How can I learn about the Monster group?
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There are several questions about the Monster group on this site, but none really answer the question in the title.
While reading about groups in a first year algebra course, I was told about the classification of finite simple groups and the existence of the Monster group, but further research on my part lead me straight into a brick wall. Any answers I could find were either far, far beyond my current knowledge, or had so little detail, I learned nothing at all. I actually feel quite frustrated with this.
I suspect this is all for a couple reasons. The Monster group is very complicated and difficult to understand, in the realm of research level mathematics. Additionally, it's not really well-understood, but this makes it an exciting object to study as a budding mathematician.
This leads to the question in the title; what is the necessary background and motivation needed to start studying the monster group? Also, what is the necessary background needed to study related topics like the moonshine conjectures and the $j$-function?
Keep in mind, I'm a second year undergraduate, though a little beyond the standard second year undergraduate program. I've studied some abstract algebra, to the level of Dummit & Foote on groups, rings and fields. I also have studied general topology and some very basic algebraic topology if that's of any use, and I'm diving into number theory right now. Hopefully this helps answers understand what "level" I'm at.
As a further note, it is obviously too early for me to know what I will be studying as a research mathematician, but I think it's unlikely that I'll become a finite group theorist. In any case, I hope that doesn't mean I'm doomed to never understand the Monster, moonshine, and the $j$-function.
group-theory soft-question
asked Aug 13 at 6:34
Nico
378310
add a comment |Â
up vote
2
down vote
favorite
There are several questions about the Monster group on this site, but none really answer the question in the title.
While reading about groups in a first year algebra course, I was told about the classification of finite simple groups and the existence of the Monster group, but further research on my part lead me straight into a brick wall. Any answers I could find were either far, far beyond my current knowledge, or had so little detail, I learned nothing at all. I actually feel quite frustrated with this.
I suspect this is all for a couple reasons. The Monster group is very complicated and difficult to understand, in the realm of research level mathematics. Additionally, it's not really well-understood, but this makes it an exciting object to study as a budding mathematician.
This leads to the question in the title; what is the necessary background and motivation needed to start studying the monster group? Also, what is the necessary background needed to study related topics like the moonshine conjectures and the $j$-function?
Keep in mind, I'm a second year undergraduate, though a little beyond the standard second year undergraduate program. I've studied some abstract algebra, to the level of Dummit & Foote on groups, rings and fields. I also have studied general topology and some very basic algebraic topology if that's of any use, and I'm diving into number theory right now. Hopefully this helps answers understand what "level" I'm at.
As a further note, it is obviously too early for me to know what I will be studying as a research mathematician, but I think it's unlikely that I'll become a finite group theorist. In any case, I hope that doesn't mean I'm doomed to never understand the Monster, moonshine, and the $j$-function.
group-theory soft-question
asked Aug 13 at 6:34
Nico
378310
I don't know the answer to your question - the Monster has many aspects, and I suspect that very few mathematicians have a thorough understanding of all of these. You could for example try and understand the paper by Griess that proves the existence of the Monster by constructing it as a group of automorphisms of a certain algebra, although that does not provide insight into all of its interesting properties. I don't agree with you statement that the Monster is not well-understood, althoguh i am sure there is more to be found out about it.
– Derek Holt
Aug 13 at 8:41
I wonder if it might be useful to start with the Mathieu groups, as a sort of a warm-up?
– MJD
Aug 13 at 9:25
Hey, have you looked yet to see what D&F says about composition series and about the classification of finite simple groups?
– MJD
Aug 13 at 12:42
Also Mark Ronan wrote a book called Symmetry and the Monster which is a nontechnical introduction to the Monster and where it comes from. It won't have any of the crucial details but if you're a second-year undergraduate it may provide important context that you will need.
– MJD
Aug 13 at 14:46
You should visit Atlas of Finite Group Representations and get acces to the GAP software.
– Somos
Aug 13 at 15:45
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
There are several questions about the Monster group on this site, but none really answer the question in the title.
