If you will be advising or teaching first-year graduate students this year, the Graduate Program Committee asks that you read the introduction and the chapter(s) of this handbook that pertain to you before the start of the school year. This contains important information to help you to be a much more effective advisor and teacher.

## Introduction

The Graduate Program Committee has prepared this handbook for preliminary advisors of new grad students and instructors in core graduate courses, to give you some knowledge and tools to help alleviate some of the pressures, fears, and low morale that often beset beginning graduate students. The transition to graduate school can be difficult, frightening, and demoralizing, and it is part of our job as faculty to help them learn to cope with it.

This handbook contains four sections: this introduction, which should be read by everyone who works with first-year students (advisors and first-year instructors); and then sections corresponding to the two main roles in which faculty interact with first-year graduate students: teaching a core graduate course and advising first-year students. Although it would not be a bad idea to read the entire handbook, all we ask is that you read this introduction and the section(s) that pertain to the role(s) you will be playing this year.

### The first year is a struggle.

First-year students have widely varying levels of preparation. Some already have Master’s degrees. Some students’ backgrounds leave them underprepared for graduate study. There is a quantum jump from college to graduate school in the mathematical sophistication and pacing of typical courses. Students struggle with having to fill in many more details than they are used to. Some have a harder time because they have been away from school for a year or more. They are adjusting to life in a different city, a different country. The great majority of those in TA positions are teaching for the first time.

Because they are in graduate school in mathematics, it is a safe bet that all of these students consider themselves to be good at math, and many have been the best in most of their math classes so far. It is also a safe bet that half of them are going to perform at or below the median in any given class here, and some of those who are performing above average will still believe they are doing poorly. This is an emotional shock that virtually all students have to cope with, and some find it nearly overwhelming.

### Workload and Time Management

First-year PhD students have a high workload. The standard at UW is that each credit represents three hours per week of student effort on average, including classes, homework, studying, and exams. This expectation may be an overestimate in some courses, but it is generally a pretty reasonable estimate for our core graduate courses, all of which carry five credits. This means that an average first-year PhD student taking 13 credits (two core courses plus a non-core course) will have to spend 39 hours on course work in an average week. Of course, it also means that most students will have to spend considerably more in some weeks (just before finals, for example), and some students will have to spend considerably more every week. When this is combined with a teaching assistantship that demands anywhere from 10 to 20 hours per week, many students feel overwhelmed by the amount of work that is required of them, especially if they are unable to budget their time efficiently.

Such factors make the first year, particularly Autumn quarter, a time of great struggle, adjustment, and anxiety for most students. It is important that all faculty, particularly first-year instructors and advisors, recognize this and do whatever they can to help alleviate the time pressure (without decreasing the amount of work that should be expected, of course). This handbook provides many specific suggestions about this.

### Crises and adjustments

Many first-year students find their workload daunting and become discouraged at some point. We hope they will turn to their instructors and advisors for advice when this happens. The chances of this increase if they know you are willing to help with their difficulties and if you keep in contact with the students.

In some cases the concerns are due to not having enough information or feedback. As a first-year instructor or advisor, you can help to make sure students have realistic information about how they are doing in their courses. Many students worry that the reason they are struggling is because they are not good enough, when it is clear to you that they are on the right track and that their struggle is par for the course; in this case help is a matter of telling them this and encouraging them to persevere.

In some cases information is not enough. The student may have to make significant adjustments. He or she may not be putting in enough effort. More likely, the effort is there but is not well distributed; too much of it is spent on some part of their commitments, leaving too little for the rest. It is also not uncommon to have overly high expectations or to try to do too much. For example, the student may be taking four courses or expecting to get a 4.0 in every course. If a student is taking three courses and finding the demands overwhelming, the right response might be to devote less time to one course. (Note that this is a course of action that will feel strange to most students; they may need reassurance that it might be appropriate to focus on some classes at the expense of other ones.) These are some scenarios under which you can present students with possible causes and solutions, leaving them with decisions. It is useful to remind students that such decisions are part of graduate study, only they can decide what is right for them, and that, subject to “Normal Progress,” there are few rules. (The rules for normal progress are summarized in the section on advising students, and the details can be found in the Graduate Program section of the departmental website.)

Teaching a core graduate course

This section is intended for faculty members teaching the four designated core graduate courses (Algebra, Real Analysis, Complex Analysis, and Manifolds).

