Advice about the Reading Course in Mathematics

[bacte2013]

Dear Physics Forum personnel,

I am a collegiate junior at US with double majors in the mathematics and computer science, and an aspiring theoretical computer scientist. My current courses in the analysis and linear algebra, and undergraduate research in the theoretical computer science fired my interest to the set theory. I initially decided to explore and study the set theory by myself, but I thought it would be a very good idea to study the subject under the experts like mathematical faculty members since I think self-studying in the mathematics, particularly in an abstract field like a set theory, all by myself might lead me to an erroneous understanding of the subject. So I contacted an emeritus professor who did very fascinating research in the set theory and mathematical logics about a guided reading, and fortunately he agreed to do so (starting on January, an hour per week, Jech/Hrbacek's Set Theory textbook) and guide my studying of the set theory.

I never did a reading course before, so I am excited and nervous at the same time. I am especially afraid that I might disappoint the professor by asking uninteresting questions or cannot following his insight or the textbook. What should I prepare myself for the reading course, and how should I interact with the professor for the reading course? What does a professor expect from the student, especially during the one-hour meeting per week?

I apologize for the grammatical error (leaving off to the library).

 

[IGU]

... I am especially afraid that I might disappoint the professor by asking uninteresting questions or cannot following his insight or the textbook. What should I prepare myself for the reading course, and how should I interact with the professor for the reading course? What does a professor expect from the student, especially during the one-hour meeting per week?

Congratulations on being a good student! Being interested and proactive will get you far. You've already taken the hardest step.

As to practical advice, the most important thing is to be prepared. Do the reading. Do the problems. Think about the material. The professor will likely provide you with the help you need. If you're having trouble understanding something, say so and you'll get help. If you're having difficulty with some problem, say so and you'll get help. If you're not having difficulty with anything, say so and you'll spend your time with the professor exploring related materials or more interesting problems. Really, any professor who would volunteer to do this is interested in getting you what you need. So your job is to do the reading, do the work, and make sure what you need is as clear as possible. I'll be very interested in hearing how this works out for you.

One thing you should keep very clear in your mind -- if you are not wasting your time then you are not wasting the professor's time. If you ever feel you are wasting your time, then speak up because that means that everybody is wasting their time. In a one on one situation like this, there's no excuse for that.

 

[bacte2013]

Congratulations on being a good student! Being interested and proactive will get you far. You've already taken the hardest step.

As to practical advice, the most important thing is to be prepared. Do the reading. Do the problems. Think about the material. The professor will likely provide you with the help you need. If you're having trouble understanding something, say so and you'll get help. If you're having difficulty with some problem, say so and you'll get help. If you're not having difficulty with anything, say so and you'll spend your time with the professor exploring related materials or more interesting problems. Really, any professor who would volunteer to do this is interested in getting you what you need. So your job is to do the reading, do the work, and make sure what you need is as clear as possible. I'll be very interested in hearing how this works out for you.

One thing you should keep very clear in your mind -- if you are not wasting your time then you are not wasting the professor's time. If you ever feel you are wasting your time, then speak up because that means that everybody is wasting their time. In a one on one situation like this, there's no excuse for that.

Thank you very much for the detailed advice! Now I can formulate my own approach and behaviors for the reading course. I am very excited to start studying the set theory under the professor one-to-one! I met him and he is very knowledgeable and friendly, which really destroys my nervousness. I am going to use this winter break to review Halmos's Naive Set Theory and learn some basics in mathematical logics.

 

[micromass]

I am going to use this winter break to review Halmos's Naive Set Theory

No need. Just start with Hrbacek and Jech right away.

 

[bacte2013]

No need. Just start with Hrbacek and Jech right away.

Why? I feel like the book I will use, "Set Theory" by Jech/Hrbacek, assume some basic knowledge in the axiomatic set theory.

 

[micromass]

Why? I feel like the book I will use, "Set Theory" by Jech/Hrbacek, assume some basic knowledge in the axiomatic set theory.

It doesn't. If you know basic set theory (like you do), then you can start the book.

 

[bacte2013]

It doesn't. If you know basic set theory (like you do), then you can start the book.

By "basic" set theory, do you mean the set-theory sections of Rudin, Zorich, and Shilov? Do you also know some books that make great supplements to J/H?

 

[micromass]

By "basic" set theory, do you mean the set-theory sections of Rudin, Zorich, and Shilov?

Yes, those will be sufficient.

 

[bacte2013]

Yes, those will be sufficient.

Thank you very much! I can't wait for this semester to end so I can dip myself to the world of set theory! In the typical reading course, is formulating my own approach to the theorems and definitions and formulating my own hypothesis to try to answer my own confusion and disjointed thoughts viewed favorably by the professor (or come as arrogant approach)?