While reading about groups in a first year algebra course, I was told about the classification of finite simple groups and the existence of the Monster group, but further research on my part lead me straight into a brick wall. Any answers I could find were either far, far beyond my current knowledge, or had so little detail, I learned nothing at all. I actually feel quite frustrated with this.
I suspect this is all for a couple reasons. The Monster group is very complicated and difficult to understand, in the realm of research level mathematics. Additionally, it's not really well-understood, but this makes it an exciting object to study as a budding mathematician.
This leads to the question in the title; what is the necessary background and motivation needed to start studying the monster group? Also, what is the necessary background needed to study related topics like the moonshine conjectures and the $j$-function?
Keep in mind, I'm a second year undergraduate, though a little beyond the standard second year undergraduate program. I've studied some abstract algebra, to the level of Dummit & Foote on groups, rings and fields. I also have studied general topology and some very basic algebraic topology if that's of any use, and I'm diving into number theory right now. Hopefully this helps answers understand what "level" I'm at.
As a further note, it is obviously too early for me to know what I will be studying as a research mathematician, but I think it's unlikely that I'll become a finite group theorist. In any case, I hope that doesn't mean I'm doomed to never understand the Monster, moonshine, and the $j$-function.
group-theory soft-question
asked Aug 13 at 6:34
Nico
378310
There are several questions about the Monster group on this site, but none really answer the question in the title.
While reading about groups in a first year algebra course, I was told about the classification of finite simple groups and the existence of the Monster group, but further research on my part lead me straight into a brick wall. Any answers I could find were either far, far beyond my current knowledge, or had so little detail, I learned nothing at all. I actually feel quite frustrated with this.
I suspect this is all for a couple reasons. The Monster group is very complicated and difficult to understand, in the realm of research level mathematics. Additionally, it's not really well-understood, but this makes it an exciting object to study as a budding mathematician.
This leads to the question in the title; what is the necessary background and motivation needed to start studying the monster group? Also, what is the necessary background needed to study related topics like the moonshine conjectures and the $j$-function?
Keep in mind, I'm a second year undergraduate, though a little beyond the standard second year undergraduate program. I've studied some abstract algebra, to the level of Dummit & Foote on groups, rings and fields. I also have studied general topology and some very basic algebraic topology if that's of any use, and I'm diving into number theory right now. Hopefully this helps answers understand what "level" I'm at.
As a further note, it is obviously too early for me to know what I will be studying as a research mathematician, but I think it's unlikely that I'll become a finite group theorist. In any case, I hope that doesn't mean I'm doomed to never understand the Monster, moonshine, and the $j$-function.
group-theory soft-question
asked Aug 13 at 6:34
Nico
378310
asked Aug 13 at 6:34
Nico
378310
asked Aug 13 at 6:34
Nico
378310
asked Aug 13 at 6:34
Nico
378310
378310
I don't know the answer to your question - the Monster has many aspects, and I suspect that very few mathematicians have a thorough understanding of all of these. You could for example try and understand the paper by Griess that proves the existence of the Monster by constructing it as a group of automorphisms of a certain algebra, although that does not provide insight into all of its interesting properties. I don't agree with you statement that the Monster is not well-understood, althoguh i am sure there is more to be found out about it.
– Derek Holt
Aug 13 at 8:41
I wonder if it might be useful to start with the Mathieu groups, as a sort of a warm-up?
– MJD
Aug 13 at 9:25
Hey, have you looked yet to see what D&F says about composition series and about the classification of finite simple groups?
– MJD
Aug 13 at 12:42
Also Mark Ronan wrote a book called Symmetry and the Monster which is a nontechnical introduction to the Monster and where it comes from. It won't have any of the crucial details but if you're a second-year undergraduate it may provide important context that you will need.
– MJD
Aug 13 at 14:46
You should visit Atlas of Finite Group Representations and get acces to the GAP software.
– Somos
Aug 13 at 15:45
add a comment |Â
I don't know the answer to your question - the Monster has many aspects, and I suspect that very few mathematicians have a thorough understanding of all of these. You could for example try and understand the paper by Griess that proves the existence of the Monster by constructing it as a group of automorphisms of a certain algebra, although that does not provide insight into all of its interesting properties. I don't agree with you statement that the Monster is not well-understood, althoguh i am sure there is more to be found out about it.