As mentioned in the Introduction, the first year is a time of struggle and anxiety for most students, and their morale can get dangerously low, especially late in Autumn Quarter. It is important to be sensitive to this, to be alert for signs that a student is starting to lose the ability or will to continue, and to be ready to help. More specifically, here are some suggestions for core instructors.

### What you can do to help

- Make yourself visible and available. Go to the math faculty/grad student picnic in September: one of its purposes is for new grad students to meet faculty. Go to tea a few times a week. Chat with your students.
- Provide information at the beginning of the course. Hand out a syllabus containing at least the following: specific prerequisites, with references to reading material and UW courses; an outline of the course content; expectations regarding homework (how much, when due, what kinds of problems); information regarding exams (when, in class or take home, open book or closed book, how long, what kinds of questions); grading policy; office hours; and how and when they can best get in touch with you. Repeat and expand on this information in the first lecture. Explain the range of grades and their meanings (see “Grades” below). Because these courses are linked to preliminary exams, it is also a good idea to discuss the content of the prelim and how it relates to the content of the course, and to return to this discussion at intervals throughout the year.
- Keep in mind the backgrounds of your students. Make an effort not to lose the less prepared students. If you address their needs, most of them will likely rise to the challenge before too long. If a student is simply not prepared for the 500-level course in your subject, he or she should take the appropriate 400-level course. Since we try to identify these students beforehand, it is not very likely that you will have them in your 500-level class; however, such cases do arise. If they are there, we need to be aware of it within the first week or so of Autumn quarter, while there is still time for them to transfer to a lower-level course. Discuss any such cases at once with the Graduate Program Coordinator.
- Review basic material at the beginning of the course. It may be a good idea to go over some of the prerequisite material. Do you spend two days or two weeks lecturing on this? With or without proofs? Do you cover a wide range of prerequisites or focus on the topics that are the most important, or those the audience is least familiar with? Consider using handouts and/or early homework to ensure a common ground for you and the audience.
- Start slowly. Start out at a pace that is not too much faster than you would conduct an advanced undergraduate course, and include more details in your lectures than you would later in the year. Gradually pick up the pace, perhaps reaching full speed by the end of Autumn quarter.
- Encourage the students to work in groups. Though this may seem quite natural and obvious, a large number of students will be used to working on assignments in isolation. We also want to encourage a collaborative atmosphere and welcoming climate among our graduate students. A few words from an instructor about the usefulness of discussing problems with other students can go a long way.
- Encourage attendance at office hours. Simply stating when you will be available in your office is probably not enough. Many students will not be used to seeking help, and will be uncomfortable looking for advice outside of the classroom. Even if you know yourself to be an easy-going, supportive person, they may feel intimidated by you – after all, you obviously understand all the confusing ideas they are struggling with, and they believe you expect them to understand as well as you. Taking a few minutes to talk to them about how classes are going when you see them in the halls or at tea can be a good way to make them more comfortable asking questions. It is not a bad idea to require students to come see you at least once during the first quarter, or even every quarter.
- Provide frequent feedback. For most first-year students, the core graduate courses will be the most challenging and difficult courses they have ever taken. Most are not sure about acceptable levels of performance, and many have very high expectations. This seems to lead to their becoming convinced, at some point during Autumn quarter, that they are failing. This quite common – and usually unwarranted – feeling can lead to severe morale problems. Abundant and accurate feedback from instructors can serve two purposes: it can reassure some students that they are not doing as poorly as they believe they are, and for those students who truly are unprepared for the class, early feedback can lead them to consider whether they might be better off in a 400-level course or, later in the year, lead them to decide to focus their effort on the courses they are most likely to succeed in.
- Request mid-quarter feedback from the class. An anonymous questionnaire for the students to fill out around the fourth week of Autumn Quarter, perhaps followed by a short in-class discussion, can elicit an enormous amount of useful information about how things are going for the students. You might think they will tell you in person if they wish you would do something differently, but you’d probably be wrong: most students are simply not confident enough to take the initiative in giving feedback. If you request feedback, you might get suggestions that are easy to implement and will dramatically improve the learning climate in your classroom. And if you get complaints or suggestions that reveal unrealistic expectations on the students’ part, it can be the occasion for a valuable and educational discussion. You would probably have gotten the same information on the end-of-quarter student course evaluations, but by then it would be too late to fix any problems.
- Contain your requirements to 15 hours. Adjust the demands of your course, in particular the homework assignments, to conform to the guideline that the total time spent on a five-credit course should average no more than 15 hours per week, including the three class hours.

