# Guidelines for NCM schools

**Guidelines for Annual Fundation Schools (AFS)**

Basic knowledge in algebra, analysis and topology forms the core of all Advanced Instructional Schools organised by NCM. The main objectives of AFS are to bring up students with diverse background to a common level and help them acquire basic knowledge in these subjects required in Advanced Instructional Schools.

The Annual Foundation Schools are aimed at first and second year Ph.D. students. Nine basic subjects are spread over AFS-I, II and III. The material covered in AFS-II assumes that covered in AFS-I and similarly AFS-III assumes material covered in AFS-II. Each speaker is required to deliver at least 6 lectures of 1 hour duration or 4 lectures of one and a half hour duration and conduct two tutorials of two hours duration each with the help of one or two course associates. Typically, there are 4 speakers for each subject. A course associate is expected to help for at least two weeks. Course associates may help in the tutorials in more than one subject.

Basic information about these schools is given in the following table.

Annual Foundation Schools |
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School | Duration | Month | Subjects to be covered |

AFS-I | 24 days | Dec | Group Theory, Real Analysis, General Topology |

AFS-II | 24 days | May | Ring Theory, Functional Anal. Differential Topology |

AFS-III | 24 days | June | Galois Theory, Complex Anal. Algebraic Topology |

A Model for Weekly Schedule for AFS |
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09.30 | 11.00 | 11.30 | 1.00 | 2.30 | 3.30 | 4.00 | 5.00 |

Algebra-L1 |
T E A |
Analysis-L1 |
L U N C H |
Algebra-T1 |
T E A |
Algebra-T2 |
S |

Topology-L1 | Algebra-L2 | Analysis-T1 | Analysis-T2 | ||||

Analysis-L2 | Topology-L2 | Topology-T1 | Topology-T2 | ||||

Algebra-L3 | Analysis-L3 | Algebra-T3 | Algebra-T4 | ||||

Topology-L3 | Algebra-L4 | Analysis-T3 | Analysis-T4 | ||||

Analysis-L4 | Topology-L4 | Topology-T4 | Topology-T4 |

**Guidelines for Advanced Instructional Schools (AIS)**

Advanced Instructional Schools are organised for those students who have undergone training in the Annual Foundation Schools or who have studied the topics taught in these schools. An AIS is normally devoted to one subject or two inter-related subjects. The duration of any Advanced Instructional School will be 18 working days. These are organised during the months of May, June, July and December. An AIS is like a Ph.D. course and it assumes the contents covered in the three Annual Foundation Schools. The syllabus of each AIS is designed by the organisers.

A typical AIS features 6 minicourses of 6 lectures each. Each speaker is supposed to deliver at least 6 lectures and conduct two tutorials of two hours each.

A Model for Daily Schedule for an AIS |
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9.30-11.00 |
11.00-11.30 |
11.30-1.00 |
1.00-2.30 |
2.30-3.30 |
3.30-4.00 |
4.00-5.00 |
5.00-5.30 |

Lecture 1 | Tea | Lecture 2 | Lunch | Tutorial | Tea | Tutorial | Snacks |

**Guidelines for NCM Workshops** **(NCMW)**

Normally every AIS has a follow up workshop of one or two weeks’ duration. These are organised during the months of August-November and January-April so that there is no clash with other programmes.

Workshops are devoted to current research topics. The workshops assume the syllabus covered in an AIS in the same subject. These are meant for senior Ph.D. students, post doctoral fellows and young teachers who have enough knowledge to follow the advanced material to be covered in the workshop. The purpose of organising workshop is to help young researchers get started in a new research area. The speakers are supposed to do literature survey and suggest open problems through their mini-courses.

Each speaker is supposed to deliver a minicourse of at least 6 lectures.

A Model for Daily Schedule for an NCM Workshop |
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9.30-11.00 | 11.00-11.30 | 11.30-1.00 | 1.00-2.00 | 2.00-3.30 | 3.30-4.00 | 4.00-5.00 | 5.00-5.30 |

Speaker 1 | Tea | Speaker 2 | Lunch | Speaker 3 | Tea | Discussion | Snacks |

**Guidelines for**** I****nstructional**** Schools for Teachers (IST)**

The ISTs were started by NBHM in 2006. It was realised by reading the feedbacks from teacher participants in the AFS and AIS that there is a need to have separate instructional schools for mathematics teachers in colleges and universities since their background and needs are somewhat different from those of research scholars. It is difficult for teachers to get leave for more than two weeks at a time. The duration of each IST is two or three weeks. These will be organised when teachers have vacation. These will cover advanced topics taught at M.Sc. level in the first week and more advanced material will be covered in the second week.

Each IST is devoted to one subject. These schools are for teachers of age at most 35 years. Preference will be given to teachers who are pursuing a doctoral degree. Only NET/SET qualified teachers will be admitted into these schools.

A typical two week long IST is conducted by atmost 4 speakers and two course associates. Each speaker delivers a course of at least 6 lectures of 90 minutes each and conducts at least three tutorials of two hours each.

A Model for Daily Schedule for an IST |
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9.30-11.00 |
11.00-11.30 |
11.30-1.00 |
1.00-2.30 |
2.30-3.30 |
3.30-4.00 |
4.00-5.00 |
5.00-5.30 |

Lecture 1 | Tea | Lecture 2 | Lunch | Tutorial | Tea | Tutorial | Snacks |

**Guidelines for ****Teacher’s Enrichment Workshops (TEW) **

TEWs are conducted by NCM with the financial support from Advancement of Arts and Sciences from India, which is known as **ARSI**.

During the Ramanujan-125 celebrations, Teachers’s Enrichment Workshops (TEW) have been started in few metro cities. The objectives of these workshops are to introduce college mathematics teachers to interesting topics in the basic subjects they teach. These lectures present interesting connections with other fields of mathematics or novel ways to teach a topic from the syllabus. The trained teachers may then deliver these lectures to some of the better students in their classes. The material covered in these lectures may be a starting point of reading projects that some good students in colleges may undertake.

A typical TEW has four courses of 6 lectures each. Each speaker is supposed to deliver at least 6 lectures.

A Model for Daily Schedule for TEW |
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9:30 | 10:30 | 11:00 | 12:00 | 1:00 | 2:30 | 3:30 | 4:00 | 5:00-5:30 |

Speaker 1 | Tea | Speaker 2 | Speaker 3 | Lunch | Speaker 4 | Tea | Discussion | Snacks |