.3670742938849725

###### top Share

63.42064564712246

###### count

70

###### MATH

###### size

22

###### gpa

2.977459424628873

###### top Share

44.52710820759676

###### count

88.5

##### 1094

###### school

###### size

758

###### gpa

3.3891454428111527

###### top Share

64.36369814389255

###### count

71

###### MATH

###### size

19

###### gpa

2.861322177541941

###### top Share

40.26350030907326

###### count

108

##### 1104

###### school

###### size

793

###### gpa

3.384661458923085

###### top Share

64.6614752434143

###### count

66

###### MATH

###### size

23

###### gpa

2.9531575824731964

###### top Share

43.549837152646596

###### count

98

##### 1114

###### school

###### size

804

###### gpa

3.3696004653806844

###### top Share

64.0389334741844

###### count

68

###### MATH

###### size

26

###### gpa

2.9090822348911582

###### top Share

41.14706210117883

###### count

83.5

##### 1124

###### school

###### size

821

###### gpa

3.406589342026613

###### top Share

66.35774230127205

###### count

67

###### MATH

###### size

28

###### gpa

2.9109864595893504

###### top Share

42.40580272314707

###### count

75

##### 1144

###### school

###### size

878

###### gpa

3.4092443327803017

###### top Share

65.95978235963416

###### count

64

###### MATH

###### size

30

###### gpa

2.926152797086596

###### top Share

42.17363619414386

###### count

79

##### 1154

###### school

###### size

935

###### gpa

3.4282378385810093

###### top Share

67.66674668721691

###### count

63

###### MATH

###### size

33

###### gpa

2.9834698949629033

###### top Share

46.71989715257013

###### count

69

##### 1164

###### school

###### size

965

###### gpa

3.46491230798535

###### top Share

69.92376287143657

###### count

68

###### MATH

###### size

32

###### gpa

2.995223360849456

###### top Share

46.38098813836469

###### count

83

##### 1184

###### school

###### size

1010

###### gpa

3.47925290354517

###### top Share

70.86270937115944

###### count

68

###### MATH

###### size

36

###### gpa

3.0650838986714333

###### top Share

47.42689290604571

###### count

83.5

##### 1194

###### school

###### size

1040

###### gpa

3.4906527436719808

###### top Share

71.74728845515045

###### count

67

###### MATH

###### size

38

###### gpa

3.133406260873163

###### top Share

53.17595010634325

###### count

71.5

##### 1204

###### school

###### size

1012

###### gpa

3.703747431523761

###### top Share

84.59811226304916

###### count

65.5

###### MATH

###### size

29

###### gpa

3.478717830475146

###### top Share

69.61236805388549

###### count

83

##### 1224

###### school

###### size

1171

###### gpa

3.5627882428500937

###### top Share

76.37271640560496

###### count

64

###### MATH

###### size

34

###### gpa

3.1555898753466907

###### top Share

53.444319815085976

###### count

87.5

##### 1234

###### school

###### size

1188

###### gpa

3.5799441677552393

###### top Share

77.18256448537606

###### count

65

###### MATH

###### size

41

###### gpa

3.178489266862151

###### top Share

56.06874885619616

###### count

67

##### 1244

###### school

###### size

1241

###### gpa

3.5975573126929192

###### top Share

78.29036874847135

###### count

65

###### MATH

###### size

43

###### gpa

3.228240949537157

###### top Share

55.86451059486035

###### count

68

##### 1254

###### school

###### size

1289

###### gpa

3.6126423469389106

###### top Share

79.48050408754871

###### count

66

###### MATH

###### size

39

###### gpa

3.180435541912479

###### top Share

53.878371816747475

###### count

89

##### 1264

###### school

###### size

1283

###### gpa

3.6229729166451925

###### top Share

80.13669149396227

###### count

66

###### MATH

###### size

42

###### gpa

3.13598176627681

###### top Share

52.25969905887213

###### count

80

## instructor Trends

```json
[
  {
    "uid": "instructor_eb98a96c05ac474b321e9170",
    "name": "SEAN PAUL",
    "count": 54,
    "terms": [
      {
        "term": "1074",
        "count": 16,
        "sections": 1,
        "gpa": 2.9375
      },
      {
        "term": "1114",
        "count": 13,
        "sections": 1,
        "gpa": 3.3461538461538463
      },
      {
        "term": "1184",
        "count": 13,
        "sections": 1,
        "gpa": 4
      },
      {
        "term": "1234",
        "count": 12,
        "sections": 1,
        "gpa": 3.4583333333333335
      }
    ]
  },
  {
    "uid": "instructor_bc7acc9f38e7d8108854c8c5",
    "name": "TULLIA DYMARZ",
    "count": 33,
    "terms": [
      {
        "term": "1224",
        "count": 12,
        "sections": 1,
        "gpa": 3.75
      },
      {
        "term": "1264",
        "count": 21,
        "sections": 1,
        "gpa": 3.5
      }
    ]
  },
  {
    "uid": "instructor_b9a630b0e3b3db4a0fe1de98",
    "name": "GLORIA MARI-BEFFA",
    "count": 30,
    "terms": [
      {
        "term": "1084",
        "count": 10,
        "sections": 1,
        "gpa": 3.55
      },
      {
        "term": "1204",
        "count": 20,
        "sections": 1,
        "gpa": 3.45
      }
    ]
  },
  {
    "uid": "instructor_679f753cde11c003a592a1a8",
    "name": "SIGURD ANGENENT",
    "count": 26,
    "terms": [
      {
        "term": "1194",
        "count": 26,
        "sections": 1,
        "gpa": 2.4615384615384617
      }
    ]
  },
  {
    "uid": "instructor_180bf94a3d2f4343128d8704",
    "name": "JEFF VIACLOVSKY",
    "count": 24,
    "terms": [
      {
        "term": "1124",
        "count": 11,
        "sections": 1,
        "gpa": 3.772727272727273
      },
      {
        "term": "1154",
        "count": 13,
        "sections": 1,
        "gpa": 3.269230769230769
      }
    ]
  },
  {
    "uid": "instructor_867c99b8678bdc2384dafdc3",
    "name": "RUOBING ZHANG",
    "count": 21,
    "terms": [
      {
        "term": "1254",
        "count": 21,
        "sections": 1,
        "gpa": 3.4523809523809526
      }
    ]
  },
  {
    "uid": "instructor_890abb761fbcec59b9793bf4",
    "name": "GAVIN BALL",
    "count": 13,
    "terms": [
      {
        "term": "1244",
        "count": 13,
        "sections": 1,
        "gpa": 3.230769230769231
      }
    ]
  },
  {
    "uid": "instructor_f46a07add28199b6227df820",
    "name": "MUSTAFA KALAFAT",
    "count": 11,
    "terms": [
      {
        "term": "1104",
        "count": 11,
        "sections": 1,
        "gpa": 3.8636363636363638
      }
    ]
  },
  {
    "uid": "instructor_7ffa168f48f2427ebb92a0ca",
    "name": "RUIFANG SONG",
    "count": 8,
    "terms": [
      {
        "term": "1144",
        "count": 8,
        "sections": 1,
        "gpa": 3.25
      }
    ]
  },
  {
    "uid": "instructor_3753748fa7dd09581055ebda",
    "name": "MANUEL GONZALEZ VILLA",
    "count": 7,
    "terms": [
      {
        "term": "1164",
        "count": 7,
        "sections": 1,
        "gpa": 4
      }
    ]
  }
]
```

## following

| code     | title                     |
| -------- | ------------------------- |
| MATH 621 | INTRODUCTION TO MANIFOLDS |