### Grades

- Satisfactory grades are between 3.0 and 4.0. Departmental rules require that for a course to count toward making normal progress, the student must obtain a grade of 3.0 or higher in the course. Consequently, a student who performs satisfactorily in a core course should be assigned a grade between 3.0 and 4.0. Since course grades play an important role in the Graduate Program Committee’s evaluation of student progress, at least for students in years one and two, it is helpful if you have a reasonable spread in your grades. Grades of 3.8 and above carry added significance – see The 3.8 rule below.
- You may have some students in your class who have already completed prelims but now want to see the material from your core course. They may not want to put full effort into the course since their priorities may be elsewhere (finding an advisor, etc.), but the Graduate Program Committee thinks that students should be encouraged to take more than just two core courses. So your grading scale should allow for such students to get satisfactory grades.
- Failing grade. The Graduate School requires a grade of 2.7 or better for a course to count for a degree, and an overall GPA of 3.0 to obtain a degree. The department views grades below 3.0 as unsatisfactory. So the usual practice is to assign a 2.7 to indicate an unsatisfactory performance, counting toward a degree but not toward normal progress requirements. An extremely poor performance can lead to a grade below 2.7, but such grades are only rarely assigned.
- The 3.8 rule. A graduate student may obtain a “course pass” in one (and only one) prelim by getting 3.8 or above in each of the three quarters of the corresponding core course. A course pass should mean that the student’s understanding of the material is so unquestionably solid that there is no reason to make them go through the additional exercise of studying for and taking the prelim. A different way of phrasing this: the student’s understanding and mathematical maturity are strong enough that they can benefit more from other activities over the summer, as compared to studying for the prelim: taking Math 600 and heading toward a research direction, for example.
- Because of the 3.8 rule, you should be looking very carefully at students in the range 3.6–3.8 at the end of each quarter, and thinking about which ones should remain on track for a course pass. We recommend being a little generous with 3.8 in the Autumn quarter. Do not give any 3.7’s in the Autumn – choose instead between 3.6 and 3.8, with a bias toward 3.8. If someone gets 3.7 in the Autumn and later puts in sterling performances that clearly place them in the over-3.8 bracket, the 3.7 will tie your hands (although as a last resort, you can go back and change the Autumn grade). If you nudge someone up to a 3.8 in the Autumn and it later becomes clear that they do not belong there, they will earn a lower grade in a later quarter.

### 400-level alternatives

If students find themselves struggling in a core graduate course because they simply do not have adequate preparation, they should be encouraged to consider taking an alternative 400-level course. For each of our core graduate courses, there is at least one appropriate 400-level course that can be taken for graduate credit instead:

Instead of |
Consider substituting |

504/5/6 | 402/3/4 |

524/5/6 | 424/5/6 |

534/5/6 | 424/5/6 or 427/8 |

544/5/6 | 424/5/6 or 441/2/3 |

If you believe this may be the most appropriate option for a student, it is important that you inform the student’s advisor or the Graduate Program Coordinator as soon as possible, preferably by the 5th day of classes (if the quarter starts on a Wednesday, this is the following Tuesday). Figuring this out early enough to be helpful usually will require some serious feedback from you early in the first quarter. Consider giving a diagnostic homework assignment and scheduling individual conferences with all students during the first week for this purpose.

### Evaluating the students

At the end of each quarter you will be asked to provide the Graduate Program Committee with a short statement (a few sentences) about each student. These statements keep the Graduate Program Coordinator and the Committee informed of each student’s progress. They also alert the committee early on to possible candidates for departmental awards. Along with these statements, the Committee will appreciate any general comments about the class, such as your impression of their ability, enthusiasm, and willingness to work compared to other years; how you read their morale; and any feedback you have on how much time the students are putting into their courses.

If you have any Master’s students taking your course and they apply to transfer to the PhD program, you will probably be asked to write a letter addressing the following: how do they compare with the other students in the course; how do they compare with other students in our PhD program; and should they be admitted to the PhD program?

