Acknowledgement

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The present set of notes was developed as a result of Higher Algebra courses

that I taught during the academic years 1987-88, 1989-90 and 1991-92. The

distinctive feature of these notes is that proofs are not supplied. There

are two reasons for this. First, I would hope that the serious student who

really intends to master the material will actually try to supply many of the

missing proofs. Indeed, I have tried to break down the exposition in such

a way that by the time a proof is called for, there is little doubt as to the

basic idea of the proof. The real reason, however, for not supplying proofs

is that if I have the proofs already in hard copy, then my basic laziness often

encourages me not to spend any time in preparing to present the proofs in

class. In other words, if I can simply read the proofs to the students, why

not? Of course, the main reason for this is obvious; I end up looking like a

fool.

Anyway, I am thankful to the many graduate students who checked and

critiqued these notes. I am particularly indebted to Francis Fung for his

scores of incisive remarks, observations and corrections. Nontheless, these

notes are probably far from their final form; they will surely undergo many

future changes, if only motivited by the suggestions of colleagues and future

graduate students.

Finally, I wish to single out Shan Zhu, who helped with some of the

more labor-intensive aspects of the preparation of some of the early drafts

of these notes. Without his help, the inertial drag inherent in my nature

would surely have prevented the production of this set of notes.

David B. Surowski,

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Chapter 1

Group Theory

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