– Derek Holt
Aug 13 at 8:41
I wonder if it might be useful to start with the Mathieu groups, as a sort of a warm-up?
– MJD
Aug 13 at 9:25
Hey, have you looked yet to see what D&F says about composition series and about the classification of finite simple groups?
– MJD
Aug 13 at 12:42
Also Mark Ronan wrote a book called Symmetry and the Monster which is a nontechnical introduction to the Monster and where it comes from. It won't have any of the crucial details but if you're a second-year undergraduate it may provide important context that you will need.
– MJD
Aug 13 at 14:46
You should visit Atlas of Finite Group Representations and get acces to the GAP software.
– Somos
Aug 13 at 15:45
I don't know the answer to your question - the Monster has many aspects, and I suspect that very few mathematicians have a thorough understanding of all of these. You could for example try and understand the paper by Griess that proves the existence of the Monster by constructing it as a group of automorphisms of a certain algebra, although that does not provide insight into all of its interesting properties. I don't agree with you statement that the Monster is not well-understood, althoguh i am sure there is more to be found out about it.
– Derek Holt
Aug 13 at 8:41
I don't know the answer to your question - the Monster has many aspects, and I suspect that very few mathematicians have a thorough understanding of all of these. You could for example try and understand the paper by Griess that proves the existence of the Monster by constructing it as a group of automorphisms of a certain algebra, although that does not provide insight into all of its interesting properties. I don't agree with you statement that the Monster is not well-understood, althoguh i am sure there is more to be found out about it.
– Derek Holt
Aug 13 at 8:41
I wonder if it might be useful to start with the Mathieu groups, as a sort of a warm-up?
– MJD
Aug 13 at 9:25
I wonder if it might be useful to start with the Mathieu groups, as a sort of a warm-up?
– MJD
Aug 13 at 9:25
Hey, have you looked yet to see what D&F says about composition series and about the classification of finite simple groups?
– MJD
Aug 13 at 12:42
Hey, have you looked yet to see what D&F says about composition series and about the classification of finite simple groups?
– MJD
Aug 13 at 12:42
Also Mark Ronan wrote a book called Symmetry and the Monster which is a nontechnical introduction to the Monster and where it comes from. It won't have any of the crucial details but if you're a second-year undergraduate it may provide important context that you will need.
– MJD
Aug 13 at 14:46
Also Mark Ronan wrote a book called Symmetry and the Monster which is a nontechnical introduction to the Monster and where it comes from. It won't have any of the crucial details but if you're a second-year undergraduate it may provide important context that you will need.
– MJD
Aug 13 at 14:46
You should visit Atlas of Finite Group Representations and get acces to the GAP software.
– Somos
Aug 13 at 15:45
You should visit Atlas of Finite Group Representations and get acces to the GAP software.
– Somos
Aug 13 at 15:45
add a comment |Â
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I don't know the answer to your question - the Monster has many aspects, and I suspect that very few mathematicians have a thorough understanding of all of these. You could for example try and understand the paper by Griess that proves the existence of the Monster by constructing it as a group of automorphisms of a certain algebra, although that does not provide insight into all of its interesting properties. I don't agree with you statement that the Monster is not well-understood, althoguh i am sure there is more to be found out about it.
– Derek Holt
Aug 13 at 8:41
I wonder if it might be useful to start with the Mathieu groups, as a sort of a warm-up?
– MJD
Aug 13 at 9:25
Hey, have you looked yet to see what D&F says about composition series and about the classification of finite simple groups?
– MJD
Aug 13 at 12:42
Also Mark Ronan wrote a book called Symmetry and the Monster which is a nontechnical introduction to the Monster and where it comes from. It won't have any of the crucial details but if you're a second-year undergraduate it may provide important context that you will need.
– MJD
Aug 13 at 14:46
You should visit Atlas of Finite Group Representations and get acces to the GAP software.
– Somos
Aug 13 at 15:45