If you are aware of students in your class who have already completed prelims, we do not need detailed information about their performance.

### Your TA

Your TA is there to assist you and your students in a variety of ways, not just as a grader. In particular, you should consider asking the TA to have regular office hours, run problem sessions or discussion groups, and/or be otherwise available to help students with their course work. He or she can help you with grading homework or exams, but we recommend that you grade the exams since this is a very effective way of getting first-hand information on how your students are doing. Be sure to get frequent feedback from your TA on student performances, difficulties with specific concepts, etc.

This chapter applies to advisors of both MS and PhD students. If you are assigned to be the preliminary advisor of a new student, we ask that you read this entire chapter before starting to advise the student. In the past, first-year students have complained that they get very little advising – their advisors sign their quarterly plans without asking any questions, and otherwise ignore them. We hope that this handbook will help you to be a more effective and more supportive advisor. This is an important part of graduate education, and all of us who are involved in the graduate program need to do our share. If you feel for some reason unable to put in the required time and effort, you may ask to have the student transferred to another advisor.

Every new student is assigned a “preliminary advisor” by the Graduate Program Coordinator. Usually these assignments are based on mathematical interests expressed by the students when they apply; occasionally they are based on other connections between a student and a particular faculty member. For PhD students, the preliminary advisor will be responsible for the student until some time in the second or third year, at which time the student will choose a PhD thesis advisor. During their second year, some MS students will choose a Master’s advisor in their field of concentration to chair the student’s supervisory committee. MS students who transfer to the PhD program may stay with their preliminary advisor until they choose a PhD advisor.

For both PhD and MS students, a student may change preliminary advisors at any time if another faculty member agrees to take over as advisor. To make the change official, the student needs to fill out a form, available in the Student Services Office, C-36. There are many reasons why a student might decide to change advisors, and you should not assume that such a change implies any reflection on your personal advising style or capabilities.

### Finding out about the program

In order to be an effective advisor, you should know at least as much about the program requirements as the student does. The authoritative source for program information is the Graduate Program section of the departmental website. There you will find up-to-date information about the programs, including pages for each of the following. We urge you to look these over before you meet your advisee.

- Degree Requirements: The bottom line – this lists the courses, exams, and other requirements necessary for getting a Master’s degree or PhD. See also Master’s Degree Options, below.
- Normal Progress: The milestones that students must pass at specified times in order to be considered to be making normal progress through the program. For first-year PhD students, the most important requirements are (a) pass (meaning a grade of 3.0 or higher) all three quarters of at least two of our four core graduate courses during the first year, (b) pass at least eight courses during the first year, and (c) pass two prelims (not both in analysis) by September of the second year (one of them can be a “course pass,” obtained by earning grades of 3.8 or better in each of the three quarters of the corresponding core graduate course).
- For most Master’s students, the requirements for normal progress can be summarized as follows: complete at least eight one-quarter courses satisfactorily (3.0 or better) by the end of the first year, and finish the degree by the end of the second. See the website for the particulars.
- Exams: Here you’ll find detailed information about all the exams that have to be taken by PhD students: language exams, preliminary exams, the general exam, and the final exam. The prelims are most relevant to new students.
- Registration Guidelines: The rules describing what courses students can sign up for. The important thing here is that first-year students are expected to sign up for three courses (not counting seminars) each quarter; this may include Math 600, and for PhD students it may include at most one 400-level math course. (MS students may take more than one 400-level course at a time.) Every supported student needs to sign up for a minimum of 10 credits each quarter.
- Transferring to the PhD program: Details about how Master’s students may apply to transfer to the PhD program. The deadline for completed applications is the end of the second week of Spring quarter.
- Frequently Asked Questions about the programs.

### Finding out about the student

Before you advise a student, you should find out about the student’s background and goals. The first source of information is the student’s application, available on-line. To access this, you need to have filled out an access form for the Graduate School – if you’ve done this in the past, you should still have access. Otherwise, get the form from the staff in C-36. If you have any questions about what you see in the student’s file, consult with the chair of Graduate Admissions: he or she might be able to give you some more insight into the student’s circumstances based on experiences gained during the admissions process. Finally, the best source of up-to-date first-hand information is the student; see the next paragraphs.

### Meeting with new graduate students

New students arrive at least a week before the beginning of Autumn quarter for orientation and TA training, and they are told who their advisor is during orientation (typically one week before classes start). Please contact the student to set up a meeting. The two days before classes start might be good times for this; otherwise, you must meet in the first week of Autumn quarter, preferably on the first day.

The first meeting is an excellent opportunity to find out more about the student. You can start by asking questions: “What kind of mathematics are you interested in? Is there a specific field you would like to work in? What are your career goals and hopes? Which advanced courses have you taken? Have you been away from mathematics any period of time?” And more immediately, “Have you thought about what courses you want to take this year?” Give the student plenty of opportunity to ask questions, too – it is important that the meeting be a conversation between the two of you, not just a question/answer session. Ideally, the student will feel comfortable and understand that you are on their side. Keep in mind that incoming students will often not have answers to questions such as the area they want to specialize in or what they want to do after getting their degree; and, even if they do, the answer is likely to change with time.

### What advice to give

As you start to form a picture of the student’s background and objectives, you will be able to give advice. The main priorities are: what courses will they take in Autumn, and what is their plan for the rest of the year? For PhD students, their plan should prepare them to pass two prelims (not both in analysis) by the following September; for MS students, their plan should include one core course in year 1, one core course in year 2. Their plan, especially for PhD students, should also help them start to look for a research direction; this can either be through core courses or through the third course they take each quarter.

- Students who want to take more than three courses are probably setting themselves up for disappointment; you should let them know that almost all students find three of our courses, together with TA duties, as much as they can handle. They should be strongly discouraged from taking more than three courses. The only exception is if a student needs to take an English course to become qualified to teach; then the student might in addition take three math courses.
- Students who want to just take two core courses (and nothing else) will not be making normal progress. Although two core courses would give a student 10 credits, enough for full time enrollment, one of the goals in our revision of the prelim system was to give first-year students some flexibility for their third course, to allow them to explore other mathematical areas, perhaps starting the search for an area of research. If they just take two core courses, they are losing that opportunity. Math 600 is always an option for a third course.

Expect first-year students to be overwhelmed by the amount of work and to experience some crises until they have adjusted their expectations and found a way to budget their time. (See Crises and Adjustments in the Introduction.) Check in with them a few times during Autumn quarter to see how things are going.

### Master’s degree options

The Math Department has four different Master’s degree programs: MA (non-thesis), MS (thesis or non-thesis), and MS in Optimization (non-thesis). As of Autumn 2014, the last one is very difficult to complete: it requires courses that are not offered very frequently. You should probably steer your students away from it.

By far the largest number of terminal Master’s students opt for the MS non-thesis degree. Students who are contemplating transferring to the PhD program should be working toward an MS non-thesis also. (Indeed, many of our PhD students get this degree as well.) You should be aware of which degree your advisee is aiming for.

Here is a brief description of the requirements for the various degrees; more detailed information can be found on the web.

- MA (non-thesis): Twelve approved one-quarter courses, including two courses in each of algebra, analysis, and one other field. At least six courses must be from at most three 500-level core courses.
- MS (non-thesis): A total of fifteen one-quarter math courses from a designated list. These must include two quarters of each of two core graduate courses and one three quarter, 500-level sequence in an approved area of specialization. An oral final exam. A written exam may be substituted with approval of the Graduate Program Coordinator.
- MS (thesis): Same as MS non-thesis, except that the three quarter, 500-level sequence is replaced by Math 700 and an expository thesis. An oral thesis defense.
- MS (optimization): (It is currently difficult to satisfy the requirements for this degree: it requires AMath 507 which is only offered every other year. We are working on revising the requirements.)

### Transferring to the PhD Program

All Master’s students are eligible to apply to transfer to the PhD program in the Spring. There is a special application form for this purpose, which must be turned in to the Student Services Office by the end of the second week of Spring quarter. There are more details on the Graduate Program web page.

### Typical programs for PhD students

Most PhD students’ schedules for the first year will look roughly as follows:

- Two core graduate courses
- One of the following:
- A 400-level course
- A third core graduate course
- An intermediate graduate course
- Math 600

The specific course choices will depend, of course, on the student’s background and interests. **All first-year PhD students must take at least two year-long core sequences during their first year** (unless they pass at least one prelim before classes start). Any exceptions require the permission of the Graduate Program Coordinator.

The second-year program is more flexible. Students who are done with prelims might be encouraged to take at least the first quarter or two of another core course, to expose themselves to the material, and knowing that they do not need to put in the work to get a stellar grade in it.

### Core graduate courses

There are four core graduate courses:

- 504/5/6: Modern Algebra (Prerequisite: 402/3/4)
- 524/5/6: Real Analysis (Prerequisite: 424/5/6)
- 534/5/6: Complex Analysis (Prerequisite: 424/5/6)
- 544/5/6: Topology and Geometry of Manifolds (Prerequisites: 402/3/4, 424/5/6)

The prerequisites for these are the following 400-level UW sequences:

- 402/3/4: Introduction to Modern Algebra
- 424/5/6: Fundamental Concepts of Analysis

All PhD students should know the material in 402/3/4 and 424/5/6. If a new student is missing a relatively small part of this material, you can direct them to the standard books. If an incoming student is missing most of either 402/3/4 or 424/5/6, you should advise them to take that sequence before attempting any core course for which it is a prerequisite. (The approach to the grey area between “relatively small” and “most” will vary with the student!)

If a student seems to be missing significant portions of both 402/3/4 and 424/5/6, then he or she might need to switch to the Master’s program; a PhD student may not enroll in more than one 400-level course without the permission of the Graduate Program Coordinator. (Applicants who are in this situation are not usually admitted to our PhD program but channeled into the Master’s track.) If you think your advisee might be in this situation, please inform the GPC immediately.

### Manifolds

This course presents first-year students with additional early challenges, which we explain below. We recommend that you communicate to any student taking this course what additional challenges to expect and when.

Manifolds starts out with a rather swift introduction to topological spaces, and then goes on to make liberal and sophisticated use of that material without a long gestation period. It is designed under the assumption that students are comfortable with (not just that they have been exposed to) abstract metric spaces. They should have little trouble if they recently took a good undergraduate real analysis course along the lines of Rudin’s Principles of Mathematical Analysis or our Math 424/5/6. But many students had a watered-down version of that course, or took it many years ago, and so do not have the familiarity with metric spaces that they need, and these students will find the first quarter quite challenging. If they are not sure whether their preparation is sufficient, they might be advised to take Real Analysis simultaneously (in which metric spaces are covered in some depth). If it is clear that they are not ready, they should probably put off Manifolds until their second year, and instead take a course that will prepare them for Manifolds. Any one of 524/5/6, 424/5/6 (Real Analysis) or 441/2/3 (Topology and Geometry) should provide sufficient preparation for taking Manifolds the following year.

The second quarter of Manifolds, in which the subject switches to differentiable manifolds, presents a similar difficulty. In this case the prerequisite material is advanced multivariable calculus and abstract linear algebra, and one of the hardest things about the course is the way in which analysis, algebra, and topology are combined. Once again, a student who has had solid versions of the prerequisite courses should be able to handle the new material with only moderate difficulty; but many students discover at this point that they didn’t learn calculus or linear algebra nearly as well as they thought they had, or that synthesizing all of these subjects is more of a challenge than they are ready for. Any student who feels shaky about this material will be helped by doing a little extra studying during Winter break.

### 400-level alternatives

A few PhD students are not prepared to take two core graduate courses. They should consider taking one core course plus an alternative 400-level course:

Instead of |
Consider substituting |

504/5/6 | 402/3/4 |

524/5/6 | 424/5/6 |

534/5/6 | 424/5/6 or 427/8 |

544/5/6 | 424/5/6 or 441/2/3 |

Note that a PhD student must have permission from the Graduate Program Coordinator to take more than one 400-level course.

If switching to a 400-level course is the most appropriate option, it is important to recognize this as early as possible. If you feel this might be appropriate for a particular student, be sure to talk with the student about the situation, and inform the student’s instructor and the Graduate Program Coordinator as soon as possible.

### Typical programs for MS students

Most Master’s students’ first-year schedules will consist of two 400-level courses and one 500-level course. Other combinations are possible. For example, a Master’s student’s background might be strong enough to allow the student to take two 500-level courses and one 400-level course. However, be wary of Master’s students who want to attempt too much too soon; the Admissions Committee carefully considers the level of preparation of students before deciding whether to admit them to the PhD progrman or the Master’s. Taking more than one 500-level course during the Autumn quarter often sets the student up for a failure from which they never recover. Most students admitted to the Master’s program are not ready for more than one 500-level course during their first year. In any case, it is vital that the proper determination be made early in the first year so that students will not be wasting their time being taught material they already know, or being taught material that is so far over their heads that they are not benefiting from it.

If a student’s background appears too weak to take any 500-level courses during the first year, you should bring this to the attention of the Graduate Program Coordinator. Although there is no rule against taking three 400-level courses, doing so will probably make it more difficult to complete an MS degree in two years, because the second-year curriculum would have to include two core graduate courses and either an intermediate graduate course or a Master’s thesis. It might be possible to finish the degree by writing a Master’s thesis during the summer following the second year, or the student may be willing to continue for a third year without departmental support. The department does not ordinarily support Master’s students beyond the second year.

### Course choices

The only 400-level courses that count toward the MS degrees are the following:

- 402/3/4: Introduction to Modern Algebra
- 424/5/6: Fundamental Concepts of Analysis (real analysis) 427/8: Complex Analysis
- 441/2/3: Topology and Geometry

The first two, 402/3/4 and 424/5/6, are the most important, for they cover most of the prerequisite material for our core (500-level) graduate courses. Every Master’s student should take these courses unless they have already had a very solid course in one or the other of these subjects. In evaluating whether a student should be allowed to skip one of these courses, you should consider not only the titles of courses the student has taken previously, but also the textbooks used, the topics covered, the grades obtained, the university at which the courses were offered, and how long ago the courses were taken. In particular, students should not skip 424/5/6 unless they are familiar with uniform convergence, metric spaces, compactness and connectedness, the theory of multivariable calculus, and either the Riemann or the Lebesgue integral in several variables. In a strong course, they will have seen measure theory. Similarly, they should not skip 402/3/4 unless they are comfortable with finite group theory, elementary ring theory, abstract linear algebra including dual spaces and Jordan canonical forms, and ideally, Galois theory.

427/8 is taught at a somewhat less abstract level, and is not a prerequisite for any of our core courses. It is a good choice for a student who has not had any exposure to complex analysis.

441/2/3 covers general topology and the differential geometry of curves and surfaces. It is an excellent choice for a student who is interested in geometry or topology and who is not yet ready for the rigors of 544/5/6.

Most first-year Master’s students should be able to enroll in one 500-level course in addition to two at the 400 level. The 500-level course should generally be chosen from among Modern Algebra (504/5/6), Real Analysis (524/5/6), and Complex Analysis (534/5/6), depending on the student’s background, interests, and preparation. The other core graduate course (Manifolds) is considerably more demanding, and is not usually appropriate for first-year Master’s students.

### Quarterly plans

Departmental registration guidelines for graduate students state: “All students must meet with their advisors each quarter to discuss their course schedules for the quarter and to obtain the advisors’ signatures on the form entitled Quarterly Plan.” The Quarterly Plan should be turned in by the fifth day of classes, so you’ll have to make plans to meet with the student some time during the first week.

When looking over the Quarterly Plan, you should make sure the student has signed up for three graded courses that are applicable to the degree. You should also make sure that he or she is taking at least two core graduate courses, and that the overall program makes sense in terms of the student’s background and interests. Exceptions require the approval of the Graduate Program Coordinator.

The Quarterly Plan is meant to serve an entirely non-bureaucratic purpose: keeping you involved in the students’ course selections and giving you an opportunity to meet with them early in the quarter. The students should understand that this is not just a matter of obtaining your signature by putting the form in your mailbox. In particular, the Graduate Program Committee makes the following request:

Never sign a Quarterly Plan without having had a substantial face-to-face discussion about the student’s progress to date, current choice of courses, and future plans.

Regular meetings. Advisors should keep in regular contact with their students. The nature and the extent of the contact will vary. It could consist of a couple of formal meetings each quarter. It will likely involve chatting with them in the corridors, at tea, and anywhere else that you see your students. Some professors take all of their advisees to lunch together, to help interactions among students at different stages of their careers. In general, advisors of first-year students should make an effort to “run into” students informally – attend tea frequently, take advantage of (or invent) any excuse to go to their offices, etc.

It comes down to this: keep in touch so you know what your advisees are up to, and provide advice and guidance as needed.